Characterization of High Speed Digital Signals in Multilayer Printed

Calibration
of Automatic
Network Analysis and Computer Aided
Microwave Measurement
by
Jeffery S. Kasten
A thesis submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirementsfor the Degreeof
Master of Science
Department of Electrical and Computer Engineering
Raleigh, NC
1991
Approved By:
Chairman of Advisory Committee
Abstract
KASTEN, JEFFERY S. Calibration of Automatic Network Analysis and Computer
Aided Microwave Measurement. (Under the direction of Dr. Michael B. Steer.)
This work representsdevelopmentof new calibration methodsfor Network Analysis suitable for removal of systematic measurementerrors presentin noninsertable
measurementmedium. The primary goal is a minimum set of calibration standards
derived using symmetry arguments. Preparation includes a review of Network Anal,ysis calibr~tion methods for one and two port measurementsystems.
Two calibration algorithms result from this study. They are verified by measurement of know standards where possible and applied to a Printed Circuit Board
(PCB) measurementfixture to characterizea PCB plated through hole; via. Specifically, the work presentedhere is Through-Symmetry-Line (TSL); symmetry arguments allow synthesis of open and short circuit calibration standards, Enhanced
TSL; complex characteristic impedance is determined for the Line standard, extension to the Through-Reflect- Line algorithm, and Through-Symmetric Fixture
(TSF); exploiting a fixtures symmet!y can reduce calibration standards to one.
Additionally, the program Signal Processingfor Automatic Network Analysis
(SPANA) was createdfor developingcalibration algorithms as well as aid microwave
measurements. SPANA allows the user t~ concentrate on algorithms rather than
frequent tasks such as data input/output, result plotting, printing etc.
11
Acknowledgements
Thank you Dr. Steerfor the time and effort you spent keepingmy path straight.
I wondered if I could ever finish. I'm astonished as I look back becausewithout
your help it could never have happened. This work was funded in part by Bell
Northern Research,ResearchTriangle Park, North Carolina and many thanks to
Real Pomerleaufor his trust in NCSU and the massivediscussionsregarding every
aspect of !ife. Of courseI can not forget Heyward Riedell and the great times we
had in 537 among other classes.Thanks to John Stonick, Pryson Pate, Ruddy, Pat
and all those other fishing people who shared the great times.
Thank you Mom and Dad. I will never forget the roadsideradio contacts that
kept my sanity and thanks for the first and last financial boosts. But most of all to
my wife Nancy who stood by me and who has given me the greatest achievementof
all - my daughter Lacey Mercedes.I love you!
"
~
List of Symbols
c
Speed of light
eij
Error Coefficient
Sij
Scattering Parameter
Tij
Chain Scattering Parameter
Z
Impedance
,8
Propagation Factor
I
Propagation Constant
r
ReflectionCoefficient
f
Dielectric Constant
A
Wavelength
7r
Constant Pi
p
Reflection Coefficient
f.A)
Frequency
ANA
Automatic Network Analyzer
APC- 7 7 millimeter Coaxial Connector
DUT
Device Under Test
ETRL
Enhanced Through-Reflect-Line
ETSL
Enhanced Through-Symmetry-Line
III
-
.
IV
List of Symbols Continued
GHz
Giga Hertz
LRL
Line-Reflect-Line
MHz
Mega Hertz
MMIC
Monolithic MicrowaveIntegrated Circuit
.
OSL
Open-Short-Load
PCB
Printed Circuit Board
,
SPANA Signal Processingfor Automatic Network Analysis
SMA
3.5 millimeter,Coaxial Connector
TEM
TransverseElectromagnetic
TD R
Time Domain Reflectometry
TMR
Thru-Match-Reflect
TRL
Thru-Reflect-Line
TSD
TSF
Through-Short-Delay
Through-Symmetric Fixture
TSL
Through-Symmetry-Line
TTT
Triple Through
.
c'
1
Chapter
1
Introd uction
1.1
Motivation
, ,
Computer technolog"':(
increaseseachyear and we can associatethis to the increased
computational power. These increasesare spawned by increasedclock speedsrequiring knowledge of transmission line effects to successfullydesign and fabricate
systems. We must include effects such as transmission line discontinuities or at
the very least delay associatedwith the lines. There exist two methods of predicting these effects. One, the discontinuity can be studied analytically by calculating
its parameters based on electromagneticfield theory -
analytic modeling. Two,
the discontinuity parameters are measured- empirical model. Analytic models
provide a compact representationof the discontinuity yet they still require experimental verification. So regardlessof the modeling method chosen,measurementof
transmission line effectsis required.
The discontinuity parameters can be described with scattering parameters (s
parameters) and measurementof scattering parameters is a .well define process.
S parameters are measuredwith a network analyzer where by a single frequency
sinusoid is applied to the network and the energy reflected from and transmitted
2
through the network define its s parameters. The introduction of the Automatic
Network Analyzer (ANA), has given engineers the measurementtool needed to
study transmission line effectswith high degree01accuracy.
Inherent to ANA's is the abilit':l;to remove systematic etror by measuring several known networks (standards). This process is referred to by several names;
calibration, error correction or de-embedding. The calibration of automatic network analysis is a g~neral concept having direct application to the AN A 's and in
this study we considerits application to the measurementof Printed Circuit Board
(PCB) discontinuities.
The ANA calibration is done with coaxial standards but PCB transmissionline
structures are microstrip or stripline. This requires conversionfrom coaxial to PCB
structures and this introduces systematic error. The premise of PCB error correction is to determine the error associatedwith this conversionand remove it. An
application of ANA calibration could produce this result, however,manufacturing
of printed circuit boards imparts limitation.
PCB manufacturing does not allow insertion of calibration standards without
physically altering the board, i.e. destructive measurementssuch as cutting the
board and inserting conventionalstandards. Additionally, the number of measurements can be large if many printed circuit board discontinuities are being studied.
Fortunately PCB manufacturing has an important property. They are manufactured with repeatable uniformity on an individual board. With this in mind we are
3
motivated to investigate PCB calibration.
Calibration of automatic network analysishas been a popular researchtopic over
the last two decadeswith the automatic network analyz~rintroduced in the 1960's.
During the early to mid 1970'semphasiswasplaced on the ANA"calibration methods
,
and in the 1980's authors reported fixture calibration methods. Our intention is to
contribute to the rapid growth of fixture calibration methods by addressingprinted
circuit board fixture ,calibration. In the following section we provide an overview of
this report.
1.2
Thesis
Overview
The purposeof this report is two fold. First, two decadesof researchhas introduce a
considerableamount of information concerningcalibration of network analysis. The
purposeof Chapter 2 is to review calibration methods by organizingthis information
into two categories-
one and two port calibration. As an introduction to this,
we discussthe history of the Automatic Network Analyzer. One port calibration is
discussedand concludeswith a discussionof previous authors choiceof standardsand
their motivation. Two port calibration begins with a thorough review of AN A error
models and concludeswith fixture two port models and a discussionabout fixture
calibration standards. The secondfocus of this report is application of symmetrical
arguments to printed circuit board fixture calibration.
Printed circuit board is a noninsertablemeasurementmedium and is easily cal-
4
ibrated using symmetrical arguments. Chapter 3 defines symmetrical arguments
and develops new calibration methods exploiting symmetry.
Chapter 5 contains
the results from experimental verification of algorithm~ developed in Chapter 3.
Chapter 4 introduces SPAN A: Signal Proc~ssing of Automatic Network Analysis;
the computer program where algorithms are implemented and other data manipu"
lations are carried(out.
Finally, we conclude with summary of work accomplished
and suggestions for future work in Chapter 6.
This report also contains three appendices. One contains a discussion of decascading error networks and lists the necessary transformations.
The next is a
user's manual for SPANA giving semantic information about available commands.
The final appendix discusses the SPANA "shell" command where an example shell
subroutine is presented.
1.3
Original
Contributions
The original contributions reported here include:
i) the Through-Symmetry-Line
de-embedding algorithm whereby symmetric ar-
guments are used to synthesize either open or short circuit reflection coefficients,
ii) the development of Enhanced Through-Symmetry-Line
de-embedding algo-
rithm that calculates the complex characteristic impedance of the line standard
using the experimentally determined propagation constant and the free-space
5
capacitanceof the line standard,
iii) the direct application of this enhancementto the Through-Reflect-Line deembedding algorithm and Line-Reflect-Line algorithm,
iv) the developmentof Through-Symmetric Fixture de-embeddingalgorithm for
use on secondorder symmetric fixtures, and
v) the developmentof the computer program SPANA for algorithm implementation and other data manipulations.
6
Chapter
Review
2.1
Literature
2
of Calibration
Theory
Review
The determination of network parametersor network analysisis fundamental to the
understanding and designof all microwavesystems. It providesa tool for verification
of theoretical research and gives design engineersdata needed to complete their
tasks.
Before the introduction of the network analyzer in the late 1960's, one-port
impedance measurementsdominated the measurement arena. Slotted lines and
graphical interpretation were used by engineersuntil the developmentof the network analyzer. It was well understood impedancescould be measuredthrough an
unknown junction. If the unknown junction is losslessand representedby an effective impedance, then reflection coefficient measurementswith a matched load and
short circuit at the output of the junction give sufficient information to determine
the unknown impedance. In 1953,Deschampsdevelopeda graphical method to determine impedance if the junction is lossless.Through his result it was possible to
determine the unknown impedanceby synthesizing the matched load using several
offset shorts [1]. A similar processfor lossyjunctions was introduced by Storer et al.
7
[2] in 1953, whereby the junction parameters (input, output reflection coefficients,
and transmission coefficIent) could be determined by graphical means. Finally, in
1956Wentworth and Barthel combinedthis previous work and introduced a simplified graphical calibration technique [3].
Graphical methods provide insight into processeseffecting microwavemeasurement yet they are tedious and based on the users interpretation. To advancethe
state of the art in microwavemeasurementit was necessaryto considerother methods for microwave measurement. In the mid 1960's, scattering parameters (s parameters) began finding use in the circuit design community replacing reflection
and transmission coefficients. The need to measuretwo-port network parameters
becameincreasingly necessarywhile existing one-port graphical methods provided
no extension to two-port measurement. There is little doubt why automatic microwave measurementis essential and history shows two-port network analysis is
inherently calibratable.
In the late 1960's Hackborn introduced the automatic network analyzer [5]
(ANA) capableof measuringscattering parametersof two port networks. The ANA
produced accurate s parameter measurementsand offered calibration as a way to
assure accuracy. Calibration was analytic and performed by computer control as
compared to previous graphical methods and the automatic measurementsignificantly increasedmeasurementspeed.By modeling the network analyzer systematic
error, Hackborn developedthe foundation of calibration in use today.
8
Imperfections in the network analyzer were modeled as deviations from an ideal
analyzer and referred to as error representation networks, see Fig. 2.1.1. Error
for each ANA port was modeled with a correspondingscattering matrix with four
complexparametersand easilyrepresentedwith a signal flow diagram, seeFig. 2.1.2.
Since graphical calibration used known standards e.g. matched load, short circuits
or offset short circuits, it would seemappropriate to measuresimilar standards with
the new ANA in order to determine the error networks i.e. calibrate. This is exactly
what Hackborn did.
First for one port calibration, he measuredreflection coefficientswith the error
network terminated with an ideal short circuit, offset short and sliding matched
load. These three measurementswere sufficient to determine the error network
and repeating this procedure for the secondport gave six calibration terms (error
s parameters or products.
This result was sufficient for one port measurements
on either AN A port but for full two port measurementstwo additional calibration
terms neededto be calculated. A measurementof forward and reversetransmission
coefficients with the error networks connectedtogether (through connection) completed the two port calibration procedure. Finally, the removal of the error involved
an iterative solution of nonlinear equations basedon the signal flow diagram of the
device placed betweenthe port error networks. Soon after this work was published,
Kruppa and Sodomskyrevealed Hackborn's iterative solution was in fact explicit
[8].
9
Device
Under
Test
Port #1
Port #2
Test Unit
RF Source
-
~
1
'--
Ref
~
~
Test
Network
Analyzer
8
.
I
lopay
Freq
COny
Digital
Computer
Figure 2.1.1: Automatic Network Analyzer (ANA) for measuring scattering of two.
port networks, after Hackborn, 1968.
10
)
"
,
Port #1 Error
I
Ideal
ANA
Port
#1
Port #2 Error
I I
I
I
I
I
I
I
I
I
I I
I
I
I
I
Measuremen~
Port #1
I
Ideal
ANA
Port
#2
Measurement
Port #2
Figure 2.1.2: Signal flow graph representationof the ANA measurementerror. Error
networks corrupt ideal ANA, after Hackborn, 1968.
J
11
Since the introduction of Hackborn's AN A many authors have consideredits
use and studied network analyzers of diffe!"entcomponent topologies. Hackborn's
error models have ~tood the test of time only receiving minor improvements. His
contributions include one and two port error ~odels representedby signal flow
diagrams and a calibration algorithm for removing these errors.
The history of network analysiscalibration showsa significant changeas methods
of network analyzer calibration becamewidely accepted. At this point, authors began consideringfixture calibration rather than AN A calibration sincemany devices
to be measuredwere in transmission media different from the analyzer i.e. planar
devicesand coaxial analyzers. One and two port error models were still valid, only
the physical interpretation of the error terms changed.This resulted in direct application of network analyzer calibration methods to fixture measurements.However
this was only moderately successfuland new procedureswere developed.
2.1.1
Introduction
to Calibration
of Network Analysis
For a thorough study of the calibration of network analysis, we need to investigate
.
subtopics forming the calibration process. First we look at one port measurements
and discuss general methods of accomplishing one port calibration followed by a
review of previous investigators. Secondwe expand one port results to two port
and discussthe motivation of major contributors who evolved the Hackborn error
model.
"
,
"
12
~~
,~~,~(r~
2.1.2
,~~~~Ij
;ij~~~iJj:
The measurement of reflection coefficients or impedance at microwave frequencies
~j'ij~f:~ftl~;~;~
'~X~}t~fl~
tLJ'Jy~~S~fi~
The One Port
Error
Model
requires the determination of systematic error and then removing it i.e. calibrating.
$iftt{~~~~
Here we state one port calibration in a general fashion and then review calibration
':~J;;g~I~{~j~]
~:t:i%~~~?J::g;s~
methods developedby previous authors. The Hackborn one port error model shown
;i:\-;-~:iz~3[frifjJ~
~:;7t:;~;J!~~~;
in Fig. 2.1.3, has been examined by many authors. The measuredreflection coef-
,Jj~k;j~~~~~~
~i;~j;;~~~~f;i
ficient PM is related to the desiredreflection coefficient PL by the familiar bilinear
~ri£~;~~
,,1i~iWI1A~
!~.,~
transform .
""~,,,,-~~";%';&'
!~t~~"":iI;
:;~f':f1;:";:;',
,::c."
","
';",
:',
'!:;
PM =
eoo -
PL~e
1-
(211
. .)
PLel1
.
RearrangIng,
';(~(':':c:";;;
j",c,.,
;~,.""",
"';C"';iC'2'i\
PL --
- PM
eOO
~e
-
ellPM
~e -- eOOe11
- eOIelO
,,~{~;j;:~';:'~
~',,;
;f;r~l~~~
(2 .1.2)
(2.1.3)
-",,~,
.~iJt'JJ
::)~~~!t~~
:;J;:*fii~~~
we can see the desired reflection coefficient is altered by the error network com-
.,jJ~~!J~~-3;l;:$*
prised of scattering
,:;,'-:,~~~£;
parameters
eOO,
ell, and the product eOlelO.Two methods exit
for calculating the error network: (1) classical three termination, (2) redundant
terminations, or the impedance associatedwith PL can be determine without calculating the error network by using properties of the bilinear transform. Let us
consider these in more detail.
.'~;'i.'
"
,
13
One Port Error Network
a
p=1?m
a
PI
Figure 2.1.3: Signal flow graph for one port error network. Desired load reflection
coefficient PI is masked by error coefficientseij and Pm is the measuredreflection
coefficient.
J
14
Classical Result of One Port Calibration
Classical one port calibration is the calculation of these terms based on measurements made with three known terminations (standards) connectedto the reference
plane. The standards have associatedreflection coefficientsr 1,r 2 and r 3 and corresponding measuredreflection coefficientsMl, M2 and M3. Thesereflection coefficients with (2.1.2) form three simultaneousequations for the error terms with the
solution:
ell
A-I
= A'f";-=r-;
(2.1.4)
- (M2- Ml)(1 - ellrl)(1 - ellr2)
eOlelO -
r
2-
r
1
(2.1.5)
and
eOO
with
A=
-- M 1 - :~~~
I-ell
(
~-=-=.!:!-
r3 - r2
)(
M3
-
(2.1.6)
Ml
M2 - Ml
)
(2.1.7)
A final measurementand evaluation of (2.1.2) with the desiredload in place yields
the error corrected reflection coefficient. When a sweepfrequency measurementis
required, these error terms are calculated for each frequency thereby providing an
error corrected reflection coefficient versusfrequency.
Use of Redundant Standards
Three standards are necessaryand sufficient but sensitiveto experimental error. In
1974 Bauer and Penfield introduced the use of redundant standardsto improve the
c
J
15
calibration accuracy [9]. Although their results utilized impedanceparametersit is
a simple task to apply redundancy here.
An estimate of the error terms can be obtained by rearranging 2-.1.2yielding the
error function
eri
= PMi
- eoo+ PLi(~e - ellPMi)
(2.1.8)
with i = 1,2,3,... , N the number of standards and ~e as in 2.1.3. A least squares
minimization of 2.1.8 yields the error terms which are then used to calculate the
error corrected reflection coefficientgiven by 2.1.2.
Use of Bilinear Transformation
Properties
Perhaps the greatest deviation from the classical procedure is the use of bilinear
transformation to determineone port impedance. Although this is not a calibration
it doesproduce a result which correctsfor measurementerrors. Becausethe bilinear
transform method does not begin with a scattering parameter signal flow diagram
of the error network, laborious solution of simultaneous equations is not required.
If Zl, Z2 and Z3 are the impedancescorresponding to the standard reflection coefficients used above and M1, M2 and M3 are the associatedmeasuredreflection
coefficientsthen by using the crossratio property of the bilinear transform [10],
(~~ )(~~ ) = (M - )(
Ml
Z - Z3
Z2 - Zl
M - M3
M2
-
M3
)
M2 - M1
(2.1.9)
16
we can
directly find the load impedance Z from the measure of its reflection coeffi-
cient M.
Z = Zl - ZaQ
(2.1.10)
1-Q
Q=
~-=~~-~/~~
M-MaM2-Ml
Z2-Z1
The classical corrected reflection
coefficient can be used to determine this impedance
however the converse is not true because the reflection
the output
and bilinear
results of this area of microwave
is frequently
discussed by previous
port calibration.
of
authors
transform
methods encompass the
measurement.
The classical one port
and it is directly
extendable
to two
This extension will be discussed in subsequent sections, but first,
discussion of one port calibration
2.1.3
coefficient is a function
impedance of the error network which we do not know.
Classical one port, redundancy,
published
(2.1.11)
standards will conclude the one port methods.
One Port Calibration
Standards
Previous authors introduced three known terminations for use with the classical
one port calibration.
The investigators
were motivated to use their standards
various reasons. In 1968, Hackborn introduced
the one port
for
model and his choicefor
standards was influencedby need. A direct short circuit, offset short, and a sliding
load were used [5]. He chose the sliding matched load because it compensates for
an imperfect
[6, 7].
load. Since then authors have studied the sliding load in great detail
~
17
In 1971, Kruppa and Sodomsky used open and short circuits, and a matched
load [8]. Their apparent motivation was the simplicity these ideal standardsoffer
to the calibration equations. In 1973, Da Silva and McPhun replaced the sliding
load with a direct short circuit and two offset shorts [11]. A short circuit was
convenient and required less space. Shurmer was similarly motivated to avoid the
sliding load. His standards included an open circuit, direct short, and offset short
[12]. Gould et al. used matched load, short circuit, and mismatch load standards
and they were placed directly at the referenceplane. Gould chosethese standards
becausetheir characteristicsvary slightly with frequency and therefore reduce the
need for accurate frequencymeasurements[13]. In 1974,Kasa analyzedthe sliding
termination and found it was possibleto use a known load with two different sliding
terminations [6].
In each case,the authors indicated the standard terminations where known either by an ideal assumption or appropriate model. For example, short circuits or
offset shorts are assumedideal with reflection coefficientsof r
=
-1
or expj e.
An open circuit standard is assumedideal or the parasitic capacitanceassociated
with the fringing electric field determined. Of coursethis capacitanceis geometric
and frequency dependentand can be difficult to determine. To improve calibration
accuracy we need to increasethe certainty of the standards used.
In 1978, Da Silva and McPhun examinedredundant measurementsas a method
to reduce the uncertainty of their standards i.e. combinations of short and offset
J
'-"
18
short circuit terminations, or open and offset open circuit terminations [14]. Their
motivation was straight forward; offset standards require knowledgeof the propagation constant of the offset line. A fourth standard (one redundant standard) gave
sufficient information to determinethe line propagation constant and if a fifth standard was used, it was possibleto determine the reflection coefficientof an unknown
termination such as an imperfect open circuit.
We can use any combination of at least three standards and the choice is influenced by the accuracy of the standards. Many of these authors provided an
extension of their one port result to a two port calibration procedure with Hackborn leading the way. Using a format similar to our one port calibration discussion,
we will discusstwo port calibration.
Two port calibration, containing additional error terms, has undergonechanges
since the Hackborn model. First, let's examine the Hackborn two port model then
discussthe motivation of authors following him, and finally, look at the most recent
model.
2.1.4
ANA
Two
Port
Error
Models
Common to all two port calibration methods is the attempt to model system imperfections with error networks. Thesenetworks, being system dependent,have taken
on different descriptions to suit the system designer. Hackborn extended his one
port model to two ports by connecting the referenceports together and measuring
J
;7~
19
forward and reversetransmissionfrom port one to two. Fig. 2.1.4 showsthe signal
flow graph his through connection. Thesemeasurementsweresufficient to calibrate
his ANA giving a total of eight error terms,six oneport error termsand two transmission terms. This eight term result is derived assumingno leakagepath exits
between ports. This assumptionseemsintuitively impossible.
In 1973 Shurmer introduced the concept of leakageand developeda six term
two port error model [12], or simply a "one path" model. Shurmer's motivation
was straight forward, his network analyzer was not automatic. That is, he used two
hardware configurations, one for reflection and another for transmission measurements. This required a reversal of input-output connectionsof a device under test
( dut) to measureits s parameters. Fig. 2.1.5 shows the "one path" model introduced by Shurmer. If leakagewas important for this model why not Hackborn's
eight term model? Rehnmark, in 1974,introduced the ten term model by including
forward and reverseleakagein the Hackborn model [15], seeFig. 2.1.6.
Automatic network analyzersused today model systemerror with a twelve term
model which is a Shurmer one path for each direction. This idea was introduced
in 1978by Fitzpatrick and is shown in Fig. 2.1.7 [16]. However,it is not the most
comprehensivemodel in existence. Digressing for a moment, we need to discus,s
componentsusedin constructing an automatic network analyzer to fully understand
this comprehensivemodel.
True automatic network analysisfrees the user from interchanging the dut con-
L
J
20
Port #1 Error
Port #2 Error
Ideal
ANA
Port
#1
Ideal
ANA
Port
#2
I
I
I
Figure 2.1.4: Through connection of the eight term error model. Each port is
describedwith four s parameters,Sfj2, after Hackborn, 1968.
Figure 2.1.5: One path error model. Six error terms, fij embedthe device s parameters, Sij and for full characterization the device must be reversed.
-
J
21
e30
(1)
RF IN (1)
I
1
I
~1m
or
(2)
~2m
(1)
811
m
or
(2)
~2m
I
I
I
I
I
MeasurementI
Port#1
I
I
I
I
RFIN(2)
12
I
03
Device
Under
T t
es
I
I
I
I Measurement
I
Port#2
I
I
I
Figure 2.1.6: Ten term error model. Extension of Hackborn model by including the
leakageto and from eachport, e30and eO3,after Rehnmark, 74.
J
22
1
e30
RF IN
I
I
e1
~1m
~1
I
I
MeasurementI
Port #1
I
I
Device
Under
T t
es
I
I
er
r
e30
I
I
I
I Measurement
I Port #2
.
I
I
I
I
RF IN
~2m
~2m
I
I
Figure
12
I
I
2.1.7: Twelve term error model. Introduce by Fitzpatrick,
this model is a
dual "one path". Full characterization of the device is done without interchanging
ports.
J
23
nections. This useful feature is possibleby redirecting the microwavesourcebetween
measurementports and possibly using one complex ratio detector to determine amplitude and phaseinformation for both ports. Under this condition .two switchesare
neededas shown in Fig. 2.1.8. In 1979, Salehexamined this test set indicating the
measurementport impedanceslooking into PI and P2 can be functions of the switch
positions [17]. In other words, a general error model would require terms modeling each s parameter measured,Fig. 2.1.9, and a solution of systemsof nonlinear
equations would be necessaryfor calibration. Fortunately, test sets can be designed
while not requiring this general model. For example, by using two detectors it is
accurate to use the twelve term model mentioned above.
Up to this point, we have discussedtwo port error models neededfor calibrating
network analysis. Each author has developed a calibration method based upon
their model yet they have chosen from the "available" one port standards. We
find new standarQswereintroduced after thesemodels had becomewidely accepted
and calibration of network analysis began focusing on fixture calibration. The next
level of discussionapplies these models to fixture calibration assumingthe network
analyzer has been previously calibrated using one of the above models. This is
important to note since it will be shown fixture error models are comparatively
simple with regards to the number of error terms. In fact, Chapter 3 developsnew
calibration methods exploit the simplicity of fixture error models.
Source
Reference
~Source Switch
~2 and~2
~1and~1
P1
r--
""
24
\
DeVi;
P2
~ ~-~ ,,~d~
: Hr-~~
I
est
~ 1and~2
~2 and~1
DetectorSwi;!
Detector
Figure 2.1.8: Automatic Network Analyzer using sourceand detector switches. In
general,impedancelooking into PI and P2 is not constantthereforerequiring error
models for each s parameter.
RF IN
e4
512m
IN
511
m
e1o
es
RF IN
R
m
e13
16
522m
Figure 2.1.9: Sixteen term error model. Error models are used for each s parameter
measured,after Saleh,79.
25
2.1.5
Fixture
Two Port Error Models
The s parameter measurementof an arbitrary two port network can be divided into
two tiers. First we have the calibration of the network analyzer, i.e. measurement
and calculation of ANA error terms, and secondwe need to interface our arbitrary
network to the network analyzer. This interface or adaptor is commonly referred
to as the fixture. For example, if we were interested in measuringthe s parameters
of a microstrip transmission line we need a fixture to adapt from a coaxial AN A
to microstrip and then back again, Fig. 2.1.10. Fixturing introduces error into our
measurementand with modeling and additional calibration measurementswe can
removethis error.' This fixture calibration is sometimesreferred to as de-embedding
becausethe device to be measuredis embeddedwithin the fixture. From this point
on the terms calibration and de-embeddingwill be interchangeable.
Fig. 2.1.11 showsthe fixture error model. It is composedof two error networks,
one for each measurementport, error networks A and B. As we have seenfrom the
classicalone port calibration, there are six independent error terms for this model
and we can use one port calibration standards to calculate them. This result is
accurate if forward and reverse transmission through the fixture are equal. Fig.
2.1.12 shows a signal flow graph for the fixture error, and application of Mason's
rule verifies this fact. In general, a fixture is passiveand reciprocal so it must have
equivalent forward and reversetransmission coefficients.This is the only difference
betweenHackborn's ANA two port error model and the six term fixture model. The
"
;,.
J
26
C1
/
Coaxial Reference
Planes"""
C2
S
ound
lanes
Embedded
M2
Microstrip
L'
Mlcrostn p
Ine
;,,;
.,
"'e
Reference
Planes
[~
J
.
.f~o
Figure 2.1.10: Example of microstrip two port fixture.
.
.~~~j
i
,
,
)
27
I
I
I
I
Calibrated
A
ANA:
I
'
Port #1
/
I
I
I
I
I
I
I
I
!
II
I
I
I
I
I
I
B
!
I
I
.
.
::
~
:
Calibrated
ANA
Port #2
I
Fixture
Fixture
Port
#1
Port
#2
I
I
Figure 2.1.11: Block diagram of a two port fixture, A and B contain the fixture
error networks and the measurement planes are fixture ports 1 and 2.
I
:
Fixture
Error::
Network #1
!!
Calibrated
ANA
Port #1
I
Fixture Error
.:
Network #2
,
I
I
Fixture
Port
#1
I
:
alibrated
ANA
Port #2
I
I
: :
I
I
I
Fixture
Port
#2
Figure 2.1.12: Six term signal flow graph with error terms, eij.
"
J
28
AN A, however, can only be minimally
Additionally,
modeled by the eight term two port model.
fixtures can be constructed
smaller than internal
where port-to-port
AN A coupling therefore
coupling is significantly
is not necessary to alter the fixture
error model.
Unfortunately
many fixtures
use the classical one port
two port fixture
standards
calibration
in microwave
standards
or de-embedding
consider a micros trip fixture.
load standard
encountered
standards.
To strengthen
this point,
We have seen it is advantageous to use a matched
assumes we know its reflection
coefficient.
load and a sliding
must use other standards.
can not
and there exits a need for unique
since it allows direct measurement
effective matched
measurement
Similarly
of one error term.
This of course
In micros trip we can not fabricate
termination
is physically
an open circuit
standard
impractical
is difficult
an
so we
to model
so we need to avoid it as well.
2.1.6
Fixture
Two Port De-embedding
How can we de-embed planar fixtures?
be used so standards
unique
Most classical one port standards
to two port
sections of different geometries are typical
our fixture
fixtures
a distributed
are needed.
de-embedding
with a known two port (transmission
error networks we introduce
Standards
Transmission
standards.
line
By measuring
line) inserted between the fixture
de-embedding
In 1975 Franzen and Speciale introduced
can not
distributed
standard.
standards
for calibrating
~
29
their ANA. Although their method is not a two-tier approach it is significant because they were the first to introduce distributed standards. Their technique was
conveniently called Through-Short-Delay or TSD [18].
At this point we would like to briefly outline the next discussionof various fixture
calibration procedures. First we will look at the standards used and consider the
authors motivation and secondwe will examinethe disadvantagesencounteredwhen
using them.
TSD - Through-Short-Delay
TSD is based on both reflection and transmission measurementsand it offers two
advantages.First, a matched load standard in not required and secondit usesmechanically simple standards. In addition, Franzen and Specialefound an addition
delay line could be used to insure consistency within their measurements. TSD
is not without disadvantage. The delay standard was assumedlosslessand nonreflecting i.e. the propagation constant was pure delay and the impedance was the
measurementsystem or 50 ohms. Also, TSD although not mentioned by these two,
requires information from two delays;the through connectionand the actual delay.
If the phase differencebetween thesetwo is near zero or 180 degreesthe algorithm
will fail to return a valid result. This is a limitation of any de-embeddingtechnique
using a delay type standard. Franzen and Specialedid not apply their results to a
planar fixture but their work is significant. In 1976, Bianco et al. consideredthe
planar problem first hand by applying distributed standards to a microstrip fixture
~
30
[19].
Line-Offset Open-Line
Bianco used a total of three distributed standards; two delay lines and one offset
open circuit for de-embeddingstandards. Just as with TSD, the delay lines were
nonreflecting but they were not assumedlossless,in fact, the propagation constant
and open circuit reflection coefficient could be determined for the microstrip line.
The mechanicsof their de-embeddingrequired a separatemeasurementfor each
inserted delay line and a one port measurementwith the error networks terminated
with the offset open circuit. Of course their algorithm was subjected to the 180
degreebandwidth limitation with an added problem. When two delays are used
it is assumeduniform and they have equivalent characteristic impedances. It is
interesting to note this result was reintroduced in 1979by Engen and Hoer under
the familiar name Thru-Reflect-Line [20].
TRL
- Thru-Reflect-Line
TRL as developedby Engen and Hoer used only one delay standard with a through
connectionand an arbitrary reflection to calibrate their network analyzer. The delay
standard could be arbitrary, with its propagation constant unknown, however,the
line was assumednonreflecting. The reflection standard could be any repeatable
reflecting load and they suggestedeither an open or short circuit. Again, this result
was stated by Bianco but Engen was the first to consider algorithm singularities
,
(
31
associatedwith distributed standards.
Neither the Bianco or Engen work had been applied directly to a fixture. Benet,
in 1982,introduced the universal Monolithic Microwave Integrated.Circuit test fixture requiring severaldistributed standardsfor calibration yet they choseyet another
calibration algorithm.
Open-Short-Five
Offset Lines
Benet developedthe open-short-fiveoffset line calibration using a one tier approach
[21]. As discussedbefore, the one tier calibration is usually centeredon the twelve
term ANA error model six for each direction of measurement. To determine the
six terms Benet measuredthe fixture's responsewith open and short circuits at the
fixture referenceplane and then a minimum of three offset thru lines were inserted
and measured. As an approximation, the offset lines causedthe measuredreflection
of the fixture to scribe a circle and at the center was an additional error term.
Two additional offset lines were used to allow a least squaresfit of the circle to
these measurements. Returning to the open and short circuit error equations, he
showedtwo additional error terms could be determined. Finally, by approximation
he determined the propagation constant of the thru lines and the remaining error
terms. Benet's contribution showedinsertable distributed standards could be used
to calibrate a test fixture. Next we will seea two tier de-embeddingmethod obtains
a similar result and requires fewer assumptions.
!
32
Open-Short-Modeled
Through Line
Under some circumstancesthe fixture can not be calibrated using insertable standards such as a transistor test fixture. Here the fixture cannot be separatedto insert
the de-embeddingstandards. In 1982Vaitkus and Scheitlin proposeda two-tier deembeddingmethod for this noninsertablefixture [22]. The AN A wasfirst calibrated
using OS1 and its twelve term error model and then fixture de-embeddingmeasurements were done. Their standards were an open and short circuit and a modeled
through line [22]. The error model was simply a one port error network for each
fixture port and two leakage terms to compensatefor a leakagepath around the
transistor chip. This is a simplification of Rehnmark's ten term ANA error model.
c
Vaitkus and Scheitlin exploited two points - the fixture passivity and the identical
forward and reverseleakage. This alloweda reduction of the number of error terms
to seven. Comparing this de-embeddingresult with Benet's, simplification is possible if a two tier calibration/de-embedding method is applied becausethe fixture
offers a reducednumber of error terms.
A through line standard had beenpreviously used by others but Vaitkus differed
by using a modeled through line and determined its equivalent circuit by optimization. A bond wire through line connectedthe fixture ports together and the
equivalent circuit was optimized to fit the measuredfixture s parameters. A similar
procedure was performed on the bond wire short circuits. Vaitkus and Scheitlin
produced results using a through line standard but a generalexamination of Open-
33
Short-Through line was introduced later by Vaitkus himself [23] in 1986. Rather
than model the through line, he assumedknowledgeof the line propagation constant,
the short circuit inductance, and the open circuit fringing capacitance.
Double Through Line
In 1987, Pennock et al. introduced a de-embeddingtechnique for characterizing
transitions betweennovel transmission media [24]. Their motivation was a lack of
conventional standards and a need to reduce the total needed. In 1976, Bianco et
al. eluded that transition parameters could be determined to within a multiplicative constant if only two through line standards are used [19]. They also showed
measurementof an additional through line was a linear combination of the first two
and the constant could not be determined. Pennock exploited the multiplicative
constant and proceededto use two line standards for their de-embedding.
Their fixture error model was the commonly usedsix-term, two-port error model
completely characterizewith three standards. Pennockshowedthe Bianco constant
was a ratio of two error terms. In fact, this ratio is nearly equal to unity for
reasonabletransitions and Pennock proceededto de-embedthe fixture under this
assumption.
This result is not without problems. First, as stated before,distributed standards
must avoid A/2 singularities and second,the line must be refiectionless.Additionally,
the line attenuation constant is known or assumedequal (losslessline).
34
TTT - Triple Through
In 1988, Meys introduced a fixture de-embeddingmethod using an auxiliary two
port and matched load for standards [25]. Beginning with the standard two port
error model, the A and B error networks are connectedtogether and measured.
Also, the auxiliary two port C is cascadedto either side of A and B to form the
measuredtwo ports BC and CA. Theseand the AB two port provide necessarybut
not sufficient information to determine the error networks. The reflection coefficient
for the auxiliary two port terminated with a matched load is sufficient to determine
the error networks.
The use of a matched load is undesirable but Meys points out if the C two
port exhibits low SWR we can assumeits reflection coefficientis zero and eliminate
the matched load requirement. Since distributed standards are not used TTT is
inherently broad-band.
Results of Eul and Schiek
In 1988, Eul and Schiek examined the conventional two port measurementsystem
from a linear algebraicpoint of view. Their worked showedresults noted by previous
authors such as a needfor at least three de- embeddingtwo ports for completecharacterization and previous de-embeddingtechniques. Their main contribution was
the study of redundancy [26]. When three standards are inserted betweenthe error
networks and subsequentlymeasured,the total number of unique measuredquan-
,
35
tities is twelve, yet there are only eight linearly independenterror terms. This redundant information can be used to reducethe required knowledgeof the standards
and as a result they proposed severalde-embeddingmethodsThru-Match-Reflect is
one example.
TMR - Thru-Match-Reflect
Thru-Match-Reflect usesa through connection,a matchedload (or any other known
reflection coefficient) and an arbitrary reflection. It offersthe broad-band advantage
of these standards howeverwe need a prior knowledgeof at least one standard i.e.
the matched load. The reader is referred to [26] for discussionof the calibration
algorithm used with these standard combinations.
2.2
Conclusion
The review of calibration theory encompassedone port measurements,automatic
network analyzer error models, calibration methods and fixture de-embedding.It is
clear calibration of network analysishas beenan dynamic study coveringmuch of our
recent measurementhistory. It contains a variety of methods becausethe results
of one may not be applicable to another or someonehas a unique de-embedding
requirement. It is important to note when approaching a calibration dilemma one
should look at the problem from a known/unknown point of view. In other words,
consider the total number of unknownsin the measurementsystem and then decide
36
on the variety of standards that are available. We feel this review provides the
insight into calibration methods and hopefully given the reader a "what if we use
..." attitude towards their calibration of network analysis. Using this philosophy,
the next chapter developsnew calibration methods.
t":?:1'if':";
~1:~
".
l
.
37
Chapter
Calibration
3
Using a Symmetric
Fixture
3.1 Introduction
As we have seen from Chapter 2, it is clear a calibration can take many forms.
Naturally, we feel another calibration topic remains untouched -
exploitation of
the symmetrical nature of measurementfixtures. As with past calibration methods,
there was a need for something "new" and we are similarly motivated with this
study.
Chapter 3 concentrateson discussingadvantagesof symmetry arguments, reviewing symmetrical de-embeddingmethods, and the developmentof two new symmetrical de-embeddingalgorithms. In addition, we will re-examineTRL calibration
and develop a practical enhancement.
3.2
Motivation
for Using Symmetrical
Arguments
When consideringthe history of calibration of network analysis, two directions have
been pursued by the measurementcommunity. On one hand, there was a need
to compensatefor imperfections in calibration standards, and on the other hand,
calibration accuracy is directly related to a prior knowledge of the standards and
38
if at all possible choosethe minimum necessary.A symmetrical argument allows a
reduction in required standards thereby improving the certainty. In fact, later in
this chapter we show it is possibly to reduce the total number of standards to one.
With this in mind, when can we use a symmetric argument or when is a fixture
symmetric?
3.3
Evolution
from
an Asymmetric
to Symmetric
Fixture
A symmetric fixture is a special caseof the general asymmetric fixture. In Fig.
3.3.1, we seethe conventional two port error network and its correspondingsignal
flow graph. It is composedof two error networks A and B and in general, the
individual signal paths 8ija and 8ijb are unique forcing the fixture s parameters8ijl
to be unequal to eachother. This representsan asymmetric fixture.
A fixture is symmetric if the port 1 and 2 reflection coefficientsare equal and
the fixture is reciprocal, i.e. if 8111
=
8221 and 8211
= 8121'
Reciprocity
is true
when the fixture is passive and non-magnetic and these symmetrical equalities are
possible with two orders of symmetry; first and second order.
Using Mason's non-touching loop rule [4] we see the fixture s parameters are
related to the individual error terms,
8 111 -
811a + 821a812a811b
1 8 8
-
22a lIb
8221 -- 822b + 822a821b812b
1 - 822a8lIb
(3.3.1)
(3.3.2)
39
I
I
A
:
:
::
I
1
B
:
:
I
I
I
Po
#1
ort
#2
I
I
I
I
I
I
::
I
I
I
(a)
I
I
I
8
21f
I
I
I
~,
I
8121
I
I
I
I
(b)
Figure 3.3.1: Two port error model for an asymmetric fixture (a). Fixture error can
be described with eight error terms Sija and Sijb. Port 1 and 2 are the calibrated
ANA measurement ports. (b) Sijj are the measured fixture s parameters.
40
S21J
=
S21aS21b
1-
(3.3.3)
S22aS11b
and
S12J =
S12aS12b
(3.3.4)
1 - S22aS11b
Equating 3.3.1 and 3.3.2 and applying reciprocity we find one equation in six complex
unknowns.
Slla(l - S22aS11b)
+ SllbS~la= S22b(1-
S22aS11b)
+ SllbS~la
(3.3.5)
This is the symmetry condition equation representingan under determined system.
This implies symmetry can be produced with an infinite number of six error parameters. Fortunately, symmetry correspondsto the physical nature of the fixture
which limits the symmetric solutions to two - first and secondorder symmetry as
discussedbelow.
\
3.3.1
First
Order
Symmetric
Fixture
A first-order symmetric fixture has identical fixture halvesthat are asymmetric, see
Fig. 3.3.2. The port two error network, B, is now a port reverseof A, or B = A R.
This is true if Slla = S22b,S22a= Sllb and S~la= S~lb' Moreover, these conditions
satisfy the symmetrycondition (3.3.5). A "coaxialto microstrip" - "microstrip to
coaxial" fixture is an example of first order symmetrical fixturing. Most important,
the signal flow graph showssymmetry reducesthe number of error terms to three,
the A network only. In other words, symmetry reducesthe number of error terms
41
I
R
A
-
I
A
f
"';
I
;"",
I
:
1
'"
I
Po
ort
#1
#2
""'fi'i
"""~
ik~
I
I
:
I
Tii
I
::
I
~
,?,~~";j",;j
I
I
I
I
I
I
I
I
I
I
I;;{~~g;,1~
~~,";,;.;~.o;;:
S
I
I
I
~:;I'~ii)~*
I
f
I
21
I
l~~;1i!1~jj;;,:
I
I
""~;"
~;;;:-~~
IIJ
c:(
,
~
~~
~
(b)
Figure 3.3.2: Two port error model for a first order symmetric fixture (a). Fixture
error networks are describedby three s parameters 5ija. (b) 5111and 5211are the
measuredfixture s parameters.
.iR
""
42
for a two port fixture, and this reduction is strictly a function of the manufacturing
repeatability with direct application to printed circuit board measurements.
3.3.2
Second
Order
Symmetric
Fixture
If the fixture halvesare identical and symmetric, the fixture is secondorder symmetric. This implies network B is equal to A or all reflection s parameters, Siia or Siib,
are equal,( = S11)and all transmission s parameters are equal, Sija or Sijb, (= S21)'
seeFig. 3.3.3. A secondorder fixture satisfiesthe symmetry condition (3.3.5). A
lumped element transistor test fixture is an example of secondorder symmetrical
fixturing.
3.4
Review of Symmetrical
Methods
Previous authors have examined symmetric fixtures. In 1982, Souza et. al. used
a microstrip first order fixture to develop a method to calculate the fixture half.
Their results are based on further assumptions. First, the microstrip line used in
the fixture is reflectionless(50 n characteristic impedance) and secondthe fixture
half has a low return loss [27]. Howeverif the fixture introduces significant error,
this result is not applicable. In other words, if the fixture microstrip line impedance
is different from 50 ohms, both assumptionsare invalid.
In 1983, Pollard and Lane indirectly used a first order symmetry assumption
by modelling their fixture half with a pi equivalent circuit with different shunt
'c
43
A
I
I
I
:
:
::
1
:
:
A
I
I
I
Po
#1
ort
#2
\
I
I
I
I
I
::
I
I
Figure 3.3.3: Two port error network for a second order symmetric
error is described with two s parameters Sll and S21.
c
I
I
fixture.
Fixture
44
capacitances[35]. Their calibration standards are an open and short circuit and
a through connection. The fixture input impedance equations for the open and
short standards give sufficient information to extract the pi equiv~lent parameters
if secondorder frequency terms are neglected. As with the Souzaresult, they use
assumptions in addition to symmetry. Their result is invalid when the fixture is
considerably long or can not be modeled with a lumped element circuit. In 1986,
Ehlers was the first to apply symmetry without additional fixture assumptions.
Ehlers studied a finline first order symmetric fixture. The standards include a
through connection and either a matched load or a reflectionlesstransmission line
[37]. He pointed out a symmetric fixture requires two standards for calibration.
This is true only if the matched load or a reflectionlesstransmission line can be
fabricated. If neither are accurately possible (as is the casefor microstrip fixtures)
then an additional standard is needed.For the finline examplehis result is adequate.
Most recently, in 1989,Enders developedan iterative de-embeddingmethod using three line standardsto determine the parametersof a first order fixture [36]. His
result affirms symmetry is useful for calibrating fixtures and in the next section we
will apply symmetrical arguments and distributed calibration standards. A second
order fixturing was examined by Martin and Dukeman in 1987. They found a second order fixture requiresonly one standard; a through connection[31]. Their result
uses extensive matrix renormizations and in a following section a similar result is
developedbasedon signal flow theory.
45
3.5
Development
of Through-Symmetry-Line
- TSL Using
First Order Symmetry
3.5.1
Using Symmetry
to Replace the TRL Reflect Stan-
dard
As we have seenbefore, the calibration of a planar measurementfixture, e.g. microstrip and stripline, requires distributed standards. The preferredmethod for pla'"
nar fixture de-embeddingis Thru-Reflect-Line (TRL) or Line-Reflect-Line (LRL)
becausethe distributed standards are easily modeled and constructed. A typical
microstrip fixture, shown in Fig. 3.5.1, is a first order symmetric fixture. Identical
coax to microstrip transitions and identical microstrip line lengths are the requirements for symmetry. Thesecan easily be achievedup to low microwavefrequencies
and at higher frequenciesthrough careful design.
Becausefirst order symmetry allows the fixture to be representedby three error
terms, three standards are needed. Symmetry permits synthesisof TRL reflection
standards thereby eliminating their need. TRL standards are shownin Fig. 3.5.2a through connection, a reflection and a referencetransmissionline of length 1. The
reflection is arbitrary and is typically a short circuit. For the symmetrical through
connection, we can calculate the reflection coefficient with the microstrip ports terminated in ideal open or short circuits. Either synthesizedreflection coefficient can
replace the TRL reflection standard. Conforming to the naming of de-embedding
46
/
""
Coaxial Reference
Planes
S
Ground
lanes
~
/'"
Micr,ostrip
Line
"
1""'--
"'"
L
/
--I
Microstrip
Reference
Planes
Figure 3.5.1: Typical microstrip fixture.
47
I
I
I
I
ThroughConnection
Calibrated
ANA
Port #1
A
I
I
I
I
I
I
Calibrated
ANA
Port #2
B
I
I
(a)
I
I
"
,
I
Arbitrary Reflection
[
I
"c
'"
:
ArB
~
,.
!,
II
I
I
(b)
I
I
I
I
A
Line
B
I
I
I
I
(c)
Figure 3.5.2: TRL calibration standards. (a) Through connection, (b) Arbitrary
reflection, r, placed at eachfixture port and (c) Line connection.
48
methods we will refer to this method using thesesynthesizedstandardsas ThroughSymmetry-Line or TSL.
3.5.2
Synthesize Reflection
Standards
The TSL standards are through and line connections,Fig. 3.5.3. These are similar
to Souzaet al. [27]however their result is based on symmetry and a low fixture
return loss assumption. Note, the symmetry reflection coefficientscan be used with
the LRL algorithm with similar results. Next we will expound the derivation of
ideal open and short circuit reflection coefficients.
Referring to the signal flow graphsof Fig. 3.5.4, we considerthe through connection s parametersgiven by, Sll/(
= S22/) and S21/(= S12/),andthe actualparameters
of the A network being E, a and "'{ for Slla, S21a= S12aand S22arespectively. In
addition, the input reflection coefficient with an ideal short circuit placed at port
1b of A is
Pac= IS-
- a2
(3.5.1)
1+"'{
Previously we used Mason's rule to relate the fixture parametersto the individual
network parametersin (3.3.1) - (3.3.4). Here a similar result is given for the first
order symmetric fixture.
Sll/
S21/
= +
a2"'{ 2
IS
=
(3.5.2)
1-"'{
a2
2
1-"'{
(3.5.3)
.
,f
.
i'!
Through Connection
:?tk;:;;;ii';?J('cZ:;'~§!
I
:*1'~~"!:;~f~;;f~;;}~~;
F;"'~""""
,.~~i;"'f'C:'"'-;;;:;tc
r{i':5;iff1}~:~~~i.
49
Calibrated
R
A
ANA
A
I
I
Port #1
Calibrated
ANA
Port #2
(a)
~
R
A
A
(b)
Figure '3.5.3: TSL calibration standards. (a) Through connection and (b) Line
connection. TRL reflection standard is synthesizedusing symmetry.
50
I
I
I
I
8
I
I.
211
Calibrated
ANA
Port
#1a
Calibrated
ANA
Port
#2a
8211
I
I
I
I
a
I
:
:
(a)
1
I
I
:
:
I
I
a
I
I
::
Po
#1
ort
#2a
a
I
I
:::
I
I
#1b
I
I
a
P
sc
I
:
a
I
I
I
I
(b) #2b
a
I
I
= J?.
a
b
I
I
I
I
I
I
-1
(c)
Figure 3.5.4: TSL signal flow graphs. {a) Measuredfixture s parameters,(b) Fixture
error model describedby parameter 8,a and, and (c) Signal flow graph with ideal
short circuit placed at fixture port lb.
,
51
Combining (3.5.1), (3.5.2) and (3.5.3), the short circuit reflection coefficient can be
expressedas a function of fixture s parameters (measured).
P"c= Sll/
-
(3.5.4)
S21/
A similar results holds for an ideal open circuit placed at port lb.
Pac= Sll/ + S21/
(3.5.5)
Compared to TRL, TSL reducesthe number of standards neededand requires
fewer connectionsto the microstrip ports improving the repeatability of this connection. Moreover, P"cand Paccan be derived for any fixture exhibiting first or second
order symmetry including other planar measurementfixtures. Since these reflection coefficientsare derived mathematically, it is possibleto "insert" ideal open and
short circuits within a non-insertable medium such as a dielectric loaded waveguide.
The reader is directed to Chapter 5 for experimental verification of a symmetrically
synthesized short circuit. In the next section TSL is enhancedand this result is
directly applicable to TRL and LRL.
3.6
3.6.1
Enhanced Through-Symmetry-Line
Motivation:
Failure
of TRL
- ETSL (ETRL)
Assumptions
The development of ETSL, hence ETRL, is necessarybecauseof assumptions inherent to the TRL algorithm. As introduced in 1979 by Engen and Hoer [20], the
52
algorithm requiresthe characteristic impedanceof the line standard be equal to the
measurementsystem impedance. If not, its value has to be determined. Also, the
algorithm assumesa real characteristic impedance with no frequency dependence.
If the fixture to be calibrated is composedof dispersivetransmissionlines, e.g. microstrip, it becomesnecessaryto determine the complex characteristic impedance
Zc as a function of frequency. We presentan enhancementof the TSL algorithm by
determining the characteristic impedanceand so it is termed Enhanced ThroughSymmetry-Line -
ETSL. For the sakeof discussionwe will consider an embedded
microstrip fixture. Application of ETSL to an embeddedmicrostrip fixture follows
in Chapter 5.
An approximate value of Zc can be made using time domain refiectometry
(TDR), however, TDR can not determine frequency variations of the microstrip
characteristic impedance which can vary by as much as 5 percent from DC to 10
GHz for a typical microstrip line [32].Also, accurate modeling of Zc is complicated
by severalfactors; acceptedmodels predict different frequency variations; material
parameters may not be known; and ideal microstrip geometry may be corrupted
by dielectric coveringssuch as a passivation or solder resist layer as in the caseof
printed circuit boards, see Fig. 3.6.1. ETSL determines the complex characteristic impedance using the free-spacecapacitanceof the microstrip geometry and an
experimentally determined propagation constant, , = cx+ j,8.
The impedance calculated in this fashion, if used in the conventional TRL al-
"
I
53
i:'
j
~;
,r
~
'Z
Metal Thickness = 3.6 mil
Resist Layer Thickness
=
4. mil
+
'
'
'dth = 8. mil
+
=
!~~l.~e~1
+
+
GP Thickness= 1. mil
&":j
Solder Resist Layer
[Z3
Substrate Dielectric
.
Metal(copper)
t,
Figure 3.6.1: Embeddedmicrostrip encounteredin printed circuit board technology.
54
gorithm, compensatesfor the algorithm assumptions. By using a free-spacecapacitance explicit knowledgeof the dielectric parametersi.e. relative dielectric constant
and losstangent are not necessary.Also, we can determinecharacteristicimpedances
of atypical geometriessuch as embeddedmicrostrip or any uniform TEM transmission line. Additionally, by incorporating the propagation constant we embody the
effect loss has on the characteristic impedance(complex Zc). In short, this method
can be used to determine characteristic impedancesof any arbitrary uniform TEM
transmission line. In the next section we develop the characteristic impedance algorithm with microstrip being the transmissionline.
3.6.2
Calculation
of Complex
Characteristic
Impedance
Microstrip lines are non-homogeneoustransmission lines supporting a quasi-TEM
mode [32]. Howeverthe TSL algorithmrequiresthe equivalentTEM modecharacteristic impedance. For uniform TEM transmission lines characteristic impedance
is related to the free-spacecapacitanceand the effective dielectric constant by [33]
Zo
Zc = -;;=
(3.6.1)
yfe
with
1
Zo = ;:;voC
(3.6.2)
where Zc is the dielectric loaded characteristic impedanceof the line, Zo is its freespacecharacteristic impedance, Co is the free-spacecapacitance,c is the velocity of
light and fe is the effective dielectric constant. Co is a geometrical dependentfactor
55
and is the capacitanceof the structure in a dielectric-freemedium. It is well known
the effective dielectric constant is related to the propagation constant I by [28]
fe
where I
=
(3.6.3)
-rc2
2
!.IJ
= a + j fJ is availablefrom measurementas a by product of the TRL
algorithm. Recently, Mondal and Chen reported the TRL algorithm can be used to
determine the propagation constant of the TRL line standard. That is [29]
)
In (A~_~~~~
]
1=
1
(3.6.4)
where
A = TIlt'
T221+ TIll.
T22t - T2It . TI21 - T12t . T2Il
(3.6.5)
Tijl and Tijt are the chain scatteringparametersfor the line and through calibration
standards respectively, and 1is the length of the line standard. Conversionfrom s
to t parametersis given by,
(
)
T11
T12
T21
T22
= -1
s21
(
-~
Sll
)
(3.6.6)
-S22
1
where
~
= SllS22 -
S12S21
(3.6.7)
This result can be derived for any fixture, symmetric or otherwise,and it is a natural
progressionto incorporate this information to determine the complex characteristic
impedance. Combining (3.6.1)- (3.6.3) and taking the negative root
Zc
=
)!.IJ
2rY
C VOl
(3.6.8)
56
The negative root is chosen because the result must be positive when the line is
lossless and the impedance is positive real. This characteristic impedance is used to
overcome impedance assumptions of TRL and is applicable to the TSL algorithm.
The reader is directed to Chapter 5 where this derivation is experimentally verified with a fifty 11 coaxial example. Also, Chapter 5 contains complex micros trip
characteristic impedance calculated with the verified algorithm.
Next we examine
singularities encountered when distributed standards are used and expand on the
effect they have on calculating the propagation constant.
3.6.3
Calculation
of Propagation
Constant
Inherent to the TRL algorithm is the need to separate the error networks with a
transmission line. The line standard must be sufficiently long to produced a measurable phase difference between through and line fixtures.
Naturally,
at lower
frequencies this measurement is limited by the network analyzer measurement accuracy. Additionally, if the electrical length of the line is near 180 degrees it appears
transparent.
TRL returns invalid results in either case. Intuitively
the "farthest"
we can be from 180 degrees (or zero) would be a phase difference of 90 degrees and
reliable propagation constants can be extracted from 20 to 160 degree phase differences [30]. By choosing line standards with electrical lengths within this range the
characteristic impedance can be determined with no effect from the singularities.
,
57
3.6.4
Modifying
TSL Algorithm
Again, the TRL (TSL) algorithm requires a reflectionlessline. This is achieved
by transforming each calibration measurementfrom the measuI;ementreference
impedance to Zc. Application of TRL then determines the s parameters of the
error network referencedto Zc. To completecalibration, the s parametersof the error network are returned to the measurementreferenceimpedancesystem, (usually
50 ohms).
3.7
Development
of Through-Symmetric
Fixture
- TSF
Using Second Order Symmetry
What if the fixture is second order symmetric? Again, we define second order
symmetry as a first order fixture with symmetric halves. As we have just seen,
symmetry can be used to reduce the number of standards needed. When second
order symmetry is valid the two port error network is representedby two error terms.
Naturally, this allowsus to usefewerde-embeddingstandards,in fact, a secondorder
fixture requires only one measurementconfiguration, a through connection, thus in
conformancewith the practice of naming calibration procedures,we designatethe
new technique Through Symmetric Fixture - TSF method.
Fig. 3.7.1 showsthe signal flow graph for the fixture s parameters Sijf and the
correspondingtwo port error model. Each error is identical and symmetric therefore
58
I
I
I
I
8
I
I.
21f
Calibrated
ANA
Port
#1a
Calibrated
ANA
Port
#1a
821f
I
I
I
I
I
I
a
I
:
:
(a)
1
:
:
I
I
a
::
I
I
Po
#1
ort
2a
I
I
I
a
I
I
!
!
I
I
#1b
(b) #2b
a
I
I
Figure 3.7.1: Signal flow graphs used by TSF. (a) Measured fixture s parameters
and (b) fixture error network describedby s parameters c5and c¥.
59
the scattering matrix of each fixture half is
[Sija]
= [:
:]
(3.7.1)
The goal of TSF is to determine the error t~rms (a and 8) and is based on
Mason's non-touching loop rule, unlike the matrix renormalizations used by Martin
and Dukeman [31]. S parameter measurementsof the through connection yield two
independent quantities, Sllf and S21/, as Sllf = S22f and S12f = S21f becauseof
symmetry and reciprocity. This is sufficient to determine Sija. For clarity, we will
let the subscript t (t
Sijt
- through) represent the measuredfixture
s parameters f, i.e.
= Sijf.
The signal flow graph provides two algebraic relationships for the known quan-
tities as functions of the error terms,
Sllt
a28
= 8 + 1""=-";5"2
(3.7.2)
S21t
= 1-a282
(3.7.3)
8=
-~!-
(3.7.4)
c~~
Rearranging
a
1 + S21t
b2 - Silt
= V/S21t--~
rt
( 3.7.5)
where
b = 1 + S21t
(3.7.6)
60
The squareroot gives two possiblesolutions and the root choicedependsupon the
electrical length (Le) of the through connection. The positive root is valid when
nA < Le <
(2n + l)A
2
(3.7.7)
where
n=0,1,2,...
(3.7.8)
otherwise the negative root is correct. This choice of roots is based on a physical
constraint. The a term is the transmission coefficient of the error network and at
low frequency the phaseof a must be negative therefore the positive root choicein
this interval.
Equation (3.7.4) containsa singularity limiting the bandwidth of TSF. When the
fixture S21tis nearly equal to -1 (3.7.4) returns invalid results for [j. This can occur
when the fixture length is n)'/2. This singularity can be avoidedif the length of the
fixture is constructed so it is not an integer half wavelengthlong at any frequency
in a desired measurementrange. TSF can be used on a lumped-elementtransistor
test fixture where this restriction does not exist. Similar singularity restrictions
exist when other distributed de-embeddingtechniquesare employed. The reader is
directed to Chapter 5 where TSF is experimentally verified.
3.8
Conclusion
In Chapter 3, we havepresentednew de-embeddingalgorithms. By using symmetric
arguments, it is possibleto reducethe required calibration standards. It was shown
"
61
that reflection standards can be synthesizedfrom a through measurement. Also,
the complex characteristic impedance of uniform TEM transmission lines can be
determined if the transmission line free-spacecapacitanceis known. Taking this
impedanceinto account, we can enhancethe TSL or TRL algorithms.
Computer implementation of these algorithms is necessaryfor verification purposes. The next chapter developsSPANA or Signal Processingof Automatic Network Analysis -
a command level program useful for algorithm implementation
and other computer aided data manipulation.
62
Chapter 4
SPAN A: Computer Program
Aided
4.1
Introduction
Microwave
for Computer
Measurement
to SPANA
Computer processingof microwavemeasurementsis necessaryto free the engineer
from the costly measurementtime. It is very reasonableto assumecomputer processingis needed since a n frequency two port measurementcan produce sixty
four kilobytes (64K) of data. SPANA (Signal Processingfor Automatic Network
Analysis) has been developedto meet the needsof automatic microwavemeasuring
systems.
SPANA is a tool to be used for processingmeasuredS parameter data and its
prime use is to implement de-embeddingalgorithms. SPANA also performs various
tasks such as input/output of data, data format conversions,and others. Written
in FORTRAN in a modular fashion, SPANA is conduciveto future expansion.
SPANA is by the simplest definitions an operating system and the operations
are carried out by using a command language. These commandsallow the user
to interact with the data freely. One of the most important assetsof SPANA is
its macro capability. A macro is a series of commands sequentially read from a
'J
R"
"'
63
command file -
a macro. SPANA is adaptable to outside programmers since it
maintains all data 110 and freesthe programmer to concentrateon data processing.
4.2
Structure
SPANA has two program levels and eachlevel has the capability to inform the user
if a syntax error occurs. At the top is the command interpreter and its task is to
determine which commandis to be executed. The next layer is the actual command
function which may in turn nest severalsub-layersto complete the function. When
a command is completed, control is returned back to the command interpreter for
subsequentcommand processing. It is important to note SPANA is not a menu
driven program but rather a commandinterpreter. Commandsavailablein SPANA
are given in the next section.
4.3
Tools available in SPANA
To useSPANA, data is input to the program by "GETing" a measurementset. After
this it is processedby executing other SPANA commands and the results of data
manipulation can be "PUT" to a file. For example, calibration using TSF requiresa
measurementfor the through standard and the embeddeddevice. Two "GETs" and
a call to DMB2 (with appropriate TYPE) will calculate the error networks and the
de-embeddeddevice. "PUTting" theseresults will savethem for later use. Below is a
list of the functions and a brief description of their purpose. The reader is directed
to Appendix B for a complete discussionof the semantics of each command and
['
"
64
Appendix C where the "SHELL" commandis examplefor the potential programmer.
65
Function
Purpose
1.
HELP
On-line help
2.
GET
Input data
3.
PUT
Output data
4.
DISPlay
Display data statistics
5.
DELete
Delete data
6.
PTOR
Polar to Rectangular conversion
7.
RTOP
Rectangular to Polar conversion
8.
STaY
S parametersto Y parameters
9.
SYMmetrize
Symmetrize data
10. PULl
Reducesize of data
11. WINdow
Smoothing of data
12. STRiP
Produce X- Y data file
13. De-embedDMB2
Two-Port error correction
14. De-embedDMB3
Three-Port error correction
15. BuiLD
Produce error standard
16. SIGMA
Statistical calculations
17. GAIN
Two-port gain calculations
18. PIE
Conversionfrom S to pi equivalent circuit
19. INTP
Linear interpolation betweendata points
20. STOP
Exit SPANA
66
4.4
Conclusion
This chapter introduced SPANA with its purpose to aid microwavemeasurements.
The ability to execute command macrosis essentialto extensive measurementcalculations and SPANA can be modified by adding commandsto the interpreter and
writing correspondingsub-layers.
",
67
Chapter
Results
5
and Discussion
5.1 Introduction
In this chapter the calibration techniques developed in Chapter 3 are verified.
Through-Symmetry-Line and EnhancedThrough-Symmetry-Line are applied to an
embeddedmicrostrip fixture commonly encounteredin Printed Circuit Board technology. The error networks determined from these methods are removed from a
PCB via and a pi equivalent circuit is imposed on the via measurements.Finally,
Through-Symmetric Fixture is applied to a secondorder symmetric fixture and the
results are compareddirectly with measuredfixture halves and a de-embeddedlow
pass filter. The use of scattering parametersis common to all results. With exception of TSF and the coaxial verification, a frequency range of 45 Mhz to 10 Ghz is
used for the TSL and ETSL measurements.
5.2
5.2.1
Verification of Through-Symmetry-Line
De-embedding
Introduction
In the following sectionsthe Through Symmetry Line calibration method is applied
to a PCB embeddedmicrostrip fixture. As discussedbefore, this fixture is noninsertable and cannot be comparedwith a direct measurementof the error networks.
The symmetry verification and comparison of a synthesized and measured short
68
circuit are given with discussionand finally TSL is applied to de-embedthe PCB
VIa.
5.2.2 Measurement and Fixture
Design
Coaxial ports are used on all measurementsto allow connection to the Automatic
Network Analyzer (HP 8510) which is integrated within a computer controlled measurement setup show in Fig. 5.2.1. After the two port s parametersare measured,
the data was transferred to a MicroVax where they were processedby SPANA. The
two-tier nature of this measurement,i.e. coaxial calibration then post measurement
de-embedding,is convenientwith this measurementsystem.
Keeping with the symmetrical definitions of Chapter 3, the first order symmetric
fixture is shown in Fig. 5.2.2 (along with a detail of the embeddedmicrostrip cross
section Fig. 5.2.3) is used throughout the chapter. The microstrip dimensionsare
width (w)=8 mils, height (h)=5.6 mils, metal thickness( t)=3.6 mils and the covering
dielectric layer (solder resist layer) is approximately 4 mils thick. The length
(~ of
the microstrip portion of the fixture is 1000mils. Thesephysical dimensions(except
length) were usedbecausePCB manufacturing resourcesrequired them. Note, these
dimensions were intended to result in a 50 11characteristic impedance and as we
will seethis is not the case. The microstrip length can be arbitrarily chosenwith
only coaxial connector clearancerestricting the minimum value.
The network analyzer is calibrated to the coaxial referenceplanes Cl and C2
using the network analyzer Open Short Load calibration procedure. The fixture is
connectedto the coaxial referenceplanes and a full two port s parameter measurement is made. The magnitude and phaseof the fixture s parametersSIll, S22fand
S2lf are shown in Fig. 5.2.4, 5.2.5and 5.2.6 with the exceptionof Sl2f which is
69
HP 8510
ANA
HP-IB
Controller
1
2
RS-232
-
Lr~~~~
r1_~~1
-
Mijrr;!1'@\V/b
...
usr1
usr2
usr3
Figure 5.2.1: S parameter measurementsetup. The HP 8510 measuresdevice s
parameters, then the data is transmitted to the MicroVax for further processing.
70
Coaxial Reference
C1
,.-/
Planes""",
C2
S
M1
Ground
lanes
Embedded
Microstrip
Line
M2
..
Mlcrostnp
Reference
Planes
Figure 5.2.2: First order symmetric fixture used throughout Chapter 5. Cl and C2
are the calibrated coaxial measurementplanes and Ml and M2 are the microstrip
referenceplanes. Embeddedstructures are inserted at Ml and M2.
71
Metal Thickness= 3.6 mil
Resist Layer Thickness= 4. mil
,
Microstrip Width = 8. mil
,
=
!~~~.~~~I
+
+
GP Thickness = 1. mil
~
Solder Resist Layer
[III]
Substrate Dielectric
.
Metal(copper)
Figure 5.2.3: Detail crosssection of the embeddedmicrostrip.
i
I
I
72
O.
-10.
-..
(])
9- - 20.
Q)
"'C
:J
+-'
c:
0)
- 30.
ro
~
-40.
-50.
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.2.4: Embedded microstrip fixture s parameters. Magnitude of (0) Sllf,
(+) S21f and (~) S22f.
73
200.
120.
-.
g>
40.
0
--Q)
(/)
co
~
..c
CL
- 40.
-120.
-200.
O.
2.0
4.0
6.0
8.0
10.
Frequency (GHz)
Figure 5.2.5: Cont. Embeddedmicrostrip fixture s parameters. Phaseof 821f.
"
i,
74
200.
120.
-..
~
40.
0
--
a.>
(/)
~
.c:
a.. -4 0 .
-120.
:.'
- 200.
O.
:J
'h
'"
~'
2.0
4.0
6.0
8.0
10.
Frequency (GHz)
Figure 5.2.6: Cont. embeddedmicrostrip fixture s parameters. Phase of (0) Sllf
and (~) S22f.
,.
..
.
75
identical to S21fand has been omitted.
Symmetry requires the Siif parametersbe equal and from Fig 5.2.4-5.2.6 this is
true with minor deviations at frequencieswerethe fixture is resonant(f=0,.8, 4.5 and
8 GHz). Theseresonancesare associatedwith discontinuity capacitancesand for the
purposesof this discussion,we may model the fixture with discontinuity capacitances
at either coaxial port and a uniform transmission line between them, Fig. 5.2.7.
These capacitancesreduce the electrical length of the line and when the effective
line length is an odd multiple of half wavelengths,the Siif values exhibit minima.
Sensitivity of the fixture symmetry at these frequenciesis due to differencesin the
discontinuity capacitances. Additionally, at other frequenciesreflection from the
microstrip line dominate the reflection terms. When designinga symmetrical fixture,
one can apply commonsensearguments,to reducethe discontinuity capacitanceand
use short lengths of microstrip. The symmetry of the network is exemplified by the
synthesizedshort circuit verification.
5.2.3
Synthesis of Open and Short Circuit Reflection Coefficients
The Through Symmetry Line algorithm synthesizesthe reflection standard needed
in the TRL calibration method by using symmetry. To verify this is possible a low
inductance short circuit was placed at the microstrip referenceplane MI, shownon
Fig. 5.2.2. The measuredshort circuit reflection coefficient is comparedin magnitude and phase with the synthesizedvalue in Fig. 5.2.8 and 5.2.9. In addition, the
synthesizedopen circuit is also shown. The magnitude minimum is slightly different
between measuredand calculated. This minimum correspondsto the resonanceof
the discontinuity capacitancewith the inductive input impedanceof the short circuit
c
76
Uniform Transmission Line
Zc = ??
Cd
Cd
Figure 5.2.7: Approximate model for fixture. The fixture transmissionline is effectively terminated with equal discontinuity capacitances Cd.
"
(0
77
O.
-1.2
ro
e, - 2.4
0,)
"'C
:J
+-'
C
0>
- 3.6
ro
~
-4.8
- 6.0
O.
4.0
10.
Frequency
Figure
5.2.8:
microstrip
synthesized
Magnitude
reference
comparison
plane.
(+)
and (/:::.) synthesized
of synthesized
Measured
open circuit
short
and measured
circuit
reflection
reflection
coefficient.
short
circuit
coefficient,
at
(0)
78
200.
120.
-..
~
40.
0
--Q)
U)
ro
..c:
a..
-4
0.
-120.
-200.
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.2.9: Phase comparison of synthesized and measuredshort circuit at microstrip referenceplane. (0) Phaseof synthesizedshort circuit reflection coefficient,
( +) measuredshort circuit and (~) synthesizedopen circuit.
,
-
,
L
.,
{
I
,
i
'---
-
80
1
Coaxial Reference Planes
'
~~
S
A
M.
t.
2
, ~~~""'"
Icros np
Reference Plan
.
1
Ground
Planes
.
= 348 mils:
L = 1348 mils
.
:L\ L
I
..
1
..
'\
Embedded
Microstrip
Line
(a)
Vi,
(b)
Figure 5.2.10: Diagram of the fixture with line standard inserted (a) and via (b).
J
81
Microstrip Metal Thickness
Resist Layer Thickness = 4. mil
t
3.6 mil
H = 5 6 "I
. ml
.
t
:&"",;
Y
G
Pp
per
mc"'c
"-o",",cc-,,"""
Thif~~~ISS
~
...J;~~er
!
::,;;;::1;"",-:;;;;:-:,
Via Length = 62.5 mil
~~
.
1~-~~-1~11'
"t~~"i
o
C
T
11'
~~t;
"","'i.;);t:i)"!!t'
t~~~~~
..;,,'
..-'"
(a)
T
.,..1~
~-
[S:I Solder Resist Layer
D Substrate Dielectric
Metal (copper)
C
"';C""':~'f~'
:,,!:?,C'cc,::;
'11'
cc,')i;"";:i'"
-",~'.,.,.,..,.",
*~?;":!t:
--
'c,
-(b)
Figure 5.2.11:Detail crosssectionof printed circuit boardvia (a) and the pi equivalent circuit (b).
"
82
via s parameters, see Appendix A for complete discussionof error removal by decascading. This extraction is doneby converting the via s parametersto admittance
parameters,which form a pi equivalentcircuit, and then inverting theseadmittances.
The resulting shunt capacitance(in pF) and seriesinductive reactance(in .os) are
shown in Fig. 5.2.12 and Fig. 5.2.13respectively.
When interpreting the TSL results, considerwe are fitting a pi equivalent model
to the via and at higher frequenciesthis is inaccurate. The seriesreactancebehaves
as an inductor through two GHz and the capacitanceis constant to five. The increasingcapacitance(with frequency)is associatedwith the increasedenergy stored
in the fringe electric fields and the non-ideal inductance arisesfrom resonanceswith
other parasitic capacitances(Cp, 5.2.11).
A final note about the characteristic impedance of the line standard used in
TSL. As mentioned in Chapter 3, the TRL algorithm requires the line standard
be reflectionless or we need to determine the impedance. The TSL results were
determined using Time Domain Reflectometry (TDR) and found to be 57 .os. This
is different from the manufactures50 .0 designgoal but its effect can be removedas
describedin ETSL section.
5.2.5
Conclusion
The Through-Symmetry-Line de-embeddingmethod has been usedto calculate the
pi equivalent circuit of a printed circuit board via. The close agreementbetween
measuredand synthesizedshort circuits verifies a symmetrical argumentcan be used
to modify the TRL algorithm to TSL.
83
5.0
~
4.0
J-LL
c..
---
Q)
3.0
(.)
c
co
'0
~
co
2.0
()
C
:J
ffi
1.0
O.
O.
4.0
Frequency
Figure 5.2.12: Shunt capacitancefor a via pi equivalent circuit.
10.
--
84
100.
-I
~
80.
-(/)
E
Q
..c:
60.
a>
(J
c
ro
~
a>
40.
a:
(/)
a>
.~
20.
U)
o.
O.
2.0
4.0
6.0
Frequency (GHz)
8.0
10.
Figure 5.2.13: Seriesinductive reactancefor a via pi equivalent circuit.
~ .
85
5.3
Verification
of the Enhanced Through-Symmetry-Line
De-embedding
5.3.1
Method
Introduction
This section contains verification of the impedance enhancement to TSL and its
use in the new ETSL algorithm. Verification is done by calculating the impedance
of a precision 50 n air-line as well as other transmission line parameters including
dielectric and propagation constants.
5.3.2
Coaxial Transmission Line Parameters
Fixturing
for this verification is shown in Fig. 5.3.1. It includes two fixture halves
each composed of 7 millimeter coaxial connectors (APC- 7) to female 3.5 millimeter coaxial connectors (SMA) and a male SMA to APC- 7 adaptors. The through
connection is the connection of the fixture halves and the air line was inserted between the halves for a line connection. The air line length is 10.21 cm and the air
dielectric allows accurate calculation of the half wavelength singularities. These are
f
= This
1.4691i
fixturing
GHz,
was
where
chosen
i =
1,2,3,
for two reasons. First, the precision air line connec-
tions were APC- 7 requiring a similar mating connector. Secondly, it was desirable
to have a fixture of a non-zero length thus allowing direct application to the microstrip fixture used in the previous TSL results. Next we will present the coaxial
transmission line parameters.
i
i
86
Through Connection
APC- 7 to Female SMA
I~
~I
~=Js~:~~~~t~~~~~
APC-7 to Male SMA
(a)
Line Connection
~
10.21cmAirLi~1
fdJ(=[~~~==~Wl~~J~~~:~
(b)
Figure 5.3.1: Coaxial fixturing usedto verify TSL impedanceenhancement.(a)
Through connection and (b) 10.21cm precision 50 n air line inserted in fixture.
87
Attenuation
Constant (a)
The through and line connectionswere measuredover a 15 to 3000MHz frequency
range and the propagation constant was calculated. Fig. 5.3.2 showsthe attenuation constant, a, with per meter units. Several observationscan be made. It is
clear over this frequency range we encounter two of the predicted half wavelength
singularities since the per meter attenuation values are unrealistically high. These
constitute invalid regions. The secondobservation is low attenuation values within
valid regions. This is typical of precision coaxial lines. Finally, we seeat low frequencies(below 200 MHz) we cannot measuresignificant phasedifferencebetween
the through and line connection.
Propagation
Factor (,8)
The calculated propagation factor, ,8 = ,8/,80,has been normalized with respect to
a free-spacepropagation factor, ,80= 27rf / c wherec is the speedof light, to reveal
its accuracy. The precision air line should have a free-spacepropagation factor and
the normalized ,8 should be unity. This result is shown in Fig. 5.3.3.
Relative Dielectric
Constant (Er)
Using the propagation constant, , = a + j,8, and equation 3.6.3 we have calculated
the relative dielectric constant shown in Fig. 5.3.4. The figure showswe are calculating the constant correctly since it is nearly unity over much of the frequency
range. Naturally, an air dielectric coaxial line should have a unity relative dielectric
constant. Up to this point, these results have been derived using previous authors
work. Building on their work, we can take the processfurther by calculating the
characteristic impedanceof the coaxial line as developedin Chapter 3. Given the
~
~~~
~--
-
88
0.75
0.50
E
0.25
-~
.c
..Q- O.
<1:
- 0.25
-0.50
15.
610.
1200.
Frequency
1800.
2400.
3000.
(MHz)
Figure 5.3.2: Attenuation factor, a, for the precision air line. Calculated using 3.6.4.
-
89
1.8
1.5
~
+-'
Q)
m
1.3
"'0
Q)
N
~
E
~
1.0
0
z
0.75
0.50
15.
610.
1200.
1800.
2400.
3000.
Frequency (MHz)
Figure 5.3.3: Normalized beta for the precision air line. Calculated using 3.6.4.
'0
-
90
1.3
1.2
c
co
U)
c
8
1.1
(,)
~
(,)
Q)
""Q)
1.0
0
Q)
>
~
0.90
a:
0.80
15.
610.
1200.
1800.
2400.
3000.
Frequency (MHz)
Figure 5.3.4: Relative dielectric constant for the precision air line. Calculated using
3.6.3.
'"
91
propagation constant and the coaxial free-spacecapacitancewe calculatethe coaxial
characteristic impedanceand compareit with the designed50 0 value.
Characteristic
Impedance (Zc)
For conveniencewe rewrite the characteristic impedanceequation from Chapter 3
(3.6.8).
JW
Zc = 2/"1
(5.3.1)
C vOl
The free-spacecapacitance, Co, is a function of the inner and outer radii of
the conductors. Measuring these radii is difficult and we chosenot to attempt
their measurement. The capacitancecan be calculated assumingthe coaxial line
impedanceto be 50 Os. This is valid becausethe coaxial designerswould have chosen
the radii to give a 50 0 impedance. We have seenthe capacitanceis a function of
the impedance in Chapter 3 and using (3.6.2) we calculate the coaxial free-space
capacitance to be 66.71 pF 1m. Applying this to (5.3.1) yields the characteristic
impedance. Fig. 5.3.5 and 5.3.6 show the real and imaginary valuesof the coaxial
characteristic impedance. The real value is within one tenth of an 0 to 50 Os and
the imaginary is essentiallyzero showinggood agreementwith expectedvalues. Now
we can apply this impedancecalculation to the embeddedmicrostrip fixture usedin
the TSL results.
5.3.3
Embedded Microstrip
Transmission
Line Parameters
This section presents transmission line results calculated in the same manner as
the coaxial example above. The fixturing used here is identical to the TSL fixture.
With TSL, we determined the characteristic impedanceof the line standards using
-"
92
58.
-'-(/)
E
..c
G
--
55.
Q)
()
c:
co
53.
.~
50.
-c
Q)
c..
E
(/)
~
Q)
()
co
~
..c
48.
()
'
Q)
a:
45.
15.
610.
1200.
1800.
2400.
3000.
Frequency (MHz)
Figure 5.3.5: Real portion of the coaxial characteristic impedance. Calculated using
the free-spacecapacitanceand equation 5.3.1.
-
93
1.5
.-'-.
(/)
~
1.0
0
-(l)
()
@
0.50
"'C
(l)
Q..
E
.~
O.
(/)
'c
(l)
()
co
Ci3
- 0.50
..c:
()
'-v-'
E
- 1.0
15.
610.
1200.
1800.
2400.
3000.
Frequency (MHz)
Figure 5.3.6: Imaginary portion of the coaxial characteristic impedance. Calculated
using the free-spacecapacitanceand equation 5.3.1.
'"
-"
94
TDR and here we will seethe impedanceis complex and the embeddedmicrostrip
lines are dispersive. The ~l used in this section is five cm. This value is necessary
to extract reliable results at the lowest measurementfrequency,45 MHz yet it does
increasethe number of invalid regions. The results showtheseregio~sexist but have
little effect on calculating the embeddedmicrostrip transmissionline parameters.
Attenuation
and Propagation
Constants (a and ,8)
The embeddedmicrostrip attenuation constant is shownin Fig. 5.3.7, with units of
dB/cm. Also, Fig. 5.3.8 showsthe normalized propagation factor for the transmission line. The normalized ,8 (,8 = ,81,80and ,80
= 27r f I c) is a decreasing function
of frequency therefore the line is dispersive. Additionally, values are greater than
unity therefore the effective dielectric constant must also be greater than one.
Effective Dielectric Constant (fr)
As with the coaxial line, we calculate the real and imaginary parts of the embedded microstrip effective dielectric constant, Re(fel I) and I m( fel I) Figs. 5.3.9 and
5.3.10 respectively. The singularity effects are more pronouncedhere but they are
still not significant. The decreasingRe(fell) representsdispersionand is intuitively
clear since the amount of electric field contained in the air above the microstrip
increaseswith frequency therefore lowering the effective dielectric constant. Moreover, Im( fell) increases to a constant value for similar reasons. Note, Im( fell)
= 0.1
correspondsto a loss tangent of 0.03.
Characteristic
Impedance (Zc)
The free-spacecapacitancehas beencalculated as describedby Bahl and Stuchly [33]
and for this study hasbeenfound to be 31.59pF 1m. Given this and the propagation
-"
95
~
.
0.20
(
E
u
--
0)
"'C
-co
-a.
- 0.04
<{
-0.20
O.
4.0
10.
Frequency
Figure 5.3.7: Attenuation constant, a, for a 5 cm embeddedmicrostrip. Calculated
using 3.6.4.
- "
96
2.0
1.9
Ctj
0.>
ro
1.9
-0
0.>
N
Ctj
E
~
1.8
0
z
1.8
1.7
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.3.8: Normalized propagation factor for a 5 cm embeddedmicrostrip. The
decreasingvalue indicates dispersion. Calculated using 3.6.4.
"
97
4.0
"'-'
~;
3' 8
.-'-.
k
"""*",,;,,,-,~~
0
I
3 6
i.~~~
I'
34
~~
~.
I
Q)
3.0
O.
4.0
10.
Frequency
Figure 5.3.9: Real portion of the effective dielectric constant for a 5 cm embedded
microstrip. Again, a decreasingvalue indicates dispersion. Calculatedusing 3.6.3.
98
0.50
-'"'"
-"
0.30
c:
ro
-"
U)
c:
0
(J
0.10
0
.~
-"
(.)
Q)
B - 0.10
Q)
>
-"
-
2(.) - 0.30
w
'-"""'
E
-0.50
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.3.10: Imaginary portion of the effective dielectric constant for a 5 cm
embeddedmicrostrip. Calculated using 3.6.3.
99
constant we calculate the complex characteristic impedance Zc with results given
in Fig. 5.3.11. and Fig. 5.3.12 The characteristic impedance is complex with
increasing real and decreasingimaginary parts. These relationships are causedby
the dielectric coveringwhich effectively containsmuch of the fringe .electricfield. At
higher frequencies,the electric field occupiesmore of the free-spaceabovethe cover
layer and the embeddedmicrostrip exhibits microstrip behavior.
5.3.4
ETSL De-embedding
Results
Finally, we apply this characteristic impedance profile to the line standard used
in TSL and de-embedthe same PCB via. Shunt capacitanceand seriesinductive
reactance are shown in Fig. 5.3.13 and Fig. 5.3.14respectively.
5.3.5
Conclusion
The calculation of transmission line parameters for a precision 50 n coaxial line
indicates it is possible to determine the impedanceusing a free-spacecapacitance.
Application of this calculation to the embeddedmicrostrip makes it possible to
calculate the complex characteristic impedanceand then use it to improve the TSL
algorithm. Enhanced Through-Symmetry-Line has been used to de-embeda PCB
via from a symmetric fixture.
The effect of loss in transmission lines is indicated by dispersion and complex
characteristic impedances. Also, loss reducesthe effect of TRL singularities associated with half wavelength line standards. Up to now we have referred to these
invalid regionsas singularities yet the results only showminor perturbations in these
regions. In fact, they are not mathematical singularities becausethe line standard
has higher per unit length loss than the through standard. At half wavelengthfre-
100
~'
60.
.-'-.
cn
E
.c:
0
"-
59.
a.>
0
c::
~
"'C
58.
a.>
c.
E
.2
57.
cn
"t::
a.>
0
~
Co
.c:
56.
()
'
a.>
a:
55.
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.3.11: Real portion of the characteristic impedance for a 5 cm embedded
microstrip. Calculated using the free-spacecapacitanceand equation 5.3.1. TDR
result for this line is 57 !1s.
101
3.0
-...-'-I
(/)
.§
2.4
0
""-
Q)
u
ffi
"'0
Q)
Q..
1.8
.~
1.2
E
(/)
.~
Q)
u
~
CiS
..c
0.60
()'-.,.-J
E
O.
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.3.12: Imaginary portion of the characteristic impedancefor a 5 cm embedded microstrip. Calculated using the free-spacecapacitanceand equation 5.3.1.
-l
~
w
U--c..
Q)
u
c::
~
u
~
~
()
c::
~
U)
5.0
4.0
3.0
2.0
1.0
O.
O.
4.0
Frequency
Figure 5.3.13: Shunt capacitancefor a via pi equivalent circuit.
10.
102
103
:..,
100.
~
(/)
I-
w
80.
-U)
E
..c:
0
--
60.
Q)
()
c:
~
t5
~
40.
Q)
a:
U)
Q)
.~
20.
U)
O.
O.
2.0
4.0
6.0
8.0
10.
Frequency (GHz)
Figure 5.3.14: Seriesinductive reactancefor a via pi equivalent circuit.
"
104
quencies,the line appearstransparent only contributing an additional attenuation.
A direct comparison of the via inductive reactancebetween TSL and ETSL is
shown in Fig. 5.3.15. Their differenceis over the middle to upper frequency range.
It is in this region the complex impedanceis farthest from the J:DR 57 n value.
We can calculate the compleximpedanceof a uniform transmissionline and include
dispersion.
5.4
Results of Through-Symmetric
Fixture De-embedding
Method
5.4.1
Introduction
This section contains verification of the TSF algorithm over a frequency range of
45 to 800 MHz. Also, TSF usesdifferent fixturing so we will discussits design and
measurement. Verification is done by direct measurementof both the fixture halves
and a de-embeddedlow passfilter.
5.4.2 Measurement
and Fixture
Design
It was shown in Chapter 3, TSF requires a secondorder symmetric fixture. This
forces the fixture halves to be symmetric and identical. The fixture was designed
to introduce significant error in the embeddedmeasurementand still maintain the
symmetry requirement. This was accomplishedwith a shunt inductive discontinuity
placed between an APC-7 to female SMA adaptor and a male SMA to APC- 7
adaptor, see Fig. 5.4.1. These connector combinations allow direct measurement
and subsequentcomparisonwith the error networks calculated with TSF.
105
-1
70.
(/)
.W
"'0
~
56.
-1
(/)
.-
"'Ci)'
42 .
E
..c
0
--
~
c:
28.
~
()
~
Q)
cr:
14.
U)
Q)
~
Q)
(/)
O.
O.
2.0
4.0
Frequency
6.0
8.0
10.
(GHz)
Figure 5.3.15: Comparisonof via inductive reactancecalculated with (0) TSL and
(/::,.)ETSL.
106
Through Connection
SMA Through
APC- 7 to Male SMA
~~I~::t~~i;~=[~I~~~:~I::J::)5j~=:[~:]~
At~~~;~~
SM~Inductance
(a)
Embedded Filter
500 MHz Low Pass Filter
~J~~~~i1ri1~~~~~~I~~=~):J~=~~~~
(b)
Figure5.4.1: Fixturing for verificationof TSF. (a) Fixture throughconnectionand
(b) embedded500 MHz low passfilter. The fixture halve is composedof two adaptors
(APC-7 to male SMA) and the shunt inductor (10 nano henries) mounted in a SMA
through.
107
The approximate inductance is 10 nR and connectedas a shunt element appears
as a short circuit at low frequenciesand open at higher frequencies. This creates
significant error yet it is possibleto construct two of thesefixture halvesand satisfy
the symmetrical requirements. Fig. 5.4.2 and 5.4.3 show the mag~itude and phase
of Sijl respectively for the fixture s parameters. Only SIll and S211need be shown
because S221
= SIll
and S121
= S21/i the
fixture is symmetric. The next section
presents results of the TSF algorithm.
5.4.3
TSF De-embedding Results
TSF was applied to the embeddedlow pass filter (DUT) and results are shown in
Figs. 5.4.4 - 5.4.11. These graphs show the significant effect the fixture error networks impose and comparison,in magnitude and phase,betweendirect measurement
and the TSF de-embeddedfilter.
5.4.4
Conclusion
This section has shown when a fixture is secondorder symmetric, TSF can be used
to remove the fixture error from a DUT. TSF algorithm is not without singularities
however they did not influence this measurementbecausethey existed beyond the
measurementrange.
5.5
Conclusion
In this chapter we have presentedexperimental results for eachof the symmetrical
de-embeddingmethods developedin Chapter 3. TSL and ETSL were applied to a
embedded microstrip fixture and the impedance enhancementto TSL was verified
108
O.
- 8.0
-co
e- - 16.
Q)
"'0
:J
C
0')
- 24.
co
~
- 32.
- 40.
45.
200.
350.
500.
Frequency
(MHz)
650.
Figure 5.4.2: Magnitude of the TSF fixture s parameters, (0)
8111
800.
and (6) 8211'
~~
109
.~
~!jj~~
¥f:"t%i#iJ:~o1'
W
~_"'k
200.
~
40.
0
<D
U)
Ctj
.c
0-
-4
0.
- 200.
45.
350.
800.
Frequency
Figure 5.4.3: Phaseof the TSF fixture s parameters, (0)
811/ and (6)
821/'
l
110
O.
- 12.
-Q)
e- - 24.
Q)
'"C
:J
."
~
,-,j
.-c
0)
- 36.
co
~
-48.
- 60.
45.
350.
800.
Frequency
Figure 5.4.4: Magnitude of the filter 821, (0) direct measurementand (D.) embedded. The fixture error significantly alters the filter measurement.
'-J
no
111
"
200.
120.
-..
~
0
--Q)
CJ)
CO
..c
0-
40.
- 40.
-120.
- 200.
45.
200.
350.
500.
650.
800.
Frequency (MHz)
Figure 5.4.5: Phaseof the filter 821,(0) direct measurementand (6) embedded.
/--
112
O.
- 8.0
OJ
9- - 16.
(1)
"'0
:J
c:
0)
- 24.
cu
~
-32.
-40.
45.
200.
350.
500.
650.
800.
Frequency (MHz)
Figure 5.4.6: Magnitude of the filter 811,(0) direct measurementand (~) embedded.
.Co
113
200.
-as'
40.
0
-Q)
U)
ro
.c -40 .
0..
- 200.
45.
350.
800.
Frequency
Figure 5.4.7: Phaseof the filter Sll' (0) direct measurementand (I:::.)embedded.
~
114
O.
- 12.
-.
0)
~
-24.
Q)
-c
::J
-"
C
0')
- 36.
ro
~
-48.
- 60.
45.
350.
800.
Frequency
Figure 5.4.8: Magnitude of the filter 521, (0) direct measurementand (6) deembedded.
;
~;;~C,J;C:/i:
~-
~
115
200.
120.
--g>
0
--
40.
Q)
(/)
ro
..c
- 40.
0-
-120.
-200.
45.
200.
350.
500.
650.
800.
Frequency (MHz)
Figure 5.4.9: Phaseof the filter 821,(0) direct measurementand (6) de-embedded.
, \,
c:
;:c;
yO
ttf:;;:~
r£J;1o.~
0
.
- 8.0
--(1)
e.
- 16.
Q)
"'0
:J
--
C
0)
- 24.
ro
~
c;';
r
-
- 32 .
,cc
""-
-40.
45.
350.
800.
Frequency
Figure 5.4.10: Magnitude of the filter Sll, (0) direct measurementand (.6.) deembedded.
i
~~~~~3~
"c"",L"~",c'
::i;;~ttfi?i~~
117
~
200.
120.
-..
as>
40.
"c~
0
-Q)
U)
r'
ro
..c.
a..
- 40.
-
1
20
",'C
.
~,;"
,;1~t
-200.
45.
200.
350.
500.
650.
800.
Frequency (MHz)
Figure 5.4.11: Phaseof the filter 511,(0) direct measurementand (6) de-embedded.
118
with a 50 n coaxial example. The complex characteristic impedanceof an embedded
microstrip was calculatedand this result is not a function of symmetry and is directly
applicable to TRL and LRL de-embeddingmethods.
It was also shownTSF can be usedto de-embeda secondorder symmetric fixture.
This was accomplishedby designinga secondorder fixture with essentiallya lumped
element. The next chapter concludesthe work done here and hopes to encourage
others to pursue symmetrical argumentswhen consideringfixture design.
I
yO
119
l
v
Chapter
6
Conclusion
6.1
Summary
The objective of this study was to study calibration of automatic network analysis.
This work consistsof two parts: the organization of existing calibration methods,
and development of fixture calibration methods addressingprinted circuit board
concerns.
In the first part, the exiting methods were organizedby categorizingcalibration
methods into one or two port error models. Two port error models were further
divided to automatic network analyzermodels and fixture models. To completethe
categorization calibration standards used for by previous authors were presented
and discussionof their motivation was given.
In the secondpart of this study, symmetrical calibration methods were developed to combat the noninsertablenature of printed circuit board measurement,i.e.
use a minimum number of standards and do so without physically inserting them.
Through-Symmetry-Line was possible becausethe PCB fixture was symmetric allowing a third standard to be synthesizedfrom two standards namely the through
and line. The synthesizedshort circuit was experimentally verified indicating symmetry can be used to reduce the number of standards.
TSL was enhancedby calculating the complex characteristic impedanceof the
line standards. In order to verify this enhancement, a precision 50 ohm coaxial
air line was measuredand its transmission line parameters were calculated. Ex-
i
I
120
0
cellent agreementbetween expected coaxial parameters an calculated validate the
enhancement. The transmissionline parameters for an embeddedmicrostrip were
subsequentlydetermined. This enhancementis not a function of the symmetry and
can be applied to TRL and LRL de-embeddingmethods. Both TSL and ETSL were
used to de- embed the pi equivalent circuit of a PCB via. Finally, their result was
compared and the differencenoted.
n
The final symmetrical method, Through-Symmetric Fixture was applied to directly measurablefixtures and embeddeddevice (low pass filter). Again excellent
agreement between measuredand calculated responsesshow TSF is successfulat
removing error from a secondorder fixture. In all cases,SPANA wasused to implement the algorithms and presentthe data for this report.
6.2
Discussion
In general, calibration of network analysis models the systematic error of the measurement system. Under most circumstancesthe random measurementerror is
negligible but random processeffecting the uniformity of transmission lines should
be considered. This further strengthens the desirability to reduce the standards
needed.
Most new methodshavebeendevelopedout of need. If a matchedload cannot be
fabricated then consideranother standard to replace it. Having a review of existing
techniques allows one to chosethe most accurate method. When investigating a
new measurement system it is valuable to keep a "what if we use a ..." attitude
when selecting standards. In addition, by using a two tier calibration method the
choice of algorithms is bountiful.
121
6.3
Suggestion
for Further
Study
Additional areasof study include:
i) effect of random variation of transmission line parameters OJ!de- embedding
results, and
ii) applying symmetrical de-embeddingmethods to wafer probe calibration.
,
I
I
122
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63-66, May 1978.
[17] A. M. Saleh, "Explicit formulas for error correction in microwave measuring sets with switching-dependentport mismatches," IEEE- Trans. Instrum.
Meas., vol. IM-28, no. 1, pp. 67-71, March 1979.
[18] N. R. Franzen and R. A. Spaciale, "A new proceedurefor system calibration and error removal in automated s-parameter measurements,"Proc. 5th
EuropeanMicrowave Conf., pp. 69-73, 1975.
[19] B. Bianco, M. Parodi, S. Ridella and F. Selvaggi, "Launcher and microstrip
characterization," IEEE Trans. Instrum. Meas., vol. IM-25, no. 4, pp. 320323, December1976.
[20] G. F. Engen and C. A. Hoer, "Thru-refiect-line: an improved technique for
calibrating the dual six-port automatic network analyzer," IEEE Trans. Microwave Theory Tech.,vol. MTT-27, no. 12, pp. 987-993, December1979.
[21] J. A. Benet, "The design and calibration of a universal mmic test fixture,"
IEEE MTT -S International Microwave SymposiumDig., pp. 36-41, 1982.
[22] R. Vaitkus and D. Scheitlin, "A two-tier deembeddingtechnique for packaged transistors," IEEE MTT -S International Microwave Symposium Dig.,
pp. 328-330, 1982.
[23] R. L. Vaitkus, "Wide-band de-embeddingwith a short, an open, and a through
line," Proc. of the IEEE, vol. 74, no. 1, pp. 71-74, January 1986.
i
i
I
125
[24] S. R. Pennock,
C. M. D. Rycroft,
characterisation
Coni,
for de-embedding
pp. 355-360,
[25] R. P. Meys,
Trans.
P. R. Shepherd
purposes,"
and T. Rozzi,
Proc.
"Transition
17th European
Microwave
1987.
"A triple-through
Microwave
method
Theory
Tech., vol.
for characterizing
MTT-36,
test fixtures,"
no. 6, pp.
IEEE
1043-1046,
June
of a rigorous
the-
1988.
[26] H. J. Eul
and B. Schiek,
ory for de-embedding
Microwave
Coni,
[27] J. R. Souza
microstrip
"Thru-match-reflect:
and network
pp. 909-914,
lEE
analyzer
calibration,"
Proc.
18th.
Europ.
1988.
and E. C. Talboys,
transition,"
one result
"S-parameter
Proc.,
characterisation
of coaxial
vol. 129, Pt. H, no. 1, pp. 37-40,
to
February
1982.
[28] B. Bianco,
A. Corana,
calibration
Instrum.
procedures
S. Ridella
for measurements
Meas., vol. IM-27,
and T. H. Chen,
crowave
de-embedding
Tech., vol. MTT-36,
[30] Hewlett
Packard,
for non-coaxial
[31] A. R. Martin
symmetric
procedure,"
"Network
analysis:
measurements,"
and M. Dukeman,
ixture,"
"Propagation
no. 4, pp. 706-714,
Microwave
Product
"Evaluation
of reflection
no. 4, pp. 354-358,
[29] J. P. Mondal
fixture
and C. Simicich,
coefficient,"
December
constant
IEEE
April
applying
Note
"Measurement
J., pp. 299-306,
of errors
IEEE
Trans.
1978.
determination
Trans.
in
Microwave
in miTheory
1988.
the HP 8510B
8510-8,
pp. 1-22,
of device
May
1987.
trl
calibration
1987.
parameters
using
a
126
[32] W.J. Getsinger, "Measurement and modeling of the apparent characteristic
impedance of microstrip," IEEE Trans. Microwave Theory Tech.,vol. MTT31, pp. 624-632, August 1983.
')
[33] I. Bahl and S. Stuchly, "Analysis of a microstrip covered.with a lossy dielectric," IEEE Trans. Microwave Theory Tech.,vol. MTT-28, pp. 104-109,
"(
February 1980.
[34] T. Wang, R.F. Harrington and J .R. Mautz, "Quasi-static analysis of a microstrip via through a hole in a ground plane," IEEE Trans. Microwave Theory
Tech.,vol. MTT-36, pp. 1008-1013,June 1988.
[35] R. D. Pollard and R. Q. Lane, "The calibration of a universal test fixture,"
IEEE MTT -S International Microwave SymposiumDig., pp. 498-500, 1983.
[36] A. Enders, "An Accurate MeasurementTechniquefor Line Properties, Junction Effects, and Dielectric and Magnetic Material Parameters," IEEE Trans.
Microwave Theory Tech.,vol. MTT -37, no. 3, pp. 598-605, March 1989.
[37] E. R. Ehlers, "Symmetric Test Fixture Calibration," IEEE MTT -S International Microwave SymposiumDig., pp. 275-278, 1986.
~
--J
-;;
127
!,
Appendix
A
/
~t;
De-cascading:
Removal
of fixture
error
:;
In this appendix, the equation necessaryto removethe de- embed the device under
test (DUT) from the fixture is given. All de-embeddingresults given in Chapter 5
were produced by de-cascadingthe error networks from the embeddeddevice.
The DUT is inserted betweenthe fixture halves and the embeddeds parameters
are measured,[8emb].De- embeddingis carried out by using cascadables parameters
(t-parameters). These are obtained by application of the standard s to t transform
(T
11
T12
)
=-
1
(
821
T21 T22
1
-
822
)
(A.I)
811-~
where,
~
= 811822 -
812821
(A.2)
The error networks A and B and the embedded DUT are transformed so [8A]
becomes[TA], [8B] becomes[TB], and [8emb]correspondsto [Temb].
After conversionthe embeddedDUT is given by the following equation.
[Temb]= [TA][TDuT][TB]
(A.3)
Pre and post multiplication of this equation with inversesof A and B yield the
T -parametersof the DUT
[TDuT]
= [TA]-I[Temb][TB]-1
(AA)
128
and thus its S parameters
[
811
812
821
822
.J
]
1 [ T21
= -T11
For first order symmetric fixtures B
T11T22
1
-
T21T12
]
(A.5)
-TI2.
= AR and secondorder B
= A.
r
J
,
r
129
Appendix
:J
B
SPAN A Semantic Command
Description
This appendix is a user's manual for SPANA. Its purpose is to inform the user of
the command syntax and the required command line parameters. SPANA is not
casesensitive and for clarity this appendix will use bold face charactersto indicate
command syntax.
Someof the functions require commandparametersin addition to the command
itself for example.
*dmb2 meas=l type=l
dest=2 stan=3
The command parameters provide the function with information. Each command parameter is separated with a spaceor white spacecharacter and the argument to the right of the parameter is the data passedto the function. A complete
command line is required but parameter order can be arbitrary. If a command
syntax occurs the line will be aborted and a messagedisplayed.
Help. Example: help more
Purpose. HELP is the on-line help facility for listing the commandsavailablein
SPANA aswell as a brief descriptionof eachcommand. The possiblehelp arguments
are shown below.
Arguments.
more
page2
* help
,.
130
###########################
HELP #########################
Commands Available:
COMMAND
J
KEYWORD DESCRIPTION
DISPLAY
DISP
EXTRAPOLATEEXT
FFT
FFT
PLOT
PLOT
GET
GET
HELP
H or?
PUT
PUT
CONTACT
Describes Data
Extrapolates
Data
Does FFT on Data
Plots data
Reads data from file
Displays this help file
Outputs data
For more information
on a command type
More information
is available
by typing
or by typing
HELP PAGE2
"keyword"
HELP
HELP MORE
##########################################################
r
Steer
Steer
Steer
Kasten
SIK
SIK
Steer
)
,
b
,
131
~:
~;
t,
~
!
* help page2
######################
~
HELP PAGE2 ########################
..
,
I
Commands Available:
:
!
i
.)
!
COMMAND
KEYWORD DESCRIPTION
CONTACT
DE-EMBED DMB2 or 3 De-embeds DUT data
BUILD
BLD
Makes standard from data
POLAR>RECT PTOR
Polar to rect conversion
S/K
Kasten
Kasten
RECT>POLAR
SYMMETRIZE RTOP
SYM
Rect
to polardataconversion
Symmetrize
Kasten
Steer
WINDOW
Smooths Data
Kasten
i
[
!
I
~
.
WIN
For more information
More information
is
on a command type
available
by typing
"keyword"
HELP
HELP MORE
##########################################################
* help more
#######################
The following
read
read
write
eof
end
title:
HELP MORE ########################
input/output
filename:
filename:
prompt:
the
: the
If
available:
file
filename
is opened for input
previously
opened file
is now used for
input
the file
filename
is opened for output
: the input data file
is closed
: the input data file
is temporarily
closed
write
line to output
file
write
echo on
echo off:
commands are
: the
the
prt is
line
to terminal
flag prt is set
flag prt is cleared
set all lines
input
are
echoed.
##########################################################
\
~.
I
132
B.O.1
(,
get
Example: get meas=l file=dut.s2p format=magang
Purpose. GET is used to input a measurementset into SPANA.
Arguments.
.
help
meas
=
n1
file
=
filename
format
=
magang
=
a+jb
MEAS designatesthe measurementset (n1) data will be loaded into. The argument must be lessthan the maximum number of measurementsets. GET will over
write an existing measurementset.
FILE designates the input filename. Acceptable filenames include directory
paths and a total number of charactersless than thirty.
SPANA allows descriptive information to be placed above the data. Each line
of this text must begin with a comment delimiter (! or #) in the first or second
column howeverthe first line in the file is taken as the data identifier and it is used
in the PUT and DISPlay functions. Any subsequentcomment lines will be ignored
and GET will begin reading the data when it encounters the first uncommented
line. The data is read in until the end of file is encountered. Below is an example
file.
~
~
133
! S parametersfor DUT (This is an example data identifier)
J
! This line will be ignored
1.500
0.015
35.5
0.995
95.4
0.995
95.4
0.02
20.5
If the data is in the frequency or time domain than the independent variable is
assumedto be in megahertz or nanosecondsrespectively.
FORMAT, an optional parameter, designatesdata format in the file. It can be
either magnitude-angle form (magang) or real-imaginary (a+jb).
GET defaults
to magnitude-angle form if format is not specified. ZC format is used when a
characteristic impedance,gamma and permittivity file is to be read in. It is assumed
the input values are in real-imaginary form.
The command get help will give the on-line help information about the get
function. Reprinted below.
###########################
GET #########################
Usage:
GET HELP
: This Message
GET MEASurement_set
=
n1 FILE=ssssss
: GETs MEASurement set n1 from FILE
: Input
is Real-Imaginary
format
GET MEASurement_set
=
n1 FILE=ssssss
: GETs MEASurement set n1 from
: Input is Magnitude
format
GET MEASurement_set
=
1.
If
n1 FILE=ssssss
no FORMAT is
given
ssssss
FORMAT=time
FILE ssssss
: GETs MEASurement set n1 from FILE
: Input
is Magnitude-Angle
format
Note:
FORMAT=a+jb
FORMAT=zc
ssssss
magang is
assumed
"
,
134
fc
~c
"
~:
f
:
Default
units
are
MHz
and
#########################################################
r
i
2.
J
c
!.
(
~
nanoseconds
J
135
B.O.2
put
Example: put meas=n file=dut.s2p
Purpose. PUT is used to output a measurementset to the terminal screenor to a
specifiedfilename.
Arguments.
help
meas
=
n1
file
=
filename
inline
=
n2
option
=
1 for option
,
MEAS designatesthe measurementset (n1) to be processed. The argument
must be less than the maximum number of measurementsets. If MEAS is the only
argument then the measurementset will be put to the terminal screenand attached
to the beginning of the data will be the PUT banner.
FILE designatesthe filename to which the data will be written to. The filename
just as for GET can be any acceptablename including a directory path provided the
total number of characters is less than thirty. Below are two banners PUT would
attach to the beginning of PUT file.
!
S
parameters for DUT
! MEASUREMENT SET
1
!
!
!
!
!
!
!
!
!
!
1
Two-port
S parameters
Frequency-Domain
Data:
Magnitude-Angle
Number of Frequency
points:
1
Frequency
Interval:
O.
MHz
Low
Frequency:
1000.00
MHz
High Frequency:
1000.00
MHz
Valid
Measurement
Data
Characteristic
Impedance:
50.0000
Identifier:
S parameters
for
DUT
Form
~
')
136
I
!
FREQ
!
(MHz)
I
1000.0
811
Mag Angle
0.0194
-151.31
Mag
0.9735
821
Angle
-102.56
I
1
"'
'--
\
Mag
0.97470
812
Angle
-102.43
822
Mag
0.01784
Angle
136.54
137
! Three
port
de-embeded
!1 MEASUREMENT SET
9
!
!
!
!
!
!
!
!
!
result
(DMB3).
Part
Three-port
8 parameters
Frequency-Domain
Data:
Magnitude-Angle
Number of Frequency
points:
1
Frequency
Interval:
O.
MHz
Low
Frequency:
1000.00
MHz
High Frequency:
1000.00
MHz
Valid
De-embeded
Data
Characteristic
Impedance:
50.0000
1 of
3.
Form
Identifier:
!
Three
! FREQ
!
!
! (MHz)
I
1000.0000
The banner
port
de-embeded result
(DMB3).
Part 1 of 3.
Sll
812
S13
S21
S22
S23
S31
S32
S33
Mag
Angle
Mag
Angle
Mag
Angle
0.59842
0.22104
0.21382
-169.85
-33.48
-33.49
preceding
0.22104
0.75168
0.30034
-33.48
-167.80
-30.96
0.21382
0.30034
0.72729
the data depends on measurement
command for information
about possible statistics)
-33.49
-30.96
-168.10
statistics
(see display
with the above examples showing
two and three port data. The file format (magang, a+jb, zc or time) is specified by
the format
type of the measurement
The INLINE
taining
argument
set to be written
out.
is used to place the data on one line with the line con-
all the data for one frequency
or time point.
This is default for two port
data but may be used for three and four port data output.
OPTION
acteristic
can be used to reduce a ZC format measurement
set to only the char-
impedance and gamma. The option is default to zero and does not reduce
if an option value of one is entered the option is executed.
The command
function.
Reprinted
put
help
below.
will give the on-line help information
about the put
~
138
###########################
PUT #########################
Usage:
PUT HELP
: This
Message
PUT MEASurement_set
= nl
: Types MEASurement
on terminal
=
PUT MEASurement_set
nl
INLINE
: Puts results
and higher
on a single
PUT MEASurement_set
: Outputs
results
= nl
using
OPTION = n2
special
option
PUT
=
FILE=ssssss
MEASurement_set
: PUTs MEASurement
nl
set
nl
line
in
used
FILE
with
three
ssssss
#########################################################
ports
'"
139
B.O.3
disp
Example: disp=l
Purpose. Display is used to list measurementparameters for one set or all.
Arguments.
help
all
n1
J
If a measurementset number (n1) is given then the measurementstatistics will
be displayed. Statistics available include the following.
1, 2, 3 or 4 port S or Y parameters
System characteristic impedance
Start jStop frequency or time
Number of data points
)
Data status (measured,convertedor de-embedded)
Domain of data (frequency or time)
Data format (magang, a+jb)
If the all argument is given then statistics will be displayed for all available measurement sets. Below is a sample display output and the on-line help for disp (disp
help ).
OJ-
140
!
1
MEASUREMENTSET
1
!
Two-port
S parameters
!
Frequency-Domain
Data: Magnitude-Angle
!
Number of Frequency points:
1
!
Frequency Interval:
0.00
MHz
!
Low Frequency:
1000.00
MHz
!
High Frequency:
1000.00
MHz
!
Valid Measurement Data
!
Characteristic
Impedance:
50.0000
! Identifier:
!
S
parameters
for
Form
DUT
#########################
DISPlay
#####################
Usage:
DISP HELP
: This Message
DISP
: DISPlay data about
DISP n
: DISPlay data about
all
Measurement
Measurement
set
sets
n
#########################################################
c
Qy
141
B.O.4
del
Example: del meas=l
Purpose. Deleteis a housecleaningtool and is usedto deletean exiting measurement
set making it available for reuse.
Arguments.
help
meas= n1
SPANA will delete the measurementset designated by n1. This deletion is
permanent and should be used with caution. Note: del doesnot delete files stored
on disk. If del help is entered, the on-line help for delete will be displayed and is
reprinted below.
###########################
DEL #########################
Usage:
DEL HELP
: This Message
=
DEL MEASurement_set
nl
: DELetes MEASurement set
nl
#########################################################
"c
t
142
B.O.5
ptor
Example: ptor meas=l
Purpose. PTOR is for conversionfrom polar to rectangular format.
Arguments.
help
meas
= n1
MEAS designatesthe measurementset to be converted. This is destructive since
the measurementset is overwritten. PTOR will not convert a measurementset if
it is currently in magang format. Note: ZC format can be convertedhowever time
format can not.
On-line help is available for PTOR by entering ptor help. The help messageis
reprinted below.
#######################
PTOR ######################
Usage:
PTOR HELP
: This Message
PTOR MEAS_set
= nl
#####################################################
r
Or
143
B.O.6 rtop
Example: rtop meas=l
Purpose. RTOP is for conversionfrom rectangular to polar format.
Arguments.
help
meas
= n1
MEAS designatesthe measurementset to be converted. This is destructive since
the measurementset is overwritten. RTOP will not convert a measurementset if it
is currently in a+jb format. Note: ZC format can be convertedhowevertime format
can not.
On-line help is available for RTOP by entering rtop help. The help messageis
reprinted below.
r
#######################
RTOP ######################
Usage:
.
RTOP HELP
: This
Message
RTOP MEAS_set
= n1
#####################################################
Or
I
144
B.O.7
stoy
Example: stoy meas=l dest=2 rect
Purpose. STay is used to convert S parameter sets to Y parameters.
Arguments.
help
meas = n1
dest
J
= n2
rect
r
magang
MEAS designatesthe measurementset to be convertedand the result is placein
the DEST measurementset. The default format is equal to the MEAS set however
by using either RECT or MAGANG arguments the result format can be forced
accordingly. Note: This conversionis only valid for S parameter measurementsets.
On-line help is availablefor STay by entering stoy help. The help messageis
reprinted below.
#######################
STaY ######################
Usage:
STaY HELP
: This Message
STay MEAS_set = n1 DEST_set = n2
: Convert S parameters
data to Y parameters
:
using current
format.
STay MEAS_set = n1 DEST_set = n2 RECTangular
: Convert
S parameters data to Y parameters
:
outputing
data in complex rectangular
form.
STaY MEAS_set = n1 DEST_set = n2 MAGANG
: Convert S parameters
data to Y parameters
:
outputing
data in magnitude-angle
form.
#####################################################
";-
145
B.O.8
sym
Example: gym meas=l dest=2
Purpose. gYM is used to symmetrize the specifiedmeasurementset.
Arguments.
help
meas
dest
= n1
= n2
Symmetrization of a MEAS set is done by replacing 11 and 22 and 21 and 12
#
with the respectiveaverageof the two. The format of the DEST set will default to
the MEAS format.
On-line help is available for gYM by entering gym help. The help message is
reprinted
below.
####################
SYMmetrize
####################
Usage:
SYM HELP
: This Message
SYM MEAS_set = nl DEST_set = n2
: Averages data in measurement set nl
output
in measurement set n2
Output in columns 1 and 4 = average
columns 1 and 4
Output in columns 2 and 3 = average
columns 2 and 3
Averaging
is done in real imaginary
returned
in the input format.
and puts
of data
in
input
of data
in
input
form
and data
#####################################################
is
D;'-
,r
i
146
B.O.9
'pul
Example: pul meas=l dest=2 every=10
Purpose. PUL is used to reduce the size of a measurementset.
Arguments.
help
meas= n1
dest= n2
every= n3
MEAS signifies the measurementset to be reduced and DEST set will contain
the result. EVERY specifieswhich data points to take, ie. take EVERY 8th one.
Number of DEST points equals integer(numberJevery).
#######################
PULl ######################
Usage:
PUL HELP
: This
Message
PUL MEAS_set
= nl
DEST_set
= n2
EVERY = n3
#####################################################
'')
147
B.O.I0
win
Example: win meas=l dest=2 parm=ll
size=81
Purpose. Windowing is used to smooth a parameter in an existing measurement
set.
Arguments.
help
meas
=
n1
dest
=
n2
parm
=
11
=
21
=
12
=
22
=
n3
size
MEAS designatesthe measurementset to be smoothed with the result to be
place in the DEST measurementset. Windowing is done on the a+jb form of of the
specifiedPARM so both real and imaginary or magnitude and phaseare smoothed
together. The argument PARM is neededto designatewhich columnsof data within
the measurementset are to be smoothed. 11, 21, 12, and 22 correspondrespectively
to columns 1-2, 3-4, 5-6, and 7-8 of the measurementset. This is done so to allow
any data format to be windowed.
SIZE is the width of the window and it is a number of samplesand needsto be
odd.
On-line help is available for WIN by entering win help. The help messageis
reprinted below.
~
148
#######################
WINdow ######################
Usage:
WIN HELP
: This
Message
WIN
MEASurement_set
PARAmeter
Note:
Window
=
nl
= ?? window
size
is
=
DESTination_set
SIZE
an odd number
of
#####################################################
~
~
n2
= n3
samples.
,
i
:
'"'
149
B.O.II
strp
Example: strp meas=l type=logmag file=temp.stp parm=21
Purpose. STRP is used to generateX- Y data from a specifiedmeasurementset.
Arguments.
help
meas
=
n1
parm
=
11
=
21
=
12
=
22
file
=
filename
type
=
logmag
=
linmag
=
ang
=
real
=
lmag
MEAS designatesthe measurementset where the Y data is located with the
X data assumedfrequency or time depending on the measurementset domain.
PARM specifieswhich column pair to use 11, 21, 12 and 22 for 1-2, 3-4, 5-6 and
7-8 respectively and finally TYPE gives the output format of the Y data. Note:
Linmag, logmag and ang types apply to magnitude-angleformat data and real and
!
I
i
r
,,
i
i
,
i
l
! "
I
,
i
,
imag types correspond to a+jb format. Time format is either linmag, logmag or
real type.
,
'.
~
m
150
On-line help is available for STRP by entering strp help. The help messageis
reprinted below.
#########################
STRiP #########################
Usage:
J
STRP HELP
: This Message
=
STRP MEASurement_set
nl
PARM = n2 TYPE = n3
: Strips
parameter
and places
along
file
designated
FILE=ssssss
either
magnitude
or
with
frequency
(x,y)
phase
in the
#########################################################
151
B.O.12
dmb2
Example: dmb2 meas=1 dest=2 type=4 h=5.6 1=2000w=8 t=3.6
Purpose. DMB2 contains all the two port de-embeddingroutines and their purpose
is to do error correction.
Arguments.
~
152
~(
help
meas
=
n1
dest
=
n2
error
=
n3
stan
=
n4
thru
=
n5
line
=
nB
zmeas
=
n7
reflect
=
n7
type
=
1
=
2
=
3
=
4
t
=?
w
=?
h
=?
I
= ?
eps
=?
zc
=?
The de-embeddingroutines are executed by providing the required arguments
and possibly some optional arguments. The de-embeddingtypes 1-4 require the
following; MEAS set, DEST set and TYPE choice and someform of standard in-
J
if
153
formation. The MEAS set contains the raw S parameters of the device under test
(dut) and the result or error correctedparametersare placedin the DEST set. If the
ERROR set is specified the de-embeddingroutines will place the error two-port to
this measurementset. Only argument semanticswill be discussedhere with a detail
discussionof de-embeddingtechniquesleft to the De-embeddingTheory section of
this manual.
,
d
154
type 1 Microstrip
Open-Short-Load
Required arguments.
stan
=
n4
Type 1 (Microstrip Open-Short-Load) requires a STAN meas~rementset containing the reflection coefficientsfor the three standards (open, short and load or
matched termination). This STAN set is generated using the BLD command (see
BLD for further information). Of coursethe result is placed in the MEAS set.
type 2 Through-Symmetric-Fixture
Required arguments.
stan
=
n4
Type 2 (Through-Symmetric-Fixture) requires a STAN measurementset containing the through connectionmeasurementof the embeddingfixture.
type 3 Through-Symmetric-Line
)
Required arguments
thru
=
n5
line
=
n6
t
=?
w
=?
h
[enhanced]
Optional arguments
zmeas
=
short
= n7
zc
=?
n7
=?
eps =?
Type 3 (Through-Symmetric-Line
[enhanced])is a combinationof type 3 deembeddingroutines. The combinationsexist becauseof the optional arguments.
155
(
First the requiredarguments,type 3 needstwo S parametermeasurements,
THRU
set and LINE set, and some physical information; w=microstrip width, t=metal
thickness, h=dielectric height and eps=dielectric constant. Note: All dimensions
are in mils. The default type 3 calculatesthe microstrip characteristic impedance
(zcmic) based on the physical parameters. This zcmic can be replaced by a fixed
impedance ZC=?? or a measurementset ZMEAS. The ZMEAS characteristic
impedanceis contained in position 11 of the measurementset and is usually generated by type 4 de-embedding.If zcmic is not used w, t, h, epsneednot be specified.
The SHORT argument specifiesa measurementset containing the measuredreflection coefficient(in the SII position) with a physical short placed at the microstrip
port of the embeddingfixture. If SHORT is not specifiedthen the symmetrical option is used. Seethe De-embeddingTheory section for more information.
type 4 Through-Symmetric-Line
Required arguments.
thru
=
n4
line
=
n5
t
=?
w
=?
h
=?
I
=?
Type 4 (Through-Symmetric-Line) is used generally to determine the characteristic impedance of the microstrip. This in turn is used with type 3 de-embedding.
Type 4 requires two S parameter measurementsets, THRU set and LINE set as well
as the physical parameters w=microstrip width, t=metal thickness, h=dielectric
156
height and l=difference betweenthe physical lengths of the line and thru standards.
Reminder, all dimensions are in mils. For example if the thru microstrip is 1000
mils long and the line strip is 3000mils long one would use 2000 mils as the length
(1).
The characteristic impedance,propagation factor (gamma) and effective dielectric constant are outputs of type 4 and are placed in the last availablemeasurement
set. Typing disp all will inform the user what measurementset this is. This measurement set is assumedempty at all times and any previous data is overwritten
by type 4. This measurementset can be PUT just as any normal measurement
set however if it is subsequentlyread in by GET the user will have to specify the
FORMAT=ZC option to correctly input the data. Seethe command descriptions
for PUT and GET for further information about this I/O operation.
This finishes the argument semanticsdiscussionand below is a reprint of the
on-line help availablefor DMB2 (type dmb2 help).
############
Two Port
De-embedding
(DMB2)
############
Usage:
DMB HELP
: This
DMB MEAS
=
Type 1:
Microstrip
Type 3:
Through-Symmetric-Line
Message
n1 DEST
=
=
n2 TYPE
n3 ERROR
= ??
(opt)
Open-Short-Load
=
STAN = n4
STAN
n4
Type 2:
Through-Symmetric-Fixture
THRU
=
n4 LINE
=
=
(enhanced)
n5 W(idth)
=
? H(eight)
=
?
? ZC = optional
ZMEAS= n6 (optional)
SHORT= n7 (optional)
Type 4: Through-Symmetric-Line
THRU = n4 LINE = n5 W(idth) = ? H(eight)
= ?
T(hicknes)
= ? L(ength) = ?
T(hicknes)
Note:
All
? EPSilon
dimensions
are
=
in mils
#####################################################
r-
I
157
B.O.13
bId
Example: bId open=1 shor=2 term=3 dest=4
Purpose. BLD is used to build the three termination standard neededfor TYPE 1
de-embedding.
Arguments.
help
~
dest
=
nl
open
=
n2
shor
=
n3
term
=
n4
OPEN, SHOR and TERM designate the measurement sets containing open,
short and termination reflection coefficientmeasurementsrespectively. These measurements are located in the SII position for all three standards.
[
#######################
BuiLD ######################
Usage:
BLD HELP
: This
Message
BLD OPEN_set
DEST_set
= n1
=
SHOR_set
= n2
TERM_set
= n3
n4
#####################################################
,
158
B.O.14
stop
Example: stop
Purpose. Stop is used to exit SPANA
(
\.
159
B.O.I5
dmb3
Example: Incomplete write up.
Purpose. Three port de-embedding.
#######
De-embedding
DMB3
of Three
Ports
##############
Usage:
DMB3 HELP
: This Message
DMB3 MEASAl = nl MEASBl = n2 MEASCl = n3 LOADl = n4
MEASA2 = n5 MEASB2 = n6 MEASC2 = n7 LOAD2 = n8
DEST = n9
Note:
The output
will
be a three port.
Three
measurement sets are required
to store all
of the parameters.
n9, (n9+1) and (n9+2) are
used to store the output
#####################################################
DMB3
PURPOSE:
De-embeds
a three
port.
3
0
0
I
I
0
1
0
Six
two
measal:
measa2:
measbl:
(
,
,'~~
.,
lioO""
..
I
1
__1
I
1
1
1
1
1
1
1
1
port
measurements
0
2
0
are
required
for
maximum
accuracy.
Two port
between
ports
of reflection
coefficient
Port
2 of the three
port
network
analyzer.
2 and 3 with
a termination
fgama.
is connected
to port
1 of
Two port
between
ports
of reflection
coefficient
Port
2 of the three
port
network
analyzer.
2 and 3 with
a termination
sgama.
is connected
to port
1 of
Two port
between
ports
of reflection
coefficient
Port
1 of the three
port
1 and 3 with
a termination
fgamb.
is connected
to port
1 of
at
port
1
at
port
1
at
port
2
the
the
the
160
network
measa2:
measc1:
measc2:
analyzer.
Two port
between
ports
of reflection
coefficient
Port
1 of the three
port
network
analyzer.
1 and 3 with
a termination
sgamb.
is connected
to port
1 of
Two port
between
ports
of reflection
coefficient
Port
1 of the three
port
network
analyzer.
1 and 2 with
a termination
fgamc.
is connected
to port
1 of
Two port
between
ports
of reflection
coefficient
Port
1 of the three
port
network
analyzer.
1 and 2 with
a termination
sgamc.
is connected
to port
1 of
The reflection
coefficient
arranged
as follows.
is
passed
in
two
2 port
at
port
2
at
port
3
at
port
3
the
the
the
measurement
sets
load1:
freq.
Ifgamal
/_fgama
Ifgambl
/_fgamb
Ifgamcl
/_fgamc
freq.
Isgamal
/_sgama
Isgambl
/_sgamb
Isgamcl
/_sgamc
o.
-0.7857
O. O. O.
-0.7857
o.
o.
o.
O. -0.05263
O.
O.
O.
load2:
e.g.
1000.
0.090909
O. -0.666666
example:
files:
load1.s2p:
1000.
0.090909
load2.s2p:
1000.
0.16666
O.
-0.666666
O. -0.818181
o.
measa1.s2p:
1000.00
0.752
-167.520
0.303
-31.421
0.303
-31.421
0.727
-167.821
measa2.s2p:
1000.00
0.751
-167.280
0.305
-31.770
0.305
-31.770
0.726
-167.587
measb1.s2p:
1000.00
0.627
-175.038
0.137
-21.762
0.137
-21.762
0.788
-175.525
measb2.s2p:
1000.00
0.653
-177.033
0.093
-15.439
0.093
-15.439
0.839
-178.065
measc1.s2p:
1000.00
0.639
-176.141
0.118
-18.531
0.118
co
-18.531
0.842
-176.896
161
measc2.s2p:
1000.00
0.599
Script
of
-170.085
spana
0.218
-33.007
0.218
-33.007
0.754
-168.193
session:
spana
#########################
SPANA #########################
get meas 1 file=load1.s2p
get meas 2 file=load2.s2p
get meas 3 file=measa1.s2p
get meas 4 file=measa2.s2p
get meas 5 file=measb1.s2p
get meas 6 file=measb2.s2p
get me as 7 file=measc1.s2p
get meas 8 file=measc2.s2p
dmb3 measa1=3
measa2=4 measb1=5
load1=1
load2=2
dest=9
* put
meas
!
measc1=7
(DMB3).
Part
measc2=8
9
! Three
port
de-embeded
! MEASUREMENT SET
1
9
!
!
!
!
!
!
!
!
measb2=6
result
Three-port
S parameters
Frequency-Domain
Data:
Magnitude-Angle
Number of Frequency
points:
1
Frequency
Interval:
o.
MHz
Low
Frequency:
1000.00
MHz
High Frequency:
1000.00
MHz
Valid
De-embeded
Data
Characteristic
Impedance:
50.0000
1 of
3.
Form
Identifier:
!
Three port de-embeded result
(DMB3).
Part 1 of 3.
! FREQ
S11
S12
813
!
821
S22
S23
!
831
832
833
! (MHz)
Mag
Angle
Mag
Angle
Mag
Angle
1
1000.0000 0.59842 -169.85
0.22104
-33.48 0.21382
-33.49
0.22104
-33.48
0.75168 -167.80
0.30034
-30.96
0.21382
-33.49 0.30034
-30.96 0.72729 -168.10
\
162
B.O.16
gain
Example: Incomplete write up.
#######################
GAIN ######################
Usage:
GAIN HELP
: This Message
GAIN MEAS_set
=
n1
[GAIN
=
n2J
[MERIT
=
n3J
[NOISE
: Get gain, noise and figure
of merit
information
: of a amp described
by the two-port
measurement
:
S parameters
in measurement set n1.
:
:
:
:
The gain
information
is put in set
figure
of merit
information
in set
noise
information
in set n4.
The parameters
in [J s are optional.
n2 and
n3 and
#####################################################
the
the
= n4J
163
."
l
!
B.O.17
sigma
Example:
Incomplete
write up.
######################
SIGMA #######################
Usage:
SIGMA HELP
: This Message
SIGMA MEAS = n1 X = n2 XX = n3 mean = n4 stddev = n5
: Each entry of measurement set n1 is added to set
n2 and its square is added to set n3.
From these
accumulated
values the mean (put in set n4) and
standard
deviation
(put in set n5) are calculated.
SIGMA CLEAR X = n2 XX = n3
: Clears measurement sets n2 and n3
#####################################################
\
164
B.O.IS
pie
Example: pie meas=1 dest=2
Purpose. PIE is used to calculate a pi equivalent circuit for a given S parameter
measurementset.
Arguments.
help
meas
=
n1
dest
=
n2
MEAS specifiesthe S parameter measurementset to be convertedand the result
is placed in the DEST measurementset. It is important to note the S parameters
must be of a network accurately modeled by a pi circuit or the results will be
erroneous. Below is a reprint of the on- line help available for PIE (pie help).
#######################
PIE
#########################
Usage:
PIE HELP
: This
Message
PIE
MEAS_set
= nl
DEST_set
= n2
#####################################################
165
Appendix
SPAN A "shell"
C
Syntax
The SPAN A shell feature is available to prototype user subprograms.
The code
follow.
c
.
c
c
SPSHELL
c
c
PURPOSE:Used to implement special
calculations
c
.
c
c
subroutine
spshell(parmx,parmy,parmf,arg,noarg,ident)
c
real
parmx(mxarg,mxparm,mxmeas),parmy(mxarg,mxparm,mxmeas)
real
arg(mxarg,mxmeas),parmf(mxform,mxmeas)
integer
noarg(mxmeas),tmparg
common/parmax/mxarg,mxmeas,mxparm,mxform
c
character*30
str
character*80
ident(mxmeas)
logical
kf,fin,prt,ofile,rfile,pecho
common/freerd/nwrite,ntype,aval,ival,ich,kf,fin,prt
166
+
,ofile,rfile,pecho,str
c
logical
lmeas,ldest
integer
meas,dest
complex
s(2,2),y(2,2),ptor,zl,z2,z3,yl,y2,y3
real
twopi
twopi=3.14159265*2.0
call
tread
c
if(str(1:4)
c
.eq.'HELP'.or.str(1:4)
call
.eq.'help')then
qsmode(2)
write(ntype,50)
if(prt)write(nwrite,50)
50
format
(
+
'
#######################
+
'
Usage:'
+
'
+
:
+
'
+
'
HELP'
,I,
This Message' ,II,
SHELL MEAS_set
'
,II,
,II,
SHELL
+'
SHELL ######################'
Options:
= nl
DEST_set = n2',II,
X = ? Y = ? etc.
input
parameters'
,II
)#####################################################'
return
endif
c
c
Reset
c
input)
parameter
flags
(used
to
test
that
all
parameters
have
been
,
~
167
c
lmeas=.false.
ldest=.false.
c
C
r
Parse
rest
of command line
c
100
if(fin)goto
150
if(str(1:4).eq.
call
'MEAS'.or.str(1:4)
.eq.'meas')then
fread
meas=ival
if(meas.lt.l.or.meas.gt.mxmeas.or.parmf(3,meas)
write(ntype,*)'
goto
Measurment
Set
.eq.O.)then
not
available'
600
endif
lmeas=.true.
elseif(str(1:4)
call
.eq.'DEST'
.or.str(1:4).eq.'dest')then
fread
dest=ival
if(dest.lt.l.or.dest.gt.mxmeas)then
write(ntype,*)'
goto
600
endif
ldest=.true.
endif
call
fread
goto
100
Destination
Set
not
available'
-~-~--T
'"
)
168
c
c
Check that
all
parameters
have
been specified
c
150
if(lmeas
.eqv.
.false.
vrite(ntype,*)'
goto
.or.ldest
Not
.eqv.
enough parameters
.false.)then
specified'
600
endif
c
do
10 n=1,noarg(meas)
c
~
c
Begin shell
calculations
here
c
arg(n,dest)=arg(n,meas)/1000.
c
parmx(n,1,dest)=parmx(n,1,meas)
parmy(n,1,dest)=parmy(n,1,meas)
parmx(n,2,dest)=parmx(n,2,meas)
parmy(n,2,dest)=parmy(n,2,meas)
parmx(n,3,dest)=20.*alog10(parmx(n,3,meas))/100.
parmy(n,3,dest)=parmy(n,3,meas)
10
continue
noarg(dest)
=noarg
(meas)
c
c
Set-up
descripter
c
parmf(1,dest)=7
"
)
169
parmf(3,dest)=2
c
-"
c
a+jb
format
c
parmf(2,dest)=2
c
"c
Characteristic
Impedance
c
parmf(4,dest)=parmf(4,meas)
c
c
Identifier
c
ident(dest)='freq
conversion
and
alpha/
in
db/cm'
return
c
600
write(ntype,*)'
Command Error
--
Command Ignored'
return
end
""""C"C""",;;"",~