Lecture 12: Microstrip. ADS and LineCalc.

Whites, EE 481/581
Lecture 12
Page 1 of 15
Lecture 12: Microstrip. ADS and LineCalc.
One of the most widely used planar microwave circuit
interconnections is microstrip. These are commonly formed by a
strip conductor (land) on a dielectric substrate, which is backed
by a ground plane (Fig. 3.25a):
t
d
r
W
We will often assume the land has zero thickness, t.
In practical circuits there will often be metallic walls and covers
to protect the circuit. We will ignore these effects, as does the
text.
Unlike stripline, a microstrip has more than one dielectric in
which the EM fields are located (Fig 3.25b):
E
r
H
This presents a difficulty. Notice that if the field propagates as a
TEM wave, then
© 2016 Keith W. Whites
Whites, EE 481/581
Lecture 12
vp 
Page 2 of 15
c0
r
But which  r do we use?
The answer is neither because there is actually no purely TEM
wave on the microstrip, but something that closely approximates
it called a “quasi-TEM” mode. At “lower frequencies,” this
mode is almost exactly TEM. Conversely, when the frequency
becomes too high, there are appreciable axial components of E
and/or H making the mode no longer quasi-TEM. This property
leads to dispersive behavior, among other effects.
Numerical and other analysis have been performed on microstrip
since approximately 1965. Some techniques, such as the method
of moments, produce very accurate numerical solutions to
equations derived directly from Maxwell’s equations and
incorporate the exact cross-sectional geometry and materials of
the microstrip.
From these solutions, simple and quite accurate analytical
expressions for Z 0 , v p , etc. have been developed primarily by
curve fitting.
The result of these analyses is that at relatively “low” frequency,
the wave propagates as a quasi-TEM mode with an effective
relative permittivity,  r ,e :
Whites, EE 481/581
Lecture 12
 r ,e 
r 1 r 1

2
2
Page 3 of 15
1
1  12 d W
(3.195),(1)
The phase velocity and phase constant, respectively, are:
c
(3.193),(2)
vp  0
 r ,e
  k0  r ,e
(3.194),(3)
as for a typical TEM mode.
In general,
1   r ,e   r
(4)
The upper bound occurs if the entire space above the microstrip
has the same permittivity as the substrate, while the lower bound
occurs if in this situation the material is chosen to be free space.
The characteristic impedance of the quasi-TEM mode on the
microstrip can be approximated as
 60
 8d W 

ln

 

W 4d 
  r ,e 
Z0  
120


  r ,e W  1.393  0.667 ln  W  1.444  
d

d

W
1
d
W
1
d
(3.196),(5)
Whites, EE 481/581
Lecture 12
Page 4 of 15
Alternatively, given a desired Z 0 and  r , the necessary W d can
be computed from (3.197) in the text, and given below.
Again, (1) and (5) were obtained by curve fitting to numerically
rigorous solutions. Equation (5) can be accurate to better than
1%.
Example N12.1. Design a 50-  microstrip on Rogers
RO4003C laminate with 1/2-oz copper and a standard thickness
slightly less than 1 mm.
Referring to the attached RO4003C data sheet from Rogers
Corporation, we find that  r  3.38  0.05 and d  0.032". We
will ignore all losses (dielectric and metallic).
What does “1/2-oz copper” mean? Referring to the attached
technical bulletin from the Rogers Corporation, copper foil
thickness is more accurately measured through an areal mass.
The term “1/2-oz copper” actually means “1/2 oz of copper
distributed over a 1-ft2 area.”
For 1-oz copper, t  34 m. For 2-oz copper, double this
number and for ½-oz copper divide by 2.
Whites, EE 481/581
Lecture 12
Page 5 of 15
We will use (3.197) to compute the required W d to achieve a
50- characteristic impedance:
 8e A
W
 e2 A  2 d  2
W 

r 1 
0.61   W
d  2 
2
 B  1  ln  2 B  1 

ln  B  1  0.39 
  
 r   d
2 r 
(3.197),(6)
To apply this equation, we first need to compute the constants A
and B:
Z r 1 r 1
0.11 


A 0
0.23
(7)

  1.376
60
2
r 1
r 
B
377
 6.442
2Z 0  r
(8)
Next, we will arbitrarily assume that W d  2 and use the
simpler equation in (6). We find that
W
8e1.376
 21.376
 2.317 .
d e
2
Is this result less than 2? The answer is no. So, we need to
recompute W d using the bottom equation in (6). We find here
that W d  2.316 , which is greater than 2 as assumed.
So, with this result and d  0.032", then W  2.316  0.032"
 0.0741".
Whites, EE 481/581
Lecture 12
Page 6 of 15
A more common unit for width and thickness dimensions in
microwave circuits is “mil” where
1
1 mil 
"  25.4 m
1000
Therefore,
74.1
W  0.0741" 
"  74.1 mils (  1.88 mm).
1000
This completes the design of the 50- microstrip.
Whites, EE 481/581
Lecture 12
Page 7 of 15
Whites, EE 481/581
Lecture 12
Page 8 of 15
ADS and LineCalc
A considerable part of a microwave design engineer’s time is
spent simulating the behavior of a circuit using computer tools.
We will extensively use Advanced Design System (ADS) from
Agilent Technologies in this course. ADS 2015 can be
downloaded and run from your laptop, when on campus.
One useful tool within ADS is LineCalc. Given the physical
dimensions and material properties, LineCalc will accurately
compute Z 0 and  r ,e for microstrip as well as for a large number
of other planar waveguides. Conversely, it can synthesize a land
width given the other parameters such as Z 0 , d, t,  r , and
frequency.
LineCalc uses accurate analysis techniques to make these
calculations and can include the effect of losses, land thickness,
the presence of side and top walls, etc.
Also, LineCalc does not assume a TEM mode. Consequently,
you may find at “high” frequencies that the microstrip becomes
dispersive where Z 0 and  r ,e are functions of frequency.
Whites, EE 481/581
Lecture 12
Page 9 of 15
The effective relative permittivity calculated by LineCalc is
K_Eff = 2.692, as shown above. Compare this to the value
predicted by the approximate expression (1)
 1 r 1
1
 r ,e  r

2
2
1  12 d W

3.38  1 3.38  1

2
2
1
 2.666
32
73.24
LineCalc predicts W = 73.25 mil. Compare this to Example
N12.1 where W = 74.1 mils was calculated using the accurate
but approximate expression (3.197).
1  12
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Lecture 12
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Lecture 12
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Advanced Circuit Materials Division
100 S. Roosevelt Avenue
Chandler, AZ 85226
Tel: 480-961-1382, Fax: 480-961-4533
www.rogerscorp.com
Data Sheet
Advanced Circuit Materials
®
RO4000 Series High Frequency Circuit Materials
Features:
Benefits:
RO4000® materials are reinforced
hydrocarbon/ceramic laminates
•
Designed for performance sensitive, high volume applications
Low dielectric tolerance and low loss
•
•
•
Excellent electrical performance
Allows applications wth higher operating frequencies
Ideal for broadband applications
Stable electrical properties vs. frequency
•
Controlled impedance transmission lines
Lead-free process compatible
•
No blistering or delamination
Low Z-axis expansion
•
Reliable plated through holes
Low in-plane expansion coefficient
•
Remains stable over an entire range of circuit processing temperatures
Volume manufacturing process
•
•
RO4000 laminates can be fabricated using stardard glass epoxy processes
Competitively priced
Typical Applications:
•
Cellular Base Station Antennas and Power Amplifiers
•
RF Identification Tags
•
Automotive Radar and Sensors
•
LNB’s for Direct Broadcast Satellites
RO4000® hydrocarbon ceramic laminates are designed to offer superior high frequency performance and low cost circuit
fabrication. The result is a low loss material which can be fabricated using standard epoxy/glass (FR-4) processes offered at
competitive prices.
The selection of laminates typically available to designers is significantly reduced once operational frequencies increase to
500 MHz and above. RO4000 material possesses the properties needed by designers of RF microwave circuits and matching
networks and controlled impedance transmission lines. Low dielectric loss allows RO4000 series material to be used in many
applications where higher operating frequencies limit the use of conventional circuit board laminates. The temperature
coefficient of dielectric constant is among the lowest of any circuit board material (Chart 1), and the dielectric constant is
stable over a broad frequency range (Chart 2). This makes it an ideal substrate for broadband applications.
RO4000 material’s thermal coefficient of expansion (CTE) provides several key benefits to the circuit designer. The expansion
coefficient of RO4000 material is similar to that of copper which allows the material to exhibit excellent dimensional stability,
a property needed for mixed dielectric multilayer boards constructions. The low Z-axis CTE of RO4000 laminates provides
reliable plated through-hole quality, even in severe thermal shock applications. RO4000 series material has a Tg of >280°C
(536°F) so its expansion characteristics remain stable over the entire range of circuit processing temperatures.
RO4000 series laminates can easily be fabricated into printed circuit boards using standard FR-4 circuit board processing
techniques. Unlike PTFE based high performance materials, RO4000 series
laminates do not require specialized via preparation processes such as
sodium etch. This material is a rigid, thermoset laminate that is capable
of being processed by automated handling systems and scrubbing
equipment used for copper surface preparation.
RO4003™ laminates are currently offered in various configurations utilizing
both 1080 and 1674 glass fabric styles, with all configurations meeting the
same laminate electrical performance specification. Specifically designed
as a drop-in replacement for the RO4003C™ material, RO4350B™ laminates
utilize RoHS compliant flame-retardant technology for applications requiring
UL 94V-0 certification. These materials conform to the requirements of IPC4103, slash sheet /10 for RO4003C and /11 for RO4350B materials.
The world runs better with Rogers.®
Chart 2: RO4000 Series Materials
Dielectric Constant vs. Frequency
Chart 3: Microstrip Insertion Loss
(0.030” Dielectric Thickness)
0.000
-0.200
-0.400
dB/Inch
-0.600
-0.800
-1.000
-1.200
-1.400
-1.600
0
2
4
6
8
10
12
14
16
18
Frequency, GHz
RO3003
PTFE Woven Glass
RO4003
RO4350
BT Glass
Epoxy/PPO
BT/Epoxy
FR4
Property
Typical Value
RO4003C
Dielectric Constant, εr
(Process specification)
3.38 ± 0.05
Direction
Units
Condition
Test Method
Z
--
10 GHz/23°C
IPC-TM-650
2.5.5.5
(2)
Clamped Stripline
RO4350B
(1)
3.48 ± 0.05
3.55
3.66
Z
--
FSR/23°C
IPC-TM-650
2.5.5.6
Full Sheet Resonance
Dissipation Factor tan, δ
0.0027
0.0021
0.0037
0.0031
Z
--
10 GHz/23°C
2.5 GHz/23°C
IPC-TM-650
2.5.5.5
Thermal Coefficient of εr
+40
+50
Z
ppm/°C
-50°C to 150°C
IPC-TM-650
2.5.5.5
Volume Resistivity
1.7 X 1010
1.2 X 1010
MΩ•cm
COND A
IPC-TM-650
2.5.17.1
Surface Resistivity
4.2 X 109
5.7 X 109
MΩ
COND A
IPC-TM-650
2.5.17.1
Electrical Strength
31.2
(780)
31.2
(780)
Z
KV/mm
(V/mil)
0.51mm
(0.020”)
IPC-TM-650
2.5.6.2
Tensile Modulus
26,889
(3900)
11,473
(1664)
Y
MPa
(kpsi)
RT
ASTM D638
Tensile Strength
141
(20.4)
175
(25.4)
Y
MPa
(kpsi)
RT
ASTM D638
Flexural Strength
276
(40)
255
(37)
Dimensional Stability
<0.3
<0.5
X,Y
mm/m
(mils/inch)
after etch
+E2/150°C
IPC-TM-650
2.4.39A
11
14
46
14
16
35
X
Y
Z
ppm/°C
-55 to 288°C
IPC-TM-650
2.1.41
>280
>280
°C DSC
A
IPC-TM-650
2.4.24
(3)
Dielectric Constant, εr
(Recommended for use in circuit design)
Coefficient of
Thermal Expansion
Tg
MPa
(kpsi)
IPC-TM-650
2.4.4
Td
425
390
°C TGA
Thermal Conductivity
0.71
0.69
W/m/°K
80°C
ASTM C518
Moisture Absorption
0.06
0.06
%
48 hrs immersion
0.060” sample
Temperature 50°C
ASTM D570
Density
1.79
1.86
gm/cm3
23°C
ASTM D792
Copper Peel Strength
1.05
(6.0)
0.88
(5.0)
N/mm
(pli)
after solder float
1 oz. EDC Foil
IPC-TM-650
2.4.8
Flammability
N/A
(4)
Lead-Free Process
Compatible
Yes
V-0
ASTM D3850
UL 94
Yes
(1) Dielectric constant typical value does not apply to 0.004” (0.101mm) laminates. Dielectric constant specification value for 0.004” RO4350B material is
3.33 ± 0.05.
(2) The IPC clamped stripline method can potentially lower the actual dielectric constant due to presence of airgaps between the laminates under test
and the resonator card. Dielectric constant in practice may be higher than the values listed.
(3) The design Dk is an average number from several different tested lots of material and on the most common thickness/s. If more detailed information is
required please contact Rogers Corporation. Refer to Rogers’ technical paper “Dielectric Properties of High Frequency Materials” available at http://
www.rogerscorp.com/acm
(4) ** Note on 94V-0 ** RO4350B LoPro™ laminates do not share the same UL designation as standard RO4350B laminates. A separate UL qualification may
be necessary.
Typical values are a representation of an average value for the population of the property. For specification values contact Rogers Corporation.
RO4000 LoPro laminate uses a modified version of RO4000 resin system to bond reverse treated foil. Values shown above are RO4000 laminates with out the
addition of the LoPro resin. For double-sided board, the LoPro foil results in a thickness increase of approximately 0.0007” (0.018mm) and the DK is approximately 2.4. Therefore, effective Dk is highly dependent on core thickness.
Prolonged exposure in an oxidative environment may cause changes to the dielectric properties of hydrocarbon based materials. The rate of change
increases at higher temperatures and is highly dependent on the circuit design. Although Rogers’ high frequency materials have been used successfully in
innumerable applications and reports of oxidation resulting in performance problems are extremely rare, Rogers recommends that the customer evaluate
each material and design combination to determine fitness for use over the entire life of the end product.
Standard Thickness
Standard Panel Size
Standard Copper Cladding
RO4003C:
0.008” (0.203mm), 0.012 (0.305mm), 0.016”
(0.406mm), 0.020” (0.508mm) 0.032” (0.813mm),
0.060” (1.524mm)
RO4350B:
*0.004” (0.101mm), 0.0066” (0.168mm) 0.010”
(0.254mm), 0.0133” (0.338mm), 0.0166” (0.422mm),
0.020”(0.508mm), 0.030” (0.762mm), 0.060”
(1.524mm)
12” X 18” (305 X457 mm)
24” X 18” (610 X 457 mm)
24” X 36” (610 X 915 mm)
48” X 36” (1.224 m X 915 mm)
½ oz. (17μm), 1 oz. (35μm) and
2 oz. (70μm) electrodeposited
copper foil
.
LoPro Reverse Treated EDC for PIM
Sensitive Applications:
½ oz (17mm), 1 oz (35 μm)
*0. 004” material in not available in
panel sizes larger than 24”x18” (610
X 457mm).
Material clad with LoPro foil add .0007” (0.018mm)
to dielectric thickeness
Note: LoPro EDC foil adds .00035” to
the panel thickness per side.
World Class Performance
Rogers Corporation (NYSE:ROG), headquartered in Rogers, Conn., is a global technology leader in the development and manufacture of high performance, specialty material-based products for a variety of applications in diverse markets including: portable
communications, communications infrastructure, computer and office equipment, consumer products, ground transportation,
aerospace and defense. In an ever-changing world, where product design and manufacturing often take place on different
sides of the planet, Rogers has the global reach to meet customer needs. Rogers operates facilities in the United States, Europe
and Asia. The world runs better with Rogers.®
CONTACT INFORMATION:
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Japan:
Taiwan:
Korea:
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China:
China:
China:
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The information in this data sheet is intended to assist you in designing with Rogers’ circuit material laminates. It is not intended
to and does not create any warranties express or implied, including any warranty of merchantability or fitness for a particular
purpose or that the results shown on this data sheet will be achieved by a user for a particular purpose. The user should determine
the suitability of Rogers’ circuit material laminates for each application.
Prolonged exposure in an oxidative environment may cause changes to the dielectric properties of hydrocarbon based materials. The rate of change increases at higher temperatures and is highly dependent on the circuit design. Although Rogers’ high
frequency materials have been used successfully in innumerable applications and reports of oxidation resulting in performance
problems are extremely rare, Rogers recommends that the customer evaluate each material and design combination to determine fitness for use over the entire life of the end product.
These commodities, technology and software are exported from the United States in accordance with the Export Administration
regulations. Diversion contrary to U.S. law prohibited.
LoPro, RO4000, RO4003, RO4350, RO4350B and RO4003C are licensed trademarks of Rogers Corporation.
The world runs better with Rogers. and the Rogers’ logo are licensed trademarks of Rogers Corporation.
© 1995, 1996, 1997, 1999, 2002, 2005, 2006, 2007, 2010 Rogers Corporation,
Printed in U.S.A., All rights reserved.
Revised 05/2010 0891-0110-0.5CC
Publication #92-004