Transmission Lines, Antenna Tuners, and Impedance_pptx

Transmission Lines, Antenna Tuners, and Impedance_pptx

Transmission Lines, Antenna
Tuners, and Impedance
Matching
3/12/2009
Larry Benko, W0QE
1
Understanding Transmission Lines
• Presentation about antenna tuners and
impedance matching will follow
• Need to understand transmission lines first
• Concepts are interdependent and not separable
• Software simulation is invaluable for better
understanding of the concepts
• Inexpensive test equipment allows measurements
that only a lab could make 10 years ago
3/12/2009
Larry Benko, W0QE
2
Transmission Lines and
Coaxial Cable
• Deliver RF signals to another location efficiently
• Early transmitters did not use transmission lines
• 2/4 wire open wire lines, flexible coax, hard line,
twisted pair, microstrip, wave guide, etc.
• Computer motherboards, Ethernet, USB cables
• Nearly all digital signals are RF these days
3/12/2009
Larry Benko, W0QE
3
Who Can You Believe?
• Too much misinformation and incomplete
information exists
• Transient conditions and steady state are often
mixed together which is incorrect
• All concepts presented have been measured in
hardware and simulated in software, often in
multiple programs, with total agreement
• Please challenge me on any topic
3/12/2009
Larry Benko, W0QE
4
Software Tools
(free except EZNec, WinSmith and TLW)
• LTspice IV (previously SwitcherCAD)
– http://www.linear.com/designtools/software/
• TLW v3.0 on ARRL Antenna Handbook CDROM
• WinSmith 2.0
– http://www.scitechpublishing.com
• Collection of Smith Chart stuff
– http://sss-mag.com/smith.html
• SuperSmith
– http://www.tonnesoftware.com/
3/12/2009
Larry Benko, W0QE
5
Software Tools
(free except EZNec, WinSmith and TLW)
• VNA Help SWR Calculator
– http://www.vnahelp.com/products.html
• RFSim99
– http://www.practicalrf.com/$Newsletter/eletters/February2006/RFSim99.htm
• EZNEC
– http://www.eznec.com
– other NEC programs 4NEC2, NEC4Win etc.
• Coax loss & power handling calculator
– http://www.timesmicrowave.com/cgi-bin/calculate.pl
3/12/2009
Larry Benko, W0QE
6
Hardware Tools
• AIM4170B Antenna Analyzer
– http://www.arraysolutions.com/Products/AIM4170B.htm
– Several other good analyzers available
• Time Domain Reflectometer (home brew)
3/12/2009
Larry Benko, W0QE
7
Weaknesses in Software Tools
• LTSpice:
– Transmission line loss constant with frequency
– Q of components is constant with frequency
– Can’t model transmission line shielding
• TLW:
– Q of components is constant with frequency
• WinSmith:
– Transmission line loss is constant with frequency
• Weaknesses are minimal
3/12/2009
Larry Benko, W0QE
8
How Do Transmission Lines Work?
• At every point along the line the currents in each
wire are the same magnitude and 180 degrees
out of phase
• For coax, the currents are on the outside of the
center conductor and the inside of the shield
• AC current flow produces a magnetic field that
opposes current flow
• Transmission line currents produce the minimum
magnetic field which also minimizes radiation
3/12/2009
Larry Benko, W0QE
9
Other Currents on the Line
• A current can flow on both wires equally and is in
phase for open wire line or on the outside of the
shield for coax
• This is an antenna current that does radiate and
is generally unwanted
• Common mode chokes are used to keep this
current at acceptable levels
3/12/2009
Larry Benko, W0QE
10
Terminology of Currents
• Transmission line currents are also known as
differential or metallic currents
• Common mode currents are also known as
longitudinal or antenna currents
• Both types of currents can coexist but there is
always a small conversion from one type to the
other which can cause problems
3/12/2009
Larry Benko, W0QE
11
Properties of coaxial cable
•
•
•
•
•
•
•
•
•
•
•
Characteristic impedance
Attenuation (matched loss) vs. frequency
Power rating (current rating) matched vs. frequency
Dielectric material (voltage breakdown, temperature rating)
Center conductor (size and composition)
Shield(s) material (shielding effectiveness)
Outside jacket (weather, temperature, abrasion rating)
Minimum bend radius, flexibility
Physical size and connector compatibility
Velocity factor
Not all properties are important for a particular application
3/12/2009
Larry Benko, W0QE
12
Characteristic (Surge) Impedance
• Load impedance where no wave is reflected back
into the coax
– Next 3 slides
• Notice how the ratio of the voltage divided by the
current is the surge impedance of the
transmission line and is independent of the load
impedance at the far end!
3/12/2009
Larry Benko, W0QE
13
File LosslessReflections-50.asc
V(Vin1) under I(R1)
3/12/2009
V(Vout2) under I(R2)
Larry Benko, W0QE
14
File LosslessReflections-100.asc
V(Vin1) under I(R1)
No further
reflections
due to R1
3/12/2009
Larry Benko, W0QE
15
File LosslessReflections-25.asc
V(Vin1) under I(R1)
No further
reflections
due to R1
3/12/2009
Larry Benko, W0QE
16
Surge Impedance Continued
• All forward & reflected waves have a V/I ratio that
equals the surge impedance of the line!
• Maximum power is delivered into the load when
the load impedance matches the surge
impedance of the transmission line
• Maximum power is delivered into a matched
transmission line if the transmitter output
impedance matches the surge impedance
– Continued next slide
3/12/2009
Larry Benko, W0QE
17
Surge Impedance Again
• Zo = L/C per unit length, equivalent circuit no loss
 138 
 OD 
 ∗ log10

• Zo = 
 ID 
 ε 
for round coax
• Why a particular impedance?
– Maximum power 30Ω, minimum loss 77Ω, max. voltage
breakdown 60Ω (1929 Bell Laboratories Study)
– Maximum power per pound of copper 52Ω (F. Terman?)
– Today 75Ω, 50Ω, 52Ω, 53.5Ω, 25Ω, 80Ω, 93Ω, etc.
3/12/2009
Larry Benko, W0QE
18
100W 50Ω output transmitter driving lossless coax with
various load impedances and no impedance matching
SWR
1
1.25
1.5
1.7
2
3
4
5
10
20
50
3/12/2009
Example Load
Power into dB relative
Impedance(s)
Load
to 100W
0
50 + j0
100.0
-0.05
40 + j0, 62.5 + j0
98.8
-0.18
33.3 + j0, 75 + j0
96.0
-0.30
85 + j0
93.3
-0.51
25 + j0, 100 + j0, 40 +/- j30
88.9
-1.25
150 + j0
75.0
-1.94
200 + j0
64.0
-2.55
10 + j0
55.6
-4.81
5.0 + j0
33.1
-7.41
400 + j0
18.1
1.0 + j0
7.7
-11.14
Larry Benko, W0QE
19
SWR by other names
• SWR (standing wave ratio)
– Maximum voltage in the line = forward + reflected
voltage
– Minimum voltage in the line = forward - reflected voltage
– SWR is the maximum divided by the minimum voltage
• Reflection coefficient, return loss, and SWR
–
–
–
–
Different ways to tell the exact same story
ρ (reflection coefficient) = Vr/Vf or Ir/If
SWR = (1 + ρ)/ (1 - ρ)
RL (return loss) = -20 log10(ρ)
• SWR decreases from load to source if line has loss
3/12/2009
Larry Benko, W0QE
20
Equating SWR, ρ, & Return Loss
SWR
1
1.01
1.02
1.05
1.1
1.25
1.5
2
3
4
5
10
20
50
3/12/2009
Reflection Coefficient (ρ)
0.000
0.005
0.010
0.024
0.048
0.111
0.200
0.333
0.500
0.600
0.667
0.818
0.905
0.961
Larry Benko, W0QE
Return Loss (RL)
infinity
46.06
40.09
32.26
26.44
19.08
13.98
9.54
6.02
4.44
3.52
1.74
0.87
0.35
21
Effect of Reflections
• For continuous transmissions the signals
reflected back into the transmission line can
arrive at the transmitter with an amplitude from
zero to the original transmitter amplitude and at
any phase angle
• The impedance seen by the transmitter varies
and for high SWRs can be either very low or high
causing driving problems for the transmitter
3/12/2009
Larry Benko, W0QE
22
Reflection Examples
• Frequency = 14.0MHz, load = 73 + j87Ω, load
SWR = 4.0:1, & various lengths of RG-213
• 11.6’ (.25 λ) => 14.5 + j17.0 (Tx SWR = 3.85:1)
• 14’ = 13.1 – j1.2 (Tx SWR = 3.82:1)
• 25.8’ = 184.2 – j4.1 (Tx SWR = 3.68)
• 23.18’ (.5 λ) => 74.8 + j81.8 (Tx SWR = 3.71:1)
• 46.37’ (1 λ) = > 76.1 + j76.8 (Tx SWR = 3.47:1)
• 200’ => 20.5 + j1.9 (Tx SWR = 2.44:1)
3/12/2009
Larry Benko, W0QE
23
Loss
• At HF loss in coax is predominantly due to the
RF resistance of the center conductor
• Matched loss at HF is frequency dependent and
increases ~ as the square root of frequency
• Following example shows losses with and
without matching for a 100W transmitter
3/12/2009
Larry Benko, W0QE
24
Reconciling the Loss
Loss
Matched
Loss 12.5
ohm Load
TLW v.3.00
.59dB
LTSpice IV
.62dB
= 1.16 + 1.50dB
Method
HP8753B VNA
.59dB
Impedance
seen by Tx
2.70dB
2.66dB
Z = 110 - j80
Z = 108 - j74
2.69dB
Z = 107 - j69
• Cable was 36’1” of RG-58/U (Zo=52Ω) & the tests
were done/simulated at 14.0MHz with no matching
• Amazing agreement between hardware & software
3/12/2009
Larry Benko, W0QE
25
Loss with No Matching
• 50Ω load
– Power output = 87.2W
– Dissipative (heat) loss in transmission line = 12.8W
– Mismatched non-dissipative circuit loss ~ 0W
• 12.5 Ω load (4:1 load SWR)
– Power output = 56.0W
– Dissipative (heat) loss in transmission line = 15.7W
– Mismatched non-dissipative circuit loss = 28.3W
3/12/2009
Larry Benko, W0QE
26
Loss with Matching
• Matching at transmitter end of transmission line
– 12.5 Ω load = 78.1W
– Dissipative loss in line = 21.9W
• Matching at load end of transmission line
– 12.5 Ω load = 87.2W
– Dissipative loss in line = 12.8W
• Power output difference is 0.5dB between load &
source matching
• Higher SWRs and loss line increase differences
3/12/2009
Larry Benko, W0QE
27
Overall Circuit Loss
• Dissipative loss in the transmission line
– Increases with SWR and driving power
– Transmission line loss is primarily a function of the
square of the currents summed over length at HF
• Non-dissipative loss at source end due to
mismatch
– Drive with impedance which is the conjugate match to
mismatched line to deliver max. power (antenna tuner)
– Reducing the mismatch loss via impedance matching
increases dissipative loss in line
3/12/2009
Larry Benko, W0QE
28
10:1 SWR Example
• 1λ RG-58A (Belden 8259) 46.368’ long @ 14.0MHz
connected to a 5 + j0 Ω load with an optional tuner
at the antenna, in the shack, or no tuner at all
• Do calculation in both TLW & LTSpice showing
consistency in methods
• 0.87dB vs 3.10dB vs 5.68dB (82W vs 49W vs 27W)
for a 100W equivalent transmitter not including any
SWR power foldback
3/12/2009
Larry Benko, W0QE
29
Options to the Previous Example
•
•
•
•
RG-58A :0.87dB vs 3.10dB vs 5.68dB
RG-213: 0.36dB vs 1.54dB vs 5.17dB
LMR-500: 0.16dB vs 0.74dB vs 4.95dB
4:1 xfmr (.2dB loss) @ antenna:
N/A vs 1.38dB vs 1.95dB
• RG-213 + 4:1 xfmr (.2dB) @ antenna:
N/A vs 0.71dB vs 1.44dB
• Many other choices
3/12/2009
Larry Benko, W0QE
30
Measuring Line Zo and Loss
• Measuring surge impedance (Zo)
–
–
–
–
Open far end of line, measure Z1 @ phase angle A1
Short far end of line, measure Z2 @ phase angle A2
Zo = square root (Z1 * Z2) @ phase angle (A1 + A2)/2
Usually phase is close to zero
• Measuring Loss
– Open far end of line, measure return loss RL1
– Short far end of line, measure return loss RL2
– Loss = ( RL1 + RL2 )/4
3/12/2009
Larry Benko, W0QE
31
Shielding in Transmission Lines
• At every point currents are equal and out of phase
resulting in very little radiation and pickup
• Coaxial transmission line currents are on the
outside of the center conductor and inside of shield
• Current on the outside of the coax does affect the
currents on the inside very minimally & vice versa
• Currents on the outside of the shield do radiate
3/12/2009
Larry Benko, W0QE
32
Strength of Transmission Line Currents
• Coax is electrically λ/4 @ 11.5MHz
• SWR < 1.5:1 above 3.6MHz (Wow!)
– Next slide
• Currents flow where impedance is minimum
3/12/2009
Larry Benko, W0QE
33
Impedance measured by AIM4170
3/12/2009
Larry Benko, W0QE
34
Shield Test
• Sig. Gen. #1 = 14.0MHz @ -20dBm
– transmission line currents = 447uA
• Sig. Gen. #2 = 14.1MHz @ +21dBm (adjusted)
– to produce common mode current of 447uA via Probe #1
3/12/2009
Larry Benko, W0QE
35
Shield Test Results
Test
12’2”
Belden
RG-58A/U
14’9”
double shield
silver RG-142
Spectrum
Analyzer #1
Spectrum
Analyzer #2
-20dBm @ 14.0MHz
-103dBm @ 14.0MHz
-67dBm @ 14.1MHz
-54dBm @ 14.1MHz
-103dBm @ 14.1MHz
-54dBm @ 14.1MHz
-20dBm @ 14.0MHz
nil @ 14.0MHz
Both tests had 447uA of transmission line current @
14.0MHz & 447uA of common mode current @ 14.1MHz
3/12/2009
Larry Benko, W0QE
36
3 Wire Model for Coax
• Dipoles fed from coax without a balun or nonsymmetrical antenna or feed line
• Add simulation wire for the outside of the shield
• Some antenna designs depend on a common
mode current to work as advertised
3/12/2009
Larry Benko, W0QE
37
dB (Decibel)
• Relative measurement, ratio of power or intensity
without units
• Used in acoustics, optics, and electronics
• Convert to voltages or currents, dB = 10*log10(Po/Pi),
dB = 20*log10(Vo/Vi) if impedance is constant
• 2x = 3dB, 4x = 6dB, 8x = 9dB, 10x = 10dB, 5x =7dB,
100x = 20dB, .0001x = -40dB etc.
• Absolute dB terms (dBm, dBrnC0, dBW, dBV, dBuV)
• Impedance issues, double termination = -3.52dB
3/12/2009
Larry Benko, W0QE
38
Transmission Line Conclusion
• Was presentation too advanced?
• Antenna Tuner discussion to follow if any interest
3/12/2009
Larry Benko, W0QE
39
Antenna Tuners and
Impedance Matching
3/12/2009
Larry Benko, W0QE
40
Impedance Matching
• Generally increases RF power transfer
• Flexible or specific purpose
• All impedances can be matched at one frequency
– 2 reactive components or 2 pieces of transmission line
– Other circuits may match with “nicer” component values
• Matching circuits may provide
– Additional harmonic suppression and filtering
– Common mode current suppression or balance
• No single circuit is the “best” for all uses
3/12/2009
Larry Benko, W0QE
41
Antenna Tuners
•
•
•
•
Impedance matching via adjustable components
Increase RF power transfer to load
Allow transmitters to operate at full power output
Generally do not affect the antenna pattern
unless common mode currents change
• Located at transmitter, antenna, or in between
• Comprised of high Q low loss components
• Cascading tuners need to be done carefully
3/12/2009
Larry Benko, W0QE
42
Antenna Tuner Topologies
•
•
•
•
•
•
•
•
C-L-C high pass, “Tee” tuner
L-C low or high pass, “L” tuner (need to reverse)
Tapped low/medium Q resonant circuit tuner
Parallel L-C resonant tapped coil tuner
“L” network with auto-transformer
Single component L or C with mistuned antenna
Transmission line sections and stubs
Balanced versions of the above, static bleed
3/12/2009
Larry Benko, W0QE
43
Smith Chart
• Smith Chart basics
–
–
–
–
Zo at center, constant SWR = circles
X axis is reflection coefficient (-1 to +1)
Top half is inductive, bottom half is capacitive
Need to think in terms of Z = R +/-jX & Y = G +/-jB
• The Smith Chart allows the user to see graphical
solutions to matching problems which enhances
the understanding of impedance matching
• Smith Chart could easily be an entire presentation
3/12/2009
Larry Benko, W0QE
44
Series
Capacitor
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
45
Series
Inductor
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
46
Shunt
Capacitor
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
47
Shunt
Inductor
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
48
Series
Transmission
Line
(50Ω)
Ω)
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
49
Series
Transmission
Line
(200Ω)
Ω)
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
50
2:1 Turns
Transformer
Step Up
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
51
Open
Stub
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
52
Shorted
Stub
10MHz = Green
20MHz = Red
30MHz = Blue
3/12/2009
Larry Benko, W0QE
53
Smith Chart Regions
L type circuits
3/12/2009
Larry Benko, W0QE
54
Effect of Transmission Lines
• Series lengths of lossless transmission lines (Zo)
trace clockwise circles geometrically centered at Zo
• 180 electrical degrees of line = 1 revolution
• Loss in line causes circle to become a spiral to Zo
• Shunt lengths of shorted or open transmission line
look like shunt L & C components with medium Q
• The reactance in a non-resonant antenna can be
used as part of the matching network
3/12/2009
Larry Benko, W0QE
55
Matching Example #1
• Match 100 + j100 (load) to 50 + j0 @ 14MHz
–
–
–
–
–
–
How many ways with 2 or fewer components?
Can it be done with 1 component?
Why are some matches better than others?
What happens if the frequency is changed?
What is load SWR?
Maximum voltages and currents increase as the square
root of SWR
• Some match types will track impedance changes
versus frequency better
3/12/2009
Larry Benko, W0QE
56
Matching Example #1 Solutions
•
•
•
•
•
•
•
Ckt. A: C = 155pF, L=.99uH
Ckt. C: L = 3.1uH, C = 131pF
Starting at load, 41° of 50Ω line in series with .89uH
Starting at load, 79° of 50Ω line then shunt .36uH
Starting at load, 131° of 50Ω line then shunt 355pF
Starting at load, 64° of 75Ω line in series with .78uH
Finally just 129 degrees of series 122Ω line
3/12/2009
Larry Benko, W0QE
57
Matching Example #2
• Dipole for 80m that is approximately a half
wavelength long with the center 40’ high and the
ends at 25’ over average ground
• The dipole will be fed with a minimum of 80’ of
transmission line and if coax is used there will be a
good balun at the antenna
• Problem is to effect a match from 3.5 to 4.0MHz
with SWR at the transmitter below 1.7:1 while
feeding the antenna efficiently
3/12/2009
Larry Benko, W0QE
58
Dipole Feed Point
Impedance
3/12/2009
Larry Benko, W0QE
59
Matching Example #2 Solution #1
• Lengthening the dipole 13%, fed with .5λ of 300Ω
open wire line, followed by a good 1:1 balun and
then Ckt. C with a fixed L = 14.5uH & variable C
between 100 & 350pF yields transmitter SWRs less
than 1.3:1 over the entire 80m band
• The “L” network might have to be adjusted slightly
to account for the balun
• TLW total loss estimate <.3dB
3/12/2009
Larry Benko, W0QE
60
Matching Example #2 Solution #2
• Starting with the 127.5’ dipole, 1:1 balun at the
antenna, & 80’5” of RG-213 to a tuner
–
–
–
–
3.5 MHz:
3.7 MHz:
3.8 MHz:
4.0 MHz:
Ckt. A, L = 5.0uH, C = 350pF, Loss = .95dB
No tuner, Loss = .4dB
Series C = 970pF, Loss = .5dB
Series C = 290pF, Loss = 1.14dB
• Not a bad solution BUT antenna shouldn’t be used
on other bands (except 30m) due to SWR on coax
3/12/2009
Larry Benko, W0QE
61
Matching Example #2 Continued
• There are many other solutions and some may be
better than the 2 previous ones
• Building open wire line of Zo between 150Ω and
700Ω is easy and 4 wire line is good for lower
impedances with better balance
• Coax can be paralleled for lower impedances
3/12/2009
Larry Benko, W0QE
62
Final Matching Example
• 160m dipole 150’ high sloping down at ~25 degrees
• Resonant at 1.86 MHz and want to cover entire
160m band
• Matching to be done at the transmitter
• Impedance measured through 160m high pass 9
pole filter due to AM broadcast interference of
+30dBm after effects of filter were calibrated out
3/12/2009
Larry Benko, W0QE
63
160m
High
Pass
Filter
(200W)
3/12/2009
Larry Benko, W0QE
64
160m Dipole
Measured in
Shack
2.0 MHz
5.97:1 SWR
1.8 MHz
3.66:1 SWR
1.86 MHz
1.76:1 SWR
3/12/2009
Larry Benko, W0QE
65
No Adjustment
Match
No adjustments,
SWR<1.7:1
3/12/2009
Larry Benko, W0QE
66
“Tee”
Tuner
2 adjustments,
SWR=1.0:1
3/12/2009
Larry Benko, W0QE
67
The
“Beast”
Special
purpose
160m
tuner
3/12/2009
Larry Benko, W0QE
68
Antenna Tuners and Impedance
Matching Conclusion
• Is anyone still awake?
• We could do more examples ☺
• Topics for the future?
Tuning without generating QRM
Other ideas?
3/12/2009
Larry Benko, W0QE
69