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Agilent’s Electronic Measurement Group is now Keysight Technologies.

Keysight Technologies Inc. is the world's leading electronic measurement company, transforming today's measurement experience through innovation in wireless, modular, and software solutions. The company's 9,500 employees serve customers in more than 100 countries. Visit us at www.keysight.com.

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Impedance Matching Applications

– RF and Microwave Design

• Impedance matching for power transfer, low noise, gain and

efficiency. You are here because you want to do this better.

– Internet of Things IoT

• Lots of gadgets with antennas to match to IoT chips

• Economic and easy to realize

– 5th Generation Wireless

• Broad band matching

• Multi-antenna matching

– RF chipset integration

• Reference design for demanding clients

© Keysight

Technologies 2015 3

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Impedance Matching for Maximum Power Transfer Conjugate Matching

Zsource Zload

Matching Network

Zin = Z*source

Zout = Z*load

© Keysight

Technologies 2015 4

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Impedance Matching for Minimum Noise

Zout = Zopt

Matching Network

Zsource

Zin = Z*source

Zopt

© Keysight

Technologies 2015 5

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Impedance Matching for Impedance Dependent Spec (e.g. Efficiency, EVM, ACPR, BER) from load pull contour analysis

Zload

Matching Network

Zcontour = Zin

Zout = Z*load

Zcontour

© Keysight

Technologies 2015 6

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Designing Impedance Matching Problem

1. Designing impedance matching networks is routine in RF and

microwave engineering. But always tedious and time consuming!

2. Broadband matching over 25% fractional bandwidths into frequency-

varying complex impedances is very tedious and the math is difficult

3. Brute force optimization on a previous design may not converge over

bandwidth because of multiple local minimums, inappropriate starting

topologies and initial values

4. Matching between non-unilateral devices requires iterative input,

output and interstage matching procedures because output matching

affects the input impedance of each device

5. Implementation of distributed matching network on microstrips adds

additional complexity to calculate physical dimensions for the layout

Routine, always tedious and always time consuming

© Keysight

Technologies 2015 7

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Impedance Matching Network Design

Zsource Zload

Matching

Network

1-Stage

Zsource Zload

Input

Matching

Network

Output

Matching

Network

2-Stage

Antenna

Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

3-Stage

Increasing Levels of Difficulty

© Keysight

Technologies 2015 8

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Fano’s Limits on Matching Reactive Loads and BW

© Keysight

Technologies 2015 9

Reactive loads are harder to match over wide BW

Γ𝑚𝑖𝑛= 𝑒−𝜋(𝑄𝑙𝑜𝑎𝑑𝑒𝑑/𝑄𝑜𝑓_𝑙𝑜𝑎𝑑)= 𝑒− (

𝜋

𝑄𝑜𝑓𝑙𝑜𝑎𝑑 𝑥 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙𝐵𝑊)

𝑅𝐿𝑑𝐵= −20𝑙𝑜𝑔Γ𝑚𝑖𝑛

𝑄𝑙𝑜𝑎𝑑𝑒𝑑 = 𝑓𝑐𝑒𝑛𝑡𝑒𝑟

𝑓𝑢𝑝𝑝𝑒𝑟−𝑓𝑙𝑜𝑤𝑒𝑟 =

1

𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙_𝐵𝑊 𝑄𝑜𝑓_𝑙𝑜𝑎𝑑 = 𝑋𝑙𝑜𝑎𝑑

𝑅𝑙𝑜𝑎𝑑 = 𝐵𝑙𝑜𝑎𝑑

𝐺𝑙𝑜𝑎𝑑

Fractional BW = 𝑓𝑢𝑝𝑝𝑒𝑟−𝑓𝑙𝑜𝑤𝑒𝑟

𝑓𝑐𝑒𝑛𝑡𝑒𝑟 =

1

𝑄𝑙𝑜𝑎𝑑𝑒𝑑

“To achieve -20 dB return loss over an octave BW, the

reactive part of load must be less than 2.047x of the

resistive part“

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A very difficult impedance matching problem

Antenna

Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Transistor

Non-unilateral

Unstable

Transistor

Non-unilateral

Design the input, interstage and output

matching networks for 40% fractional BW

and 20 dB return loss

Multi-stage broadband matching of frequency-dependent complex

impedances at input, interstage and output

© Keysight

Technologies 2015 10

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Multi-stage broadband matching of complex frequency dependent impedances over 40% BW from 2 to 3 GHz

Antenna

Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Complex impedance RLC equivalent circuit

R=72 , C=10pF, L=0.405nH, Fc= 2.5GHz

2 port

S-parameters

+ stabilizing

circuit for

unconditional

stability

2 port

S-parameters 50

© Keysight


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Automatic Impedance Network Synthesis Demo

© Keysight


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Impedance Matching Solution- Automatic Synthesis 1. Automatic circuit synthesis quickly evaluate multiple matching topologies

within minutes to arrive at the most economic and realizable implementation

2. Direct filter synthesis can include frequency response shaping in the design

of matching networks, (e.g. for rejection of harmonics; low frequency gain

suppression) by selective placement of transmission zeros

3. Synthesis techniques used in previous demo

1. Real Frequency Technique- finds the best fit RL or RC model of impedance

terminations from S-parameter data

2. Fit Chebyshev rational functions for required conjugate matching networks

3. Continued fraction expansion synthesis from poles and zeros of (2)

4. Norton Transforms to match resistive parts and absorb reactive components

5. Richards Transforms to convert lumped to distributed topology

6. Pattern/Gradient Optimization to correct for finite component Q, termination

modeling errors to achieve -20db return loss in the pass band

© Keysight


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Impedance Matching Network Strategies Matching Network Type

1. L-C Pi Network

2. L-C Tee Network

3. TRL 1/4 Wave

4. TRL Single/Double Stub

5. L-C Bandpass

6. L-C Pseudo Lowpass

7. TRL Pseudo Lowpass

8. TRL Stepped Impedance

9. Custom network of your own with

optimizable parameters

Strategies for Impedance Matching

A. Use simpler topologies 1-4 for

narrow BW

B. Use more advanced topologies 5-

8 for wider BW

C. Optimize for required return loss

over BW.

D. If return loss not achieved, try

another topology or increase

order of matching network

(i.e. with more sections)

© Keysight


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LC Pi & Tee Matching Networks

1. L-C Pi Network

2. L-C Tee Network

– Useful for narrow band matching with some control of BW by setting Q value

– Synthesis automatically determines 𝑄𝑚𝑖𝑛 for widest bandwidth achievable and

LC network topology with calculated LC component values

– At the center frequency there are two exact network solutions for the minimum

Q case, usually results in one element vanishing .Inductive and capacitive

tendency buttons selects between the two solutions depending on the need to

pass or block DC

– For a specified higher-Q value, all three pi or tee parts will be present, and

optimization will be more effective at broadening the bandwidth

𝑄= 𝑓𝑐𝑒𝑛𝑡𝑒𝑟

𝑓𝑢𝑝𝑝𝑒𝑟−𝑓𝑙𝑜𝑤𝑒𝑟 =

1

𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙_𝐵𝑊 > 𝑄𝑚𝑖𝑛 =

1

2

𝑅𝐿

𝑅𝑆− 1 𝑜𝑟

1

2

𝑅𝑆

𝑅𝐿− 1

© Keysight


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Distributed Matching Networks

– Single ¼ wavelength series

transmission line

– Narrow band matching of resistive

terminations without transformer

– Some capacity for narrow band

complex terminations

TRL ¼ Wave and TRL Single/Double Stub

– 1 to 3 elements of alternating shorted

stubs and series line

– Matches any complex source and

load at a single frequency

– Distributed equivalent of LC Pi and

Tee networks

© Keysight


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LC Bandpass Matching Network – General LC matching network of

arbitrary order ( 1 to 14, typically two

components per order)

– Good for broadband problems with

frequency dependent complex terminations

– Uses real frequency technique and continued fractional expansion to

synthesize network topology and component values

– Synthesis steps:

1. Finds best-fit RLC model for terminations using Real Frequency Technique

2. Find poles and zeros of required bandpass matching network transfer function

using a Chebyshev approximation

3. Synthesize network and LC values using Continued-fraction Expansion

4. Absorb termination reactance to reduce one or more network elements

5. Optimize for return loss over BW using pattern and gradient methods

© Keysight


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LC Bandpass Matching Network (cont:) – LC bandpass matching is very sensitive

to order. Test with even or odd order.

Algorithm will use the next higher order

if needed

– Technique based on work by Fano, Levy and Cuthbert

– Synthesis algorithm does not perform resistance transformation, only

reactance cancellation

– Resistance transformation is handled by

a. Using an impedance transformer if the impedance is very far apart

b. Remove required transformer using Norton circuit transforms

c. Force removal of required transformer by increasing network loss until removal is

possible. Quality of match suffers, but can be resolved by specifying higher order

– Optimization adjusts the network to compensate for LC finite Q and

termination modeling errors

© Keysight


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LC Pseudo Lowpass Matching Network – Alternating shunt C and series L

matching network

– 1 to 14 order, about 2

components per order

– Suitable for wideband matching with complex termination without using

transformers

– Synthesis steps

1. Terminations modeled as series RL or parallel RC network

2. Poles and zeros for low pass Chebyshev transfer function between

terminations are found

3. Poles and zeros are transformed to pseudo bandpass, resulting in doubling of

poles and zeros, but accounts for unequal termination resistance and does

not require a transformer

– Optimization corrects for the simpler modeling of terminations which may

result in poorer initial match compared to the LC bandpass technique

© Keysight


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Distributed Matching Networks

– Distributed form of LC pseudo

lowpass with series line and open

stubs for microstrip/stripline realization

– Same algorithm for initial network

synthesis as LC pseudo lowpass

– Synthesized lumped network is

converted to distributed form

– Optimization corrects for

discrepancies from conversion

TRL Pseudo Lowpass and TRL Stepped Impedance

– Series of transmission lines of

different characteristic impdeances

– 1 to 30 order, one line per order

– Similar to TRL ¼ Wave but much

better for broadband matching of

complex terminations

– Synthesis results in lines with

monotonic changing Zo

© Keysight


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Putting Impedance Matching Synthesis to Work

© Keysight


Antenna

Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Complex RLC equivalent circuit

R=72 , C=10pF, L=0.405nH, Fc= 2.5GHz

2 port

S-parameters

+ stabilizing

circuit for

unconditional

stability

2 port

S-parameters 50

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Making sure transistor are unconditionally stable Stability Factor K>1, Stability Measure B1>0

– Stage 1

K<1, B>0, Unstable – Stage 2

K>1, B1>1

– Stable above 1.75GHz

© Keysight


– Stage 1

Stabilized

K>1, B>0,

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Putting Impedance Matching Synthesis to Work Matching BW setting and Antenna impedance definition

© Keysight


Antenna

Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Antenna RLC series equivalent circuit

R=72 , C=10pF, L=0.405nH,

Fc= 1

2𝜋√𝐿𝐶 =2.5GHz

2 port

S-parameters

+ stabilizing

circuit for

unconditional

stability

2 port

S-parameters 50

Matching BW = 1GHz

Fc= 2.5GHz

BW/Fc= 40% fractional BW

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Putting Impedance Matching Synthesis to Work (cont) Selecting topologies for Input, Interstage and Output Matching

© Keysight


Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Antenna

50

Try TRL Pseudo Lowpass of Orders 2, 3, 3 respectively

Min Zo = 20 and Max Zo = 120 for realizability

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Putting Impedance Matching Synthesis to Work (cont) Defining 1st (stabilized) and 2nd Stage Transistor Networks

© Keysight


Zload

Interstage

Matching

Network

Input

Matching

Network

Output

Matching

Network

Antenna

50

Add stabilized

transistor circuit for 1st

device stage after

input matching section

Add transistor S-

parameter file for 2nd

device after interstage

matching section

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Synthesized Input, Interstage and Output Distributed Matching networks

© Keysight


TRL matching network

Synthesized Microstrip matching schematic from above TRL network

Microstrip matching layout

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Optimization to correct for microstrip conversion discrepancy

© Keysight


TRL matching network

Before

Opt

After

Opt Microstrip matching network

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Summary

© Keysight


• Synthesize Broadband Input, Interstage, Output Matching Networks

• Generate Microstrip Layout, Optimize Response

• Completed in under 1 hour

-20dB return loss from 2 – 3 GHz, Gain >35dB

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Watch my YouTube How To Video

– www.youtube.com/watch?v=s8oPvj0VLCQ

– Download Genesys Impedance Synthesis tool for free

– Put it to the test on your current impedance matching problems

– Be 10x more productive in designing impedance matching networks

than your colleagues who did not attend this webcast

© Keysight


Learn How to Design Impedance Matching Network Quickly

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More Resources

31

www.keysight.com/find/eesof-innovations-in-eda

© Keysight

Technologies 2015

References

1. R.M. Fano, "Theoretical Limitations of the Broadband Matching of Arbitrary Impedances", J.

Franklin Inst., February 1950.

2. R. Levy, "Explicit formulas for Chebyshev impedance-matching networks," Proc. IEEE, June

1964.

3. T. R. Cuthbert, Jr., Circuit Design Using Personal Computers, John Wiley, New York, 1983.

4. R. M. Cottee and W. T. Jones, "Synthesis of lumped and distributed networks for impedance

matching of complex loads", IEEE Trans. Circuits Sys., May 1979.

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