Zload - Keysight
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How-Siang Yap Genesys Product Planner Keysight EEsof EDA 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. 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 Page 3 Impedance Matching for Maximum Power Transfer Conjugate Matching Zsource Zload Matching Network Zin = Z*source Zout = Z*load © Keysight Technologies 2015 Page 4 Impedance Matching for Minimum Noise Zopt Zsource Matching Network Zin = Z*source Zout = Zopt © Keysight Technologies 2015 Page 5 Impedance Matching for Impedance Dependent Spec (e.g. Efficiency, EVM, ACPR, BER) from load pull contour analysis Zcontour Zload Matching Network Zout = Z*load Zcontour = Zin © Keysight Technologies 2015 Page 6 Designing Impedance Matching Problem Routine, always tedious and always time consuming 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 frequencyvarying 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 © Keysight Technologies 2015 Page 7 Impedance Matching Network Design Increasing Levels of Difficulty 1-Stage Matching Network Zsource 2-Stage Zload Input Matching Network Output Matching Network Zsource Zload 3-Stage Antenna Input Matching Network Interstage Matching Network Output Matching Network Zload © Keysight Technologies 2015 Page 8 Fano’s Limits on Matching Reactive Loads and BW Reactive loads are harder to match over wide BW Γπππ = π −π(πππππππ /πππ_ππππ) = π − (π π ) π₯ πΉππππ‘ππππππ΅π ππππππ “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“ πππππππ = πππππ‘ππ ππ’ππππ −ππππ€ππ Fractional BW = 1 = πΉππππ‘πππππ_π΅π ππ’ππππ −ππππ€ππ πππππ‘ππ =π 1 πππ_ππππ = πππππ π ππππ = π΅ππππ πΊππππ π πΏππ΅ = −20πππΓπππ ππππππ © Keysight Technologies 2015 Page 9 A very difficult impedance matching problem Multi-stage broadband matching of frequency-dependent complex impedances at input, interstage and output Antenna Design the input, interstage and output matching networks for 40% fractional BW and 20 dB return loss Interstage Matching Network Input Matching Network Transistor Non-unilateral Unstable Output Matching Network Transistor Non-unilateral Zload © Keysight Technologies 2015 Page 10 Multi-stage broadband matching of complex frequency dependent impedances over 40% BW from 2 to 3 GHz Antenna Complex impedance RLC equivalent circuit R=72 ο, C=10pF, L=0.405nH, Fc= 2.5GHz Input Matching Network Interstage Matching Network 2 port S-parameters + stabilizing circuit for unconditional stability Output Matching Network 2 port S-parameters Zload 50 ο © Keysight Technologies 2015 Page 11 Automatic Impedance Network Synthesis Demo © Keysight Technologies 2015 Page 12 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 Technologies 2015 Page 13 Impedance Matching Network Strategies Matching Network Type 1. L-C Pi Network Strategies for Impedance Matching A. Use simpler topologies 1-4 for narrow BW 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 B. Use more advanced topologies 58 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) 8. TRL Stepped Impedance 9. Custom network of your own with optimizable parameters © Keysight Technologies 2015 Page 14 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 π= πππππ‘ππ ππ’ππππ −ππππ€ππ 1 = πΉππππ‘πππππ_π΅π > ππππ = 1 2 π πΏ π π − 1 ππ 1 2 π π π πΏ −1 – Synthesis automatically determines ππππ 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 © Keysight Technologies 2015 Page 15 Distributed Matching Networks TRL ¼ Wave and TRL Single/Double Stub – Single ¼ wavelength series transmission line – 1 to 3 elements of alternating shorted stubs and series line – Narrow band matching of resistive terminations without transformer – Matches any complex source and load at a single frequency – Some capacity for narrow band complex terminations – Distributed equivalent of LC Pi and Tee networks © Keysight Technologies 2015 Page 16 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 Technologies 2015 Page 17 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 Technologies 2015 Page 18 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 Technologies 2015 Page 19 Distributed Matching Networks TRL Pseudo Lowpass and TRL Stepped Impedance – 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 – 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 Technologies 2015 Page 20 Putting Impedance Matching Synthesis to Work Antenna Complex RLC equivalent circuit R=72 ο, C=10pF, L=0.405nH, Fc= 2.5GHz Input Matching Network Interstage Matching Network 2 port S-parameters + stabilizing circuit for unconditional stability Output Matching Network 2 port S-parameters Zload 50 ο © Keysight Technologies 2015 Page 21 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 – Stage 1 Stabilized K>1, B>0, © Keysight Technologies 2015 Page 22 Putting Impedance Matching Synthesis to Work Matching BW setting and Antenna impedance definition Antenna Matching BW = 1GHz Fc= 2.5GHz BW/Fc= 40% fractional BW Input Matching Network Interstage Matching Network 2 port S-parameters + stabilizing circuit for unconditional stability Antenna RLC series equivalent circuit R=72 ο, C=10pF, L=0.405nH, 1 Fc= 2π√πΏπΆ =2.5GHz Output Matching Network 2 port S-parameters Zload 50 ο © Keysight Technologies 2015 Page 23 Putting Impedance Matching Synthesis to Work (cont) Selecting topologies for Input, Interstage and Output Matching Antenna Try TRL Pseudo Lowpass of Orders 2, 3, 3 respectively Min Zo = 20 ο and Max Zo = 120 ο for realizability Input Matching Network Interstage Matching Network Output Matching Network Zload 50 ο © Keysight Technologies 2015 Page 24 Putting Impedance Matching Synthesis to Work (cont) Defining 1st (stabilized) and 2nd Stage Transistor Networks Antenna Input Matching Network Interstage Matching Network Output Matching Network Zload 50 ο Add stabilized transistor circuit for 1st device stage after input matching section Add transistor Sparameter file for 2nd device after interstage matching section © Keysight Technologies 2015 Page 25 Synthesized Input, Interstage and Output Distributed Matching networks TRL matching network Synthesized Microstrip matching schematic from above TRL network Microstrip matching layout © Keysight Technologies 2015 Page 26 Optimization to correct for microstrip conversion discrepancy TRL matching network Before Opt Microstrip matching network After Opt © Keysight Technologies 2015 Page 27 Microstrip Layout Realization Demo © Keysight Technologies 2015 Page 28 Summary • 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 © Keysight Technologies 2015 Page 29 Watch my YouTube How To Video Learn How to Design Impedance Matching Network Quickly – 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 Technologies 2015 Page 30 More Resources www.keysight.com/find/eesof-innovations-in-eda References 1. 2. 3. 4. R.M. Fano, "Theoretical Limitations of the Broadband Matching of Arbitrary Impedances", J. Franklin Inst., February 1950. R. Levy, "Explicit formulas for Chebyshev impedance-matching networks," Proc. IEEE, June 1964. T. R. Cuthbert, Jr., Circuit Design Using Personal Computers, John Wiley, New York, 1983. 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. © Keysight Technologies 2015 Page 31
