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by: D'angelo Will


D'angelo Will
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This 39 page Class Notes was uploaded by D'angelo Will on Thursday October 22, 2015. The Class Notes belongs to PORT 1 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/226878/port-1-university-of-california-santa-barbara in Portuguese at University of California Santa Barbara.




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Date Created: 10/22/15
6976 High Speed Communication Circuits and Systems Lecture 3 SParameters and Impedance Transformers Michael Perrott Massachusetts Institute of Technology Copyright 2003 by Michael H Perrott What Happens When the Wave Hits a Boundary 39 Reflections can occur Incident Wave V y Reflected Wave E I Hv X L I i h h MH Perrot39t MIT OCW What Happens When the Wave Hits a Boundary 39 At boundary 39 Orientation of Hfield flips with respect to Efield Current reverses direction with respect to voltage Incident Wave Y I y Reflected Wave 2 I gt E I Hv X is L y a h NIH Perrot39t MIT OCW What Happens At The Load Location 39 Voltage and currents at load are ratioed according to the load impedance Incident Wave Ii Voltage at Load 2 h L Vi W Vi Current at Load 1 quot y X J Reflected Wave I Ratio at Load Z i ZL V i Vr Z lt L E Ii I vrg M H Perrott 39r MIT ocw Relate to Characteristic Impedance 39 From previous slide WWE 1VrVz39 Ii Ir IZ 1 ITIZ L 39 Voltage and current ratio in transmission line set by it characteristic impedance V V I 2 T ZO T 2 Vr Li Ir Vi 39 Substituting 1V7Vz39 Z0 ZL MH Perrott MIT OCW Define Reflection Coefficient I I I V 39 Definition FL 2 L 39 No reflection if FL 0 39 Relation to load and characteristic impedances 1 r Z0 L ZL 1 rL 39 Alternate expression ZL Z0 r L ZLZO 39 No reflection if ZL Z0 MH Perrott MIT OCW Parameterization of High Speed CircuitsPassives 39 Circuits or passive structures are often connected to transmission lines at high frequencies 39 How do you describe their behavior I 39 Transmission Line 1 MH Perrott Linear Network Transmission Line 2 MIT OCW Calculate Response to Input Voltage Sources 39 Assume source impedances match their respective transmission lines Same value Same value by definition by definition Linear Network z1 MCD 22 2 Transmission Line 1 Transmission Line 2 MH Perrott MIT OCW Calculate Response to Input Voltage Sources 39 Sources create incident waves on their respective transmission line 39 Circuitpassive network causes 39 Reflections on same transmission line 39 Feedthrough to other transmission line Linear Network VIZ Zz I Vr2 MH Perrott MIT OCW Calculate Response to Input Voltage Sources 39 Reflections on same transmission line are parameterized by PL 39 Note that FL is generally different on each side of the circuitpassive network Linear Network How do we parameterize feedthrough to the other transmission line MH Perrot39t MIT OCW SParameters Definition 39 Model circuitpassive network using 2port techniques 39 Similar idea to TheveninNorton modeling 112 Linear Network Q J Vi2 39 Defining equations Vrl Vil V22 311 312 VZ1 VZ1 VZ2 V V V 7 2 2 S21 21 S22 22 VZ2 VZ1 VZ2 MH Permit MIT OCW SParameters CalculationMeasurement 112 Linear Network J Vi2 v h 22 i 2 gt T Vr2 V22 V72 2 S21 V21 VZ2 VZ2 VZ1 2 i 322 T l L2 V22 Z V 39 Z1 V22 MHPermtt MAT OCW MBHB Permit Note Alternate Form for 21 and S12 FLZ V Wn2 Linear Network J Vi2 Z2 2 MQD 4 22 L 2R gt T Vr2 SGt W712 set Wnl d Vrl V72 2 I Vi L2 Z V Z1 Vin2 I Ll 21 Z V i 321 2 1 Z2 Vinl i 522 MIT OCW Block Diagram of SParameter 2Port Model SParameter TwoPort Model 521 512 Z1 22 I J 39 Key issue twoport is parameterized with respect to the left and right side load impedances Z1 and 22 39 Need to recalculate 11 821 etc if Z1 or Z2 changes 39 Typical assumption is that Z1 Z2 50 Ohms MH Perrott MIT OCW Macromodeling for Distributed Linear Networks Z1 Linear 22 Linear 23 i Circuits amp Circuits amp Passives Passives length d1 1 length d2 2 length d3 39 Key parameters for a transmission line 39 Characteristic impedance only impacts Sparameter calculations 39 Delay function of length and u s 39 Loss ignore for now 39 Key parameters for circuitspassives 39 Sparameters We would like an overall macromodel for simulation MH Perrott MIT OCW Macromodeling for Distributed Linear Networks Z1 Linear 22 Linear 23 Circuits amp Circuits amp Passives Passives length d1 1 length d2 2 length d3 1 1 A d1 dela d dela d delay1 velocity V2 J us 2 V3 J us 3 J LCd1 H8d1 39 Model transmission line as a delay element 39 If lossy could also add an attenuation factor which is a function of its length 39 Model circuitspassives with Sparameter 2ports 39 Model source and load with custom blocks MH Perrott MIT OCW Macromodeling for Distributed Linear Networks Z1 Linear 22 Linear Z3 Circuitsamp Circuitsamp Passives Passives length d1 1 length d2 2 length d3 1 1 1 ZL 1 dela a d dela J d delay1 velocity V2 H8 2 V3 he 3 LCd1 H8d1 ZLZ1 ZRZz ZLZz ZRZs vs E 21 i E Ev I I out e 4 t T Sparam Sparam Z Z Zs39Z1 2 port 2 port L 3 5 zszl E 1 lt2 ZLZs 5 T E l awle Vr1 Viz 4 ldelay2 lt Vr1 Viz lt delay3 l4 MH Permit WT OCW Note for CppSim Simulations ZLZ1 ZRZz ZL22 ZRZ3 VS Z1 i i Z1Zs a Vn Va Vn Vrz T E S39IOaram Sparam E Zs39Z1 2p0rt 2port I E E ZsZ1 E 1 2 E E 39 CppSim does blockbyblock computation 39 Feedback introduces artificial delays in simulation 39 Prevent artificial delays by 39 Ordering blocks according to inputtooutput signal flow 39 Creating an additional signal in CppSim modules to pass previous sample values 39 Note both are already done for you in Homework 1 MH Perrott MIT OCW SParameter Calculations Example 1 Transmission VH Line Junction Viz Z1 39 E 22 h i I 7 h 5 Vr1 JV Vr2 Derive S Parameter 2Port 39 SetVi20 39 SetVi1 0 Z2 Z1 Z1 Z2 Vrl I lvz39l 2 MW V72 2 F2VL 2 2 EVA Vr2 W1W1 1l 1Vz391 inl W2Vr2 1 r2 i2 ii 511 ii 322 r2 r1 Z1 i 521 iZ 21 F1 MH nun OCW Z2 312 Z 11 F2 SParameter Calculations Example 2 Transmission Line Vi1 Junction with Capacitor Vi2 Q Z1 Z2 h h C Vr1 E I E Vr2 l Derive S Parameter 2Port 39 Same as before ii 511 r1 522 r2i Z Z i 521 111 i 512 212 Z2 Z1 39 But now Zz1sC Zl r Z113C39 Z2 1 Zz1SC 21 2 Z11sC Z2 MH Permit MIT OCW ECEl45N218A Notes Set 4 l 2 Port Parameters Twoways of describing device A 03 Equivalent CircuitModel Physically based Includes bias dependence Includes frequency dependence Includes size dependence scalability Ideal for IC design Weakness Model necessarily simpli ed some errors Thus weak for highly resonant designs 27Port Model Matrix of tabular data vs frequency Need one matrix for each bias point and device size Clumsy 7 huge data sets required Traditional microwave method Exact 2 Port descriptions These are black box mathematical descriptions port 1 1 gt port o 2 Inside might be a transistor a FET a transmission line or just about anything The terminal characteristics are V1 V2 11 amp 12 7 there are 2 degrees of freedom Rev 1 107 Prof S LongECEUCSB ECEl45N218A Notes Set 4 2 Admittance Parameters UH l Yll Y12 l lel M Yzzl LVZJ Example Simple FET Model m W AA vvv Rds By inspection l jwcgs jwcgd gm jwcgd Easy I Y11 2 1 1 V20 ReVll07 ijgd Gds ijng V10 Prof S LongECEUCSB ECEl45N218A Notes Set 4 3 Impedance Parameters l V1 l le Zizl l Il l lvzl lZ21 Zzzl llzl Example R1 R2 0 E R3 By inspection I R1R3 R3 l R3 R2R3l V V 2112 1 21 2 1 21 Il 120 120 But y z and h parameters are not suitable for high frequency measurement Problem How can you get a true open or short at the circuit terminals Any real short is inductive Any real open is capacitive To make matters worse if you are trying to measure a high freq active device a short or open can make it oscillate Solution Use termination in Zo instead Broadband Not very sensitive to parasitic LC Kills re ections Rede ne parameters to use fwd and rev voltage waves Measurement can use directional couplers Revll07 Prof S LongECEUCSB ECEl45N218A Notes Set 4 4 S Parameters Z0 Z0 1 gt 4 2 b 2 0 z 0 input re ection coeff a2 0 rev transm gain a10 l b1 l Sll SlZ H al l ibzi i521 522 iiazi fwd transm gain a2 0 output F a1 0 Note that Zo must be de ned We don t really need transmission lines Our objective now is to demystify Sparameters 7 they are easy Recall Vx Vx V x Ex 2 m Z0 Z amplitude not rms values 0 phasor quantities We can normalize the amplitude of waves to Z0 i ax V x forward wave 420 bx V x reverse wave JZO 1 Why So that E axa x power 1n forward wave if a 1414 then power in wave is 1 watt or ams 1 Rev 1 107 Prof S LongECEUCSB ECEl45N218A Notes Set 4 5 likewise bXbX 2 is the power in the reverse wave So in terms of total voltage VX and current 1X vx lo ax bx ix 42 0 Ix ax bx or axvxz39x ij OVxZoIx 1 1 bx 5vx zx NEW 20100 Re ection So how is F defined in terms of the S parameters At port 1 h 11 F1 1 1 2511511 512a2 We need to eliminate a2 How 512 If ZL Zo FL 2 0 b so therefore a 0 1f port 2 is terminated in Z0 2 F1 2 511 a1 1120 Same with at port 2 with 82 b2 522 2 F2 a2 1110 ReVll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 6 Transmission 72 SZIal 522 So the forward transmission 821 can be found by setting a 0 terminate output b2 a1 521 a2 0 Reverse transmission similarly is found by setting a1 0 terminate input in Z0 1 1 Sllal 521a2 512 2i 5 2 1110 ReV1107 Prof S LongECEUCSB ECEl45N218A Notes Set 4 7 Some comments on power measurement Power can vary over a large range therefore it is often specified on a logarithmic scale There must be a point of reference on the scale the power measurements are usually with reference to 1 mW The unit is called meaning dB relative to 1 mW of power Thus 0 dBm 1 mW 10 dBm 10 mW 10 dBm 01 mW etc dBm 10 log10 P What is the difference between dB and dBm To convert mW to dBm To convert dBm to mW dB is a power ratio 7 used to describe a gain or loss for example G 10 loglo PomPin dB Return Loss 2010g10lFl dB But dB says nothing about the absolute power level Don t confuse their usage Revll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 8 Now de ne available power PAVS maX power output from a source with 39 A Z v that can be absorbed into a load let ZS Z0 ZL Z ZO in this case because maximum power transfer occurs when we have a conjugate match Z0 Vgen Z0 vgenz generator load 2 Vgen 1 Plead PAVS g Zo Or in terms of a and b SO ReV1107 Prof S LongECEUCSB ECEl45N218A Notes Set 4 9 o 239 We see that the available power is independent of load impedance Even if the load is not matched available power remains constant Actual power in the load is reduced however 0 239 Generator output power is calibrated and displayed as available power Actual Load Power 1 2 1 2 1 P a Re V Load 2 1 2 l l or S 2 PLaad PAVS1 1139 Re ected Power b1 a1 11 1 1 PR Elbll2 ZEIaIIZISulZ PAVSISIIIZ IS I2 Power re ected from input El 11 Power incident on input lall2 Power re ected from network output Ibz 2 5222 Power incident on output lazl2 Silnilarly 1 a22 Power incident on output 2 Re ected power from load lbllz Power re ected from input port 1 Elbzlz Power incident on load from the network Revll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 10 I T 611 512 b1 lt P Also by de nltlon transducer gain load GT even if avs 1 load isn t matched to network and 2 input of network not matched to generator Here PLaad ib2i21irL2 21 is de ned in terms of transducer gain for the special case of where ZL Z0 39521l2 Ibz39z 2 lull a2 0 l Elbzlz 2 power incident on load and is absorbed since FL0 1 2 Elall 2 source avallable power 395le2 transducer gain with source and load Z0 Similarly 2 lslzl reverse transducer power ga1n ReVll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 11 Reference Planes Microwave transistor in package On board S 511 5121 521 522 39l connection to instruments Define X 0 at both ports De ning the reference planes differently changes the Sparameters ReV1107 Prof S LongECEUCSB ECE145N218A Notes Set 4 12 phase shifts 509 microstrip transmission lines connections to instruments here 27M 6 x 1 1 m 1 27M 62 x2 2 26 96 Sue 1 Sne i 2 5121610914492 512261292 The re ection parameters are shifted in phase by twice the electrical length because the incident wave travels twice over this length upon re ection The transmission parameters have the sum of the electrical lengths since the transmitted wave must pass through both lengths ReVll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 l3 Comment on electrical length The microwave literature will say a line is 430 long at 5 GHZ What does this mean zf Z Electr1cal length E 360 Aref Recall fl v so fwf 22 u z gtE 360 ref360 V Z V fref ET Zf360 a line which is 1 ns long has an electrical lengthE 3600 at frzf 1 GHZ and an electrical lengthE 360 at Fref 100 MHz Why notjust say T 1 ns you should be conversant with both terminologies Converting to physical length f lref Vp V lref 7p E de 1 thus physical length Electrical length in wavelengths lref 01 Revll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 14 How to Calculate S Parameters Quickly b 511 1 a1a20 b1S11a1S12a2 First Comment We must kill a2 in order to measure or calculate S S gtb2 a2 if ZL Z0 then FL is zero and so 612 FLbz 0 So b 511 Z Li a1 ZLZO is the input impedance with Z0 Z L So ifwe say that Zin ZLZO then ZinlzLzo Z0 511 Z Z Fin in ZLZO 0 or 1 Z 511 in ZLZO 1 Sn The same comment clearly applies for 522 The Smith Chart is often used to plot SH 522 ReV1107 Prof S LongECEUCSB ECE145N218A Notes Set 4 Example 49 Given Z0 509 what is Sn 4Q o vw gt E 509 0 ZinZLZO 549 54 50 i 11 54 50 104 S39 391 t 39 s 1m1 ar argumen S glve 22 Find S21 b 2 521 I 120 11 4 rS ZS Z0 1 2 gt ZL Z0 ng lt gt b1 b2 ReV1107 Prof S LongECEUCSB ECEl45N218A Notes Set 4 16 What is al in this case V V We know that a1 1 and Vfr J20 2 So a Vgen 1 2 20 V C0n51der the load b2 of Why 0 b2 gt e 2 ZL Vout a2 FLbZ But FL 0 because ZL Z0 so 612 0 VoutVViwlz 2JZ o b2 Jzo b2 Now calculate VomVgen Vaut lZO 32 VZO3210132202 But a 0 because the load impedance Z0 so Vaut xZo 2101 Substitute for a1 Vgen 2 Z0 11 Va 2 Mo 321 h ReVll07 Prof S LongECEUCSB ECE145N218A Notes Set 4 17 2V thus S21 am when ZL ZS Z0 gen Why the factor of 2 Z0 V gen 20 VgenZ generator load We see that the generator voltage is split between the source and load in the matched case Here we see that VoutVgen 12 but the transducer gain must be equal to l PLOADPAVS lSulz is the transducer gain in this situation If we insert an ampli er into the network the signal has been increased by an amount 821 V Vout 21 VgenZ generator load ReVll07 Prof S LongECEUCSB ECEl45N218A Notes Set 4 18 So lSzilz is the FORWARD INSERTION GAIN or FORWARD TRANSDUCER GAIN in a system of impedance Z0 EXAMPLE Find S21 50 4 V gen 821 2 VoutVgen VoutVgen 50104 048 S21 096 0 OR we could let VIgen 2 Then S21 Vom What about a reference plane extension 50lX1041 Vgen 321 2 VoutVgen gt gt lt Sn S11 ezjel Sn Fm0 Szz FOUT0 22 SZZ eljez and 27139 27239 612 542 74 62 272 Si S2Iej399192 S2Ie Z7IJ39Z1Z2 ReVll07 Prof S LongECEUCSB ECEl45N218A Notes Set 4 19 EXAMPLE Find the 4 S parameters of the following circuit J Z0 Vgen SH Find Zin with ZL Z0 then calculate input re ection coef cient ZINlZLZO 1SClZo 21V 1 S ZIN Zo Zo 11 ZIN Zo 211 1 0 turning the crank joaCZo 2 11 1DCZO 2 22 will be the same due to symmetry Note that we calculated ZIN with port 2 terminated in Z0 This is part ofthe de nition of 11 so is essential ReVll07 Prof S LongECEUCSB


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