PHD Modeling. Electrical & Computer Engineering University of Illinois. Copyright by Jose E. Schutt Aine, All Rights Reserved

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1 ECE 598 JS Lecture PHD Modeling Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois i 1

2 TWO PORT NETWORK REPRESENTATION Z Parameters V Z I Z I V Z I Z I 1 1 Y Parameters I Y V Y V I Y V Y V At microwave frequencies, it is more difficult to measure total voltages and currents. - Short and open circuits are difficult to achieve at high frequencies. - Most active devices are not short-or open-circuit itstable.

3 S Parameters - Definitions a = 1 Ei 1 Ei a = Z o Z o r1 b = 1 E Er b = Z o Z o Z o is the reference impedance of the system b 1 = S 11 a 1 + S 1 a b =S 1 a 1 +S a 3

4 S Parameters - Definitions b 1 S = 11 a=0 1 a a 1 1 a=0 S = 1 S = b = b 1 a1=0 S a a a1=0 To make a i = 0 i 1) Provide no excitation at port i ) Match port i to the characteristic impedance of the reference lines. CAUTION : a i and db i are the traveling waves in the reference lines. b 4

5 Generalization For a general N port B SA B N SA i ij j j1 S ij B A i j Ak 0 k j k1,..., N 5

6 Motivation Limitation: S Parameters only work for linear systems. Many networks and systems are nonlinear Applications High-speed links, power amplifiers, mixed-signal circuits Existing Methods Load pull techniques IBIS models Models are flawed and incomplete 6

7 PHD Modeling Polyharmonic distortion (PHD) modeling is a frequency-domain modeling technique To construct PHD model, DUT is stimulated by a set of harmonically related discrete tones In stimulus, fundamental tone is dominant and higher-order harmonics are smaller 7

8 Advantages of PHD Modeling Mathematical model exists and is very robust Instrumentation exists: Large signal network analyzers PHD model defines X parameters which form a superset of S parameters LSNA instruments will gradually replace all VNAs 8

9 PHD Framework Stimulus A-waves are incident and B-waves are scattered Reference System Z C Default value is 50 ohm For a given port with voltage V and current I A V Z I C B V Z I C 9

10 PHD Framework Signal is represented by a fundamental with harmonics Signals are periodic or narrowband modulated versions of a fundamental with harmonics Harmonic index: 0for dc contribution, tib ti 1for fundamental and for second harmonic 10

11 PHD Framework Define variables A B port harmonic port harmonic Introduce multivariate complex function F such that B F A, A,..., A, A,

12 PHD Framework 1

13 PHD Framework F describes a time-invariant systemdelay in time domain corresponds to phase shift in frequency domain jm j j j j B e F A e, A e,..., A e, A e,... For phase normalization, define P j ( A11) e B F A, A P, A P,..., A P, A P,... P 3 1 m

14 Harmonic Superposition In many situations, there is only one dominant large-signal input component present. The harmonic frequency components are relatively small harmonic components can be superposed Harmonic superposition principle is key to PHD model 14

15 in which h PHD Derivation B K A P G H 11 m m n Gpq, mn A11 P Re( AP ) m n H pq, mn A11 P Im( AP ) K,0,...,0 A11 F A11 A pq, mn 11 A pq, mn 11 Re Im F n A P A11 F 11,0,...,0,, n A P A11,0,...,0 Spectral mapping is nonanalytic 15

16 Since we get PHD Derivation n Re( A P ) n Im( A P ) B K A P 11 A P m A P pq, mn 11 n G A P pq, mn 11 n H A P conj A P m conj A P m j AP AP n n n n conj A P conj A P j n n 16

17 PHD Model B S A P A mn pq, mn 11 mn T A P conj A pq, mn 11 PHD Model Equation S A p1, m1 11 K A11 p m A 11 T A 1, , 1,1 : S A pq, mn 11, 11 1,1 : T A pq, mn 11 G A jh A pq, mn 11 pq, mn 11 G A jh A pq, mn 11 pq, mn 11 17

18 Index Convention S pq,mn probe port source port probe tone source tone A B port tone port tone 18

19 Large-Signal Reflection Microwave amplifier with fundamental frequency at 9.9 GHz 19

20 Compression and AM-PM Microwave amplifier with fundamental frequency at GHz 0

21 T,11 Microwave amplifier with fundamental frequency at 9.9 GHz 1