everything you've always wanted to know about...
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© 2002 Agilent Technologies - Used with Permission
Everything you've always wanted to know about Hot-S22 (but we're afraid to ask)
Jan Verspecht
Jan Verspecht bvba
Gertrudeveld 151840 SteenhuffelBelgium
email: [email protected]: http://www.janverspecht.com
Slides presented at the WorkshopIntroducing New Concepts in Nonlinear Network Design
(International Microwave Symposium 2002)
Everything you’ve always wanted to know about
“Hot-S22”(but were afraid to ask)
Jan Verspecht
Agilent Technologies
3
Outline
• Introduction: What is “Hot S22” ?
• Getting and interpreting experimental data
• Confront classic approaches with data
• Derivation of the extended “Hot S22” theory
• Confront extended “Hot S22” with data
• Conclusion
4
What is “Hot S22” ?
• D.U.T. behavior is represented by pseudo-waves (A1, B1, A2, B2)
• “Hot S22” describes the relationship between B2 and A2
• Valid under “Hot” conditions (A1 significant)
D.U.T.A1 A2B1 B2
5
Experimental investigation
• Take a real life D.U.T. (CDMA RFIC amplifier)
• Apply an A1 signal
• Apply a set of A2’s
• Look at the corresponding B2’s
• Mathematically describe the relationship between the A2’s and B2’s
• Repeat for different A1’s
6
Experimental set-up
Large-Signal Network Analyzer(LSNA, formerly known as NNMS)
RFIC
A1 B1 B2 A2
synth2synth1
• synth1 generates A1
• synth2 generates a set of A2’s
• LSNA measures all A1’s, B1’s, A2’s, B2’s
7
Interpretation of the data
? 0.3 ? 0.2 ? 0.1 0 0.1 0.2 0.3
? 0.3
? 0.2
? 0.1
0
0.1
0.2
0.3
? 0.75 ? 0.5 ? 0.25 0 0.25 0.5 0.75
? 0.75
? 0.5
? 0.25
0
0.25
0.5
0.75
A2 (V) B2 (V)
• IQ-plots of the A2’s and B2’s for a constant A1
(x-axis = real part, y-axis = imaginary part)
8
Phase normalization is good
• Normalize the phases relative to A1
• P = ej.arg(A1)
? 0.3 ? 0.2 ? 0.1 0 0.1 0.2 0.3
? 0.3
? 0.2
? 0.1
0
0.1
0.2
0.3
? 0.6 ? 0.4 ? 0.2 0
0
0.2
0.4
0.6
0.8
A2.P-1 (V) B2.P-1 (V)
9
? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0
0
0.25
0.5
0.75
1
1.25
1.5
Varying the amplitude of A1
B2.P-1 (V)
A1 increases
10
Varying the amplitude of A2
• Linear dependency versus A2
? 0.5 ? 0.25 0 0.25
? 0.6
? 0.4
? 0.2
0
0.2
0.4
? 0.5 ? 0.25 0 0.25
? 0.5 ? 0.25 0 0.25
? 0.6
? 0.4
? 0.2
0
0.2
0.4
? 0.5 ? 0.25 0 0.25
? 0.5 ? 0.25 0 0.25
? 0.6
? 0.4
? 0.2
0
0.2
0.4
? 0.5 ? 0.25 0 0.25
? 1.3 ? 1.2 ? 1.1
1.4
1.45
1.5
1.55
1.6
1.65
? 1.3 ? 1.2 ? 1.1
? 1.3 ? 1.2 ? 1.1
1.4
1.45
1.5
1.55
1.6
1.65
? 1.3 ? 1.2 ? 1.1
? 1.3 ? 1.2 ? 1.1
1.4
1.45
1.5
1.55
1.6
1.65
? 1.3 ? 1.2 ? 1.1
B2.P-1 (V)
A2.P-1 (V)
12
Classic S-parameter description
• B2 = S21 (|A1|).A1+ S22.A2
? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25
0
0.5
1
1.5B2.P-1 (V)
13
Simple “Hot S22” description
• B2 = S21(|A1|).A1+ S22(|A1|).A2
? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25
0
0.5
1
1.5B2.P-1 (V)
14
Model linearity & squeezing
• We look for a mathematical model which– is linear (superposition valid)– squeezes
• Squeezing implies that the phase of A2.P-1
matters
• We need different coefficients for the real and the imaginary part of A2.P-1
• More elegant expression results when using A2.P-1 and its conjugate
15
Mathematical expression
• B2.P-1 = S21(|A1|).A1 .P-1 + S22(|A1|).A2 .P-1 + R22(|A1|).conjugate(A2 .P-1)
• B2 = S21(|A1|).A1+S22(|A1|).A2+ R22(|A1|).P2.conjugate(A2)
16
Extended “Hot S22”
• B2 = S21(|A1|).A1+ S22(|A1|).A2+ R22(|A1|).P2.conjugate(A2)
? 1.25 ? 1 ? 0.75 ? 0.5 ? 0.25 0 0.25
0
0.5
1
1.5
B2.P-1 (V)
17
Quadratic “Hot S22”
• Further improvement is possible by using a polynomial in A2 and conj(A2)
• E.g.: quadratic “Hot S22”B2 = F.P + G.A2+ H.P2.conj(A2) +
K.P-1.A22 + L.P3.conj(A2)2 + M.P.A2.conj(A2)
• Note the presence of the P factors(theory of describing functions)
18
Comparison (highest A1 amplitude)
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
? 1.4 ? 1.3 ? 1.2
1.4
1.5
1.6
1.7
B2.P-1 (V)
ClassicS22
Simple“Hot S22”
Extended“Hot S22”
Quadratic“Hot S22”
19
Residuals
? 25 ? 20 ? 15 ? 10 ? 5 0 5
? 50
? 45
? 40
? 35
? 30
Relative Error(dB) S22
Simple“Hot S22”
Extended“Hot S22”
Quadratic“Hot S22”
Amplitude of A1 (dBm)
20
Conclusion
• An accurate “Hot S22” exists
• It has a coefficient for the conjugate of A2.P-1
• It can accurately be measured
• It describes the relationship between A2 and B2 under large-signal excitation