Stability Analysis of Microwave Circuits

Transcription

1 Stability Analysis of Microwave Circuits

2 Introduction Stability analysis is a critical step of RF design flow Classical methods are either not complete or too complex Stability analysis need to be efficient (especially in large signal) - Rigorous - Fast - User-friendly - Compatible with commercial CAD softwares Slide 2

3 Existing Methods Linear analysis small signal - K factor - Normalized Determinant Function (NDF) - Stability envelope Non-linear analysis large signal - Nyquist criterion - NDF - Bolcato, Di Paolo & Leuzzi, Mochizuki, Output power (dbm) low frequency 0 oscillation Output power (dbm) -20 f0 oscillation Output power (dbm) Frequency 1400 (MHz) Frequency (MHz) 160 Frequency (MHz) Slide 3

4 Existing Methods Linear analysis Widely used: K factor (also µ and µ now) - K>1 & <1: unconditional stability of two port network - K<1: conditional stability stability circles Unconditional stability Conditional stability Unconditional instability Limitations: Only indicates that a stable circuit will continue to be stable when loading it with passive external loads at the input or output Do not guarantee the internal stability of the circuit! Slide 4

5 Source Existing Methods Linear analysis Potentially instable architectures for which K factor is not enough Multi-stage power amplifier Multi-fingers transistor IN OUT Gate Drain Slide 5

6 H (º) H (db) Pole-Zero Identification Principle 50 H( j ) Frequency domain Identification techniques db(zsond) phase(zsond) E9 4.0E9 6.0E9 8.0E9 1.0E10 1.2E10 Freq frequency (GHz) 6 Pole-zero plot R G f 0, P in v out Node n (i,f ) in s R L H( s) n i 1 p j 1 ( s z ) ( s ) i j Im (GHz) poles zeros Re (GHz) Slide 6

7 Pole-Zero Identification Principle Complex conjugate poles with positive real part -> start-up of an oscillation Oscillation frequency = Module of the imaginary part Slide 7

8 J.M. Collantes et al. Monte-Carlo Stability Analysis of Microwave Amplifiers, 12th IEEE Wireless and Microwave Technology Conference, April 2011, Florida. A. Anakabe et al. Automatic Pole-Zero Identification for Multivariable Large-Signal Stability Analysis of RF and Microwave Circuits, European Microwave Conference, September 2010, Paris. J.M. Collantes et al. Expanding the Capabilities of Pole-Zero Identification Techniques for Stability Analysis, IEEE Microwave Theory and Techniques International Symposium, June 2009, Boston. Slide 8

9 Key Elements Suitable for both linear and non-linear stability analysis Very easy to use with any CAD tool Very easy to analyze results Notion of stability margin Oscillation mode knowledge -> Help to find the suitable stabilization strategy Parametric Analysis implemented Monte-Carlo Analysis Slide 9

10 Integration in CAD Environment GENERATOR Perturbation introduction node CIRCUIT LOAD in out Var VAR Eqn VAR1 fin=9.65 GHz Pin=12 Input frequency Input power P_1Tone cmp1198 Num=1 Z=50 Ohm P=polar(dbmtow(Pin),0) Freq=fin ampli X1 Term Term1 Num=1 Z=50 Ohm HARMONIC BALANCE HarmonicBalance HB1 Freq[1]=fin Order[1]=10 SS_MixerMode=yes SS_Start=f1 SS_Stop=f2 UseAllSS_Freqs=yes MergeSS_Freqs=yes Var VAR Eqn VAR3 f1=fstart+fin e9 f2=fend+fin Meas MeasEqn Eqn meas1 Zsond=mix(v_sond,{-1,1})/mix(I_sond.i,{-1,1}) frequency=ssfreq-fin Var VAR Eqn VAR2 fstart=4.325 GHz fend=5.325 GHz n_point=101 I_Probe I_sond v_sond I_1Tone SRC1 I_LSB=polar(0.0001,0) Start sweep frequency Stop sweep frequency Number of frequency points Nonlinear stability analysis template EDA Tool Templates for ADS STAN Automation for MWO AC simulation for linear HB simulation for non-linear STAN tool integrated in IVCAD software User-friendly GUIs Slide 10

11 Selecting the node All nodes are equal, but some nodes are more equal than others SISO transfer function exact pole/zero cancellations are possible Pole/zero cancellations are associated with the lack of controllability and/ or observability in the system Slide 11

12 Selecting the node - Recommendations In simple circuits with a clear feedback structure any node should serve for the analysis Multistage power amplifiers At least one analysis per stage Slide 12

13 Relevant information about the nature of the oscillation and the place in which it is being generated can be extracted extremely useful for circuit stabilization V bias_1 Multi-nodes V bias _ m V bias _ n Im (GHz) Im (GHz) clear -2 quasi-cancellation -2 not observable -4-4 Im (GHz) Re (GHz) Re (GHz) Re (GHz) Slide 13

14 Node n Multi-nodes v out (i,f ) in s A B FET 2 FET 1 FET 3 A- No oscillation detected in the common node FET 4 FET 5 FET 6 B- Oscillation detected in the transistor node Odd mode (parametric frequency division) will determine the stabilization strategy Slide 14

15 Re (GHz) STAN Tool Parametric Analysis with swept parameter(s) Verification for various conditions (Pin, Zload, ) Checking of critical resonances Optimization of stabilization networks R G P IN f 0, v out (i,f ) in s Z load Pin (dbm) Slide 15

16 Monte-Carlo Example: L-Band medium power FET amplifier Low frequency instability related to the input bias network Stabilization by the inclusion of a gate-bias resistor R STAB Monte Carlo sensitivity analysis for different R STAB (5 % dispersion in all circuit parameters) Imaginary Axis (MHz) R STAB = 44 Imaginary Axis (MHz) R STAB = Real Axis (MHz) Real Axis (MHz) Slide 16

17 Performances optimization Example: Ku-Band MMIC PA for active space antenna Stable original circuit Inter-branch stabilization resistances RF in RF out RC stabilization networks Natanael Ayllón Rozas Développement des méthodes de stabilisation pour la conception des circuits hyperfréquences : Application à l optimisation d un amplificateur de puissance spatial., PhD Thesis, February 2011.

18 Performances optimization Example: Ku-Band MMIC PA for active space antenna All stabilization networks removed resistances maintained for topological reasons RF in RF out Parametric frequency division /2 instability Slide 18

19 Performances optimization Example: Ku-Band MMIC PA for active space antenna Optimized version resistances maintained for topological reasons RF in RF out No oscillation detected, especially around F0/2 Stabilization resistances Slide 19

20 Example: Ku-Band MMIC PA for active space antenna Results comparison Performances optimization Original Optimized

21 Some recommendations Always do first a small signal stability analysis (AC) from low frequencies (LF) to the max gain of the devices. Do the LF part separately or use a log sweep to avoid losing information at LF if the sweep covers several decades. Do the identification in sub-bandwidths if the sweep covers several decades. Slide 21

22 Some recommendations In large-signal stab analysis use [f1, f1 + f0 + δ] but keep in mind at least two things: - Survey the evolution of the critical poles found in the AC analysis as input drive is increased. Focus the analysis on those bands. - Focus the analysis also in instabilities that are very common as f0/2 Note: In the sweep, avoid the precise case where the frequency fs of the frequency generator coincides exactly with a harmonic (not sub-harmonic) of the large signal operating frequency f0 of the circuit Slide 22

23 Some recommendations If in your circuit simulation you have some measurement files ([S] blocks) or EM-simulated block files, relax the phase tolerance (1 ) to avoid overmodeling Slide 23

24 Q & A Contact Stéphane Dellier dellier@amcad-engineering.com Phone: