Stability Analysis of Microwave Circuits 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 www.amcad-engineering.com Slide 2 Existing Methods Linear analysis “small signal” - K factor - Normalized Determinant Non-linear analysis “large signal” - Nyquist criterion - NDF - Bolcato, Di Paolo & Leuzzi, low frequency 0 oscillation -20 -40 -60 -80 -100 -20f0 oscillation -20 -40 -60 -80 -100 0 2 0 Output power (dBm) • Output power (dBm) - Function (NDF) Stability envelope 0 Output power (dBm) • 200 -40 -60 -80 -100 0 400 200 0 400 200 400 600 600 Frequency (MHz) Mochizuki, … www.amcad-engineering.com 800 1000 600 800 1000 1200 140 Frequency (MHz) 160 800 Frequency 1000 (MHz) 1200 1400 Slide 3 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 ! www.amcad-engineering.com Slide 4 Existing Methods Linear analysis • Potentially instable architectures for which K factor is not enough OUT IN www.amcad-engineering.com Gate Source Multi-fingers transistor Multi-stage power amplifier Drain Slide 5 Pole-Zero Identification Principle dB(Zsond) |H| (dB) 50 H ( j ) H (º) phase(Zsond) RL 100 f0, Pin 0 -100 0.0 2.0E9 4.0E9 6.0E9 8.0E9 1.0E10 1.2E10 Node ‘n’ v out ( i in ,fs ) Freq (GHz) frequency Pole-zero plot 6 4 i (s ) j www.amcad-engineering.com Im (GHz) (s z ) j 1 200 -200 n i 1 p RG 10 -10 Frequency domain Identification techniques H ( s) 30 poles 2 0 zeros -2 -4 -6 -0.3 -0.2 -0.1 0.0 Re (GHz) 0.1 0.2 0.3 Slide 6 Pole-Zero Identification Principle Complex conjugate poles with positive real part -> start-up of an oscillation Oscillation frequency = Module of the imaginary part www.amcad-engineering.com Slide 7 STAN Tool • 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. www.amcad-engineering.com Slide 8 STAN Tool 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 www.amcad-engineering.com Slide 9 STAN Tool Integration in CAD Environment GENERATOR Perturbation introduction node in Var Eqn VAR VAR1 fin=9.65 GHz Pin=12 Input power ampli X1 Meas Eqn Term Term1 Num=1 Z=50 Ohm I_Probe I_sond 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 LOAD out P_1Tone cmp1198 Num=1 Z=50 Ohm P=polar(dbmtow(Pin),0) Freq=fin Input frequency CIRCUIT v_sond Var Eqn I_1Tone SRC1 I_LSB=polar(0.0001,0) VAR VAR3 f1=fstart+fin+0.0001e9 f2=fend+fin MeasEqn meas1 Zsond=mix(v_sond,{-1,1})/mix(I_sond.i,{-1,1}) frequency=ssfreq-fin Var Eqn VAR VAR2 fstart=4.325 GHz fend=5.325 GHz n_point=101 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 www.amcad-engineering.com STAN tool integrated in IVCAD software User-friendly GUIs Slide 10 STAN Tool 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 STAN Tool 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 STAN Tool Multi-nodes → 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 6 6 4 4 4 2 2 2 0 clear -2 -2 -4 -6 -0.3 0 quasi-cancellation -4 -0.2 -0.1 0.0 Re (GHz) 0.1 0.2 0.3 -6 -0.3 Im (GHz) 6 Im (GHz) Im (GHz) Vbias _ n Vbias _ m Vbias_1 0 not observable -2 -4 -0.2 -0.1 0.0 Re (GHz) 0.1 0.2 0.3 -6 -0.3 -0.2 -0.1 0.0 Re (GHz) 0.1 0.2 0.3 Slide 13 STAN Tool Multi-nodes Node ‘n’ v out ( i in ,fs ) B A FET2 FET1 A- No oscillation detected in the common node FET3 FET5 FET4 FET6 BOscillation detected in the transistor node Odd mode (parametric frequency division) will determine the stabilization strategy www.amcad-engineering.com Slide 14 STAN Tool Parametric Re (GHz) • Analysis with swept parameter(s) • Verification for various conditions (Pin, Zload, …) • Checking of critical resonances • Optimization of stabilization networks RG PIN f0, v out ( i in ,fs ) Zload Pin (dBm) www.amcad-engineering.com Slide 15 STAN Tool 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 RSTAB • Monte Carlo sensitivity analysis for different RSTAB (5 % dispersion in all circuit parameters) 40 20 RSTAB = 44 0 -20 -40 -0.2 -0.1 0 Real Axis (MHz) 0.1 Imaginary Axis (MHz) Imaginary Axis (MHz) 40 20 RSTAB = 70 0 -20 -40 -0.2 -0.1 0 Real Axis (MHz) 0.1 Slide 16 STAN Tool Performances optimization Example: Ku-Band MMIC PA for active space antenna • Stable original circuit Inter-branch stabilization resistances RF in RC stabilization networks RF out 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. STAN Tool 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 STAN Tool Performances optimization Example: Ku-Band MMIC PA for active space antenna • Optimized version resistances maintained for topological reasons RF in Stabilization resistances RF out No oscillation detected, especially around F0/2 Slide 19 STAN Tool Performances optimization Example: Ku-Band MMIC PA for active space antenna • Results comparison Original Optimized STAN Tool 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. www.amcad-engineering.com Slide 21 STAN Tool 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 www.amcad-engineering.com Slide 22 STAN Tool 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 www.amcad-engineering.com Slide 23 Q&A Contact Stéphane Dellier E-mail: dellier@amcad-engineering.com Phone: +33 555 040 531 www.amcad-engineering.com