Simulation o Radio Frequency Integrated Circuits Based on: Computer-Aided Circuit Analysis Tools or RFIC Simulation: Algorithms, Features, and Limitations, IEEE Trans. CAS-II, April 2000. Outline Introduction Analyses required or RF circuits SPICE analyses and limitations Algorithms or RF simulation Time-domain methods Harmonic-balance method Mixed time-requency methods Envelope method Linear time varying analysis RF noise Commercial tools Introduction RF blocks are a big challenge in the design process Typical blocks that are analyzed Ampliiers Mixers Oscillators, Voltage Controlled Oscillators (VCOs) Phase-Locked Loops (PLLs) Filters (CT, SC, SAW) SPICE is not adequate or circuit level analysis o most RF blocks Lack o computer-aided analysis tools aggravates design problems Analyses Required or RF Circuits Rapid simulation o the periodic or quasiperiodic steady state Accurate simulation o harmonic and intermodulation distortion Simulation o noise up/down conversion due to circuit nonlinearities Phase noise/jitter simulation Simulation o oscillator turn-on transient Simulation o the capture process o PLLs Distributed element simulation
RF Ampliier Periodic Steady State Mixer Quasi-Periodic Steady State V V Time Time V Oscillator Turn-On and Steady State SPICE Analyses and Applications DC.op,.dc Dc operating point, dc transer curves Can be used or all circuits Small-signal AC.ac,.noise,.disto Frequency response o linearized circuits Can be used or ampliiers Time
SPICE Analyses and Applications SPICE Limitations Transient.tran,.our Large-signal time-domain analysis Can be used or Ampliiers Oscillators Mixers PLLs A/D, D/A converters Noise analysis at a dc operating point Cannot simulate noise mixing in mixers Cannot simulate phase noise/jitter Long transient analyses required or Periodic/quasi-periodic steady state Turn-on transients o high-q oscillators and capture process o PLLs Can accumulate signiicant numerical error Fourier analysis SPICE Limitations Requires periodic steady state and undamental requency Multiple tones must be commensurate IM3 simulation is diicult Subject to interpolation and aliasing errors Tighter tolerances required to resolve small harmonics Fourier integral gives reliable results Elements and models Transmission line is the only distributed element Models may possess discontinuities in higher-order derivatives => spectral contamination Periodic Steady-State Simulation Time-domain methods Harmonic-balance method Mixed time-requency methods Traditionally limited to small circuits Recent advances allow simulation o much larger circuits
Time-Domain Method Time-Domain Method Impose periodicity constraint v(0) = v(t) V 0 T Time A popular method is the shooting method Requires dense matrix solutions Matrix-ree methods allow simulation o ~1000 node circuits V 2 3 4 5 1 For a driven circuit period T is known For an oscillator T is an unknown Time Non-Linear Frequency Domain Analysis Harmonic Balance Balance the requency spectrum at each node Low distortion signals require ew Fourier series coeicients Smooth device models are essential or RF Time-derivatives (capacitors) become multiplication in requency domain Handle distributed elements in req. domain
Multi-Tone Frequency Domain Analysis Frequency Truncation Harmonic truncation keep a inite number o requencies containing signiicant energy One-tone spectrum Minimum number o time-domain samples dictated by the number o signiicant Fourier coeicients, not by the Nyquist rate Two-tone spectrum Oscillator Simulation with HB Problems Unknown period o oscillation Arbitrary time origin Solutions (K. Kundert, 1990) Frequency as an additional unknown Additional equation to ix phase Direct implementation convergence problems Iprobe Oscillator 0, Z( ), Use Voltage Probe Vprobe Convergence criterion Probe current equals zero Advantages Autonomous circuit orced circuit E.Ngoya, Int.J. Microw. Milim.-wave CAE,1995
Mixed Time-Frequency Methods For circuits with both mild and strongly nonlinear behavior Examples: switching mixer, switched-capacitor circuits Mixed Time-Frequency Methods Represent the envelope waveorm with ew Fourier series terms Few points needed to represent envelope Can ind them with a ew transient simulations o the ast cycle New methods Based on multi-rate partial dierential equations Uses bi-variate representations or eicient computation Envelope Method Linear Time Varying Analysis Slow inormation signal over ast carrier Startup transients o circuits with ast signals AGC circuits, PLLs Mixer example RF=0 Output Direct calculation o envelope without tracing the ast cycles Solve dierential equation in the envelope Inner loop is harmonic balance LO Periodic time varying network RF small signal LO Linear time varying network Output LO LO 2 3 LO LO 2 3 LO LO
Analysis Methods - Summary * Small signal Time- Domain Methods MNL = mildly nonlinear HNL = highly nonlinear Frequency- Domain Methods Mixed Time Freq. Method Envelope Method Linear Time Varying Method Ampliiers X X (MNL) Ampliiers X (HNL) Mixers (CT) X X X X* Mixers (NCT) X X X* Oscillators X X X PLLs, AGCs X SC Circuits X X X* CT = commensurate tones NCT = noncommensurate tones Mixing Noise Up/down conversion o noise due to mixing SPICE noise analysis does not work Cyclostationarity/requency correlation important Monte Carlo or stochastic methods Phase Noise Important or adjacent channel intererence, data recovery, and sampled data systems Most analyses are o speciic oscillators under simpliying assumptions Methods or proper phase noise calculation available in commercial simulators Commercial RFIC Circuit Simulators Commercial simulators or RFIC design gaining maturity Simulators developed rom two dierent ronts Microwave design ADS rom Agilent/EEso Harmonica rom Ansot Analog IC design Spectre-RF rom Cadence ELDO-RF rom Mentor
Conclusions SPICE-like analyses not suitable or RFIC circuit simulation Fast and eicient RFIC simulation available in commercial simulators Available tools lack system on chip solutions Simulators need to be benchmarked or accuracy and perormance Summary Harmonic balance or High dynamic range weakly-nonlinear systems RF ront-ends (LNA, Mixer) IQ modulators LC and crystal oscillators Circuits with distributed components Transmission lines, S-parameter models Time-domain PSS or Strongly nonlinear circuits Ring oscillators Frequency dividers DC-DC converters Input signals with sharp transitions