Introduction to RF Simulation and Its Applications by Kenneth S. Kundert Presenter - Saurabh Jain
What will he talk about? Challenges for RF design and simulations RF circuit characteristics Basic RF building blocks RF Analysis methods, implementation and comparison RF measurements
Main challenges for RF designs (Rx) Small signals and noise Small input signals (1µV) Input noise and noise at Rx input Coherent super heterodyne receiver Large interference signals Strong nearby transmitters on adjacent channels drive Rx into non-linearity. Quantified with inter-modulation distortion Expensive in SPICE, as long run time is needed for a good frequency resolution.
Main challenges for RF designs (Tx) Non-linearity at Tx output Spectral re-growth Harmonic distortion SPICE simulation for spectral re-growth will require long runtime to capture the needed spectrum.
RF Circuit characteristics (1) Narrow band signals (eg. cell Transmission) High frequency carriers Low frequency modulation signals High Low fc fs fc 1 2GHz forces use of small simulation time step forces long SPICE run time fs 10 30KHz However we get a sparse spectrum if narrow band signals are periodic. Leveraged in Harmonic Balance simulation methods
RF Circuit characteristics (2) Time varying Linear Signals RF designs are generally linear to prevent distortion. Some circuits like mixers perform frequency translation using periodic signals Linearization with time varying operating point allows to extend conventional small signal spice methods to RF designs. Time varying nature represents frequency translation.
RF Circuit characteristics (3) Linear passive components Tx lines, spiral inductors and substrate offer various challenges to include in simulations. Semiconductor models Accurate high frequency models for semiconductor devices needed. Modeling gate-r, thermal and flicker noise for MOS.
Basic RF blocks (Mixers) Perform frequency translation Generates images which need to be filtered out. Sideband v/s image Sideband desired signals Images undesired
Basic RF blocks (Oscillators) Generate reference signal at a given frequency Used to generate LO signal Noise performance of LO affects mixers. In a stable oscillator Amplitude deviation damps out Phase perturbations persist Special simulation techniques needed to calculate phase noise.
RF Analysis types (PSS & QPSS) Traditional DC Compute steady state solution at constant input PSS (periodic steady state) Calculate steady state response with a time varying periodic input. Quasi-PSS Usually used for multi-tonal designs.
RF Analysis types (PSS & QPSS cont..) Traditional transient simulations take long time if min( f, f 2)/ max( f 1, f 2) 1 or f 1 f 2 / max( f 1, f 2) 1 1 Small time step and long run time. PSS & QPPS directly calculate Fourier co-efficient # of co-efficient calculated K ( 2K i 1) Usually harmonics beyond 4 th or 5 th fundamental are neglected. i
Harmonic Balance method Frequency domain solution of circuit. Solution represented as Fourier series for T periodic fundamental (f=1/t) Certain non-linear component are evaluated in time domain and converted back to frequency domain using Fourier transforms.
Harmonic Balance for QPSS Extend PSS for multi tonal inputs. Two fundamental QPSS becomes k and l have no common period (linearly independent) So Fkl(V)=0 is bounded by k<k and l<l
Shooting Newton method for PSS Solves circuit equations in time domain. Iterative layer over traditional SPICE. Assume V(t) as non-constant period T stimulus v(t0+t) = φ(v(t0), t0), t0=0 v(0) = φ(v(0),0) Non-linear algebraic problem solved using Newton methods
Other methods Multi tonal PSS (QPSS) Basis for Mixed frequency time methods (MFT) Autonomous shooting methods Used for calculating oscillator time period Oscillator time period additional unknown with an additional equation to constrain the oscillator phase.
Small Signal RF Analysis (LPV) AC and NOISE analysis for SPICE are traditional small signal analysis Small signal applied to circuit at its DC point Linearized about DC point by using Taylor series Linear Periodically Varying (LPV) analysis extend this by linearizing circuit about a periodic signal. More accurate, faster and errors in linearization phase have minor affect on small signal analysis Examples PNOISE, PAC & PXF.
Small Signal RF Analysis (LPV contd ) Input signal u(t)= ul(t)+us(t) where ul(t) is large periodic wave with period TL and us(t) is small sinusoid signal Output v(t)= vl(t)+vs(t).
Small Signal RF Analysis (PAC & PXF) Periodic AC (PAC) It is used to measure response of an input to all nodes at all frequencies. Predicts output sidebands for an input Periodic transfer function (PXF) Inverse of PAC Used to measure possible images at input for an output
Other methods Transient Envelope Analysis Volterra methods Multirate partial differential equation metods (MPDE)
How do methods compare? RF simulation methods mainly harmonic balance based or shooting newton Harmonic Balance Frequency domain Better support for distributed components, like lossy T-Lines Accurate if circuit is near linear with sinusoid V,I Not good if signals have abrupt transitions (needs more harmonics to simulate) Time domain Shooting method Not efficient but new methods are being developed Good for non-linear circuits Can handle abrupt transitions as sim time step can be varied
RF Measurements (Tx functions) Conversion Gain: Generalization of Gain (Av) for periodic circuits like mixers Gain from undesired image or power etc. Use PAC or PXF
RF Measurements (Tx functions) AM/PM conversion Narrow band approximation fm fc Use PSS to get φ and PAC for L and U FM conversion
RF Measurements (Noise) Noise is critical as RF circuits deal with very small signals Characterized by Noise Figure (NF) For a mixer - Use PSS to compute steady state response for LO. Apply small signal PNOISE analysis. For Oscillator noise. PXF to determine to determine sensitivity to interference.
RF Measurements (Noise) Inter modulation distortion Apply two tonal signal (f1, f2) within circuit bandwidth Distortion products fall within the range 2f1-f2, 2f2-f1, 3f2-2f1..
RF Measurements (Noise) Compression points 1dB point where gain Drops by 1dB Inter modulation distortion can be categorized calculating n th order harmonic power versus input power P IPn P n 1 P = power of fundamental P = Difference of P1 nth harmonic power Doubling input power multiplies output power by 2 n
RF Measurements (Noise) Blockers PSS followed by PAC to compute gain of desired signal (Adjacent Channel Power Ratio) ACPR Used to measure ACP requirements Caused by non-linearities in output stage
Thank? You!