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

• 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.

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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 forces use of small simulation time step

• Low forces long SPICE run time

• However we get a sparse spectrum if narrow band signals are periodic.

– Leveraged in Harmonic Balance simulation methods

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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

– Small time step and long run time.

– PSS & QPPS directly calculate Fourier co-efficient

• # of co-efficient calculated

• Usually harmonics beyond 4th or 5th fundamental are neglected.

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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 Shooting method

Frequency domain Time domain

Better support for distributed components, like lossy T-Lines

Not efficient but new methods are being developed

Accurate if circuit is near linear with sinusoid V,I

Good for non-linear circuits

Not good if signals have abrupttransitions (needs more harmonics to simulate)

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

– Use PSS to get φ and PAC for L and U

• FM conversion

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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 gainDrops by 1dB– Inter modulation distortion can be categorized

calculating nth order harmonic power versus input power

• P = power of fundamental• = Difference of P1 – nth harmonic power

• Doubling input power multiplies output power by 2n

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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!