Introduction to RF Simulation
and Its Applications
by
Kenneth S. Kundert
Presenter - Saurabh Jain
What will he talk about?
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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)
Coherent super heterodyne receiver
– 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.
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 fc  1 2GHz
– Low frequency modulation signals fs  10  30KHz
• High fc forces use of small simulation time step
• Low fs forces long SPICE run time
• 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 1, f 2) / max( f 1, f 2)  1 or | f 1  f 2 | / max( f 1, f 2)  1
– Small time step and long run time.
– PSS & QPPS directly calculate Fourier co-efficient
• # of co-efficient calculated K   (2K  1)
i
i
• Usually harmonics beyond 4th or 5th fundamental are
neglected.
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 abrupt
transitions (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
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 nth 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
2n
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!