What is Volterra series, and what is it used for?

Hello qiushidaren,

Volterra Series is a Time domain simulator ...Accurate large Signal
Steady-state behaviour of weakly non-linear power amplifiers, mixers, oscillators, etc...

Advantage: The Volterra Series Simulator avoids repeated Fourier transforms,
hence the numerical precision in the results is considerably higher than Harmonic Balance.
So many design engineers prefer this for calculating intermodulation levels.


Find attached is a very good PDF document written by Dr. Steve Maas on
"What You Need To Know About Volterra-Series Analysis"


---manju---

Hi

reading through the paper attached one might find out that Voltera series simulator is indeed nonlinear simulator, but not time domain. It is working in frequency domain. It is used mainly for weakly nonlinear circuits, e.g. to calculate intermodulation in almost linear amplifiers (LNAs) etc. This is the area where convetional harmonic balance technique will fail to get accurate results as it is better suited for 'hard' nonlinear circuits such as mixers, frequency multipliers etc.

flyhigh

I think it is a time domain simulation. The frequency domain one is hamonic balance. The idea of volrerra series resembles the convolution which is the time domain one. The voltera series is a series of integral convolution.

Hi

taken from above attached paper

"... Furthermore, and somewhat less obviously, it can be evaluated
entirely in the frequency domain; there is no need for the repeated Fourier
transforms required by harmonic-balance analysis. As a result, Volterra
analysis is not limited by the numerical range of multitone Fourier transforms,
and since it is not iterative, it is extremely fast. Most of the computation
time is used by the linear analyses of the circuit; the time required for
generating the nonlinear currents is invariably negligible..."

So it works entirely in frequency domain. Plese read Mass's paper"!

flyhigh

Ok, thank you. I found it it the book how to write the voltera kernel in frequency domain.. sorry about that...

"Distortion analysis pf analog integrated circuit" by Piet Wambacq and Willy Sansen

Dear qiushidaren,

Volterra Series is a Taylor series with memory (Schetzen). You can use Volterra for continuous time signals as well as for discrete time signals. It can be used in time domain and frequency domain. Volterra Series can be used to represent Wiener, Hammerstein and Wiener-Hammerstein blocks.
Its applications are in Communications (sattellite channel, Linear filter in cascade with power amplifier), where it can be used for identification, predistortion and equalization. In biomedical engineering, Echo cancellation, OFDM sytems, analog to digital converters ....to mainly linearize and improve their performance.

Hope this little helps......

You might wanna look @
Polynomial Signal Processing by Mathews
Volterra and Wiener theories by Schetzen
Principles of Digital Transmission by Benedetto and Biglieri