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Limiter-Amplifier Modeling (Read 116 times)
pancho_hideboo
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Limiter-Amplifier Modeling
Apr 04th, 2006, 9:14am
 
Hi.

I would like to model limiter-amplifier by table-look up.

It is straightforward if I use DC-transfer characteristics of limiter-amplifier.
But I would like to characterise limiter with sinusoidal input.
In this case, output waveform will be like rectangular for large amplitude input.

What amplitude of output should I use in table with input sinusoidal amplitude as independent variable ?
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jbdavid
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Re: Limiter-Amplifier Modeling
Reply #1 - Apr 15th, 2006, 4:52pm
 
say you have an input sinusoid with Peak value of 1, limiting amp with a gain of 3 and a peak output amplitude of 1..

you COULD do a table look up, with
the foloowing table
-0.333 -1
0     0
0.333   1

and used a clamped extrapolation on either end

or you could assume that at 90% of full scale you start "soft limiting"
at 99% it gets pretty firm..
-1 -1
-0.9 -0.99
-0.66 -0.95
-0.3   -0.9
0       0
0.3    0.9
0.66  0.95
0.90  0.99
1.0    1.00

With this model you could even use linear extrapolation beyond the ends ..

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jbdavid
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pancho_hideboo
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Re: Limiter-Amplifier Modeling
Reply #2 - Apr 16th, 2006, 9:48pm
 
Hi.

In modeling limiter, we have two options, equivalent-lowpass and baseband models.

If we use equivalent-lowpass model, we can implement AM/AM and AM/PM characteristics easily by table look up, since we consider an envelope only for fundamental output.

But if we use baseband models for limiter, what amplitude should be used in table ?
Limiter outputs include 1st, 2nd, 3rd, ...., etc. harmonics.
I don't think we should use raw amplitude of output in table.
Rather three parameters model for limiter is better.
See page.212-213 of following.

http://btobsearch.barnesandnoble.com/booksearch/isbnInquiry.asp?z=y&btob=Y&isbn=...

We can determine three parameter by transient or PSS analysis.

For symmetric limiter
#define   Lim3(_v1, s)  ( K*(_v1)/pow(pow(K*fabs(_v1)/Limiter_High_Level_V,s)+1.0,1/s) )

Here K, Limiter_High_Level_V and s are parameter to be determined.

I will model limiter like following.

 Input signal for limiter is equivalent-lowpass representation.
 First AM/PM effect is modeled as equivalent lowpass by table look up.
 After AM/PM effect is included, AM/AM effect is modeled by baseband using three parameter model.

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jbdavid
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Re: Limiter-Amplifier Modeling
Reply #3 - Apr 19th, 2006, 9:39am
 
I normally start with first order models to support functional (is stuff hooked up right) checks..
and had no idea (from your initial question) that this was not what you were talking about.

You have moved a good bit beyond that..

The assumption in the baseband equivalent models (like the ones in the cadence libs) is that you can more easily manipulate the signal
effects in phasor space - where you model the only the complex(I&Q) signal properties superimposed on the
(known) carrier.

For time domain simulation with these models you cannot handle multiple harmonics of the signal in this way,
and my understanding is that you introduce a lot of other harmonics in the limiting amp..
thus you would be looking only on the effect of the retained harmonic.

I'm going to let others in this forum (like Jess) who can better approach the model at the level you are talking about.

jbdavid
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jbdavid
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Jess Chen
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Re: Limiter-Amplifier Modeling
Reply #4 - Apr 19th, 2006, 12:13pm
 
pancho_hideboo,

I am not sure I understand your initial question but you may find the paper listed below helpful.

http://designers-guide.org/Modeling/modeling-rf-systems.pdf

If you are asking about units, I usually build my baseband equivalent models around peak units. I am also not sure I understand the difference between what you call baseband and low pass equivalent.

If memory serves, the model you listed is a Rapp model. I usually use that model to simulate the original static nonlinearity, without suppressing the RF carrier, i.e. a passband model. However, I suppose it could be used in a baseband equivalent model but the parameters would be different and probably not easy to derive. You could sweep a PSS passband simulation to plot the peak fundamental output against the peak fundamental input, and then use the circuit optimizer to fit the baseband equivalent model to the curve. The baseband equivalent model would work with a swept DC analysis to sweep out the peak output versus peak input curve. You would need to define the integrated squared error through the waveform calculator and identify the modeling parameters for the optimizer to adjust.

I would steer away from look up table models for baseband equivalent models. The discontinuous first derivative you get from a look-up table can cause spurs and/or some amount of spectral regrowth. A smooth curve fit eliminates that problem. You do not have to use the Circuit Optimizer to fit a function to the data, as I described above. You can usually get a good fit using tools like Matlab, Mathematica, or even Excel. The trick is to chose the right model, like the Rapp model for example.

-Jess
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