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[AMPS] IMD and harmonics

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Subject: [AMPS] IMD and harmonics
From: pcmeas@hotmail.com (Arlen Mendelssohn)
Date: Wed, 06 May 1998 01:54:17 PDT
There seems to be some misunderstanding of how IMD happens.  The voltage 
output *divided-by* voltage input equation for any two port device is 
always a Taylor series expansion, which includes linear, square, cubed, 
etcetera terms in it.  If one processes a single sinusoidal signal 
through this expansion, the squared terms give rise to a second 
harmonic, the cubed terms a third harmonic, and so forth.  But then, how 
does one get intermodulation, a mixing of two signals?  If one delivers 
two pure tones to an amplifier which exhibits such a Taylor series 
expansion characteristic, one of the terms is:

( A*sin(2*pi*omega1*t) + B*sin(2*pi*omega2*t) ) ^2

where:

A,B are the peak voltages of the two separate signals,
omega1, omega2 are the angular frequencies of the two signals
pi and t are evident.
^2 is the best I could do at making a squared sign!

The expansion of this term gives us four separate frequencies: twice 
each of the original frequencies, plus the sum and difference of the 
two.

Now that we have the second harmonic of each, the very same second-order 
term can cause a mixing of one of the second harmonics with one of the 
fundamentals, producing a third order product.  Similarly, a fifth order 
product comes from the fourth power term plus the second,etc.  An 
interesting note here - a push-pull amplifier suppresses only the odd 
order harmonics.  Do you suppose it has improved IMD?  As it turns out, 
push pull amplifiers have strikingly high IMD for their relatively good 
harmonic performance.

One fallout of this is that I cannot create a third order IMD product if 
I do not create a second harmonic.  This fact is used to advantage in 
television transpose amplifiers.  The designer aims the output network 
such that it appears to the amplifying device as a short circuit at the 
second harmonic, and they can achieve miraculous levels of third order 
IMD - often 60dB down - in a class B amplifier.  The drawback, of 
course, is that tuning is very narrowband.

So if an amplifier has a stimulus of only 30 MHz, and we see some 350MHz 
signals, then some of the 350 might be IMD, but since IMD cannot exist 
without harmonics, then chasing IMD by itself would have little use, so 
the focus should be harmonics.

Harmonics at the anode may actually be a good sign.  If we want 
efficiency, we can arrange to have the ouptut network appear very high 
impedance at the odd harmonics, which tends to make the anode voltage 
appear as a square wave, which means better efficiency.  Classes D, E, 
F, etc, are all based on controlling the waveshape at the output of the 
device to be square-like.  Therefore, I put little value in observations 
of the anode voltage waveform or harmonic structure.  It is not 
representative, in most cases, of anything that would occur at the 
antenna output.

Arlen

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>>That's not an intermod problem, it's a harmonic problem.  
>
>Unless you carefully define which frequencies are there, it could be 
either,
>or both. However, if the analyser isn't being overloaded, and isn't 
telling
>lies, then from what was said, it seems there's something not quite 
right.
>It does depend a lot on the test set up and the coupling, though.
>
>73
>
>Peter G3RZP
>
>Out of circulation 2 thru 11 May.
>
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