# Tones Input In To An Amplifier

Suppose two tones are input in to an amplifier. The tones are pure sinusoids with one at frequencies 8GHz and the other at frequency 8.03GHz,(delta f =0.03GHz). Assume that the transfer characteristic of the amplifier is represented by Vout= ko + k1Vin +k2Vin^2 +k3Vin^3...+k9Vin^9. List the output frequencies of all 3rd order (those near 24 GHz) and 4th order (those near 32GHz) signals in ascending order of frequency.

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#### Solution Preview

f1 = 8.03 GHz

f2 = 8.00 GHz

Define the mid frquency f0 = (f1+f2)/2 = 8.015 GHz

define "delta f" fd = 0.015

Then,

f1 = f0 + fd

f2 = f0 - fd

The two tones at the input will give rise to output frquencies which are of the form:

(+/-) n*f1 (+/-) m*f2

where (+/-) means "Plus or Minus" and, in general, n and m can take values from 0 to 9 (since there is a maximum of 9 order in the transfer characteristics.

also, can express (+/-) n*f1 (+/-) m*f2 as

(+/-) n*(f0 + fd) (+/-) m*(f0 - fd)

There are four combinations possible because of the two (+/-) operators.

1 | + | + | +nf1+mf2 | f0(n+m)+fd(n-m)

2 | + | - | +nf1-mf2 | f0(n-m)+fd(n+m)

3 | - | + | -nf1+mf2 | f0(m-n)+fd(-n-m)

...

#### Solution Summary

Solution solves for combinations of output frequencies. 550 words.