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Tones Input In To An Amplifier

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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 solves for combinations of output frequencies. 550 words.

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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)
...