# Input Tone in to an Amplifier

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Consider a single input tone, such that: Vo = ko + k1*Vin + k2* Vin^2 + k3*Vin^3 +.... Let Vin = cos(wt). Now if a tone is put into an amplifier, and its amplitude is increased by 1.5dB, how much will the amplitude of the third order products increase in dB? Using the third order term only of the transfer polynomial, prove this third order relationship. Using the Nth order term only of the transfer polynomial, find the Nth order relationship for the Nth order products.

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##### Solution Summary

Considering Vin = Cos (wt), we can find the relationship for the n-th order products using Vo = Kn*(Vin)^n = Kn*{Cos^n(wt)}.

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Vin = Cos (wt)

Nth order:

Vo = Kn*(Vin)^n = Kn*{Cos^n(wt)}

Nth order term is the coefficient of the Cos(nwt) term.

Now we know that when you factor the Cos^n(wt) into lower powers, at the end we will get the coefficient of the Cos(nwt) ...

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