For the sets of two input frequencies given below (all in the FM broadcast band), when these are applied to an RF amplifier that has both a linear voltage gain and a second-order output, i.e.,

Vout(t) = Av * Vin + b * Vin^2

where

Vin(t) = Av * cos(w1t) + A2 * cos(w2t)

f₁ = 87.9 MHz, f₂ = 88.1 MHz

f₁ = 107.7 MHz, f₂ = 107.9 MHz

f₁ = 87.9 MHz, f₂ = 107.9 MHz

Find and list all the second-order output frequencies produced by the mixer defined by V_out.

Now add to the two terms in the Vout(t) defined in the previous problem a third-order term, so that:

Vout(t) = Av * Vin + b * Vin^2 + cVin^3

subject to the same two-tone input as before:

Vin = A1 * cos(w1t) + A2 * cos(w2t)

at the following frequencies:

f₁ = 87.9 MHz, f₂ = 88.1 MHz

f₁ = 107.7 MHz, f₂ = 107.9 MHz

f₁ = 87.9 MHz, f₂ = 107.9 MHz

f₁ = 97.9 MHz, f₂ = 98.1 MHz

Find the third-order output frequencies, and identify those which could be problematic given the width of the established FM broadcast band (87.9 to 107.9 MHz).