Figure shows the circuit diagram of a square-law modulator. The signal applied to the non linear devices

Question:

Figure shows the circuit diagram of a square-law modulator. The signal applied to the non linear devices is relatively weak, such that it can be represented by a square law: v2 (t) = a1v1 (t) + a2v21 (t), where a1 and a2 are constant, and v1 (t) is the input voltage and v2 (t) is the output voltage. The input voltage is defined by v1 (t) = Ac cos (2???ct) + m (t), where m (t) is a message signal and Ac cos (2???ct) is the carrier wave.

(a) Evaluate the output voltage v2 (t).

(b) Specify the frequency response that the tuned circuit in Figure must satisfy in order to generate an AM signal with ??c as the carrier frequency.