Question

The signal m(t) = 3cos20000πt is fed to a VCO with quiescent frequency of 3 MHz and frequency sensitivity of 20 KHz/V. Denote the output of the VCO by y(t).

Derive the output y(t)

Answer 1

The VCO takes an input signal and produces an output signal by adding the quiescent frequency to the product of the frequency sensitivity and the input signal.

Step-by-step explanation:

The VCO (Voltage Controlled Oscillator) takes an input signal, m(t) = 3cos(20000πt), and produces an output signal, y(t). We are given that the quiescent frequency of the VCO is 3 MHz and the frequency sensitivity is 20 KHz/V. To derive the output y(t), we can use the formula:

y(t) = f0 + Kv(t)

where f0 is the quiescent frequency, K is the frequency sensitivity, and v(t) is the input signal. Substituting the given values, we have:

y(t) = 3 MHz + 20 KHz/V * 3cos(20000πt)

Thus, the output y(t) is the sum of the quiescent frequency and the product of the frequency sensitivity and the input signal.