Question: In the VCO circuit shown in Fig., the voltage dependence of each varactor can be expressed as Cvar = C0(1 + α1Vvar), where Vvar denotes the average voltage across the varactor. Use the narrowband FM approximation in this problem. Also, neglect all other capacitances and assume the circuit oscillates at a frequency of ω0 for the given value of Vcont. The dc drop across the inductors is negligible.
(a) Compute the "gain" from ISS to the output frequency, ωout. That is, assume ISS changes by a small value and calculate the voltage change across the varactors and hence the change in the output frequency.
(b) Assume ISS has a noise component that can be expressed as In cos ωnt. Using the result found in (a), determine the frequency and relative magnitude of the resulting output sidebands of the oscillator.
