The RLC circuit shown in Figure P28 can be used as a narrowband filter . If the input voltage !i(t) consists of a sum of sinusoidally varying voltages with different frequencies, the narrowband filter will allow to pass only those voltages whose frequencies lie within a narrow range. The magnification ratio M of a circuit is the ratio of the amplitude of the output voltage υ_o(t) to the amplitude of the input voltage υ_i(t). It is a function of the radian frequency 2 of the input voltage. Formulas for M are derived in elementary electrical circuits courses. For this particular circuit, M is given by

 

The frequency at which M is a maximum is the frequency of the desired carrier signal. Determine this frequency as a function of R, C, and L.

Figure P28

Transcribed Image Text:

RCO M V(1 - LCo?)2 + (RCo)?