An alternative to the prototype bandpass filter illustrated in Fig. 1 is to make ω0 = 1 ra...

An alternative to the prototype bandpass filter illustrated in Fig. 1 is to make ω0 = 1 rad/s, R = 1 Ω, and L = Q henrys.

a) What is the value of C in the prototype filter circuit?

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b) What is the transfer function of the prototype filter?

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c) Use the alternative prototype circuit just described to design a passive bandpass filter that has a quality factor of 16, a center frequency of 25 krad/s, and an impedance of 10 kΩ at resonance.

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d) Draw a diagram of the scaled filter and label all the components.

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e) Use the results obtained in Problem 1 to write the transfer function of the scaled circuit.

Problem 1

The voltage transfer function of the prototype bandpass filter shown in Fig. 1 is

Show that if the circuit is scaled in both magnitude and frequency, the scaled transfer function is

Figure 1