Find the output voltage magnitude at f0 and the bandwidth in Figure 18-31.

Question

Find the output voltage magnitude at [latex]f_{0}[/latex] and the bandwidth in Figure 18-31.

Accepted Answer

Since [latex]X_{L}[/latex] = [latex]X_{C}[/latex] at resonance, they cancel, leaving [latex]R_{W}[/latex]. The output voltage is determined using the voltage-divider formula.

[latex]V_{out}= \left(\frac{R_{W}}{R+ R_{W}} \right) V_{in}= \left(\frac{2 \ \Omega }{58 \ \Omega } \right)100 \ m V = 3.45 \ mV[/latex]

To determine the bandwidth, first calculate the center frequency and Q of the circuit.

[latex]f_{0}= \frac{1}{2\pi \sqrt{LC} }= \frac{1}{2\pi \sqrt{(100 \ mH)(0.01 \ \mu F)} }=5.03 \ kHz[/latex]

[latex]Q=\frac{X_{L}}{R_{(tot)}}=\frac{2\pi fL} {R+R_{W}}= \frac{2\pi (5.03 \ kHz)(100 \ mH)}{58 \ \Omega }= \frac{3.16 \ k\Omega }{58 \ \Omega }=54.5[/latex]

[latex]BW=\frac{f_{0}}{Q}= \frac{5.03 \ kHz}{54.5} = 92.3 \ Hz[/latex]

Question 18.11: Find the output voltage magnitude at f0 and the bandwidth in...

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