8. Derive a formula for the voltage gain, g(?) = Re(Vout/Vin), and its phase ?(?), for the circuit sketched at right. Graph both quantities over the range ?L/R = 0–4. Comment on the value of the gain at small and large frequency. What sort of filter is this? Vin = V0 e^{i?t} Vout
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Without a sketch, it's hard to know exactly what the circuit looks like, but let's assume it's a simple RC (resistor-capacitor) circuit. In an RC circuit, the output voltage Vout is given by the voltage across the capacitor. The impedance of the capacitor is Show more…
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Obtain the expression for the voltage transfer function Vout(jw)/Vin(jw) for the circuit shown in terms of the symbolic components (i.e., do not substitute for the component values). Indicate what happens to the magnitude of the gain (i.e., |Vout(jw)/Vin(jw)|) as the frequency approaches zero and infinity. In the magnitude calculation, substitute for the actual component values. Note that the magnitude of a complex number (a + jb)/(c + jd) is |(a + jb)/(c + jd)| = sqrt(a^2 + b^2)/sqrt(c^2 + d^2).
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Consider the filter circuit shown in Active Figure 33.22 $\mathrm{a}$ . (a) Show that the ratio of the output voltage to the input voltage is $$ \frac{\Delta v_{\mathrm{out}}}{\Delta v_{\mathrm{in}}}=\frac{R}{\sqrt{R^{2}+\left(\frac{1}{\omega C}\right)^{2}}} $$ (b) What value does this ratio approach as the frequency decreases toward zero? What value does this ratio approach as the frequency increases without limit? (c) At what frequency is the ratio equal to one-half?
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