Consider the circuit depicted in the figure below, R V,elue where we shall asssume that the input voltage can be written as Vin(t) = Re{Voc*| with complex-valuod Vo, and likewise that the output voltage Voue(t) = ReįV4c**j with complex-valuod V1. With j = V=I, the complex impedances of resistors, ca- pacitors, and inductors in this case are respectively given by ZR = R, Zc ZL = jul. jwC" (n) Determine V1/Vo as a function the angular froqueney w given the parameters R and C. (b) Evaluate V1/V% in the limit w →0 and in the limit w o. Is the circuit above a low-pass filter, a high-pass filter, or something else? H+

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Publisher:Robert L. Boylestad
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6. Consider the circuit depieted in the figure below,
R
V,eiut
where we shall assume that the input voltage can be written as Vin(t) = Re{Voet}
with complex-valued Vg, and likewise that the output voltage Vout(t) = Re{Vje*}
with complex-valued Vị. With j = V-1, the complex impedances of resistors, ca-
pacitors, and inductors in this case are respectively given by
ZR = R,
Zc =
ZL = jwL.
(a) Determine Vı/Vo as a function the angular frequency w given the parameters R and C.
(b) Evaluate Vi/Vo in the limit w +0 and in the limit w + o0. Is the circuit above a low-pass
filter, a high-pass filter, or something else?
w
Transcribed Image Text:6. Consider the circuit depieted in the figure below, R V,eiut where we shall assume that the input voltage can be written as Vin(t) = Re{Voet} with complex-valued Vg, and likewise that the output voltage Vout(t) = Re{Vje*} with complex-valued Vị. With j = V-1, the complex impedances of resistors, ca- pacitors, and inductors in this case are respectively given by ZR = R, Zc = ZL = jwL. (a) Determine Vı/Vo as a function the angular frequency w given the parameters R and C. (b) Evaluate Vi/Vo in the limit w +0 and in the limit w + o0. Is the circuit above a low-pass filter, a high-pass filter, or something else? w
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