help with detailed answer explanation Please show all work throughout. You will

Question

help with detailed answer explanation

Please show all work throughout. You will lose credit if you do not. Basic op-amp circuit analysis You are given the following circuit: Please answer the following questions about this circuit, assuming that the source vin is sinusoidal. At low frequency, does a capacitor appear as a short or as an open? Explain using both equations and words. Using this knowledge, sketch an equivalent low-frequency circuit model. What is the gain of the circuit that you drew in part a? You must show your work in order to receive credit. At high frequency, does a capacitor appear as a short or as an open? Explain using both equations and words. Using this knowledge, sketch an equivalent high-frequency circuit model. What is the gain of the circuit that you drew in part c? You must show your work in order to receive credit. What is the gain of the complete circuit at any given frequency omega? Show that this result is consistent with your intuitive results from parts b and d by taking the limit of this expression as omega rightarrow 0 and as omega rightarrow + infinity

Explanation / Answer

A) xc = reactance offer by capacitor = 1/(2*pi*f*C)

   hence at low frequency   Xc is high , so capacitor will act as a open circuit

b)     capacitor is open circuit

Vo/Vin = -R2/R1     :::: hints :: it is inverting amplifier ::

c) xc = reactance offer by capacitor = 1/(2*pi*f*C)

   hence at high frequency   Xc is low , so capacitor will act as short circuit

d) V o = 0   

e)    Re = Xc ||R2   = R2/( -R2*WC+1)

gain   = - Re/R1 =- R2/[R1*( -R2*WC+1)]

as w --> 0   , gain =   -R2/R1

as w -->infinity   gain =0

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