Consider the oscillator shown below The two amplifiers each have a real gain of

Question

Consider the oscillator shown below The two amplifiers each have a real gain of A and can be considered as ideal Write down an expression for the loop gain of the oscillator. Find the value of the amplifier gain necessary for oscillation, and the frequency at which this oscillation will occur Shown below is an IGMF band-pass filter Its transfer function is given by:V_2/v_1=-Omega_0/squareroot2 s^2+squareroot2Omega_0s+Omega^2_0 Calculate the gain (in dB) and phase shift of the filter at the corner frequency Omega_0 = 1 rad/s. Calculate the filter's rate of fall off in dB/decade as Omega rightarrow infinity. Consider the following network function: A(s) =10^6/(s+10)(s+1000) Sketch the Bode amplitude plot of the network function. [Label your axes carefully. The frequency range of your plot should cover 10^0 to 10^5 rad/s] Sketch the Bode phase plot of the network function. [Label your axes carefully. The frequency range of your plot should cover 10^0 to 10^5 rad/s] An amplifier with an open-loop gain given by this transfer function is placed in feedback loop with a constant feedback fraction Beta = 0.1 Use your Bode plots from parts (i) and (ii) to determine the phase margin of the amplifier.

Explanation / Answer

i) loop gain = R/( 1 +sCR)* sC/(1+sCR)

ii) gain necessary fr oscillation = magnitude(AB) = 1

phase shift sumof angle is 180

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