1. Inductive Load with Phasors: For the circuit shown below,
vs(t) = Vs cos ωt L RL vo(t)
a. Find the phasor form of the output voltage vo(t) (magnitude |v˜o| and phase φ) and write
them in terms of the ratio ωL/(Rs||RL) where ω is the radian frequency of the voltage
source and Rs||RL is the parallel combination of resistors Rs and RL.
b. From the phasor result in part (a.) construct the real (physical) output voltage vo(t).
c. Using a math plotting package, make a log-log plot of the magnitude of the normalized
Rs + RL
as a function of the ratio ωL/(Rs||RL) over the range
d. Plot the phase φ on a semilog plot, also as a function of the ratio ωL/(Rs||RL), over the
same range. [That is, logarithmic in frequency and linear in phase]. It will will make
more sense if you plot the phase in units of π radians.
[Hint: Use your intuition and knowledge of the current-voltage relationship for inductors to
predict the behavior in the limits ω → 0 and ω → ∞ and compare with your analysis.]
2. Op-amp Filter: Consider the op-amp filter circuit below.
In the ideal op-amp approximation;
a. Find the complex voltage gain A(ω) = ˜vout(ω)/˜vin(ω). It is not necessary to put it into
real+imaginary or polar form. Write the simplest expression you can.
b. What is the gain in the low frequency limit A(ω → 0) and the high frequency limit
A(ω → ∞)?
c. Find expressions for the two corner frequencies.
d. Plot the magnitude of the gain on a Bode plot. That is, 20 log |A(ω)| vs. log f.
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