Phasor Domain Analysis

Quick Review of Theory

Find the time-domain voltage, Vc(t) over the capacitor by using phasor techniques.

Find the time-domain voltage over the capacitor using phasor domain techniques. The voltage and current source are both AC (sine) sources with frequency of 1MHz.

Solve for the magnitude of the current through the capacitor.

a) Write the time-domain (differential) node voltage equations for the circuit shown. Do not solve.

b) Solve for the voltage Vx(t) using phasor analysis.

Assume the source voltage is sinusoidal with a magnitude (not rms) of Vs, a phase angle of 0º, and a frequency of w. The transformer has a turns ratio of n1:n2.
a) Solve symbolically for Zeq, the equivalent impedance seen at the primary connections of the transformer, looking right. Your answer should be in the phasor domain (in terms of the frequency w).

b) Find the real (P) and reactive (Q) power dissipated in the elements to the right of the transformer. Your answer will again be symbolic.

Gain for the filter circuit shown below is defined as Vout/Vin where Vout is the voltage over the resistor RL. Find the gain in the phasor domain (as a function of jw). You must solve for Vout/Vin but you do not need to simplify once you have found that ratio.

Solution

Set-up the phasor-domain node-voltage equations for the following circuit. Do not solve.

In the circuit shown below, find the current flowing down through the inductor. The frequency of the source is 2 Mrads/sec and the phase is 0 degrees. You must use phasor analysis, but your final answer must be converted back to time-domain.

Solution

(c) 2011, Steven H. VanderLeest.