5/17/16 - AC Circuit Analysis

Today we list all the methods of circuit analysis we know for DC circuits, we are told that all the methods can apply to AC circuits as well.

Here we have a problem that we solve for using nodal analysis, we convert everything into the phasor domain and set up our equations as usual, then solve for the voltages at our essential nodes.

Next up is mesh analysis.

Given the circuit already in the phasor domain, we set up our equations to solve for the three currents. We already know one due to the current source in one of the loops and use it to simplify our systems to solve.

Next we have our lab activity. We hook up a resistor and inductor in series and observe the input voltage vs the current and voltage across the inductor as a function of time.

We're told that the cutoff frequency for this circuit is the resistance over the inductance and are told to feed an input of the cutoff frequency, 10 times, and 1/10 of it.

We calculate at the cutoff frequency, the phase shift will be exactly 45 degrees on the inductor voltage.

Here we can see that phase shift.

Next up is 1/10 of the cutoff frequency. We calculate a almost 90 degree phase shift.

Here we can see that there is a approximate 90 degree difference since as the input function comes to zero, the inductor voltage almost reaches its peak.

Next is 10 times the cutoff frequency. We calculate almost no phase shift.

As you can see, the two voltage functions are almost in phase.

Another mesh analysis problem, we solve i_1 and i_2 since i_3 we already know.

Lastly, we can see that we have source transformations as well. They follow the same principles as our DC source transformations except in the phasor domain.

And a small compilation of our drawings.