3/15/16 - Superposition and Source Transformation

To encourage students to show up on time for class, Professor Mason begins the class with a delightfully simple lab activity. We have two resistors with values of our choosing and a voltage out to measure the potential drop in between the resistors.

We construct the circuit using two 10kOhm resistors, the breadboard, and the Analog Discovery.

An input of a sinusoidal wave with an amplitude of 2V.

The voltage across the middle of the circuit from said sinusoidal input, we find that its amplitude is simply one half of the input, as expected.

Square wave input, 2V amplitude.

Same reference point, same square wave, with a one-half multiplier.

Triangle wave, same 2V amplitude.

Again same wave, with a one half multiplier.

Our observations recorded on a table, with the circuit diagram.

Professor Mason introduces a familiar concept of super positioning. It's useful to find the voltage or current at a specific element in a circuit by taking one independent source at a time. Voltage sources are replaced with a short circuit (or wire) and current sources are replaced with an open circuit (or gap), We find the effects of each independent source and add their effects together.

A simple mesh problem with a dependant source, we solve for i_1 and consequently find i_0.

Here we are given our first practice problem with super-positioning, we find the current based on the two sources and sum them up to find the total current.

Another example problem that is slightly more complicated. We find the equivalent resistance to find the current and solve for the voltage. We then add them up to find the total voltage.

Next, to confirm our calculations, we set up the circuit using the breadboard, resistors, and Analog Discovery.

We also attach the multi meter to the circuit to measure the potential.

Here we record the actual resistances of each resistor in our circuit, as well as the measured voltages from each source.

The two instances of us measuring the potential.

Here we recalculate our expected potentials with the actual resistances of the elements in the circuit, we can see that the first value matches up closely, while we failed to calculate the second value before we had to move on.

Lastly, we are introduced to the concept of source transformations. We can convert voltage sources into current sources and vice verse if the circuit is in a particular form. We can convert a voltage source in series with a resistor to create a current source in parallel and back, but we have to make sure to account for that resistance before we combine it with other elements. Source transformation is an method to drastically condense circuits down to reduce the amount of work required to solve for a specific element.