Day 7: Superposition and Source Transformation

Day 7: Superposition and Source Transformations

Time-varying Signals

Today we started off class with the Time-varying Signals lab. 

Here in the prelab, we predicted what we thought would get if we had equal resistances. Of course this is just a voltage divider, so we would expect output voltage to be half of input voltage. We predicted for Sine, square, and triangle waves.

Our simple setup with two resistors, a supply, and leads from Analog discovery to measure the voltage across the second resistor.

Sine wave input: 2V

Sine wave output: 1V

Square wave input: 2V

Square wave output: 1V

Triangle wave input: 2V

Triangle wave output: 1V

All wave inputs and outputs were just as predicted. Output was half on input. The shape of the wave was just as predicted as well: starts at origin and goes up to respective amplitudes in the shape of the wave.

Superposition

Superposition is the idea of analyzing a circuit by 'turning off' all sources except one and analyzing a circuit element that way, then doing that for each source and adding up the answers. This only works because the elements we are using are linear. We cannot directly find power using this method.

In this example, Professor mason showed us how easy it was to use superposition to calculated answers in your head. It only requires a little bit of drawing of pictures.

We showed here that circuit elements are linear. The right side of the class solved the circuit for V = 12V, the the left side solved for V = 24V. We found the current i_0. We showed that our current was half that of the other side.

Our first lab group problem of Superposition. We were able to solve this with much ease.

Here we checked our answer for the previous problem with Nodal Analysis.

Superposition II

In this lab, we analyzed, built, and tested a circuit containing multiple sources. Except in special cases, multiple sources preclude the use of analysis techniques based entirely on circuit reduction approaches. We can, however, use circuit reduction techniques in conjunction with superposition to determine the response of a circuit with multiple sources.

We were able to use the idea of source transformations, as well as superposition to find the expected voltage over the 6.8k ohm resistor. Although this took a lot of work, we eventually did get our experimental answer. The thing that was messing us up was the idea of power dividers, more specifically, dividing powers multiple times in a row.

Here are two pictures of our circuit,
as shown in the lab manual.

Actual measured resistances from
our circuit. 1.99 and .702 volts
were the measured values

 

Measure of voltage across 6.8k ohm resistor with both power supplies engaged. We got an answer very close to our expected value of 2.7V. 

Here, with only the 3V power supply engaged, we found a very accurate answer of 0.701V.

As above, we found a very accurate value for when only the 5V power supply was engaged, treating the 3V supply as a short circuit.

Finally, we worked our a problem with source transformations. This makes circuits really easy. We are able to change voltages in series with resistors to current sources in parallel with resistors. Voltage divider calculations become very useful here!