Day 7 Notes Superposition and Source Transformation/ Lab Time - varying Signals and Superposition

Part1: Lab Time-Varying Signals

Purpose: This lab aims to give a tutorial pertaining to creating some simple types of waveform generators, using an oscilloscope to measure time varying signals, and analyzing voltage divider.

Pre-Lab:

The amplitude and period of both the input and output waveform including a sinusoidal wave, triangular wave, and square wave. 

Based on the model of a voltage divider, we set-up the bread-board and analog. After a few adjustment in the waveform generator window, we create the desired type of wave and perform our measurement on the oscilloscope window. 

The sinusoidal wave. The input voltage is the blue curve and the output is the orange curve.

On the oscilloscope (measurement), the Vin (amplitude 2V, frequency 1kHz, period 1ms), the Vout (amplitude 1V, frequency 1kHz, period 1ms). The measurement results match with our expectation. 

The triangular wave. The measurement values are Vin(3V, 1kHz, 1ms), Vout(1.5V, 1kHz, 1ms), which agrees with our expectations. 

The square wave. The measurement values are Vin(2.5V, 500Hz, 2ms), and Vout(1.25V, 500Hz, 2ms), which agree with our expectation. 

Shortly, this lab is designed so that students can follow easily. We have no difficulty to get the desired values. All measurements are the same we expected. 

Part 2: 

Linearity property: A linear circuit is one whose output is linearly related (or directly proportional) to its input.

We are introduced a theory of linearity property, which is one whose output is linearly related/directly proportional to its input. Then we do a problems to verify that. Our group do with the 24V, while others groups do with 12V. Consequently, our results is as twice as other group's results.

Then we study about another technique to analyze a circuit: superposition. It states the voltage across (or current through) an element in a linear circuit is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone. We do a practical problem by using superposition. 

Part 3: Superposition Lab

 Purpose: The lab is to verify the superposition technique.

Pre-lab:

We calculate the V using the superposition and get V=2.69V

Procedure

We set up the experiment and get the measured value is 2.74V when 3V source and 5V source are applied

The 3V source is applied alone, and the value is 0.69V. Subsequently, the 5V source is applied alone, and the value is 2.03V

These are our calculated values(in red) and measured values(in green) of the resistors and the desired voltage.

 Shortly, we perform the lab successfully when our calculation meets our measured results. The experiment shows that the superposition is verified.

Part 4: Source Transformation

A source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa.

Note: When using source transformation to analysis, we do not transform the branch relating to the unknown value because it will affect the results. The reason is the source transformation is equivalent for the a and b terminal only.

After that, we do a practice problem to enforce our skill. 

Summary

In conclusion, this class we do two experiments and learn two more circuit analyzing techniques which are superposition and source transformation. These techniques are piquantly powerful to simplify a bewildering circuit. However, for the source transformation, we have to carefully transform the circuit so that the answer is not affected.