MATLAB Packet

3/17/16 - More Source Transformation, Thevenin's Theorem, and Norton's Theorem

Today we start the class with Professor Mason giving us a circuit to put into EveryCircuit.

Next we talk more about Thevenin's Theorem, given a simple circuit, we replace the independent voltage sources with a short circuit and the independent current sources with an open circuit. Then we calculate the resistance R_th by measuring the resistance between the two nodes of the resistor R_L.

Professor Mason's work on the same circuit, we can see that we combine the resistors into two on either side and can find the equivalence resistance.

We now find the voltage V_th by finding the potential difference across the load resistor. We do this by taking the resistor out of the circuit and solving for the potential at the two nodes. We used a single system since we used source transformation to simplify the circuit.

Next, we are given this circuit with the load resistor on top, we solve for the Thevenin Resistance and Voltage for the circuit.

We used Mesh analysis and are given that R_L is 1kOhm, so we solved for the resistance and then found the voltage across the 1kOhm resistor.

We constructed the circuit in EveryCircuit to double check our answers, which are identical to the app.

The next step was to set up the actual circuit and test our calculations. We obtained resistors and measured their actual resistances, then constructed a circuit based on the resistors.

After attaching the resistors to the breadboard, we again use the Analog Discovery to power the circuit and then attach a multimeter to measure the voltage drop across the load resistor.

Here we can see that our voltage is 52.3 mV, which does not match our calculated 54 mV.

Rather than recalcuating the values by hand, we modify the circuit in EveryCircuit and find the new expected voltage difference.

As one can see, our expected voltage drop is 52.5 mV while our actual is 52.3 mV.

Lastly in class, we are given a 10kOhm (really around 9kOhm) potentiometer. Professor Mason explain that the potentiometer, pot for short, has three prongs, and a band of resistive material in the the package. The middle prong has a varying resistance due to it being able to slide across the resistive material.

Here we attach the potentiometer to our breadboard and we measure the voltage drop across the potentiometer.

Here we have a chart of resistance values and our recorded voltage. We calculate the power from it using the formula P = V^2 / R.

We then plotted our values in Excel and found a reversed quadratic function.

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.