Day 8: Thevenin's Theorem

Lab 8: Thevenin's Theorem

Thevenin's Theorem takes the argument that an entire circuit can be simplified into a singular resistance and then analyzed for the load on it.

Prelab

My team was asked to find the Thevenin equivalent circuit, which consisted of both the R(thevenin) and the circuit voltage V(oc) at the two terminals a and b (top left and right corners of circuit).

This is done by first "muting" all power sources by shorting all voltages sources and opening all current courses. Afterwards, we use our resistor calculating methods to find a single "Thevenin resistance" that can act as the circuit. From there, we analyzed the circuit to find a "Thevenin Voltage".

Both of these can be seen at the bottom right.
R(TH) = 7.699k Ohms
V(TH) = 0.46 V

Procedure:

After setting up the circuit seen above, we took a resistance measurement for the entire thing to confirm it aligned with our calculated value over the terminals A and B.

Measured R(TH) = 7.57k Ohms

We also measured the V(TH) on the circuit

The value gathered is really close to the theoretical value we got!
V(TH) = 0.447V

We decided it was a good time to calculate the percent error between the two Thevenin values and how far we were from the actual.

Okay so, not bad! We were within 3% or so on each value.

We then placed a Potentiometer (9.66k ohms max) in the place of the load resistance and varied the value of R(Load) while measuring voltage across it.

Choosing a random resistance (8.12k Ohms) we calculated the 

Day 7: Super Positition

Lab 7: Super Position II

In this lab, my team and I analyzed a circuit with multiple voltage sources and utilized the Super Position method. This method essentially simplifies the circuit by drawing focus to one source and its effects on the system. By analyzing each of them individually, we can come to a complete conclusion by adding the separate results find.

Prelab

To put this into practice, we first were given a circuit to analyze on paper (whiteboard). The goal for this analysis was to find the value of V over the "6.8K" resistor.

The circled values are the actual values of the resistors that we were given. This will play into our results later.

Using the ideal values, however, we carried out our analysis of the circuit using superposition techniques. The diagram drawn on the whiteboard is the "3V" version where the 5V supply has been shorted out (replaced by a wire with no resistance). Analyzing the "5V" version and adding it gave us our answer.

From our findings, we had gotten that the voltage over the resistor was theoretically going to be 2.703V

Live Trial

After obtaining the necessary materials, my team and I put together a working circuit based on the design in the prelab. For future experimental calculation, we measured the actual resistances of each element (shown in prelab).

We then connected only one voltage source and measured the value of V from its version of the circuit.

An actual value of V(3V) = .695V is attained!

Now the same procedure is practiced with the 5V supply!

V(5V) = 1.99V actual!

Now for the final procedure...BOTH SUPPLIES!

As suspected, the value is pretty darn close!

V = 2.69V

Making a table of these values, we can see just how close we were to ideal!

All values are within 2%, which my team and I agreed was within the acceptable range for results.

Summary

To sum up, the principle of Superposition is one that takes focus on a singular source and analyzes the effect it causes on the circuit. From the live trial, we can see that the calculated results line up quite closely to the experimental results. Professor Mason made an astute remark by saying that superposition is a lot of easy work, as compared to other methods, that are a little bit of hard work. It is definitely a method I will consider, come exam time.

Day 6: Mesh/Nodal Analysis

Lab 6: Nodal Analysis

In this lab, we used nodal analysis techniques to predict circuit behavior, built said design on a bread board, and tested it for reliability with multimeters during live trials.

Prelab:

The entire procedure was basically a textbook nodal analysis problem, with the objective to find two voltages V1 and V2.

From this we found that our values were:

V1 = 2.268V

V2 = 4.268V

We then built the physical test circuit for the design seen above.

Kind of cramped, but it's true to the diagram!

After running it from the Analog Discovery kit and using two wires as probes...

Voltage over resistor 1 (V1)

Voltage over resistor 2 (V2)

After viewing the live values, we took into consideration the factors that could have attributed to them.

We measured the actual resistances of each resistor used in the lab and marked the voltages across each.

We then calculated the percent error from the theoretical value calculated and the live value we tested:

Summary:

This lab has essentially proven the effectiveness of nodal analysis from conception of a design to its testing. The values gotten from the live trial indicate that even with the tolerances set in the mass produced resistor values, one can still rely on the proposed values to appear within 1%.

Lecture:

After the lab, we learned about Mesh Analysis and its benefits.

It is basically using KVL in separate "meshes" or loops. By taking the system of equations that arises from both loops, we can find values for each current.

This is another example of using a mesh analysis technique in a larger circuit.

Day 5: Temperature Measurement System

Lab 5: Temperature Measurement System

Purpose/Prelab:

This lab was our first design centered challenge in which we had to develop a circuit that increase V(out) with a variable resistance. More specifically we had a set of criteria to meet:

• +5 voltage input to the system
• Output voltage varies by a minimum of 0.5V over a temperature range of 25 - 37 degrees celsius
• Output voltage must increase as temperature increases

In order to achieve these specifications a circuit element called a Thermistor was used rather than a standard potentiometer.

A thermistor is basically a resistor whose resistance value changes with temperature changes within it! The specific model we used was a negative one that decreased the resistance value the higher the temperature got.

Preliminary schematic of circuit

Using a handy chart supplied to us regarding the thermistor, we were able to find the predicable resistances associated with that temperature. 

Chart of decreasing resistance with increased temperature

The only thing needed after that was to find a fixed value of R to use aside the variable R(Thermistor)

After some voltage divider algebra, we found a value we were satisfied with!

We had calculated that the value of the fixed resistor was to be between 4.67k - 17.63k Ohms. Since that would not be an easy part to find in the lab, we were directed to a more realistic value of 10k ohms.

Procedure:

We first measured our thermistor to get some realistic R values from room temp to human touch temp (37 degrees Celsius)

Real value of R(Thermistor) at room temp (10.95K Ohms)

Physically touching unit to get applicable resistance (6.40K Ohms)

We then measured the fixed Resistor value (expected 10K) and put together the circuit for implementation.

Measuring R of fixed resistor (9.95K Ohms)

Prototype circuit built

Observing the V(out) values from the circuit in the footage, we can see that the resistance from the thermistor decreases the longer it is touched.

From this we obtain the values:

V(25 Degrees Celsius) = 2.41 V

V(37 Degrees Celsius) = 2.93 V

This confirms that we met the 2nd requirement for the change in voltage to be at least 0.5 V between our target temperatures.

Calculating a percentage error:

[(Experimental - Theoretical)/Theoretical]*100%

Where the experimental value is the actual change in voltage in the circuit.

Experimental = 2.93V - 2.41V = 0.52V

[(0.52V - 0.5V)/0.5]*100% = 4.00%

Lecture:

Today, we learned about Nodal analysis and it's benefits/process.

Using this we found the voltages contained at specific nodes in the circuit.

Further, if we analyze another styled circuit we can see that nodes can be combined to make nodal analysis easier.

Day 2: Resistors and Ohm's Law - Voltage-Current Characteristics

Lab 2: Resistors and Ohm's Law - Voltage-Current Characteristics

Purpose:

The purpose of this lab was to exercise our knowledge of Ohm's Law and how to use it. This was done by utilizing a resistor (100 Ohms), a multimeter, the analog discovery device, and a power supply.

Tools used in experiment

Procedure:

By setting up a simple circuit that connected the power supply to the resistor, we could measure the amount of voltage and current going circulating. This would help us understand and confirm Ohm's law a bit better.

Schematic for circuit to test Ohm's Law

After organizing the circuit, we had to get an actual reading of the resistance value of the resistor to use in calculations. Using the multimeter set to read Ohms, we verified that it was within reasonable tolerances for use (100.3 Ohms).

Measuring actual resistance

We tested a variety of Voltages from the power supply (these were already set on the supply, but we used a multimeter to test the applied levels) and made sure to read the currents that correlated (shown below).

2.97V

4.51V

5.99V

7.44V

8.98V

11.98V

Data:

From those readings we were able to put together a table for analyzing:

Summary:

By setting up a scenario in which a rated resistor was put under a specific level of voltage, we could measure and make a data analysis of its behavior. Using Ohm's Law:

A resistance can also be found and verify our trust in the equation. Further proof of this is seen in the linear trendline in the graph above.

Day 3: Dependent Sources and MOSFETs

Lab 3: Dependent Sources and MOSFETs

Procedure

Materials used in lab (Not pictured, laptop)

Schematic to build for testing MOSFET behavior

Testing actual resistance of 100 Ohm resistor

Breadboard of circuit including MOSFET and ANALOG Discovery

After building the circuit, we needed to test the relation of the dependency on the MOSFET in order to properly analyze it.

Beginning test for threshold by adding applying voltage to MOSFET gate until current increases.

Left DMM is for gate voltage applied, Right DMM is for current through MOSFET 

Increasing V(gate)

Huge spike in Current once threshold of approx 2.20V(gate) is acheived.

Increasing to higher V(gate) does very little in comparison.

It can be deduced that the threshold for which the MOSFET allows current to flow is approx. 2.20V on the Gate. This can be further seen in the data chart and graph of said data.

After obtaining a threshold voltage to begin a more aware procedure, we begin testing increments of 0.5V from 2 to 5.

Beginning procedure to characterize gate voltage and drain current.

V(gate) will begin at 2.00V for collection of data.

Increments of 0.5V were added to V(gate) for smoother plots.

Until a maximum of 5V is achieved by the Analog Discovery unit.

Analysis/Summary:

 The transistor is behaving in the manner that a Voltage Controlled Current Source would. In other words, the MOSFET will not allow any current through itself unless a specific magnitude of Voltage is applied to its Gate.

To calculate the value of g, we need to use the following formula for a Field Effect Transistor.

Where I(d) is the drain current, V(gs) is the voltage to the gate from the source, and V(t) is the threshold voltage we found. Using the last row as our values:

g = 2(35.6)/(5.00 - 2.20) = 71.2/2.80 = 25.43 milliSiemens