Day 15 (Day17 on notes)

Today we went over op amps in RC circuits, Did an Inverting Differentiator Lab, and learned about singularity functions.

The differentiator op amp is an op amp circuit where the output voltage is proportional to the rate of change of the input voltage. Also, any noise can result in high or low saturation.

The integrator op amp output voltage is proportional to the integral of the input voltage. This op amp can lead to saturation fairly quick so it requires a feedback resistor to be added.

Inverting Differentiator Lab:

The purpose of this lab is to test the behavior of the differentiator op amp. We will then compare measured output voltage with theoretical values.

The first picture is the input voltage of 1V at 1kHz and the bottom picture is the output voltage.

The first picture is the input voltage of 1V at 2kHz and the bottom picture is the output voltage.

The first picture is the input voltage of 1V at 500Hz and the bottom picture is the output voltage.

Above we see the theoretical output voltage amplitudes and in pink are the measured output voltage amplitudes. The large percent error may be due to the op amp having saturation. It can be noted that as we decreased the frequency of the input voltage, the percent error decreases so it may imply that our op amp is more efficient at lower frequencies. When taking this into account, we can conclude that the output voltage is proportional to the rate of change of the input voltage.

Above is an example of circuit analysis using singularity functions to approximate the current in the
RC circuit shown. Singularity functions are functions that are either discontinuous or have discontinuous derivatives.

Above is another example of circuit analysis that uses singularity functions.

Day 14 (Day16 on notes)

Today we learned a bit more about inductors and went over 1st order circuits. We also did a Passive RC Circuit Natural Response Lab and a Passive RL Circuit Natural Response Lab. 

Above we took a look at equivalent inductance that works like ohms laws for resistors.

We did a quick example of finding the time for a capacitor at 5V to drop to .01V which we see is about 6 seconds.

Passive RC Circuit Natural Response Lab:

The objective for this lab is to measure the response of a RC circuit when charging then manually disconnecting the power source to measure the voltage across the capacitor using an oscilloscope.

Above is our circuit set up for part b of the lab.

Part a) Here we have the capacitor fully charged at 3.5V then the voltage drop is recorded as the power source is shorted. The time constant is then measured by 36.8% of the fully charged voltage (1/e of the exponential curve).


Part b) Like in part a, we use the same method to calculate the time constant.

Above are the results we got for the lab. the large percent error in part b is expected because we were not able to switch the circuit manually fast enough to decrease error. Despite the lack of an efficient switch, we had expected to see a large uncertainty value in our results.

Above are examples of first order RL circuits. We were to find current and voltages as a function of time of the inductor and its time constant.

Passive RL Circuit Natural Response Lab.:
The purpose of this lab is to measure the response of a RL circuit and manually disconnecting the power source to measure the voltage across the inductor using an oscilloscope.

Since time in class was running out, the professor set up the circuit and displayed the oscilloscope measurements on the projector. We had made a prediction of the behavior of the voltage across the inductor (in green) with a square wave voltage input. The current (in blue) was then drawn based on the green graph.

Here is the voltage graph that was measured across the inductor which agrees with our predictions.


Here I included a table of equations from today's lecture.

Day 13 (Day15 on notes)

Today We learned about capacitors and RC circuits, did a lab on capacitor voltage-current relations, and learned inductors and also did a lab on inductor voltage-current relations.

Above we did an example where we had to find the energy stored in each capacitor and the voltage across each of the capacitors.

Capacitor Voltage-current Relations Lab:

The objective of this lab is to measure the relationship between then voltage difference across a capacitor and the current passing through it in an RC circuit when applying different types of time-varying signals.

Above we predicted what the current graph as a function of time will look like at the specified voltage function graph drawn in black.

Above is a our circuit layout and we are measuring the voltage across the capacitor.

From our oscilloscope, the input voltage is the sine wave at 1kHz and 2V in blue and the current is shown in orange.

This is our measurement of a 100Hz triangular wave at 4V in blue and current in orange.

This is our measurement of a 2kHz triangular wave at 2V in blue and current in orange.

Based on our results, we see that the current across the capacitor is not the cosine wave we had predicted. Since the capacitor is not able to charge and discharge quickly, we see that result in the current graphs. We also see this same effect in the triangular voltage input but is more "square" shaped as predicted. 

Above we do equivalent capacitance in a circuit that are like ohms laws but opposite. 

Above is a useful table or questions

Above is an example where we going current and energy in an inductor based on known voltage function and inductance.

Day 12 (Day14 on notes)

Today we looked a little further into cascaded op amps and did a lab where we design a temperature measurements system.

Here we took a look at a comparison of an op amp and a darlington transistor and looked at the over all gain that can be found as a product of individual gains.

Above we did an example for cascaded op amps where we needed to find the current i_0 as a function of v_0.

Temperature Measurement System Design Lab:
The objective of this lab is to design a temperature management system using a thermistor, a Wheatstone bridge, and an op amp. With these three components we will be able to make a system that can detect a voltage change.

Above we built a Wheatstone bridge circuit and used a potentiometer to balance the voltage change of the thermistor to be zero at room temperature. So if the thermistor heats up and decreases in resistance, we will be able to measure that voltage change.

Once the Wheatstone bridge was balanced, we added an op amp to the Wheatstone bridge to amplify the voltage change. Above we can see how the voltage change was amplified as we heated the thermistor to body temperature.

Day 10

Today we went over the different types of components we have used in the past ten class meetings and learned about op amps as well as did a lab with an op amp.

Above is a list of circuit components we have used so far.

Once we learned how op amps work, we treated the op amp as non ideal and redrew the circuit to incorporate as simplified internal to the original circuit. We then used nodal analysis to solve for the ratio of the output and source voltages.

Next we did the Inverting Voltage Amplifier Lab. The purpose of this lab is to examine how the input voltage is amplified using an OP27 op amp.

Above is our circuit layout and our data. We can see that the op amp has a voltage saturation limit at about 4.5V. The linear portion of the graph demonstrates the best operational range for this op amp. The percent error greatly increases when you go past the linear portion as expected.

Day 7

Today we did a Time Varying signals lab, a BJT Curve tracer lab, and learned the superposition, linearity, and source transformation analysis techniques.

The purpose of this lab is to learn how to use the Analog Discovery to apply and measure time varying signals as well as using the oscilloscope to measure the time varying signals.

Since the resistances are are equal, through voltage division we expect the output voltage to be half of the voltage source thus the voltage signals will be half of the amplitude. 

Here is a picture of our circuit layout.

The three images above are the measurements from the oscilloscope. Input voltages are as follows: sinusoidal = 2V at 2kHz, triangular = 3V at 1kHz, and rectangular = 2.5V at 500Hz. The amplitude on the sinusoidal wave was at the expected 1V and the same can be said for the triangular and rectangular waves as they too have half the input voltage amplitude.


Next we began the BJT Curve Tracer Lab. The objective of this lab is to find the collector current vs. collector voltage. We were given a 2N3904 transistor.

Above is the schematic we followed to build the circuit.

Using the waveform generator we created a Gummel plot of the combined collector and base currents vs. the base-emitter voltage as shown above.

Above we learned that in a linear circuit we can assume a voltage at V_0 and work backwards to calculate the voltage source. The fraction that we are off in our voltage is equal to the fraction we are off in the V_0.

Next we learned the superposition principle where we set a power source to zero then solve for current, then set the other power source to zero and find its corresponding current. We can then add up the currents for the true current of the original circuit.

Here we learned that we can transform sources based on the resistances to what an opposite equivalent power source if it were in series/parallel with that resistor to then simplify to a very simple equivalent circuit.

Day 8