Lab Day 25

During this day, we went over bode plots, which are plots in magnitude (decibels) and phase (degrees) of a transfer function versus frequency. The standard form of the Bode Plot contain many components: a gain K, a pole, a simple pole, and a quadratic pole. 

Here is a summary of rules when plotting Bode Plots:



This was the final blog entry for the class!!!

Lab Day 24

Signals With Multiple Frequency Components Lab 

In this lab we calculated the magnitude response of an electrical circuit and use this information to infer the effect of the circuit on some relatively complex input signals. We applied the following input signals types:

- a signal composed of multiple sinusoidal waves of different frequencies

- a sinusoidal signal with a time-varying frequency (aka sinusoidal sweep)

Here are the calculations for the pre-lab:

 This is a picture of our circuit:

Input voltage is a custom waveform: 20{sin(1000*pi*t)+sin(2000*pi*t)+sin(20000*pi*t)}:

 Here is the Vout across the resistor (blue) in comparison to the Vin (pink):

This is the calculation Theoretical vs Experimental with the %error.

In conclusion, we went over the transfer function, learned how to calculate gain and poles, and did a lab to see how input frequency affects the output graph.

Lab Day 23

Apparent and Power Factor Lab

The purpose of this lab was to use apparent power and power factor to quantify the AC power delivered to a load and the power dissipated by the process of transmitting this power. For the pre-lab we calculated the theoretical values of the circuit: Current, Voltage, Average Power, Apparent Power, and Power Factor.

For this circuit we will change RT values. All of the circuits will have the same input of 1V at 5Khz.

Here is the output of circuit at RT=47 Ohm.

For second part of lab we insert a 10 microF capacitor in parallel with Inductor and RL. Here is the output of circuit with input of 1V at 5Khz,

According to our experiment, higher RT value results in higher percent difference with theoretical value. However, with capacitor inserted into the circuit, the percent difference is lowered drastically. 

Lab Day 22

On this day we reviewed inductor and its parameters, went over average and maximum power calculation within AC circuits, and saw a demonstration to see how RMS values dictate maximum power of AC circuits. We did not have a lab for this day.

Lab Day 21

Inverting Voltage Amplifier Lab

In this lab assignment, we concerned with the steady-state response of electrical circuits to sinusoidal inputs. The input and output signals both have the same frequency, but the two signals can have different amplitudes and phase angles. We then measured the gain and phase responses of an inverting voltage amplifier circuit and compare these measurements with expectations bases on analysis. 

This is the pre-lab with the picture of the circuit. On the top right corner, we calculated the cutoff frequency of the circuit, the amplitude gain, and phase difference.

Picture of the 100Hz.

Picture of the 1KHz.

Picture of the 5KHz.

The chart of the bottom half shows the measurements to calculate the amplitude gain, phase difference, and it is compared with the results from the pre-lab with the %error.

OP Amp Relaxation Oscillator Lab

A "relaxation oscillator" is constructed by using some type of device that will act as a switch when a certain voltage is applied to one of its terminals. The "switching voltage" is usually the voltage across a capacitor that is being charged or discharged accordingly. 

We determined the value of R using the formula for the period T.

This is the picture of the circuit.

This is a picture showing the voltages for the OP Amp relaxation oscillator.

Lab Day 20

Phasors: Passive RL Circuit Response Lab

In this lab assignment, we measured the gain and phase responses of a passive RL circuit and compared these measurements with expectations based on analysis.

This is the pre-lab, where we showed that the amplitude gain and phase difference between the input voltage and input current are shown. Also the cutoff frequency for the circuit. 

This is a picture of our circuit.

We used the function generator to apply a sinusoidal input at Vin. The oscilloscope displayed both Vin and Vl.

We calculated the measured gains and phase differences between Iin and Vin for the three frequencies.

With the measurements we used to estimate the gain and phase difference between Vin and Iin and the gain and phase difference between Vl and Iin.

These results were compared with the value from the pre-lab, We do not have the ability to directly measure a time-varying current, so we used Iin=(Vin-Vl) / R

Lab Day 19

Impedance Lab

The purpose of this lab was to measured the impedance of three separate circuits and compare it with our calculated values. 

The output current from the 47 Ohm resistor and output voltage 100 Ohm resistor was measured.

This picture is showing the output at 10KHz.

The output current from the 47 Ohm resistor and output voltage from the microH was measured. 

This picture is showing the output at 10KHz.

 The output current from the 47 Ohm resistor and output voltage from the 0.1 microF was measured.

This picture is showing the output at 10KHz.

Here are the results from the three circuits, including their voltage and current measurements.

Conclusion: Today we went over impedance and admittance, and how to solve for them within circuits involving resistors, inductors, and capacitors.

Lab Day 18

Today we went over the components of a sinusoidal graph, learned that phasors are complex numbers that represent the amplitude and phase of sinusoidal graphs, and how to use phasors to determine sum of the magnitudes and angles. There was no lab during this day. (Function generator shown in class)

Lab Day 17

RLC Circuit Response Lab

In this lab, we emphasized modeling and testing of a second order circuit containing two resistors, a capacitor, and an inductor. The step response of the given circuit was analyzed and tested. The measured response of the circuit was compared with expectation values based on the damping ratio and natural frequency of the circuit.

This is the output of our circuit.

Pre-Lab

 We know the damping ratio by using  α = 1/2RC ω=1/(LC)^1/2  we can then calculate the damping ratio = α/ω.

In Lab

Since the capacitor and inductor in parallel, the damping ratio can be calculate by knowing the X% differently subtracting the voltage changing ratio of times the n is equal to -0.118 which is off a little.

Conclusion: Through this lab we can see how a huge discrepancy between theoretical and experimental values. This shows that what happens on paper doesn't always translate into real world phenomenons.

 

Lab Day 16

Series RLC Circuit Step Response

In this lab, we emphasized modeling and testing of  series RLC second order circuit. We analyzed and tested the step response of a given circuit. The measured response was compared with expectations based on the damping ratio and natural frequency. We then re-designed the circuit to make it critically damped without changing the frequency or DC gain. We also compared the results.

This is the pre-lab, which shows the differential equation relating Vout and Vin for the system. We then estimated the damping ratio, natural frequency, damped natural frequency and DC gain of the circuit. We also estimated the rise time and frequency of any oscillations that would expect to see in the step response of the circuit.

This is the output of our circuit.

This is the picture of our circuit.

Conclusion: Today we went over the basic principles of series RLC circuit, and did a lab to see how this type of circuit works when critically damped.

Lab Day 15

Inverting Differentiator Lab

In this lab assignment, we examined the forced response of a circuit which performs a differentiation, which is the circuit output derivative with respect to time of the input to the circuit. We then applied sinusoids of various frequencies to the circuit and compare the output with our expectations based on analysis. 

Picture of our pre-lab that determines the circuit output Vout as a function of the circuit input, Vin. The sinusoidal function we supplied is amplitude of 1 V, offset 0 and frequency 1kHz, 2kHz, and 500Hz.

Graph of frequency 1kHz Vout = 1.228V

Graph of frequency 2kHz Vout = 2.456V

Graph of frequency 500Hz Vout = 0.614V

The % error is then solve on this picture.

We measured the time difference between Vin and Vout using peak to peak method.

The time difference is 0.355 ms, then we can use it to calculate RC by applying to function Vout=RC dv/dt

Lab Day 14

Passive RC Circuit Natural Response Lab

In this lab assignment, we examined the natural response of a simple RC circuit. We used both manual switching operation and a square wave voltage source to create our circuit's natural response. We then saw the method used to create the response affects the circuit being measured.

This is the pre-lab, we estimated the initial capacitor voltage and the time constant for the circuits. Also the measured resistance and capacitor values.

This is an image of the oscilloscope window, showing the capacitor voltage for the first circuit, in which V+ is used as the voltage source.

This is the measured data and the calculated data from the pre-lab. The percent error is shown as 2.9% this is because the resistance values were a little off.

This is an image of the oscilloscope window, showing the capacitor voltage for the second circuit, in which the waveform generator is used as the voltage source.

This is the measured data and the calculated data from the pre-lab. The percent error is shown as 0.8% this is because the resistance values were a little off.

This is a picture of our circuit.