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.

Lab Day 13

Capacitor Voltage-Current Relations Lab

In this lab assignment, we measured the relationship between the voltage difference across a capacitor and the current passing through it. We applied several types of time varying signals to a series combination of a resistor of 100 ohms and a capacitor of 1 microF. The voltage difference across the resistor, provided an estimate of the current through the capacitor. This current can be related to the voltage difference across the capacitor. 

This is a picture of the circuit.

This is the pre-lab. The top graph shows a sinusoidal wave of the capacitor voltage and current. The bottom graph show a triangular wave of the capacitor voltage and current.

This is an image of the capacitor current for a 1kHz sinusoidal input. 

This is an image of the capacitor current for a 2kHz sinusoidal input. 

This is an image of the capacitor current for a 100Hz triangular input. 

This is an image of the math channel to calculate current from resistor's voltage for a 1kHz sinusoidal input. 

This is an image of the math channel to calculate current from resistor's voltage for a 2kHz sinusoidal input. 

This is an image of the math channel to calculate current from resistor's voltage for a 100Hz triangular input. 

Lab Day 12

Temperature Measurement System Design Lab 

In this lab assignment, we designed a simple temperature system which outputs a DC voltage which indicates temperature. Our system will use a thermistor to indicate the temperature. We used a Wheatstone bridge circuit to convert this resistance change to a voltage change. The voltage output of the Wheatstone bridge circuit was small relative to the amount of temperature change, so we used a difference amplifier to increase the overall sensitivity of the temperature measurement system. 

These two pictures are our circuit with the thermistor and potential transistor.  

To make the lab work we were required to test each system individually and on the Wheatstone bridge we had to make Vab as close to zero because we wanted to know the value of Vout when we increase the thermistor temperature. On the difference amplifier we built it in the same circuit as the previous lab which was with 4 same resistor to connect the amplifier and we were supposed to get Vout=Vb-Va and with a supply power Vb with 2V and Va with 1V we got Vab=0.996V. 

After we connected the two circuits together and hold the thermistor to see the Vab change by the ratio Vout=R2/R1 (Vb- Va)

This is a video showing our working circuit.

In conclusion: The ratio did not come out with Vf=10times of Vi but the voltage did increase when the thermistor was hold with our fingers.