ENGR 203 Spring 2005 Laboratory Experiment I: RC Circuit Step Response, Lab Reports of Engineering

Download ENGR 203 Spring 2005 Laboratory Experiment I: RC Circuit Step Response and more Lab Reports Engineering in PDF only on Docsity! ENGR 203 Spring 2005 Laboratory Experiment I April 21/22 2005 Due Date: April 28 or 29, 2005 Consider the following first-order RC circuit: Circuit response to a rectangular pulse (step response): Before proceeding with the lab experiment, obtain the value of the source resistance Rs (function generator). Using a 0 – 1 volt (zero-to-peak unipolar) square waveform with a 50% duty cycle (half of the time on and half of the time off) from the function generator as the input vi(t), With the oscilloscope, measure, observe, and record the voltage across resistor R, during one complete cycle of the period of repetition only, when the frequency of the waveform is: a) 10 kHz, b) 5 kHz, c) 2 kHz, and d) 1 kHz. You can use Excel to transfer the data points from the scope’s display to a file, in order to plot them later. Post-lab work and Questions: 1 Using the time-domain physical models of the resistor and the capacitor, assuming zero initial voltage across the capacitor, obtain analytically the equation that governs the behavior of the output voltage v0(t) for the lab experiment. 2 In the time-domain, solve the differential equation you derived in part 1 and obtain v0(t) when vi(t) is equal to u(t) – u(t-T/2) volts, where T is the period of repetition of the input waveform. 3 Evaluate (over an appropriate length of time) and plot (using MATLAB) v0(t) for T = 100 μsec, 200 μsec, 500 μsec, and 1 msec. 4 Using Matlab, plot the experimental data obtained in the lab. 5 Compare your analytical results with those obtained experimentally. 6 Analytically, what is the time constant of the experiment circuit configuration? What is its numerical value? What effect does Rs have on the circuit’s time constant? 7 How long does it take for the output voltage to reach the final value for the circuit configuration? How many time constants are more or less required for this to happen?