First Order RC and RL Circuits - Lab 6 | THTR 2, Lab Reports of Theatre

Download First Order RC and RL Circuits - Lab 6 | THTR 2 and more Lab Reports Theatre in PDF only on Docsity! ECE2A Fall 2008 Lab #6 6 First-Order RC and RL Circuits OBJECTIVES: To explore the concept of time constant and rise/fall times in simple RC and RL circuits, how to use the oscilloscope to make such measurements, and introduce the idea of differentiator, integrator, and frequency filtering circuits. PROCEDURE: Parts List: (1) 0.01 µF capacitor (1) 10mH inductor (1) Resistor decade box plus cables and clip leads for circuit construction. 1. RC Circuit Build the RC circuit shown below, using the decade box for the resistor, R, and a 0.01µF capacitor. Note that the 50Ω resistor is just shown for reference - it is actually inside the function generator. You can verify the capacitor value using the impedance meter in the lab. Drive the circuit with a function generator, initially set to a 1kHz square wave, with an amplitude of 2 Volts peak-to-peak. Be sure that the DC offset switch on the function generator is off (pushed in) and that the vertical scope inputs are DC coupled (not AC coupled). It will be convenient to view the input and output signals simultaneously on the oscilloscope screen, which is accomplished by the connections shown below. Set the vertical positions so that the 0 volt (ground) level is the center of the screen for both channels. 50Ω V g + Function Generator R Decade Box C To Oscilloscope Channel A To Oscilloscope Channel B V in + - V out + - Fig 1: First-order RC circuit for time-constant experiments 2 (a) RC Time Constant and Rise/Fall Time Starting with R=1kΩ, observe and record the input and output waveforms. They should be similar. Increase the resistance to 5kΩ, and record the resulting waveforms in your notebook. Calculate the time constant from this waveform, and compare with the theoretical prediction. Physically, the voltage across the capacitor rises more slowly as the resistance is increased because the flow of charge (ie. current) is reduced. Another figure of merit commonly used in such cases is the rise-time (τ r) or fall- time (τ f) , defined as the time it takes for the signal to progress from 10% to 90% of its final value. From the expression for the output voltage as a function of time, show that the rise time can be expressed as τ 10 - 90% = τ r = τ f = 2.2 RC. And verify this experimentally. The rise time can be conveniently measured by adjusting the vertical sensitivity so that the waveform fills the screen, as there are two dotted horizontal lines which mark the 10% and 90% levels. (b) The Circuit as an Integrator Now increase the resistor to 20kΩ. The time constant is now longer than the duration of the square pulse, so the output waveform does not quite reach its previous peak value. Increase the resistance again to 100kΩ, and record the resulting waveform in your notebook. You will probably have to adjust the vertical scale, since the peak amplitude will continue to shrink. Can you see what is happening? The output is now approximately a triangular wave, which is the integral of the input signal. Verify that the circuit is acting as an integrator by changing the input waveform to triangular and sine waves, making plots of both in your notebook. Change the scope from YT mode to XY mode (using the Display menu) and sketch the resulting figure. Can you explain the shape of this figure? Return to YT mode. Note that we have chosen to adjust the value of the resistance to observe the integrator behavior. We could alternatively keep the resistor fixed and change the frequency. At approximately what frequency will the circuit behave as an integrator for a resistor value of 10kΩ instead of 100kΩ? Verify your answer experimentally. (c) The Circuit as a Low-Pass Filter Although we will not discuss filters at length in ECE 2A, you can see that the simple RC circuit of figure 1 is a type of filter called a low-pass. It is so called because low frequency signals will pass through, but high frequency signals get strongly attenuated. This kind of circuit is used in stereo speakers to direct low frequency audio to the big "woofers". Plot the output voltage as a function of input frequency for a sine wave excitation over the range 100Hz to 100kHz, for R=5kΩ. Plot the result on a log scale in frequency.