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ELECTRICAL AND COMPUTER ENGINEERING EECE 263 – Basic Circuit Analysis Lab #3 – Single time constant circuits Purpose The purpose of this lab is to observe the behaviour of single time constant RL and RC circuits. Equipment The main pieces of equipment will be the function generator, oscilloscope, breadboard, and various circuit components. Reference Chart for Resistor Values Experiments Please record your results on the summary sheet provided. Part A – RC Circuit Build the following circuit on your breadboard. Start with values of R = 1kΩ and C = 47nF. For the function generator, set up a 1kHz square wave with an amplitude of 1V (2 volts peak-topeak). Rotate the AMPL knob on the function generator’s front panel and use the oscilloscope to help set the input. Use the oscilloscope to obtain a signal at the output of the function generator on one channel and a signal across the capacitor (Vout) on the second channel. Adjust the time scale so that you have only a few cycles of the square wave on the screen. Sketch what you see on the summary sheets. Adjust the time scale so that you have only one period of the square wave on the screen and measure the time constant. Then calculate the expected time constant. Record both on the summary sheet. What is the value of “Vout” after 5 time constants? Next, exchange the capacitor for two different values, one higher and one lower than the original value (for example, 10nF and 100nF). At this point you may wish to change the time-scale on the oscilloscope to see the changes better. Sketch the resulting waveforms on the summary sheets and briefly explain your observations. Part B – RL Circuit Build the following circuit on your breadboard. Start with values of R = 1kΩ and L = 2.2mH. For the function generator, set up a 10kHz square wave with an amplitude of 1V. Use the oscilloscope to obtain a signal at the output of the function generator on one channel and a signal across the inductor (Vout) on the second channel. Adjust the time scale so that you have only a few cycles of the square wave on the screen. Sketch what you see on the summary sheets. Adjust the time scale so that you have only one period of the square wave on the screen and measure the time constant. Then calculate the expected time constant. Record both on the summary sheet. What is the value of “Vout” after 5 time constants? Next, exchange the resistor for two different values, one higher and one lower than the original value (say, 330Ω and 2.7kΩ). At this point you may wish to change the time-scale on the oscilloscope to see the changes better. Sketch the resulting waveforms on the summary sheets and briefly explain your observations. Part C – Simple Filter Circuit This section is not really one of the topics that we will study in class, but I thought you might like to examine a simple but effective filter circuit. Build the following circuit on your breadboard: Attach the oscilloscope probes across the 1nF capacitor. Set the function generator to produce a sine wave with a 1 volt amplitude. Use the same procedure as in part A, but with the function generator set to the sine wave output. Start with a 1kHz signal and measure the amplitude of the output signal. Then, decrease the frequency of the output from the function generator by factors of 10, each time measuring the amplitude of the output signal. Repeat until you get down to 1 Hz. Record your results on the summary sheet. Now, increase the frequency to 10kHz, and measure the amplitude of the output signal. Finally, increase the frequency by factors of 10 and record the amplitude of the output signal at each step. Repeat until you get up to 1 MHz. Plot your results on the summary sheet. You should see three distinctive regions on your graph. What do you think is happening at low, medium, and high frequencies? This type of circuit is called a bandpass filter. It rejects low and high frequencies (For instance by using the appropriate resistor and capacitor combination, as you see in this example), but allows the medium range frequency signals to pass through to the output. The values of the resistors and capacitors determine the low and high frequency cut-off points. Later in the term we will learn more about the behavior of inductors and capacitors driven by sinusoidal signals of different frequencies. This behavior is complex in nature, and is a function of the frequency of the signal applied. Instead of a resistance, we measure the way that capacitors and inductors allow or resist the flow of current using a measure known as impedance , where f is the frequency and C is the (Z). Capacitors have an impedance of = capacitance. When the denominator of the expression for Z approaches 0, as in the case of a DC voltage, the magnitude of Z approaches infinity. In other words, the capacitor impeded the flow of current. Therefore it behaves like an open circuit. Also, it behaves like a “short” circuit when the frequency is high enough to make the “2πfC” a very large number, and hence, the impedance negligible. At midband frequencies, the capacitors in this circuit have finite impedances, and the behavior of the circuit is based on the values of these impedance in series or parallel with the other circuit components. For example, at 1kHz, the impedance of the 1µF capacitor is equal to: 1 1 = ≈ 160Ω j2πfC 2π ∗ 1k ∗ 1μ And for the 1nf capacitor: 1 1 = ≈ 160kΩ j2πfC 2π ∗ 1k ∗ 1n So, using the voltage division equation, it is possible to calculate the amplitude of Vout at this frequency. Now, based on the above example and your own results, draw the effective circuit for DC, a midband frequency, and in the limit as the frequency approaches ∞. Note that these circuits will have just resistors. They “may” have short or open circuits as well.