EENG223 ELECTRIC CIRCUITS LAB EXPERIMENT IV FIRST-ORDER CIRCUITS Objectives: 1. To study the step response of a series R

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Eeng223 Electric Circuits Lab Experiment Iv First Order Circuits Objectives 1 To Study The Step Response Of A Series R 1 (30.78 KiB) Viewed 50 times

Eeng223 Electric Circuits Lab Experiment Iv First Order Circuits Objectives 1 To Study The Step Response Of A Series R 2 (40.65 KiB) Viewed 50 times

EENG223 ELECTRIC CIRCUITS LAB EXPERIMENT IV FIRST-ORDER CIRCUITS Objectives: 1. To study the step response of a series RC circuit using a square-wave input voltage. Preliminary Work: Step Response Consider the first order RC circuit shown in Figure 1. With ) being a symmetrical square-wave voltage having period 7 and amplitude , as shown in Figure 2(a), derive an expression for the capacitor voltage v.() in the first half-cycle, as shown in Figure 2(a), by following the procedure below: (a) Derive the differential equation (DE) for the capacitor voltagev, (f) valid in the interval 0<t<T/2, wherev,()=V. Note that the initial condition for this DE is v(0)-, which is still unknown. (b) Assume that the solution has the form v()= 4+ Be". Then substitute this into the DE and determine the unknown parameters A, B and a. (c) Find the unknown initial condition F, (in terms of the parameters R, C, T and V) by imposing the symmetry condition on the solution: v(7/2)=-(0)=V₂. (d) Find the time instant (in terms of R. C, T and V) at which the capacitor voltage becomes zero in the first half-cycle. (e) Calculate the numerical values of V, and to for 7-10 ms, 1-10 V, R-10 k2 and C=0.1 µF. R-104 W Figure 1 (0) C-0.1 F

V Figure 2 V₂ T/2 T Equipment: 1 signal generator (with square-wave), 1 resistor (10 kf2), 1 capacitor (0.1 µF), 1 oscilloscope. Experimental Procedure: Step Response (a) Construct the circuit shown in Figure 1. Adjust the signal generator output to symmetrical square-wave. Then adjust its amplitude to 10 V and its frequency to 100 Hz. (b) Connect the oscilloscope probes to the signal generator output and across the capacitor. (c) Obtain a steady trace on the oscilloscope screen with at least one complete cycle of the waveforms. Sketch the waveforms on paper or take a photo of the oscilloscope screen. (d) Measure the voltage V, and the time instant , at which the capacitor voltage becomes zero. Evaluation of Experimental Results: Step Response (a) Compare the measured and calculated values of f, and V. (b) Using the measured value of V, and the expression obtained in part 1(c) of the Preliminary Work, calculate the time constant t of the circuit, and compare it with the theoretical value r -RC-10 kfx 0.1 µF-1 ms. Discussion: State whether or not the measured results in the step response of the RC circuit are in agreement. with the theoretical analysis results. Comment on the possible sources of discrepancy between theory and experiment. Conclusion State any conclusions that you may draw from this experiment regarding the connection between theory and practice. Also, discuss whether experimental results can be used to justify the mathematical models of resistors and capacitors.