Step Response of an RC Circuit ECE 2100 Circuit Analysis Laboratory updated 8 January 2008 Pre-Laboratory Assignment Consider the circuit of Figure 1. The voltage source Vs and resistance Rs comprise a circuit model of a function generator. 1. Find the circuit time constant τ for t≥0. Assuming that the capacitor is initially uncharged, find and accurately sketch vR(t) and vC(t) for t≥0. Calculate vR(t) and vC(t) for t = 0, τ, 2τ, 3τ, 4τ, and 5τ seconds. Put your results in a table under the hand analysis column: hand analysis simulation experimental % vC error (SIM vs. HA) % vC error (EXP vs. HA) vRvCvRvCvC t 0 τ 2τ 3τ 4τ 5τ Table 1. RC Circuit Data Table Find the 10-90% rise time of vC(t) (this is the time required for vC(t) to transition from 10% (0.5V) to 90% (4.5V) of its final value). 1Figure 1. RC Circuit 2. In order to simulate and physically realize the circuit of Figure 1, the circuit of Figure 2 will be used, in which the switch action is simulated by using a square wave voltage source. Using your SPICE engine, simulate the circuit of Figure 2. Your output will look like Figure 3. Figure 2. RC Circuit with Square Wave Voltage Source 2Figure 3. RC Circuit Simulation Results When the voltage source is at +5V, a closed switch is simulated; a voltage source value of 0V is used to discharge the capacitor. 3. Note that the XY location of the cursor is displayed at the lower left-hand corner of the plot window. Use that feature to fill in the simulation columns of Table 1. Find the simulated 10-90% rise time of vC(t). Procedures 1. Determine the output resistance of the function generator Rs by setting the function generator to produce a 50 Hz square wave ranging from 0 to 5V as in Figure 3. Next, connect a decade resistance box to the function generator. Begin with 500Ω and decrease the resistance until 50% of the open circuit voltage is observed. Use the results to determine Rs. 2. Construct the circuit of Figure 2. Before connecting the function generator verify that the open circuit voltage provided by the function generator is still a 50 Hz square wave ranging from 0 to 5V as in Figure 3. Print out or sketch voltages Vs(t) and vC(t) for the RC circuit. 3. Carefully measure the values needed to complete Table 1 (experimental column). Find the experimental 10-90% rise time of vC(t). 4. Change R1 to a 10 kΩ resistor. Document and explain the change in vC(t). 3Analysis 1. Compare the hand analysis, simulated, and experimental results for the 10-90% rise time of vC(t). Credits and Copyright Adapted from material developed by current and former ECE faculty, including Professor Joseph Kelemen. © 2008 Damon A. Miller. All rights reserved.