STUDY OF RC AND RL CIRCUITS Venue: Microelectronics Laboratory in E2 L2

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1 EXPERIMENT #1 STUDY OF RC AND RL CIRCUITS Venue: Microelectronics Laboratory in E2 L2 I. INTRODUCTION This laboratory is about verifying the transient behavior of RC and RL circuits. You need to revise the natural and step response of RC and RL circuits you have covered in lectures. The charging and discharging of capacitor through a resistance is verified first, finding out its theoretical value of time constant which is verified by practical calculations. The magnetizing and demagnetizing of a coil through a resistance is verified first, finding out it s the theoretical of its time constant which is verified by practical calculations. II. PRE-LAB Do the ORCAD simulations of both RC and RL circuits, calculate time constants and plot the resulting waveforms across C (in the case of RC) and the waveform of the current in the case of RL. In the ORCAD, use VPULSE as the Vs and set V1=5V, V2=-5V, TD=0, TR=0, TF=0, PER=1/FREQUENCY and PW=0.5*PER Use the following specifications while verifying the RC of Fig # in ORCAD C uf R Ohm Vs 10.0 Vpp TYPE = SQUARE WAVE FREQUENCY = 20 khz OFFSET = 0 Use the following specifications while verifying the RC of Fig # in PSPICE L1 10 mh R Ohm Vs 10.0 Vpp TYPE = SQUARE WAVE FREQUENCY = 20 khz OFFSET = 0 ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

2 III. EXPERIMENTAL METHOD Equipment Required: Square-wave generator, discrete circuit components of R1=3000Ω, L1=470uH and C1=1000pF, oscilloscope and square-wave generator Fig #1 Fig #2 IV. MEASUREMENT AND READIGNS Here derive the equation for the above vc(t) and vr(t), and plot them using MATLAB to see if they are the same as the ones obtained PSPICE and the oscilloscope in II and III respectively. From the plots in II and III find out how long (in time constant, τ) does it take for the vc(t) and vr(t) to get to 95 % of their maximum (or come down to 5 % of minimum) of their minimum values. Show with changing values of R, the resultant waveforms and effect on them. V. CONSLUSIONS Varying R in RC circuit results in what? Varying R in RL circuit results in what? How much the voltage across a charged capacitor is reduced to after one time constant, RC? How much the voltage across a resistor in RL circuit is reduced to after one time constant, L/R? ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

3 EXPERIMENT II STUDY OF RLC TRANSIENT RESPONSE Venue: Microelectronics Laboratory in E2 L2 I. INTRODUCTION This laboratory is aimed at enabling students on how to use the function generator for generating a step input with an appropriate repetition rate, to an oscilloscope to measure RLC overdamped and underdamped responses. II. PRE-LAB Write and run a PSPICE program for the circuit shown in Figure 1. In the VPULSE model, make V1=-5V, V2=5V, PW=10ms and PER= 15ms, plot the voltage across the capacitor from 0 to 5 ms in 0.1 ms increments. Print the Netlist output file and the Output waveform and attach. Write and run a PSPICE program for the circuit in Figure 2. Plot the voltage across the capacitor from 0 to 5 ms in 0.1 ms increments. Print the Netlist output file and the Output waveform and attach. Use the program above to also analyze the resistor voltage, plot the voltage across the resistor from 0 to 5 ms in 0.1 ms increments. Print the Output waveform and attach. III. BACKGROUND A series RLC circuit can be modeled as a second order differential equation, having solution under the three conditions for its roots. When its roots are real and equal, the circuit response to a step input is called Critically Damped. When its roots are real but unequal the circuit response is Over-damped. When roots are a complex conjugate pair, the circuit response is labeled Under-damped. IV. EXPERIMENTAL METHOD, MEASUREMENT AND READINGS In this experiment only the over-damped and under-damped responses are studied, the critically damped is just another form of over-damped response. ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

4 EQUIPMENT REQUIRED: Oscilloscope, Function generator, Resistor, 100 Ω, Resistor, 1.0 kω, Capacitor, 1.0 µf, Inductor, 220 mh OVER-DAMPED RLC CAPACITOR VOLTAGE SETP RESPONSE: With the RLC circuit disconnected, adjust the function generator to produce a repetitive pulse that is -5 volts for about 10 ms, then +5 volts for about 10 ms. (i.e. 10 Volts peak-to-peak, 0 Volts of DC offset, 20 ms Period or 50 Hz). For the circuit in Figure 1, calculate the output response, VC(t), t > 0, to an input step, from -5 to +5 Volts. Connect the circuit in Figure 1. Measure the final value, VC(t= ), and the initial value, VC(t=0+), from the oscilloscope and record in the Data section. Also measure the voltages VC(t=0.5 ms), VC(t=1.0 ms), and VC(t=2.0 ms) from the oscilloscope and record in the Data section. First determine α and ω0. Calculate the roots of the characteristic equation, S1, 2 and determine Vc(0), and Vc( ), and d[vc(0)]/dt. Calculate A1 and A2, and fill in the Data Table for Figure 1 below: ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

5 Quantity α DATA TABLE I OVERDAMPED RLC Calculated Value Measured Value ω 0. S1, 2 Vc(0) d[vc(0)]/dt Vc( ) A1 and A2, Equation for Vc(t) Vc(0.5ms) Vc(1ms) Vc(2ms) UNDER-DAMPED RLC CAPACITOR VOLTAGE SETP RESPONSE: Keep the function generator settings used in Part 1. For the circuit in Figure 2, calculate the output response, VC(t), t > 0, to an input step, from -5 to +5 Volts. Note that the only change to the circuit is replacing the 1 k-ohm resistor with a 100 Ohm resistor. FIGURE 2: Underdamped RLC Circuit with Step Input ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

6 First determine α and ω0. Calculate the roots of the characteristic equation, S1, 2 and determine Vc(0), and Vc( ), and d[vc(0)]/dt. Calculate A1 and A2, and fill in the Data Table for Figure 1 below: Quantity α DATA TABLE II UNDERDAMPED RLC Calculated Value Measured Value ω0 S1, 2, ωd Vc(0) d[vc(0)]/dt Vc( ) A1 and A2, Equation for Vc(t) Vc(0.5ms) Vc(1ms) Vc(2ms) V. CONCLUSIONS ECE Lab1 ECE 2201 SEMESTER II, 2011/2012

7 EXPERIMENT III RESONANCE IN RLC CIRCUITS Venue: Microelectronics Laboratory in E2 L2 I. INTRODUCTION This laboratory is about studying resonance in RLC series and parallel circuits. This experiment will be used to examine the sinusoidal frequency response of the series and parallel to see at what frequency the current through an RLC series becomes or the voltage across a parallel RLC circuit reaches maximum value. A network is in resonance when the voltage and current at the network input terminals are in phase and the input impedance of the network is purely resistive. II. PRE-LAB Do the ORCAD simulations of both RLC parallel and RLC series circuits. III. EXPERIMENTAL METHOD, MEASUREMENT AND READINGS Consider the Parallel RLC circuit of figure 1. The steady-state admittance offered by the circuit is: Y = 1/R + j( ωc 1/ωL) Resonance occurs when the voltage and current at the input terminals are in phase. This corresponds to a purely real admittance, so that the necessary condition is given by ωc 1/ωL = 0 ECE Lab III ECE 2201 SEMESTER II, 2011/2012

8 The resonant condition may be achieved by adjusting L, C, or ω. Keeping L and C constant, the resonant frequency ωo is given by: Equipment Required: Square-wave generator, discrete circuit components of R=1 KΩ, L= 27mH and C=1uF, oscilloscope and square-wave generator. Set up the RLC circuit as shown in Figure 1 Figure 1 Apply a 4.0 V (peak-to-peak) sinusoidal wave as input voltage to the circuit. Set the Source on Channel A of the oscilloscope, and the voltage across the ca[pcitance on Channel B of the oscilloscope. Vary the frequency of the sine-wave on signal generator from 500Hz to 2 KHz in small steps, until at a certain frequency the output of the circuit on Channel B, is maximum. This gives the resonant frequency of the circuit. ECE Lab III ECE 2201 SEMESTER II, 2011/2012

9 DATA TABLE I PARALLEL RESONANCE f 500 Hz 600 Hz C R L Vo V(t) reading Repeat the experiment using for the series resonant circuitry in Figure 2, and use L = and C = and R = 1 KΩ. The Vo voltage on the resistor is proportional to the series RLC circuit current. Figure 2 ECE Lab III ECE 2201 SEMESTER II, 2011/2012

10 DATA TABLE Ii SERIES RESONANCE f 500 Hz 600 Hz C R L Vo V(t) reading IV. CONCLUSIONS Find the resonant frequency using equation given in the before and compare it to the experimental value in both cases. Plot the voltage response of the circuit and obtain the bandwidth from the half-power frequencies using equation. ECE Lab III ECE 2201 SEMESTER II, 2011/2012

11 EXPERIMENT IV VERIFYING FREQUENCY RESPONSE OF ACTIVE FILTERS Venue: Microelectronics Laboratory in E2 L2 I. INTRODUCTION Filters are also called frequency-selective circuits as they are able to filter some of the input signals on the basis of frequency. They are categorized as passive or active filters the former are making use of resistors, inductors and capacitors, while the latter are making use of the OP-AMPs. The responses are obtained and plotted for both of. II. PRE-LAB Do the ORCAD simulations of Low Pass and High-Pass Filters shown below. III. EXPERIMENTAL METHOD, MEASUREMENT AND READINGS Construct the low-pass and high-pass filters of Fig. 1 and Fig. 2. Note that C2 of the lowpass filter consists of two 0.01 mf capacitors in parallel. The two 1.0 mf tantalum power-supply bypass capacitors are to be used on all circuits in this laboratory procedure. Characterize the responses of the low-pass filter and of the high-pass filter for frequencies from 10 Hz to 10 khz. ECE Lab IV ECE 2201 SEMESTER II, 2011/2012

12 DATA TABLE I LOWPASS FILTER f 10Hz 500Hz 1000 Hz 2000 Hz 3000 Hz 4000 Hz 5000 Hz 6000 Hz 7000 Hz 8000 Hz 9000 Hz Hz Vi(t) Vo Fixed ECE Lab IV ECE 2201 SEMESTER II, 2011/2012

13 DATA TABLE II HIGHPASS FILTER f 10Hz 500Hz 1000 Hz 2000 Hz 3000 Hz 4000 Hz 5000 Hz 6000 Hz 7000 Hz 8000 Hz 9000 Hz Hz Vi(t) Vo Fixed IV. CONCLUSIONS Find the cutoff frequencies of both of the circuits; obtain the readings and using exel plot the data of the above two to show they are working as LOWPASS and HIGHPASS filter. Plot the voltage response of the circuit and obtain the bandwidth from the half-power frequencies using equation. ECE Lab IV ECE 2201 SEMESTER II, 2011/2012