Department of Electrical & Computer Engineering Technology. EET 3086C Circuit Analysis Laboratory Experiments. Masood Ejaz

Transcription

1 Department of Electrical & Computer Engineering Technology EET 3086C Circuit Analysis Laboratory Experiments Masood Ejaz

2 Experiment # 1 DC Measurements of a Resistive Circuit and Proof of Thevenin Theorem Prelab: Solve the circuits theoretically (steps 1, 2, and 3) and then perform PSpice simulations to fill out appropriate tables under procedure section. Objective: To build a resistive circuit and its Thevenin equivalent to prove their equivalency for the load. Procedure: 1. Build the following resistive circuit on the breadboard and measure the indicated variables R1 1.0k R3 3.0k R5 1.0k V1 10 V R2 2.0k R4 4.7k R6 2.2k Figure 1: Resistive Circuit for Step 1 Theory Simulation Lab V R4 I R3 V R6 I R6 2. Suppose your load is comprised of resistors R4, R5, and R6. Draw the Thevenin equivalent circuit and then build it on the breadboard. Measure load current and load voltage and compare them to the corresponding values that you obtained in step 1 to show the equivalency of both the circuits for this load (Note: if exact value of R TH is not available, use the closest value or make a series combination of resistors to get to the closest value) V TH = ; R TH = 2

3 Thevenin Circuit Theory Simulation Lab V LOAD I LOAD 3. Now assume that load is just resistor R6. Repeat step 2. V TH = ; R TH = Thevenin Circuit Theory Simulation Lab V LOAD I LOAD 3

4 Discussion: You lab report discussion should include an explanation and importance of Thevenin theorem and explanation of your Thevenin equivalent circuits. If there is any discrepancy in your results, make sure to discuss that too. 4

5 Experiment # 2 Transient Response of RC and RL Circuits Prelab: Perform lab simulation using PSpice. Also, find the response equations as being asked in the lab and fill out the corresponding tables to compare simulated and theoretical results. Objective: To design first-order RC and RL circuits to observe their transient response Procedure: RC Circuit 1. For the first-order RC cicuit as shown in figure 1, derive the equations for the capacitor voltage when input is 5V (complete or step response) and when it is 0V (source-free or natural response). v c( t) [step response] = v c( t) [natural response] = 2. Build a first-order RC circuit as shown in figure 1. Use square wave as your input and choose its frequency such that pulse width of the square wave (t p ) is six times the time constant ( ) of the circuit, i.e. t 6. It can safely be assumed that this pulse width time is long enough for p the circuit to get to its steady-state value. Remember that pulse width is half of the time period of the square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage = 0V) 5

6 R2 2k R3 2k V1 = 0 V2 = 5V TD = 0 TR = 1p TF = 1p V1 R1 1k C1 10n 0 Figure 1: First-Order RC Circuit 3. Connect your oscilloscope to observe both input signal and voltage across capacitor simultaneously. Fill out the following table with your theoretical, simulated, and observed values from oscilloscope. Save your waveform. t = t = 2 t = 3 v c( t) [step response] v c( t) [natural response] Theory Simulation Lab Theory Simulation Lab RL Circuit Procedure: 1. A first-order RL circuit is shown in figure 2. Derive the equations for the inductor current when input is 5V (complete or step response) and when it is 0V (source-free or natural response). i L( t) [step response] = i L( t) [natural response] = 6

7 R1 100 R3 100 V1 = 0 V2 = 5V TD = 0 TR = 1p TF = 1p V1 R2 100 L1 1mH 0 Figure # 2: First-Order RL Circuit 2. Build the circuit from figure 2. Use square wave as your input and choose its frequency such that pulse width of the square wave (t p ) is six times the time constant ( ) of the circuit, i.e. t p 6. It can safely be assumed that this pulse width time is long enough for the circuit to get to its steady-state value. Remember that pulse width is half of the time period of the square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage = 0V) 3. Observe the current passing through the inductor. For hands-on, measure the voltage across R3 on the oscilloscope and calculate current from that. PSpice simulation can plot the current using a current probe. Fill out the following table with your theoretical, simulated, and observed values. Save your waveform. t = t = 2 t = 3 i L( t) [step response] i L( t) [natural response] Theory Simulation Lab Theory Simulation Lab Discussion: Your lab report should show the derivation of the equations. Discussion should focus on the transients in RL and RC circuits. Also discuss about discrepancies between lab and expected results. Discuss why it is important to study transient analysis of RL and RC circuits, i.e. their practical implication. 7

8 Experiment # 3 Transient Response of RLC Circuits Prelab: Solve circuits theoretically and perform simulation using PSpice. Write down your prelab calculations and observations as required in the following procedure. Objective: To design two different RLC circuits to study the response characteristics. Procedure: 4. For the first RLC circuit as shown in figure 1, calculate the values for neper frequency ( ) and resonant frequency ( o ). Determine the type of damping and calculate the root(s) of the characteristic equation. R1 1k L 100mH V1 = 0V V2 = 5V TD = 0 TR = 1p TF = 1p V1 1k R2 C 10nF 0 Figure # 1: First RLC Circuit Neper Frequency ( ) Resonant Frequency ( o ) Damping Type s 1 s 2 5. Assume that input is a square wave with values from 0 to 5V with level zero representing source-free circuit and 5V representing step circuit. Perform the analysis to calculate the capacitor voltage for both step and source-free circuits. v c (t) (step) = v c (t) (source-free) = 6. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square wave to be around six times the time constant (reciprocal of the dominant neper frequency, 8

9 i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation interval small enough to have a smooth graph. 7. Use MATLAB to plot the step and source-free responses from your expressions of capacitor voltage (one plot will be preferred else plot separately). Compare your plot with the simulated results to check the accuracy of your derived expressions. Fill out the following table. Make sure to put the simulated and MATLAB plots in your lab report. Simulation Time Step Response (positive or negative) Steady- State Time Source-free Response (positive or negative) Steady- State MATLAB 8. Build your circuit on bench and observe capacitor voltage to fill out the following table. Compare your results with the simulated and theoretical responses for validation. Bench Time Step Response (positive or negative) Steady- State Time Source-free Response (positive or negative) Steady- State 9. Now, for the second RLC circuit as shown in figure 2, calculate the values for neper frequency ( ) and resonant frequency ( o ). Determine the type of damping and calculate the root(s) of the characteristic equation. Neper Frequency ( ) Resonant Frequency ( o ) Damping Type s 1 s 2 9

10 R1 1k 2k R2 V1 = 0V V2 = 5V TD = 0 TR = 1p TF = 1p 0 V1 L1 R3 3k 100mH C1 Figure # 2: Second RLC Circuit 10. Assume that input is a square wave with values from 0 to 5V with level zero representing source-free circuit and 5V representing step circuit. Perform the analysis to calculate the voltage across R 2 for both step and source-free circuits. V R2 (t) (step) = V R2 (t) (source-free) = 11. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square wave to be around six times the time constant (reciprocal of the dominant neper frequency, i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation interval small enough to have a smooth graph. 12. Use MATLAB to plot the step and source-free responses from your expressions of the voltage across R2 (one plot will be preferred else plot separately). Compare your plot with the simulated results to check the accuracy of your derived expressions. Fill out the following table. Make sure to put the simulated and MATLAB plots in your lab report. 100nF Simulation Time Step Response (positive or negative) Steady- State Time Source-free Response (positive or negative) Steady- State MATLAB 10

11 13. Build your circuit on bench (if required) and observe voltage across R2 to fill out the following table. Compare your results with the simulated and theoretical responses for validation. Bench Time Step Response (positive or negative) Steady- State Time Source-free Response (positive or negative) Steady- State Discussion: Your lab report discussion should focus on the transients in RLC circuits. Discuss different types of damping, effect of neper ( ), resonant ( o ), and natural resonant ( d ) on the circuit response, and practical implication of this study. Compare your theoretical, simulated, and lab results and discuss if there are any discrepancies. 11

12 Experiment # 4 Sinusoidal Response of an RLC Circuit Prelab: Solve circuit theoretically and perform simulation using PSpice. Write down your prelab calculations and observations as required in the following procedure. Objective: To observe amplitude and phase change in an RLC circuit under a sinusoidal forcing function. Procedure: 1. Solve for the voltage expressions across inductor and capacitor in figure 1 R1 R2 R4 Vs k 5 V 100kHz 0Deg L1 330uH R3 1.0k C1 1.0nF Figure 1: RLC Circuit for the Experiment V L (j ) = ; v L (t) = V c (j ) = ; v c (t) = 2. Simulate the circuit in PSpice and observe waveforms across source, capacitor, and inductor. Fill out the following table with the observed values from the simulated results. V L (peak) (Volt) Phase angle L (degree) V C (peak) (Volt) Phase angle C (degree) 12

13 Note: (i) To measure phase angle of V L and V C from the simulation and oscilloscope, measure the time difference between the zero-crossing of your source waveform and the respective voltage waveforms using cursors (figure 2). Let this time be t, then using the following relationship, phase angle for each of the waveform can easily be found, T t 360 where T is the time period of each waveform (constant as long as f is constant), and is the phase angle. (ii) When you use PSpice to simulate your circuit, make sure to use fourth or fifth cycle of your voltage waveforms to measure peak voltage and phase angle, i.e. when voltages are settled down to their steady-state. From the simulation, you will see that for the first couple of cycles, v L and v C will still be in the process of settling down to their steady-state. t Figure 2: Measurement of t from simulation 13

14 3. Build circuit on the breadboard and repeat step 2. Fill out the following table with your lab results V L (peak) (Volt) Phase angle L (degree) V C (peak) (Volt) Phase angle C (degree) 4. Show the phasor relationship of the three voltages using phasor diagram Discussion: Your discussion should encompass the importance of sinusoidal analysis as well as reason to perform analysis in complex frequency domain versus time domain. You should also discuss the concept of lagging waveforms versus leading waveforms and effect of the inclusion of capacitors and inductors in the sinusoidal circuits. Exercise: Make Thevenin equivalent of your circuit assuming load to be C 1. Find load voltage and load current and show their phasor relationship. 14

15 Experiment # 5 Analysis of Series RLC Band-pass Filter Prelab: Solve circuit theoretically and perform simulation using PSpice (AC sweep with both linear and logarithmic sweep type). Write down your prelab calculations and observations as required in the following procedure. Objective: To observe the frequency response of a series RLC bandpass filter or series resonant circuit Procedure: 1. For the bandpass filter design shown in figure 1, let resonant frequency f o be KHz and required bandwidth is approximately KHz. Complete the design by calculating the following quantities: Inductance L Capacitance C Quality factor Q Lower cut-off f 1 Upper cut-off f 2 L1 C1 Vin 5Vac 0Vdc R1 10k + Vout - 0 Figure 1: Series RLC Band-pass filter 2. Fill out the following table from your calculated and simulated values. Note that the input sinusoidal source has 5Vp output. V R (f o ) V R (f 1 ) V R (f 2 ) Calculated Simulated 15

16 3. From your simulation, figure out the upper and lower frequencies corresponding to 10% of the maximum output and write them down. These will be considered as stop-band frequencies f lower_10% = ; f upper_10% = 4. Build circuit on the bench and fill out the following table with your observations. Hz f o v(f o ) f 1 v(f 1 ) f 2 v(f 1 ) f lower_10% f upper_10% v(f lower_10%) v(f upper_10%) Volt 5. From your observations, draw a rough sketch of frequency response of the circuit (v R vs. f) Discussion: In your lab report, discuss band-pass filter, its equations, its practical applications, and discrepancies between theoretical, simulated and lab results and their possible explanation. 16

17 Exercises: (i) (ii) Derive circuit equations to find out f lower_10% and f upper_10% Create two MATLAB programs to calculate different parameters for series band-pass filter as follows: Program 1 should be a function based on this lab, i.e., given the center frequency, required bandwidth, and resistor value, it should calculate values for inductor and capacitor, upper and lower cut-off frequency and quality factor. Further, it should also plot the frequency response of the circuit. Plot should be properly labeled. Program 2 should be a function that calculates center frequency, quality factor, bandwidth, upper, and lower cut-off frequencies based on the input values of resistor, capacitor and inductor. Plot the frequency response of the circuit and properly label your plot. 17