ECE 2004 Lab 5 RC and RL Networks Rev 0_5

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 1 Lab 5 Rev 0.5 10/28/2022 Lab #5 RC and RL Networks I. Introduction When performing basic analysis of RC and RL circuits, it is often assumed that the components are all ideal and modeled as such. In real-world components, the construction of these devices can introduce undesired effects, often referred to as “parasitics”. For example, Fig. 1, shows several models for a capacitor. Fig. 1a, is the traditional model for the “ideal” capacitor used in most hand calculations. Fig. 1b shows a capacitor model that includes the effects of internal leakage within the capacitor modeled as a parallel resistor, R leakage . This leakage path is the result of imperfect insulation in the dielectric layer between the two plates within the capacitor that give rise to a small amount of current flow directly through the device. This leakage path causes any charge placed on a capacitor to eventually discharge even when disconnected from a circuit. The leakage path is modeled as a large valued resistor that bypasses the ideal capacitor allowing a small amount of current to always flow. Fig. 1c shows a capacitor model that includes a series resistor, ESR. The ESR is the “equivalent series resistance” which includes resistive loss resulting from wire resistance, plate losses, and loss in the dielectric insulator. Typical values for ESR are several ohms or less. (a) Ideal (b) Including leakage (c) including losses Figure 1 Capacitor models Parasitic effects also exist within inductors. Fig. 2 shows two models for an inductor. Fig. 2a is the “ideal” model often used in basic circuit analysis. Fig. 2b is the inductor model that includes ESR due to the resistive losses in the long length of wire used to make the coil.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 2 Lab 5 Rev 0.5 10/28/2022 (a) Ideal (b) Including wire loss Figure 2 Inductor models In this laboratory exercise, the time domain response, also known as the transient response, of simple RC and RL networks will be investigated. The response includes switching effects resulting in the charging or discharging of capacitors and inductors. The switching response will be simulated using a function generator operating with a pulsed waveform. The pulsed waveform will have a pulse width long enough to simulate a switched condition with at least 10 time constants (10 τ ). Fig. 3 shows the output of the function generator configured for a pulsed waveform with 5V peak and offset of 2.5V. The frequency of the waveform is determined by period which is at least 20 time constants long (20 τ ). Allowing at least 10t within a charging, or discharging, cycle provides a long enough time for the waveform to reach its maximum, or minimum, value respectively. The time constant for simple RC and RL networks are determined by τ = RC or τ = L/R respectively. When attempting to estimate the time constant using a measured waveform from a RC or RL network, the time constant in a charging cycle is the time to reach 63.2% of the peak. 𝑓𝑓 ( 𝑡𝑡 ) = ( 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) ( 1 − 𝑝𝑝 − 𝑡𝑡 𝜏𝜏 � ) = ( 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 )(1 − 0.367) = (0.623)( 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) 𝑤𝑤ℎ𝑝𝑝𝑒𝑒 𝑡𝑡 = 𝜏𝜏 When estimating the time constant in a discharging cycle, τ is the time to reach 36.7% from the peak. 𝑓𝑓 ( 𝑡𝑡 ) = ( 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) ( 𝑝𝑝 − 𝑡𝑡 𝜏𝜏 � ) = (0.367)( 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) 𝑤𝑤ℎ𝑝𝑝𝑒𝑒 𝑡𝑡 = 𝜏𝜏 Fig. 4 shows the charging and discharging waveforms in simple RC and RL networks. The important parameter in RC networks is the voltage across the capacitor. For the RL network, the important parameter is the current flowing through the inductor.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 3 Lab 5 Rev 0.5 10/28/2022 Figure 3 Function generator waveform for simulating switched response Figure 4 Charging and discharging waveform in RC and RL networks

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 4 Lab 5 Rev 0.5 10/28/2022 II. Experimental Procedure A. Equipment List ± Keysight DSO-X 2002A Digital Storage Oscilloscope (2-channel scope) ± Keysight 33500B Waveform Generator ± Keysight 34450A Digital Multimeter (DMM) ± Keysight U8032A Triple Output Power Supply ± Agilent (Keysight) U1733C Handheld LCR Meter ± Breadboard ± Coaxial cable with BNC to BNC ± Coaxial cables with BNC to alligator clip (quantity 2) ± 100 µ F, 50V electrolytic capacitor ± 0.1 µ F ceramic capacitor ± 100 Ω, 5%, ¼-½ watt resistor ± 1 KΩ, 5%, ¼ -½ watt resistor ± 470 KΩ, 5%, ¼ -½ watt resistor ± 30-inch length of enameled wire, 22 AWG ± Wooden dowel, ¼” diameter ± Ferrite rod, ¼” diameter, Fair-rite 4061266011 ( µ r = 125) ± Plastic end caps (quantity 2) ± Box cutter B. Basic Capacitor Measurements In all measurements, if the capacitor has a polarity, check that you are properly connecting the capacitors’ (+) and (-) terminals to the instruments’ (+) terminal and (-) terminals. 1. Digital Multimeter (DMM) Measurements of Capacitor (a) Configure the power supply for 10 VDC output on one of the channels. Set the DMM to measure DC voltage. Temporarily connect (touch both leads) a 100 µ F electrolytic capacitor across the power supply terminals. Verify the proper connection of the (+) and (-) terminals. Remove the capacitor and quickly measure the voltage across the capacitor terminals. Record the measured voltage. Capacitor Voltage ___________ VDC Wait a few minutes and measure the voltage again. Record the measured voltage. Capacitor Voltage ___________ VDC

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 5 Lab 5 Rev 0.5 10/28/2022 Why did the voltage slightly drop? Using a breadboard, insert a 470k Ω resistor in a good location so that the 100 µ F capacitor can be inserted in parallel with the resistor. Again, temporarily connect the 100 µ F electrolytic capacitor across the power supply terminals to charge the capacitor. Quickly insert the capacitor into the breadboard to create a parallel RC combination. Using the DMM, measure the voltage across the terminals. Monitor the voltage across the RC circuit. Describe what you see. Why is there a change in the voltage? Discharge the capacitor by connecting (shorting) the capacitor leads together. Verify that the capacitor is fully discharged by measuring the voltage across the capacitor, which should now be 0 VDC. ( Note: when shorting the capacitor terminals together, there is a very large instantaneous current flow during this rapid discharge. This could damage capacitors with a very large energy storage (Q = CV) but is acceptable for the low-valued capacitors and voltages we use in our labs). (b) Using the DMM, configure the instrument to measure resistance. Record the measured resistance between the two terminals of the capacitor. DMM Resistance Measurement of Capacitor ___________ohms Is this resistance expected? Explain why you measured this value? 2. LCR Meter Measurements of Capacitor (a) Connect the 100 µ F electrolytic capacitor to the LCR meter using either of the techniques shown in Fig. 5. (a) Connection with meter clip leads (b) Connection with component socket Figure 5 connecting a capacitor to the LCR Meter (b) Verify that the frequency on the LCR is set to 1kHz, if not, press the Freq. button until 1 kHz is shown on the meter. With the meter in “auto” mode, the measured capacitance will be displayed

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 6 Lab 5 Rev 0.5 10/28/2022 automatically. Record the measured capacitance for the 100 µ F electrolytic capacitor in the middle column on Table 1. Table 1 Capacitor Measurements using LCR Meter Measured Value 100 µ F Electrolytic Cap 0.1 µ F Ceramic Cap Capacitance (F) Impedance ( Ω ) @ 1kHz ESR ( Ω ) (c) Configure the LCR meter to measure impedance (Z) for the 100 µ F electrolytic capacitor. This function is selected by cycling the ZLCR button. Record the measured impedance on Table 1. (d) Configure the LCR meter to measure Equivalent Series Resistance (ESR) for the 100 µ F electrolytic capacitor. This function is selected by pressing and holding the Ai/ESR button for 1 second. Record the measured ESR on Table 1. (e) Remove the electrolytic capacitor and insert the 0.1 µ F “ceramic” capacitor. (f) Record the measured capacitance, impedance and ESR for the 0.1 µ F ceramic capacitor in the right column on Table 1. 3. Transient Measurements of RC Network During Charging (a) Configure the function generator’s Channel 1 for a Square Wave with Amplitude = 5.0Vpp and an Offset = 2.5 V . Set the generator’s Channel 1 output to High Z . This should produce a waveform shown in Fig. 6. Figure 6 Function generator waveform for simulating switched response (b) Set the frequency of the generator to produce a pulsed waveform with a minimum pulse width = 10 τ , where τ = RC is the time constant calculated from the values shown in the circuit in Fig. 7.

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 7 Lab 5 Rev 0.5 10/28/2022 Record the calculated time constant, τ (in seconds), and the associated Frequency setting on your generator. Calculated time constant ( τ ) ________ seconds Generator frequency setting __________ (Hz) (c) Using the breadboard and a set of BNC-to-Alligator cables, assemble the circuit shown in Fig. 7. Using a BNC-BNC cable, connect the function generator “ Sync ” output to the oscilloscope “ Trig In ” . Using the menus, set the oscilloscope Trig ger to Ext ernal. Scope Channel 1 displays the input voltage pulse and Channel 2 is the measured voltage across the 0.1 µ F capacitor. Figure 7 Wiring diagram for measuring the transient response of a simple RC network (d) Set the timebase and trigger position on the oscilloscope to observe only the charging of the capacitor. Position the input (channel 1) on the upper part of the display and position the capacitor voltage (channel 2) on the lower part. Use the same vertical scale for channel 1 and channel 2. Record the oscilloscope display. (e) Using oscilloscope cursors, measure the time and associated voltage at several points along the charging cycle. Start by measuring the peak voltage of the charging cycle (close to the end of the cycle), record this voltage and associated time on Table 2. Next, calculate the voltage at 63.2% of this peak. Place the cursor on this voltage, record the time and voltage at this point. Lastly, move the cursor to the start of the waveform, just as the capacitor charging begins. Record the voltage and time at this point. Table 2 Measurements of RC transient response during charging Location on waveform Time (seconds) Voltage (V) Peak voltage 63% of peak voltage Start of waveform (f) Calculate the time constant, τ, by subtracting the time measured at the 63.2% point from the time measured at the start of the charging cycle. Record the measured time constant. Also calculate and record the theoretical time constant using the values for R and C.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 8 Lab 5 Rev 0.5 10/28/2022 Measured time constant, τ ___________ (seconds) Theoretical time constant, τ (= RC) __________(seconds) (g) In your report, compare the measured time constant with the theoretical value, RC. Explain why there are discrepancies. 4. Transient Measurements of RC Network During Discharging (a) Repeat the transient measurements during the discharging cycle in the RC network. Observe the discharging portion of the waveform by adjusting the oscilloscope timing offset to expose this portion of the waveform. (b) Using oscilloscope cursors, measure the time and associated voltage at several points along the discharging cycle. Start by measuring the largest voltage at the point just before discharging begins, record this voltage and associated time on Table 3. Next, calculate the 36.7% of this peak. Place the cursor on this voltage, record the voltage and time at this point. Table 3 Measurements of RC transient response during discharging Location on waveform Time (seconds) Voltage (V) Peak voltage 36.7% of peak voltage (c) Calculate the time constant, τ, by subtracting the measured time at the 36.7% point from the start time (at the peak). Record the time measured constant. Also, calculate and record the theoretical time constant using the values for R and C. Measured time constant, τ ___________ (seconds) Theoretical time constant, τ (= RC) __________(seconds) (d) In your report, compare the measured time constant with the theoretical value during the discharging cycle. Explain why there are discrepancies. Also, compare any differences between the time constants for the charging and discharging.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 9 Lab 5 Rev 0.5 10/28/2022 C. Basic Inductor Measurements 1. Building an Inductor (a) With the 30-inch length of enameled wire (magnet wire) and the box cutter, carefully scratch off the enamel paint from around the two ends of the wire, about 0.75 inch to 1 inch, to expose the underneath copper conductor, as shown in Fig. 8. (b) Create the inductor by carefully wrapping the wire around the wooden dowel. Count the total number of turns as you wrap the wire. As shown in Fig. 8, leave about 0.75-inch of wire hanging at each end in order to make connection from your inductor to the LCR meter and breadboard. Record the number of turns. Number of Turns __________________ Figure 8 Inductor (wooden dowel not shown) 2. Digital Multimeter (DMM) Measurements of Inductor (a) Using the DMM, configure the instrument to measure resistance. Record the measured resistance between the two terminals. If the measured resistance is very large, it is likely that you didn’t scrap off enough enamel paint. Record the resistance. DMM Resistance Measurement of Inductor _________ohms Is this resistance expected? Explain why you measured this value? 3. LCR Meter Measurements of Inductor (a) Verify that the frequency on the LCR is set to 1kHz, if not, press the Freq. button until 1 kHz is shown on the meter. With the meter in “auto” mode, the measured inductance will be displayed automatically. Record the measured inductance on the middle column on Table 4. Note, the inductance value for an inductor wrapped around a wooden dowel is the same as the inductance with an air core as the relative permeability for the wood and air is about the same ( µ r = 1).

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ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 10 Lab 5 Rev 0.5 10/28/2022 Table 4 Inductance measurements using LCR Meter Measured Value Inductor on Wood Inductor on Ferrite Inductance (H) Impedance ( Ω ) @ 1kHz ESR ( Ω ) (b) Configure the LCR meter to measure impedance (Z) for the inductor wrapped around wood. This function is selected by cycling the ZLCR button. Record the measured impedance on Table 4. (c) Configure the LCR meter to measure Equivalent Series Resistance (ESR) for the inductor wrapped around wood. This function is selected by pressing and holding the Ai/ESR button for 1 second. Record the measured ESR on Table 4. (d) Replace the wooden dowel with a ferrite rod. This is most easily accomplished by using the ferrite rod to push the wood dowel out. Push plastic caps on either end of the rod to hold the wire in place. Record the measured inductance, impedance and ESR for the inductor wrapped on the ferrite rod on the right-most column on Table 4. (e) For your report, discuss the difference in the measured inductance between the inductor with the wooden dowel ( µ r = 1) and the inductor with the ferrite core ( µ r = 125). 5. Transient Measurements of RL Network (a) As before, configure the function generator’s Channel 1 for a Square Wave with Amplitude = 5.0Vpp and an Offset = 2.5 V . Set the generator’s Channel 1 output to High Z . (b) Set the frequency of the generator to produce a pulsed waveform with a minimum pulse width = 10 τ , where τ = L/R is the time constant of the circuit shown in Fig. 2. Use the inductor wrapped around the ferrite core. Record the calculated time constant, τ (in seconds), and the associated Frequency setting on your generator. Calculated time constant ( τ ) ________ seconds Generator frequency setting __________ (Hz) (c) Using the breadboard and a set of BNC-to-Alligator cables, assemble the circuit shown in Fig. 9. Scope Channel 1 displays the input voltage pulse and Channel 2 is the measured voltage across the resistor. In this case, we are interested in the current flowing in the inductor and measuring the voltage across the resistor and dividing this voltage by 100 will provide a measurement of current.

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 11 Lab 5 Rev 0.5 10/28/2022 Figure 9 Wiring diagram for measuring the transient response of a simple RL network (d) Set the timebase and trigger position on the oscilloscope to observe only the charging of the inductor. As before, position the input (channel 1) on the upper part of the display and position the inductor current (channel 2) on the lower part. The inductor current is calculated by taking the voltage across the 100 Ω resistor and dividing by 100. Properly scale each waveform and record the oscilloscope display. (e) Using oscilloscope cursors, measure the time and associated voltage at several points along the charging cycle. Start by measuring the peak voltage of the charging cycle, divide voltage by the resistor value and record the associated current and time on Table 5. Next, calculate the 63.2% of this peak. Place the cursor at this point and record the current and time. Lastly, move the cursor to the start of the waveform, just as the inductor charging begins. Record the current and time at this point. Table 5 Measurements of RL transient response Location on waveform Time (seconds) Current (I) Peak current 63% of peak current Start of waveform (f) Calculate the time constant, τ, by subtracting the measured time at 63.2% point and the measured time at the start of the charging cycle. Calculated time constant, τ ___________ (seconds) Theoretical time constant, τ (= L/R) __________(seconds) (g) In your report, compare the measured time constant with the theoretical value, L/R. Explain why there are discrepancies. 6. Transient Measurements of RL Network During Discharging

ECE2004 Fundamentals of Electric Circuits © NYU Tandon School of Engineering 12 Lab 5 Rev 0.5 10/28/2022 (a) Repeat the transient measurements during the discharging cycle in the RL network. Observe the discharging portion of the waveform by adjusting the oscilloscope timing offset to expose this portion of the waveform. (b) Using oscilloscope cursors, measure the time and associated voltage at several points along the discharging cycle. Start by measuring the largest voltage at the point just before discharging begins, record the associated current and time on Table 6. Next, calculate the 36.7% of this peak. Place the cursor at this point, record the current and time on the table. Table 6 Measurements of RL transient response during discharging Location on waveform Time (seconds) Current (I) Peak current 36.7% of peak current (c) Calculate the time constant, τ, by subtracting the measured time at the 36.7% point from the start time (at the peak). Record the time measured constant. Also, calculate and record the theoretical time constant using the values for R and L. Measured time constant, τ ___________ (seconds) Theoretical time constant, τ (= L/R) __________(seconds) (d) In your report, compare the measured time constant with the theoretical value during the discharging cycle. Explain why there are discrepancies. Also, compare any differences between the time constants for the charging and discharging.

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ECE 2004 Lab 5 RC and RL Networks Rev 0_5

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