EE 221 L CIRCUIT II. by Ming Zhu

Transcription

1 EE 22 L CIRCUIT II LABORATORY 9: RC CIRCUITS, FREQUENCY RESPONSE & FILTER DESIGNS by Ming Zhu DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING UNIVERSITY OF NEVADA, LAS VEGAS OBJECTIVE Enhance the knowledge of time constant and frequency response of RC and RLC circuits, and apply them to filter designs. COMPONENTS & EQUIPMENT Power Supply Multimeter Oscilloscope Function Generator Breadboard & Jump Wires Resistors Capacitors Inductors (optional) Op Amp (optional) LM555 (or equivalent) BACKGROUND RC circuits are the simplest circuits that are related to time-constants and frequency response, and are widely used in countless electrical and electronic applications. In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

2 Refreshment on key knowledges and formulas regarding to RC circuits and frequency response are listed as follows. V in is a step input: Time constant τ = RC V C = V in ( e t RC) V R = V in e t RC V in is an AC input with frequency f : ω = 2πf V C = V in ( + j(2πf)rc ) = V in ( + jωrc ) V R = V in ( j(2πf)rc + j(2πf)rc ) = V in ( jωrc + jωrc ) ω 0: V C V in, V R 0 (Open circuit in DC) (Passive) High pass filter: ω : V C 0, V R V in (Passive) Low pass filter: DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 2

3 V out (jω) V in (jω) = + jωl R + jωrc V out = V in, when at resonance frequency: (Passive) Band pass filter: ω = LC Quality factor: Q = R L C V out V in = R 2 R + jωr 2 C (Active) Low pass filter LAB DELIVERIES PRELAB:. Review the knowledge of RC circuits and frequency response, part of which are listed in the previous section. 2. Simulate the circuit below. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 3

4 ) Calculate the time constant (τ) of the circuit. 2) Run the simulation and observe the differences between vin and vout. 3) Can you give out an approximate τ through simulation? Compare with your calculation. 3. Simulate the following circuit for the frequency response. ) Hand calculate the -3dB frequency of the circuit. 2) Make sure to set AC voltage equal to. Run the simulation for Bode plot of Vout. Compare your calculation with the simulation result. LAB EXPERIMENTS:. Implement the circuit in Prelab 2 on breadboard. ) Use the function generator to setup V in as a square signal with V pp = V and f = 0Hz. 2) Use oscilloscope to read the voltage at V out. Zoom in and look into the rising/falling edge of the achieved waveform. Measure rising, falling time (T r, T f ), and time constant. Compare the measured results to the ones in hand calculations and LTspice simulations. 3) Repeat ) and 2) with f = 0kHz. 4) Change to R = 2kΩ, C = 20nF and f = 0kHz. Repeat to calculate the time constant and observe the input/output waveform and rising/falling time. f = 0Hz R = 0kΩ C = 00nF f = 0kHz R = 0kΩ C = 00nF f =0kHz R = 2kΩ C = 20nF T r /T f (μs) T r = T f = T r = T f = T r = T f = Output Waveforms: DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 4

5 2. Implement the circuit in Prelab 3 on breadboard. ) Use the function generator to setup V in as a sine signal with V pp = 5V and f = Hz. 2) Read the output voltage through the oscilloscope. Write down its amplitude. 3) Change the input signal frequency from Hz to 0Hz, 00Hz, khz, MHz. Observe the V out waveform on the oscilloscope, and write down the amplitude at each frequency. 4) Draw the Bode Plot for the circuit frequency response. f (Hz) 0 00 k 0k 00k M V pp Hz 0 Hz 00 Hz k Hz 0k Hz 00k Hz M Hz Timer. Follow the steps below. Deliverables are in bold. All work must be typed. ) This lab exercise will introduce you to your first active circuit, meaning a circuit that requires a DC power source to operate. Skim through the LM555 timer datasheet. There are many variants of the 555 timer but most are interchangeable. It is a good idea to check the datasheet though to look for differences. For this lab, almost all 555 timer chips are suitable. You do not need to understand the internal operation of the circuit to use it. 2) The pin-out for the 555 timer is shown below in Fig. 9. The circuit you will be constructing is shown in Fig. 20. Build this circuit on a breadboard and try to keep connections short and neat. The 0 nf capacitor value is not critical and you can substitute the next higher value if you can t find 0 nf. 3) Use a Vcc voltage of 5V. Select R and C based on this equation, t = ln(3) RC.RC 4) Set the time for 0 seconds or a different value that is convenient based on available components. Connect a high value resistor from the Trigger pin to Vcc. The value is not critical but be sure to select one that is over 00k. Connect a wire to the trigger connection and leave the other end floating for now. When this pin goes low or connects to ground, the circuit is triggered and the output goes to Vcc for the set time interval as shown in the following figure. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 5

6 5) Let s connect an LED to the output so that we can see the output pulse duration. The voltage at the output pin will be 5 V. Using this and the LED s forward voltage as described in Lab #: DC Circuits, select a resistor that limits the current to 20 ma. Finally, to trigger the circuit, plug the floating end of the trigger wire into a ground connection for a moment and pull it out. The LED should light up and then turn off after the time interval. Measure the time duration using a clock or timer. (All hand calculations in all steps, Photo of circuit) Figure. Pin out of 555 timer. Figure 3. Operation of 555 timer. Figure 2. Schematic of monostable application of 555 timer. * All images on this page are taken from Wikimedia Commons and have been released into the public domain by their authors. * POSTLAB REPORT: Include the following elements in the report document: Section Element Theory of operation Include a brief description of every element and phenomenon that appear during the experiments. Prelab report 2. Hand calculation results of prelab circuit (a) and (b). 2. LTspice schematics and simulation results of the two circuits. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 6

7 Results of the experiments Experiments Experiment Results Photos of implementations and measured results 2 Photos of implementations and V that clips Vout 3 Photos of Oscilloscope measurements. Answer the questions Questions Questions Conclusions Write down your conclusions, things learned, problems encountered during the lab and how they were solved, etc. Images Paste images (e.g. scratches, drafts, screenshots, photos, etc.) in Postlab report document (only.docx,.doc or.pdf format is accepted). If the sizes of images are too large, convert them to jpg/jpeg format first, and then paste them in the document. Attachments (If needed) Zip your projects. Send through WebCampus as attachments, or provide link to the zip file on Google Drive / Dropbox, etc. REFERENCES & ACKNOWLEDGEMENT. C. K. Alexander and M. Sadiku, Fundamentals of Electric Circuits, 4 th Ed Previous EE lab instructions I appreciate the help from faculty members and TAs during the composing of this instruction manual. I would also thank students who provide valuable feedback so that we can offer better higher education to the students. DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 7