ECE 301 Lab 8 Updated W23(1)

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ECE 301 Foundations of Electric Circuits II Assignment 8 Dr. K. Scoles, Drexel University Edited by Keith Zuckerman, Winter 2023 Series RLC Bandpass Filter Assignment Goals At the end of this assignment, you will be able to: • Simulate first-order passive filters • Capture schematics within Multisim • Set up and use the Bode Analyzer for filter gain and phase measurement of both simulation and hardware Prerequisite Knowledge (ECE 201) • Basic dc and ac circuit analysis techniques • Circuit capture in Multisim Preparation • Read sections 9-4.1 and 9-9 in Ulaby’s Circuits textbook Materials Required Breadboard Hook-up wires 1 pair red-black alligator leads Resistor, capacitor from student design 100 mH inductor

Introduction [1] Filters are very important in audio and other signal processing applications. Depending on the specifics and complexity of the design, they can be used to remove unwanted high or low frequency noise, select or reject a specific frequency band, or perform other applications. Fig. 1. Gain vs frequency response for a bandpass filter. [1] The bandpass filter (Fig. 1) is designed to pass a select band of frequencies while blocking all others. It is characterized by its center frequency, ω 0 , and its bandwidth, B. The bandwidth is the difference between two critical radial frequencies, ω c1 and ω c2 , and describes the selectivity of the filter. The critical frequencies are defined to be where the gain M BP drops to a level of 0.707, or 3 dB below the peak value. A filter can be considered a two-port network, such as that in Fig. 2, with the input supplied between nodes a and b, and the output available between nodes c and d. The gain of the system is the ratio of the output voltage to the input. This is also called the transfer function of the network, H(ω). For a passive filter the magnitude of H(ω) is less than or equal to 1. Using an active filter adds the opportunity of having a gain greater than 1.

Fig. 2. Filter as a two-port network [1]. Fig. 3. A linear network performing a bandpass function using a series RLC circuit The techniques used to find the transfer function of the bandpass filter (Fig. 3) are based on the same ac circuit analysis techniques you applied in ECE 201: Transfer sources and components into the phasor domain, analyze the circuit, and determine the transfer function. From the complex transfer function you can determine the magnitude of the gain (M BP (ω)) and the phase shift introduced by the filter, Φ(ω). These two functions are graphed on a Bode plot. The transfer function for the series RCL circuit, with the output across the resistor, is

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The bandwidth and quality factor Q for the filter are given by 2 and 3, respectively. When we take into account “real” components, particularly the inductor and its parasitic resistance, the circuit performance changes (Fig. 4). Fig. 4. RLC bandpass filter with buffered input. Center frequency is 4 kHz, bandwidth is 1 kHz. Component RL represents the parasitic resistance of the inductor L1. The transfer function becomes where R T = R1 + RL. As a consequence of the additional resistance, the magnitude of the gain no longer equals 1 at ω 0 . The bandwidth and Q also change

The bandwidth is now measured 3 dB down from the reduced peak amplitude M’ BP . Note that equations 4, 5, 6, and 7 revert to the ideal cases if RL = 0. In this lab, you will initially design a series RLC bandpass filter to meet a set of specifications, perform a simulation to verify the design, then match the simulation result to straight line approximations of the Bode plot. Following your analysis, you will modify your design to account for the parasitic resistance of the inductor, then simulate and measure the filter. References [1] F. T. Ulaby, M. M. Maharbiz, Circuits , 3 nd ed., NTS Press, 2016.

ECE 301 Foundations of Electric Circuits II Assignment 8 Instructions Dr. K. Scoles, Drexel University Series RLC Bandpass Filter Simulation While you did a simulation of the RLC Bandpass filter in your pre-lab, you will repeat it here taking into account the parasitic resistance of the inductor, and in a different format. The goals are (1) to verify your design and (2) to produce a comparison of the filter’s simulated and measured performance all within the ELVISmx Bode Analyzer application. Fig. 6. An RLC bandpass filter captured in Multisim. Inductance and resistance for the nominal 100 mH inductor are shown. 1. Modify your design to produce a bandpass filter with a 10 kHz center frequency and 2 kHz bandwidth taking into account the real value and parasitic resistance of the inductor. Find values for C1 and R1. 2. Capture the schematic of Fig. 6 1. Modify the component values to match your design. You can use up to two resistors or capacitors in series or parallel to try to match the needed values as closely as possible. 2. Add “on-page connectors” (Place:Connectors:On-page connector) for the signals shown, and edit the connector names to match those in Fig. 6. On- page connectors with the same names are treated as being electrically connected.

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3. Double-click the NI ELVISmx Bode Analyzer block in the panel on the left of the schematic to open its Front Panel and configure the settings to give you a suitable sweep range. Set the Mapping to “logarithmic” to plot temporal frequency f on a log scale. 4. Select Simulate»Run to start the simulation. The gain and phase responses will be plotted (Fig. 7). Add points in the Bode Analyzer setup if your curves are not smooth. 5. Stop the simulation and enable the cursors of the ELVISmx Bode Analyzer by going to the Cursors Settings section and selecting Cursor (Sim). 6. Drag the cursor to the right, and place it as close as possible to the first point on the magnitude curve with a y-value of -3 dB (3 dB below the peak). Record f c1 . Place the cursor at the peak of the response. Record f 0 and M(f 0 ). Move the cursor to the second y-value of -3 dB. Record f c2 . Increasing the number of points may help in accurate cursor placement. 7. Keep the Bode Analyzer open with your simulation results visible. Simulated gain and phase response of a series RLC bandpass filter with center frequency of 4 kHz and bandwidth of 1 kHz.

Fig. 7. Simulated gain and phase response of a series RLC bandpass filter with center frequency of 4 kHz and bandwidth of 1 kHz. Measurement 1. Build the passive filter with the “100 mH” inductor and your C1 and R1. 1. Use the DC supply to provide +15V and -15V to the Op Amp 2. Use the function generator to provide the stimulus signal 2. Connect the Oscilloscope to measure the Response 3. Adjust the input frequency to 1kHz and record the output value. 4. Increase the frequency from 1kHz to 10kHz in steps of 1kHz and record the values in a table. 5. Increase the frequency from 10kHz to 20kHz in steps of 5kHz and record the values in a table. 6. Convert the values to dB and plot the results. Compare to simulation. Deliverables • Compare pre-lab results, done without parasitic resistance, to simulation and measurement results with the resistance. • f c1 , f 0 , M(f 0 ), f c2 , B, Q • Comment of the differences seen with and without the parasitic resistance - pre- lab vs lab. Are the results reasonable given equations 5-7? Be quantitative. • Comment also on the differences between the simulation of the circuit with parasitic resistance and the measurement results • Include the final schematic, with title block (like Fig. 6) • Include the comparison of simulated and measured results Double check the Student Deliverables Checklist for content and format of all deliverables 1. Pre-Lab analysis due in hardcopy at start of lab session 2. Assignment report due as upload to Bb Learn in Word or PDF format by start of your next lab session.