Lab 17 Series Resonance on line Ala LM 17Mar2020 rev1 (1)

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Apr 3, 2024

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Lab 17 (eBook 26) Series Resonance Name ____________________ Date ___________________ Class ___________________ READING Text, Sections 13–1 through 13–4 OBJECTIVES After performing this experiment, you will be able to: 1. Compute the resonant frequency, Q , and bandwidth of a series resonant circuit. 2. Measure the parameters listed in objective 1. 3. Explain the factors affecting the selectivity of a series resonant circuit. MATERIALS NEEDED Resistors: One 100 Ω, one 47 Ω One 0.1 μF capacitor (changed from original 0.01 μF to match figure 17-3) One 100 mH inductor REQUIRED LAB PREPARATION (PRELAB) 1. Read all sections of the lab. 2. READ document named “BRIGHTSPACE ON-LINE LAB ASSIGNMENT AND SUBMISSION PROCEDURE” available in Lab 11 folder 3. Read the text book, sections 13-1 through 13-4 4. Find the required resistors, capacitors and inductor for this lab as indicated in the Materials Needed section above 5. Review the oscilloscope “time base operation” or what is called Horizontal Control depending on the oscilloscope manufacturer. 6. Review the relationship between frequency and period, what is the period at 2KHz? What should the time/div be set to on the oscilloscope to show 1 cycle on the full screen? ANS: _______________ Lab 17 P a g e | 1

7. Complete the PreLab questions at the back of this document and hand in to teacher before going to your Lab station. SUMMARY OF THEORY The reactance of inductors increases with frequency according to the equation X L = 2π fL On the other hand, the reactance of capacitors decreases with frequency according to the equation Consider the series LC circuit shown in Figure 17–1(a) . In any LC circuit, there is a frequency at which the inductive reactance is equal to the capacitive reactance . The point at which there is equal and opposite reactance is called resonance . By setting X L = X C , substituting the relations given above, and solving for f , it is easy to show that the resonant frequency of an LC circuit is where f r is the resonant frequency . Recall that reactance phasors for inductors and capacitors are drawn in opposite directions because of the opposite phase shift that occurs between inductors and capacitors. At series resonance these two phasors are added and cancel each other . This is illustrated in Figure 17–1(b) . The current in the circuit is limited only by the total resistance of the circuit . The current in this example is 5.0 mA. If each of the impedance phasors is multiplied by this current, the result is the voltage phasor diagram as shown in Figure 17– 1(c) . Notice that the voltage across the inductor and the capacitor can be greater than the applied voltage! Figure 17–1 Lab 17 P a g e | 2

At the resonant frequency, the cancellation of the inductive and capacitive phasors leaves only the resistive phasor to limit the current in the circuit. Therefore, at resonance, the impedance of the circuit is a minimum and the current is a maximum and equal to V S / R . The phase angle between the source voltage and current is zero. If the frequency is lowered, the inductive reactance will be smaller and the capacitive reactance will be larger. The circuit is said to be capacitive because the source current leads the source voltage. If the frequency is raised, the inductive reactance increases, and the capacitive reactance decreases. The circuit is said to be inductive. The selectivity of a resonant circuit describes how the circuit responds to a group of frequencies . A highly selective circuit responds to a narrow group of frequencies and rejects other frequencies. The bandwidth of a resonant circuit is the frequency range at which the current is 70.7% of the maximum current . A highly selective circuit thus has a narrow bandwidth. The sharpness of the response to the frequencies is determined by the circuit Q . The Q for a series resonant circuit is the reactive power in either the coil or capacitor divided by the true power, which is dissipated in the total resistance of the circuit . The bandwidth and resonant frequency can be shown to be related to the circuit Q by the equation Figure 17–2 illustrates how the bandwidth can change with Q . Responses 1 and 2 have the same resonant frequency but different bandwidths. The bandwidth for curve 1 is shown. Response curve 2 has a higher Q and a smaller BW . A useful equation that relates the circuit resistance, capacitance, and inductance to Q is Figure 17–2 Lab 17 P a g e | 3

The value of R in this equation is the total equivalent series resistance in the circuit. Using this equation, the circuit response can be tailored to the application. For a highly selective circuit, the circuit resistance is held to a minimum and the L/C ratio is made high. The Q of a resonant circuit can also be computed from the equation where X L is the inductive reactance and R is again the total equivalent series resistance of the circuit. The result is the same if X C is used in the equation, since the values are the same at resonance, but usually X L is shown because the resistance of the inductor is frequently the dominant resistance of the circuit . PROCEDURE 1. See document titled” BRIGHTSPACE assignment and submissions process” which is available in Lab 11 folder, 2. These include a. Simulate the circuit in Multisim and record the required results in the appropriate table, b. Paste into a blank sheet an image of your actual breadboard as if you were doing the experiment in the Lab, and c. Submit this completed Lab document, and the simulation files via the assignment folder in Brightspace. 3. Use the Multisim spec values for all your calculation, and read the yellow highlighted comments in table below. Lab 17 P a g e | 4

Table 17–1 Listed Value Measured Value L 1 100 mH XXXXXXXXXXXXXXXXXXXXXX C 1 0.1 μF XXXXXXXXXXXXXXXXXXXXXX R 1 100 Ω Do not use R 1 in Multism Do use R 1 on your breadboard which you will photographe and then copy pasted into this document. R S 1 47 Ω XXXXXXXXXXXXXXXXXXXXXX R W ( L 1 resistance) XXXXXXXXXXXXXXXXXXXXXX Figure 17–3 COPY/PASTE image of your Breadboard here; Lab 17 P a g e | 5

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