Construct the RLC Series resonance circuit showen below in multisim. simulate th
ID: 1813286 • Letter: C
Question
Construct the RLC Series resonance circuit showen below in multisim. simulate the circuit at the frequencies shown in the table and record the current reading obtained
the inductor self-resistance RL=65 Ohms has been included in the schematic. if the inductor you choose has different DC resistance please feel free to modify the circuit.
Frequency, HZ Is(RMS)mA Vc(RMS)mV VL(RMS) mV
200
300
500
700
730
734
738
800
1000
1200
1400
Construct the RLC Series resonance circuit shown below in multisim. simulate the circuit at the frequencies shown in the table and record the current reading obtained the inductor self-resistance RL=65 Ohms has been included in the schematic. if the inductor you choose has different DC resistance please feel free to modify the circuit.Explanation / Answer
Case 1: critically damped response.
a. Set the potentiometer to the value R calculated above corresponding to a damping ratio of 1.
b. Set the function generator to 1Vpp with an offset voltage of 0.5V and a frequency of 200 Hz. Display this waveform on the oscilloscope. Measure the voltage over the capacitor and display the waveform vC(t)on the scope. Measure its characteristics: risetime, Vmin, Vmax, and Vpp. Make also a print out of the display. Compare the measured results with the one from the pre-lab and the simulations.
Case 2: overdamped response.
a. Set the potentiometer to the value R calculated above corresponding to a damping ratio of 2. Measure and display the response over the capacitor and make a print out. Determine the rise time, min and max value of the voltage vC.
b. Calculate one of the time constants of the expression (4). Usually one of the time constants is considerably larger than the other one which implies that the exponential with the smallest time constant dies out quickly. You can make use of this to find the largest time constant. Measure two points on the graph (v1,t1) and (v2,t2) as shown in Figure 6. Choose t1 sufficiently away from the origin so that one of the exponentials has decayed to zero. You can than make use of the following relationship to find the time constant:
(7)
in which Vf is the final value of the exponential (value at the time t=infinite). The expression you derived in the last lab: t=trise/2.2 is a special case of the above expressions (i.e. v1=0.1Vmax; v2=0.9Vmax).
Figure 6: method to measure the time constant.
Case 3: underdamped response
a. Set the potentiometer corresponding to the value R calculated above corresponding to a damping ratio of 0.2. Measure and display the response over the capacitor and make a print out. Determine its characteristics: voltage and time of the first peak, voltage and time of the second peak. Make a print out.
b. Determine the value of t and wd from the measured waveform (See Figure 3). Use the expression (7) to determine the value of the time constant (t=1/s).
5. Vary the potentiometer and observe the behavior of the response (display the voltage over the capacitor). Notice when the output goes from underdamped to critically damped and overdamped. In general, a critically damped response is preferred because it does not give overshoot or "ringing" and has a fast rise time. An overdamped response has a slower rise time than the other responses, while the underdamped response rises the fastest, but also give a lot of overshoot which is not desired. Record your observations in you lab notebook.
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