Name: I. INTRODUCTION See Part V, Tuned LRC Circuits. In this lab exercise, we will be working with the setup shown below in Figure 1. Function generator in squarewave mode (to CH. 1 (to CH. 2 Figure 1. Diagram of experimental setup showing tuned inductor (L2) being shock excited by square wave from function generator and small inductor (L1). In this circuit, a function generator a device that generates repetitive signals of various shapes, such as square waves, triangle waves, and sine waves is connected in its squarewave mode through a resistor to the small inductor L1. For our purposes, L1 can be just a few turns of wire (more about this later) and L2 will be the coil you used earlier (which may have included 30 or so turns). Notice that L1 is being used here as the primary of a transformer, the secondary of which is the larger inductor, L2. But unlike the usual situation in which a transformer is driven by a sinewave source (like the 60Hz AC power line), here we are driving our transformer with a square wave. When the voltage supplied by the squarewave generator changes abruptly, the magnetic flux through L2 changes abruptly, and an emf is generated in L2. This abrupt change in the flux through L2 is what we mean when we say that L2 has been shock excited by the function generator. The polarity of the emf induced in L2 by the shock excitation is, as you know, always such that it opposes the change in the flux through L2. From Part V of the theory handout called Tuned LRC Circuits, we can see that if we look at the voltage across the tuned system involving L2, C1 and C2, we should expect to see a ringdown a damped sine wave as the natural response of this system to the abrupt change in flux caused by the squarewave generator. If the only causes of the removal of energy from the ringing tuned system (L2, C1 and C2) were intrinsic to the tuned system itself, then a measurement of the time required for the amplitude of the ringdown to fall from some value to onehalf that value would give a very accurate measurement of the Q of the tuned system (see Part V of Tuned LRC Circuits). The time thus measured is called the halfamplitude decay time and will be denoted by the symbol τ 1/ 2. However, in addition to losses that are associated only with the tuned system (chiefly the resistance of the wire used to wind L2), some energy is always removed from the ringing tuned system by dissipation in the input impedance of the scope and in the circuit containing R and L1. The removal of energy from L2 by the circuit containing R and L1 is due to the fact that L1 is always linked to L2 by magnetic flux (these two coils are said to be inductively coupled). As the tuned system rings, some amount of energy is transferred from L2 to L1, and some fraction of this energy is lost by dissipation in R and in the unavoidable resistance of the windings of L1. C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 1
To minimize losses that are external to the tuned system, we will take the following precautions: Use timesten probes to look at voltages on the scope. A timesten probe is a special scope probe designed to increase by a factor of ten the load resistance that the scope places on the circuit terminals to which it is attached. This will be especially important when we want to look at the voltage across the tuned system (i.e., across L2). Make sure that L1 is loosely coupled (magnetically) to L2. In particular, we will make L1 no more than about 5 turns of wire and we will separate L1 from L2 as much as we can and still see a signal across L2. So if we follow the precautions given above, we should be able to get a good measurement of the Q of the tuned system. This measurement is the primary objective of this lab. II. PROCEDURES A. On a solderless breadboard, build the circuit shown in Figure 1. Refer to the suggestions below. Some suggestions for circuit construction: 1. For R, use a 47ohm resistor. 2. For L1, wind no more than 5 turns of enameled magnet wire no smaller than about #26 American Wire Gauge (AWG) onto a coil form such as a small plastic or cardboard tube. The turns should be contiguous. 3. For L2, used the coil you used in the lab on measuring Q by the bandpass method. 4. Use lowloss capacitors for C1 and C2. A good choice for the fixed capacitor C1 would be a silvermica capacitor of about 50100pF. (Ask your instructors about this.) For C2, use your airdielectric variable capacitor. 5. Use a timesten probe to look at the voltage across L2 on Channel 2 on the scope. B. Using a digital multimeter capable of measuring capacitance, measure the fixed capacitor C1 and the maximum and minimum capacitances of the variable capacitor C2. Record these below. C1: pf C2 max: pf C2 min: pf C. Set your variable capacitor to its maximum capacitance and shock excite your parallelresonant circuit at a rep rate of a few hundred hertz. Use the highest amplitude setting of the function generator. Adjust the sweep speed of your scope so that you can see several ringdowns. On graph paper provided by your instructors, make a sketch of what you see on the scope. (Include both CH. 1 and CH. 2.) D. Do you see a ringdown on Channel 2 on your scope at both the rising edge and the falling edge of the square wave? C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 2
E. Increase your scope s sweep speed so that you can see clearly the highfrequency oscillations in one of the ringdowns. Measure the frequency of the damped sinusoid in the ringdown and record it below. Frequency of Damped Sinusoid: F. Measure the halfamplitude decay time for the ringdown on your scope. Record it below. Halfamplitude decay time: G. Now switch your function generator to its sinewave mode and measure the resonant frequency of the paralleltuned system by sweeping the frequency of the function generator. Resonant frequency f 0 : H. Compare quantitatively your measurement of the resonant frequency with your measurement (from Step E) of the ringdown frequency. I. Using your measurement of the resonant frequency and of the halfamplitude decay time, calculate the Q of the paralleltuned system (see Part V of Tuned LRC Circuits for information about how to calculate Q from these two measurements). Q = C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 3
J. Change your variable capacitor to its smallest capacitance setting. What effect do you expect this change in the capacitance to have on the resonant frequency of the paralleltuned system? K. Switch your function generator back into its squarewave mode at a rep rate of a few hundred hertz. Adjust your scope s sweep speed, if necessary, so that you can see the highfrequency oscillations in one ringdown. Measure and record the frequency of the damped sinusoid in the ringdown. Frequency of Damped Sinusoid: L. Measure the halfamplitude decay time for this ringdown. Compare your result with your measurement of the decay time for the largest capacitance setting. Halfamplitude decay time: M. Measure the resonant frequency of the tuned system (use the same procedure that you used in Step G). Was the prediction you made in Step J correct? Resonant frequency f 0 : N. Compare quantitatively your measurement of the resonant frequency with your measurement of the ringdown frequency. C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 4
O. Calculate the Q of the paralleltuned system. Compare (quantitatively) your result in this step with your calculation of Q for the highest setting of the variable capacitor. C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 5
P. Leaving your airdielectric variable capacitor (C2) at its smallest capacitance setting, disconnect the lower terminal of L2 from ground and connect a 100ohm potentiometer (or pot ) as a variable resistor in series with L2 as shown in Figure 2. Function generator in squarewave mode (to CH. 1 r (to CH. 2 Figure 2. Diagram of modified experimental setup with small variable resistor r (a 100ohm pot) connected in series with L2. Q. Once again, shock excite your paralleltuned system using the function generator in the squarewave mode at a rep rate of a few hundred hertz. Adjust the sweep speed of your scope, if necessary, so that you can see the damped sinusoidal oscillations in a single ringdown. R. Adjust the pot repeatedly through its entire range from 0 ohms to 100 ohms. As you do this, pay particular attention to the shape of the ringdown (that is, to the halfamplitude decay time). What effect does increasing r seem to have on the decay time? S. Now measure and record the halfamplitude decay time with r set to 100 ohms. Halfamplitude decay time (r = 100 ohms): C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 6
T. In Step M, you measured the resonant frequency of the paralleltuned system with the variable capacitor at its lowest setting and r effectively set to 0 ohms. Do you expect the resonant frequency to have changed greatly now that you have changed r to 100 ohms (see page 25 of Tuned LRC Circuits)? Explain your answer briefly. Now test the prediction you just made by measuring and recording the resonant frequency as you did in Step G. Compare (quantitatively) your measurement of the resonant frequency for r = 100 ohms and for r = 0 ohms. Resonant frequency f 0 (r = 100 ohms): U. Using your results from Step S and Step T, calculate and record the value of Q for the case in which r is set to 100 ohms. Q (r = 100 ohms) = In Step O, you calculated the Q of the paralleltuned system with r effectively set to 0 ohms (and the variable capacitor set to its lowest value). Compare your two measurements of Q (i.e., with r = 0 ohms and r = 100 ohms). What effect, if any, does increasing r have on the Q of the paralleltuned system? C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 7
V. Now set r to 0 ohms and add a fixed 2.2k resistor and a variable resistor (a 200k pot) in parallel with the variable capacitor (C2), as shown in Figure 3. Keep C2 at its smallest capacitance setting. Function generator in squarewave mode (to CH. 1 200 k (to CH. 2 r 2.2 k Figure 3. Diagram of experimental setup modified by adding 2.2k fixed resistor (R2) and 200k pot (R3) in parallel with C2. W. Shock excite your paralleltuned system at a rep rate of a few hundred hertz. Adjust your scope so that you can see the damped sinusoidal oscillations in a single ringdown. X. With r set to 0 ohms, adjust the 200k pot (R3) repeatedly through its entire range from 0 ohms to 200 k. What effect does increasing R3 seem to have on the halfamplitude decay time? Y. Now set R3 to 0 ohms and measure and record the halfamplitude decay time. Halfamplitude decay time (R3 = 0 ohms): Z. Keeping R3 set to 0 ohms, measure and record the resonant frequency as you did in Step G. Resonant frequency f 0 (R3 = 0 ohms): C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 8
AA. Calculate Q for R3 = 0 ohms. Q (R3 = 0 ohms) = BB. Now set R3 to its maximum resistance (200k). Measure and record the halfamplitude decay time. Halfamplitude decay time (R3 = 200k): CC. Keeping R3 at 200k, measure and record the resonant frequency as you did in Step G. Resonant frequency f 0 (R3 = 200k): DD. Calculate Q for R3 = 200k. Q (R3 = 200k) = EE. Compare your Q values for R3 = 0 ohms and R3 = 200k (with r set to 0 ohms). What effect does increasing R3 seem to have on the Q of the paralleltuned system? C:\TEACHING\PHYS426\SPRING00\LAB4.DOC 9