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Milwaukee Area Technical CollegeElectronic Technology

Electronic Communications

Lab Exercise 2

Series and Parallel (anti-) Resonant Circuits

Objective:

The purpose of this lab unit is to compare the operating characteristics of series and parallelLCR circuits tuned near and far their resonant frequency. Recognizing the associatedfrequency response curves of band-pass and band-reject filters with respect to the load alongwith controlling circuit bandwidth using resistive damping will also be explored.

Part 1: Resonance

1. Measure the inductance and DC resistance of a 47H inductor. Also measure thecapacitance of a 470pF capacitor and record all values below. Be sure to zero theeffects of all measuring instrument leads.

L = RDC(L) = C =

2. Calculate the resonant frequency for the series LC circuit in figure 1 using measuredvalues then assemble the circuit for analysis. Disregard RS at this time.

fR =

3. Without an external damping resistor (RS) as denoted on the schematic, the value rS ofthe LC circuit is to be determined. This (little) rS is sometimes referred to as reactiveresistance and is a frequency dependent characteristic that should be considered whenchoosing an inductor. Actually, finding rS in situ will help determine the working Q of thecircuit since a nominal value is not given. Take special note to the type case used indenoting each resistance during this lab exercise.

Place channel 1 of the oscilloscope at VIN (generator output) and Channel 2 at VOUT andmanually sweep near resonancethe function generator’s frequency while maintaining 4 VP-P at the generator’soutput (VIN) at all times. Watch for a minimum output at/near thecalculated fR. Overlay the two channels using the position controls and watch the zerocrossings to ensure a zero phase relationship. This should occur near resonance and isnow called f0. Measure and record both VOUT and f0. Is there a difference between fR

and f0? Explain.

VOUT = f0 =

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Using the voltage divider equation to solve for an unknown resistance, find the value ofrS to determine Q. rS = RTHVOUT/VIN - VOUT

rS =

There should be a noticeable difference between the calculated value of rS and the DCmeasured resistance of the inductor. Can you explain this difference?

Ideally to obtain a high Q resonant circuit the inductor’s resistance should be kept at aminimum. Think about various ways for reducing reactive resistance (rS).

4. With RS set to 0 (no R added), manually sweep the generator from 500 kHz to 2.0MHz gathering the data to plot a response curve for VOUT vs frequency. Note:Collecting the data rather than graphing the result is more important at this point. It isrecommended to use 20 kHz steps between the preceding and succeeding 200 kHz ofthe resonant frequency, and 40 kHz steps beyond 200 kHz on either side of resonance.Also, record specific measurements at the point you consider f0 (this should be the

same as in step 3 if all is going well) and the two 3 dB up points labeled f1 and f2. Again,make certain that the output of the generator is maintained at 4 VP-P.

f0 = f1 = f2 =

At this time also note the phase difference between VIN and VOUT as you sweep aboveand below resonance using VIN as the reference (trigger the scope on the inputchannel). This should correspond to the reactive characteristic mnemonics of ELI andICE presented in previous courses.

5. Repeat all of step 4 but with RS equal to 22 or 24 . What conclusions can be madefrom your observations due to this change?

Now do the same for an RS of 47 .

6. Using a computer spreadsheet application, complete an individual graphical responsefor each value of RS and include a fourth where all three are superscribed forcomparison purposes labeling all characteristic frequencies on each.

7. From your data and completed graphical response curves determine the circuit Q,geometric center, bandwidth, and impedance at resonance for each value of RS.Compare theoretical results (show calculations using actual values and rS found in step3) with the experiential results and explain any large discrepancies. The geometriccenters can be found by using the data recorded for f1 and f2.

Table all the results from above including the directly measured f0 and the geometriccenter for f0.

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Part 2: Anti-Resonance

8. Using no external damping resistor (RP) for this step, assemble the parallel LCR circuitin figure 2. Use the same method and voltage divider formula in step 3 to aid in findingwhat is now referred to as rP for an anti-resonant circuit or sometimes called ZTANK. Inaddition, transform the circuit rP to its equivalent rS or rS’showing all calculations.Remember that at f0 the circuit Z is now maximum, just the opposite of what wasobserved for the series resonant circuit.

VOUT = f0 =

rP =

rS’= (transformed value)

How close is rS’to the actual rS obtained in step 3? Is it more or less?

Explain the discrepancy between the two and consider how the change made to RTH

might have an effect.

9. Considering ZTANK determined in step 8, calculate ZTotal for the circuit. ZTotal or ZT isdetermined at the resonant frequency with no load except for the output impedance ofthe signal source that would include RTH in this case. Remember that the sourceimpedance of a parallel resonant circuit is considered to be outside the tank circuittherefore loading the tank, which has an effect on the total impedance and bandwidth.

ZT =

10. Like the series resonance circuit, sweep and plot the response curves byloading/damping the circuit for RP equal to infinity (no external load), 47 k, and 10 k.Again, take specific measurements at the point you consider f0 (this should be the sameas in step 8) and the two 3dB down points labeled f1 and f2 for each sweep. Makecertain that the output of the generator is maintained at 4 VP-P.

11. Using step 7 as a guide, determine from your data the circuit Q, geometric center,bandwidth and ZT for each value of RP and compare this with theoretical values. Showall calculations, table appropriately and be prepared to explain any large discrepanciesbetween theoretical and experiential values.

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Lab Exercise 2 Circuit Figures

4Vpp

R th

1k

Rs = See Lab Procedure

C = 470pF

L = 47uH

Vout

Figure 1 (Resonance)

4Vpp

R th

10k

Rp = See Lab ProcedureC = 470pFL = 47uH

Vout

Figure 2 (Anti-Resonance)