Chapter. 20 parallel resonance-Copy (1).pdf.

Laser and optoelectronics engineering department AC course lecture 3 chapter 20

1. AC ELECTRICAL
ANALYSIS II
LECTURE 3: CH. 20 PARALLEL RESONANCE

2. Parallel RESONANCE
•Forseriesresonance,theresonantfrequencywasthefrequencyatwhichtheimpedancewasaminimum,
thecurrentamaximum,andtheinputimpedancepurelyresistive,andthenetworkhadaunitypowerfactor.
•Fortheparallelresonantcircuit,theimpedanceisrelativelyhighatresonance.

3. Parallel RESONANCE

4. Parallel RESONANCE
For unity power factor, the reactive component must be zero as defined by

5. Parallel RESONANCE
wherefpistheresonantfrequencyofaparallelresonantcircuit(forFp=
1)andfsistheresonantfrequencyforseriesresonance.
theresonantfrequencyfpisafunctionofresistance(inthiscaseRl).
Sincethefactor islessthan1,fpislessthanfsandasthe
magnitudeofRlapproacheszero,fprapidlyapproachesfs.

6. Maximum Impedance
Atf=fptheinputimpedanceofaparallelresonantcircuitwillbe
nearitsmaximumvaluebutnotquiteitsmaximumvalueduetothe
frequencydependenceofRp.Thefrequencyatwhichmaximum
impedancewilloccurisdefinedbyfmandisslightlymorethanfp,

7. Selectivity curve
Thequalityfactoroftheparallelresonantcircuitcontinuestobe
determinedbytheratioofthereactivepowertotherealpower.

8. Selectivity curve
Fortheidealcurrentsource(Rs=∞Ω)orwhenRsissufficientlylargecomparedtoRp,wecanmakethe
followingapproximation:

9. Selectivity curve
Ingeneral,thebandwidthisstillrelatedtotheresonantfrequencyandthequalityfactorby

10. EFFECT OF Ql ≥ 10
Inductive Reactance, XLp Resonant Frequency, fp(Unity Power Factor)

11. EFFECT OF Ql ≥ 10
Resonant Frequency, fm(Maximum VC) Rp

12. EFFECT OF Ql ≥ 10
ZTp Qp

13. EFFECT OF Ql ≥ 10
BW IL and IC

14. EFFECT OF Ql ≥ 10

15. Examples
EXAMPLE 20.6 Given the parallel network of Fig. 20.32 composed of “ideal” elements:
a. Determine the resonant frequency fp.
b. Find the total impedance at resonance.
c. Calculate the quality factor, bandwidth, and cutoff frequencies f1 and f2 of the system.
d. Find the voltage VC at resonance.
e. Determine the currents IL and IC at resonance.