Presentation on parallel resonance for b-tech 1st year...

1. Seminar On Basic Electrical
Engineering(TEE-201)
Topic:
Parallel Resonance
Made By: Shivam Gupta
Roll No.-33
Sec.-E

2. Contents
Parallel
Resonance
• Parallel Resonance
Introductio
n
• Introduction
Parallel RLC
Circuit
• Parallel RLC Circuit
Resonant
Frequency
• Resonant Frequency
Parallel
Resonant
Circuit
• Parallel Resonant Circuit
Frequency
Curve
• Frequency Curve
Impedence
Of a Parallel
Resonant
Circuit
• Impedence Of a Parallel Resonant Circuit
Current In
Parallel
Resonant
Circuit
• Current In Parallel Resonant Circuit
Susceptanc
e Of a
Parallel
Resonant
Circuit
• Susceptance Of a Parallel Resonant Circuit
Bandwidth
Of a Parallel
Resonant
Circuit
• Bandwidth Of a Parallel Resonant Circuit
Review
• Review

3. PARALLEL RESONANCE
The resonance that results when circuit
elements are connected with their inductance
and capacitance in parallel, so that the
impedance of the combination rises to a
maximum at the resonant frequency.

4. INTRODUCTION
• The resonant electrical circuit must have both
inductance and capacitance.
• In addition, resistance will always be present due
either to the lack of ideal elements or to the
control offered on the shape of the resonance
curve.
• When resonance occurs due to the application of
the proper frequency ( fr), the energy absorbed
by one reactive element is the same as that
released by another reactive element within the
system.

5. Resonant Frequency
 The frequency at which the inductive and
capacitive reactances of a parallel resonant
circuit are equal.
 The frequency at which the parallel
impedance of a parallel resonant circuit is
maximum.
 The frequency at which the parallel
impedance of a parallel resonant circuit has a
power factor of unity.

6. Calculation Of Resonant Frequency
Simple parallel resonant circuit (tank circuit).
Since we know the equations for determining the reactance of
each element at a given frequency, and we're looking for that point
where the two reactances are equal to each other, we can set the
two reactance formulae equal to each other and solve for
frequency algebraically.

7. XL=2πfL
XC=1/2πfC
Resonance occurs when XL = XC

8. This is a formula to tell us the resonant
frequency of a tank circuit, given the values of
inductance (L) in Henrys and capacitance (C) in
Farads.

9. Phasor diag. for parallel resonant circuit.

10. Parallel resonant circuits
• A parallel resonant circuit is resistive at the
resonant frequency.At resonance XL=XC, the
reactive components cancel. The impedance is
maximum at resonance.
• Below the resonant frequency, the parallel
resonant circuit looks inductive since the
impedance of the inductor is lower, drawing the
larger proportion of current.
• Above resonance, the capacitive rectance
decreases, drawing the larger current, thus,
taking on a capacitive characteristic.

11. Capacitive
Frequency Curve For Parallel
Resonance
Resistive
Inductive

12. Impedence Of A Parallel Resonant
Circuit
Impedance is maximum at resonance in a parallel resonant circuit, but
decreases above or below resonance. Voltage is at a peak at resonance since
voltage is proportional to impedance (E=IZ).
Impedance peaks at resonance

13. Current In A Parallel Resonance
Circuit
At resonance the current flowing through the
circuit is at its minimum as the inductive and
capacitive branch currents are equal ( IL = IC )
and are 180o out of phase.

14. We remember that the total current flowing in a
parallel RLC circuit is equal to the vector sum of the
individual branch currents and for a given frequency
is calculated as:

15. At resonance, currents IL and IL are equal and
cancelling giving a net reactive current equal to zero.
Then at resonance the above equation becomes.

16. Susceptance At Resonance
 The inductive susceptance, BL is inversely
proportional to the frequency as represented by the
hyperbolic curve.
The capacitive susceptance, BC is directly
proportional to the frequency and is therefore
represented by a straight line.
The final curve shows the plot of total susceptance of
the parallel resonance circuit versus the frequency
and is the difference between the two susceptances.

17. At the resonant frequency point were it crosses the
horizontal axis the total circuit susceptance is zero.

18. Bandwidth Of A Parallel Resonant
Circuit
BW = Δf = fh-fl = 343-281 = 62
fl = fc - Δf/2 = 312-31 = 281
fh = fc + Δf/2 = 312+31 = 343
Q = fc/BW = (312 Hz)/(62 Hz)=5
The bandwidth of the parallel resonant response curve is measured
between the half power points. This corresponds to the 70.7% voltage
points since power is proportional to E2. ((0.707)2=0.50) Since voltage is
proportional to impedance, we may use the impedance curve.

19. Review:
• At resonance parallel RLC circuit acts like an open circuit.
• Current at resonance is at it’s minimum.
• Impedence of the parallel resonant circuit is maximum
and is equal to the resistance.This resistance is known as
dynamic resistance.
• Susceptance At resonant frequency is equal to ZERO

20. THE END
THANK YOU