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LECTURE 4: PARALELL & SERIES RESONANCE by Department of Electrical Engineering Reactance
vis Frequency:
Xa)
Reactance
Frequency, f
Frequency, f
Series Resonance Frequency:
Capacitive | Inductive
AT Uy |
Xc > AL \ <7 > Xc
|
E - X.
a Inductive and Capacitive
= Reactances are equal here
a AL = Xe
Cc
om
Bb
wo
a
ao
X.-X,
(fr) Frequency, jf
Series Resonance
Impedance of a Series Resonance Circuit:
Capacitive Inductive
Pala) Mc > Xi XL > Mec
—<—al- -_
a
Cc
co
am
a
oo
=
Z=R
oO ad
f Frequency,
Dynamic (fr) 4 vf
impedance Series Resonance
Series Phase Angle Resonance Circuit :
[2 | YY Ww"
Below fa Capacitive Above fr. Inductive
At fz Lin phase with Vs
I leads Vs (ICE) Tlags Vs (ELI)
+907 Jo Le
+45° XL> Xc
(Inductive)
——————
o° > 7
Xe? KX
_A5? & apacitive)
Bandwidth is a range of frequencies within a given band, in particular that used for transmitting a signal. ( Series Resonance Circuit Bandwidth: • The frequency response of the circuits current magnitude relates to the sharpness of the resonance in a series resonance circuit. • The sharpness of the peak is measured quantitatively and is called the Quality Factor, Q of the circuit. • The Q - factor relates the maximum or peak energy stored in the circuit (reactance) to the energy dissipated (resistance) during each cycle of oscillation meaning that it is a ration of resonant frequency to bandwidth. Quality Factor & Selectivity: Series Resonance Circuit Bandwidth:
Current Amplitude
Ac > AL
R small
AL > Xe
R medium
Frequency, J
Series Resonance Example A coil having a resistance of 10Ω and inductance of 75 mH is connected in series with 40µF capacitor across a 200V a.c supply. Determine: a) At what frequency resonance occurs b) The current flowing at resonance Series Resonance Example A series circuit comprises a 10Ω resistance, a 5µF capacitor and a variable inductance L. the supply voltage is 20<0˚ volts at a frequency of 318,3 Hz. The inductance is adjusted until the p.d across the 10Ω is maximum. Determine for this condition a) The value of the inductance b) The p.d across each component c) The Q- factor Parallel RLC Circuit:
Either side of resonance the
current = IL - le
Tax I, ~ Ic
I
ne, R L
—
Atresonance the
reactive current is zero
Tutu
Xr ath
open circuit
Parallel Resonance Circuit Impedance:
Inductive Capacitive
Mec > A ML? Mec
— eal
Dynamic
impedance
a . -_
fr Frequency, j
Parallel Resonance
Susceptance at Resonance :
+/Be +iBc
A
Be = 2nfC
Inductive
Susceptance
B
Cc
3 0 ,
a
a
cr
Capacitive
Susceptance
y
“By “By
Q – Factor: • The selectivity of Q – factor for a parallel resonance circuit is the ratio of the circulating branch currents to the supply current, given by;
Bandwidth:
Por N
FL tu
Lower Upper
frequency frequency
aa
f (Hz)
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