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This lecture is part of lecture series on Electrical Circuit Analysis course. It was delivered by Prof. Mursleen Sayed at Bengal Engineering and Science University. It includes: Transfer, Function, Initial, Conditions, Rlc, Circuit, Series, Input, Output, Capacitor, Multiple
Typology: Slides
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Y(s) is the laplace of output signal ^
X(s) is the laplace of input signal ^
^
Transfer function of a series RLC circuit ^
Input signal is voltage V
g
^
Output signal is current I ^
H(s) = I/V
= 1/(R + sL + 1/sC)g = sC/(s
2 LC + sRC + 1)
^
If voltage across the capacitor is the output signal ^
H(s) = V/V
=(1/sC)/(R + sL + 1/sC)g = 1/(s
2 LC + sRC + 1)
H(s) =? ^
Poles & Zeros =? ^
H(s)=
1000 ohm V g
(^250) ohm 50 mH
μ^ 1 F
Vo
sV 10 s 05
. 0 250
o 6
o
g o^
6
2
g
o^
(^10) x 25 s 6000 s
s( 1000 V^
6
2
(^10) x 25 s 6000 s
s( 1000
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H(s) = ^
Poles ^
-p1 = -3000 –j ^
-p2 = -3000 +j ^
Zeros ^
-z1 = -
1000 ohm Vg
(^250) ohm 50 mH
μ^ 1 F
Vo
6
2
(^10) x 25 s 6000 s
s( 1000
Transfer function in Partialfraction expansion ^
Y(s) = H(s)X(s) ^
Writing the equation in the form of sum of partialfractions ^
Produces a term for each pole of H(s) ^
Produces a term for each pole of X(s) ^
Terms generated by poles of H(s) gives rise totransient component of total response ^
Terms generated by poles of X(s) gives rise tosteady-state component of total response
H(s) = ^
Source voltage is v
= 50tu(t) Vg^
^
V(s) = 50/sg
2
^
V(s) = H(s)Vo^
(s) =g
= ^
K^1
= 5
5x
-4^
0
*K 1 = 5
5x
-4^
-79.
(^0)
^
K^2
= 10
K^3
= -4x
6
2
(^10) x 25 s 6000 s
) 5000 s( 1000
2 6
2
(^50) xs (^10) x 25 s 6000 s
) 5000 s( 1000
K^ s K s (^4000) j 3000 s
K
(^4000) j 3000 s
K^
3 (^22)
1
Response of a circuit is related to H(s) through apartial fraction expansion ^
Practically driving a circuit with an increasing rampvoltage leads to failure of components ^
Ramp function should only increase to a defined maximumvalue within a finite time interval ^
If time constant of the circuit is small compared to the timetaken by the signal to reach the maximum value. A solutionassuming an unbounded ramp is valid for this finite timeinterval
Response of a circuit with delayedinput ^
-as
^
-as
^
-as
^
Circuit is time-invariant
