SECOND ORDER CIRCUIT

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SECOND ORDER CIRCUIT
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Second order circuit
Natural Response of Parallel RLC
Circuit (Source-Free Parallel RLC Circuit)
We want to solve for v(t).
Applying KCL,
Differentiate once,
? This is a second order differential equation
with constant coefficients
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Second order circuit
This is known as the CHARACTERISTIC EQUATION of
the diff. equation
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Second order circuit
Solving for s,
Which can also be written as
where
s1, s2 known as natural frequencies (nepers/s)
?? known as neper frequency, ?o known as
resonant frequency
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Second order circuit
Overdamped solution
Critically damped solution
Underdamped solution
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Second order circuit
Overdamped response
Roots to the characteristic equation are real and
negative
A1 and A2 are determined from initial conditions
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Second order circuit
Critically damped response
A3 is determined from 2 initial conditions NOT
POSSIBLE
? solution should be in different form
A1 and A2 are determined from initial conditions
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Second order circuit
Underdamped response
Roots to the characteristic equation are complex
- known as damped natural frequency
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Second order circuit
Underdamped response
Using Eulers identity ej? cos ? jsin ?
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Second order circuit
Underdamped response