EGR 261 – Inverse Laplace Transforms using MATLAB
Application of Laplace Transforms: Circuit Analysis
MATLAB is a powerful tool for analyzing circuits using Laplace
transforms. One approach might be:
• Determine the s-domain circuit (find initial conditions first)
• Use MATLAB to find complex impedances (XC = 1/(sC), XL = sL)
• Write any required circuit equations (KVL, KCL, etc)
• Use solve( ) solve the circuit equations. The result will be functions
of s.
• Use ilaplace( ) to find the corresponding time-domain expressions.
In class the s-domain relationships for each type of circuit element are
developed. They are summarized on the following slide.
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EGR 261 – Inverse Laplace Transforms using MATLAB
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s-domain circuit models
time-domain
s-domain
R
C
L
R
1/(sC)
v(0)/s
sL
Li(0)
10V
10/s
2mA
0.002/s
Lecture #22
EGR 267 – Engineering Analysis Tools
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Procedure: Circuit Analysis using the Laplace-transformed Circuit
1) Draw the circuit at t = 0-.
• Assume that the circuit is in steady state.
• Draw inductors as short circuits and capacitors as open circuits.
• Find vC(0-) and iL(0-) – these are needed for step 2.
2) Draw the s-domain circuit for t > 0.
3) Analyze the circuit as you might analyze a DC circuit (using any
circuit analysis method). Recall that the s-domain impedances sL and
1/(sC) act essentially like resistors. Determine the desired result in the
s-domain (V(s), I(s), etc).
4) Convert the result back to the time domain. In other words, use
inverse Laplace transforms to find v(t) or i(t) from V(s) or I(s).
Note: If the circuit has zero initial conditions then the voltage sources
in the capacitor and inductor models will be zero.
EGR 261 – Inverse Laplace Transforms using MATLAB
Example 1:
Use Laplace transforms and MATLAB to determine i(t) and vC(t) in the circuit
shown below (for t > 0). Assume that all initial conditions are zero.
i(t)
28 ohms
160 V
+
-
4H
0.025 F
+
VC(t)
_
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EGR 261 – Inverse Laplace Transforms using MATLAB
Example 1 (continued)
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EGR 261 – Inverse Laplace Transforms using MATLAB
Example 2:
Use Laplace transforms and MATLAB to determine ia(t) and ib(t) in the circuit
shown below (for t > 0). Assume that all initial conditions are zero.
5
15
ia(t)
10V
ib(t)
4H
20V
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EGR 261 – Inverse Laplace Transforms using MATLAB
Example 2 (continued)
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EGR 261 – Inverse Laplace Transforms using MATLAB
Example 3: (class example)
Use Laplace transforms and MATLAB to determine i(t) and v(t) in the circuit
shown below (for t > 0). Assume that vC(0) = 50V and i(0) = 100 mA.
8 mH
i(t)
336 V
+
-
10 uF
+ v(t)
4k
2k
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