Application of Laplace Transforms: Circuit Analysis
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1 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. EGR 272 – Inverse Laplace Transforms using MATLAB
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EGR 272 – 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) - PowerPoint PPT Presentation
Transcript of Application of Laplace Transforms: Circuit Analysis
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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.
EGR 272 – Inverse Laplace Transforms using MATLAB
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s-domain circuit models
time-domain s-domain
L sL
R R
C 1/(sC)
Li(0)
v(0)/s
10V 10/s
2mA 0.002/s
EGR 272 – Inverse Laplace Transforms using MATLAB
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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 272 – Inverse Laplace Transforms using MATLAB
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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.
28 ohms 4 H
0.025 F160 V
+
VC(t)
_
+-
i(t)
EGR 272 – Inverse Laplace Transforms using MATLAB
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Example 1 (continued)
EGR 272 – Inverse Laplace Transforms using MATLAB
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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.
ia(t) ib(t)
EGR 272 – Inverse Laplace Transforms using MATLAB
1 0 V 2 0 V
5 1 5
4 H
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Example 2 (continued)
EGR 272 – Inverse Laplace Transforms using MATLAB
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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.
EGR 272 – Inverse Laplace Transforms using MATLAB
2k
10 uF
336 V +-
i(t)+ v(t) -
8 mH
4k
