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TitleCircuits Solutions With Matlab
TagsElectrical Impedance Matrix (Mathematics) Operational Amplifier Electrical Network
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Page 26

7.Using MATLAB for Analysis of Steady-State Circuits with Sinusoidal Inputs

Analysis of steady-state linear circuits with sinusoidal inputs using phasors and impedances requires
complex arithmetic. MATLAB can be used to reduce the effort required to do this complex arithmetic.
Consider the circuit shown in Figure 7-1a. The input to this circuit, vs(t), is a sinusoidal voltage. At steady
state, the output, vo(t), will also be a sinusoidal voltage as shown in Figure 10.15-1a. This circuit can be
represented in the frequency domain using phasors and impedances as shown in Figure 10.15-1b.
Analysis of this circuit proceeds as follows. Let Z1 denote the impedance of the series combination of R1
and jω L. That is,

(7-1)






Figure 7-1 A steady-state circuit excited by a sinusoidal input voltage. This circuit is represented both (a)
in the time domain and (b) in the frequency domain.

Next, let Y2 denote the admittance of the parallel combination of R2 and 1/jω C. That is,

(7-2)
Let Z2 denote the corresponding impedance, that is,

(7-3)
Finally, Vo is calculated from Vs using voltage division. That is,

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