TABLE OF CONTENTS This chapter presents applications of the Laplace transform. Several examples are given to illustrate how the Laplace transformation is applied to circuit analysis. Complex impedance, complex admittance, and transfer functions are also defined.
In this section we will derive the voltage-current relationships for the three basic passive circuit devices, i.e., resistors, inductors, and capacitors in the complex frequency domain.
Resistor
The time and complex frequency domains for purely resistive circuits are shown in Figure 4.1.
Figure 4.1: Resistive circuit in time domain and complex frequency domain
Inductor
The time and complex frequency domains for purely inductive circuits is shown in Figure 4.2.
Figure 4.2: Inductive circuit in time domain and complex frequency domain
Capacitor
The time and complex frequency domains for purely capacitive circuits is shown in Figure 4.3.
Figure 4.3: Capacitive circuit in time domain and complex frequency domain
| Note | In the complex frequency domain, the terms sL and 1/sC are called complex inductive impedance, and complex capacitive impedance respectively. Likewise, the terms and sC and 1/sL are called complex capacitive admittance and complex inductive admittance respectively. |
Use the Laplace transform method to find the voltage v C( t) across the capacitor for the circuit of Figure 4.4, given that v C( 0 ?) = 6 V.
Solution:
We apply KCL at node A as shown in Figure 4.5.
