First-Order Circuits
The Source-Free RL Circuit and Source-Free RC Circuit
There are three basic, linear passive lumped a components: the resistor (R), the capacitor (C), and the inductor (L). These may be combined in the RC circuit and the RL circuit with the abbreviations indicating which components are used. These circuits, among them, exhibit a large number of important types of behavior that are fundamental too much of analog electronics. In particular, they are able to act as passive filter.
Natural response
The Natural Response of an RC Circuit
Resistive Circuit => RC Circuit
Algebraic equations => differential equations
Same Solution Methods (a) Nodal Analysis
(b) Mesh Analysis
The solution of a linear circuit, called dynamic response, can be decomposed into Natural Response + Forced Response Or in the form of Steady Response + Transient Response. The natural response is due to the initial condition of the storage component (C or L). The forced response is resulted from external input ( or force). In this chapter, a constant input (DC input) will be considered and the forced response is called step response.
: Two forms of the first orders circuit for or natural response
The Source-Free RC Circuit
•The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation.
•The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8% of its initial value.
• v decays faster for small t and slower for large t.
for finding source free RC circuit:
The Source-Free RL Circuit
•The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8% of its initial value.
• i(t) decays faster for small t and slower for large t.
•The general form is very similar to a RC source-free circuit.
This topic shows the relationship of voltage per time and current per time. In real life, both RL and RC circuits are powerful and have diverse applications. By experimentation you will understand the true power of the circuits and why engineers rely upon the resistor and capacitor for many applications also in resistor and inductor for many radios receiver.