First-Order Circuits Instructor: Chia-Ming Tsai Electronics Engineering National Chiao Tung University Hsinchu, Taiwan, R.O.C.

Contents Introduction The Source-Free RC Circuit The Source-Free RL Circuit Singularity Functions Step Response of an RC Circuit Step Response of an RL Circuit First-Order Op Amp Circuits Applications

Introduction Two types of circuits are included –The RC circuit: a circuit comprising a resistor and a capacitor –The RL circuit: a circuit comprising a resistor and an inductor First-order differential equations are produced while applying KVL and KCL to the circuits

The Source-Free RC Circuit

Cont’d The natural response of a circuit refers to the behavior of the circuit itself without external excitation sources. 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. –  = RC

Cont’d The energy stored in the capacitor is dissipated in the resistor!

Cont’d

Example 1

Example 2 t < 0 t > 0

The Source-Free RL Circuit

Cont’d The time constant for the RL circuit is

Cont’d The energy stored in the inductor is dissipated in the resistor!

Example 1

Example 1 (Cont’d)

Example 2 t < 0 t > 0Find R eq Find i(0)

Example 3 t < 0 t > 0 Find i(0), i 0 (0), v 0 (0) Find R eq

Example 3 (Cont’d) Inductor current is continuous Resistor current is discontinuous