FPGA Based Digital World - Transient Circuit Analysis

FPGA based Digital World

Welcome to FPGA based Digital World.

Analog circuit is the basis of electronics, and covers lots of area.

Transient Circuit Analysis

For transient response of a circuit, several methods are available for analysis.

Modeling in Time Doamin with ODE(Ordinary Differential Equations)

In this case, the input x(t) is a function of time, and the circuit is modeledas ODEs. The reponse y(t) of the system is achieved by solving the ODEs.

For a SISO circuit system, another way to get the response is through the convolution of input x(t) and the impulse response h(t)of the circuit, i.e.,

y(t) = x(t) * h(t)

Modeling in s-Doamin with Laplace Transform

Laplace transform converts differential equations in the time domain into algebraic equations in complex Laplace variable s-domain.

The input signal x(t) can be transformed to s-domain as X(s), and the system characteristic in s-domain is modeled by its transfer function H(s).Then the system response in s-domain is

Y(s) = H(s)X(s)

And the response in time-domain could be achieved by the inverse Laplace transform of Y(s).