Frequency Response

The Frequency Response Analysis (PLECS Standalone only) computes the frequency response of a system at discrete analysis frequencies by sequentially applying sinusoidal perturbations. The analysis is executed by following these steps:

  1. A transient simulation is used to drive the system into steady-state. The length of the simulation is determined by the Initialization time span parameter \(T_{init}\). This is used to define the operating point at which the frequency response will be calculated.

  2. Transient simulations are executed in parallel for every discrete frequency \(f_k\). All simulations start from the steady-state point reached in the previous step. The length of the perturbed simulations is defined as \(T_s + T_c\), where \(T_s\) is the Settling time span parameter, and \(T_c = N * 1/f_k\) is the number of Extraction cycles parameter times the period of the sinusoidal perturbation. An additional transient simulation with no perturbation is also executed.

  3. The Fourier analysis is computed for each discrete perturbation frequency \(\omega_k = 2\pi f_k\), of \(T_c\) period in the perturbation and response signals of both the perturbed and unperturbed simulations. Being \(U(\omega_k)\) and \(U_0(\omega_k)\) the Fourier transforms of the perturbation signal in the perturbed and unperturbed simulations, and \(Y(\omega_k)\) and \(Y_0(\omega_k)\) the Fourier transforms of the response signals in the perturbed and unperturbed simulations, respectively.

  4. The frequency response of the system is obtained as \(G(\omega_k) = (Y(\omega_k)-Y_0(\omega_k))/(U(\omega_k)-U_0(\omega_k))\).