Transfer Function Gain Calculator

Calculate the DC gain and magnitude of a first-order transfer function at a specified frequency.

s
Hz

Magnitude at f

3.0331

DC Gain (at f=0)10.00
Magnitude (dB)9.64 dB
Phase Angle-72.34 °

Magnitude at f vs Static Gain (K)

Vedi formula →

Formula

## First-Order Transfer Function A first-order system has the transfer function G(s) = K / (tau*s + 1). The magnitude and phase at any frequency characterize how the system attenuates and delays sinusoidal inputs. ### Frequency Response **|G(j*omega)| = K / sqrt(1 + (omega*tau)²)** **Phase = -arctan(omega*tau)** At the corner frequency omega = 1/tau, the magnitude drops by 3 dB from the DC gain and the phase is -45 degrees.

Esempio Risolto

A system with K=10, tau=0.5 s, evaluated at f=1 Hz.

  1. 01omega = 2*pi*1 = 6.283 rad/s
  2. 02omega*tau = 6.283 × 0.5 = 3.142
  3. 03|G| = 10 / sqrt(1 + 3.142²) = 10 / sqrt(10.87) = 10 / 3.297 = 3.033
  4. 04dB = 20*log10(3.033) = 9.64 dB
  5. 05Phase = -arctan(3.142) = -72.3°