Transfer Function Gain Calculator — सूत्र
## 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.
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.
हल किया गया उदाहरण
A system with K=10, tau=0.5 s, evaluated at f=1 Hz.
- omega = 2*pi*1 = 6.283 rad/s
- omega*tau = 6.283 × 0.5 = 3.142
- |G| = 10 / sqrt(1 + 3.142²) = 10 / sqrt(10.87) = 10 / 3.297 = 3.033
- dB = 20*log10(3.033) = 9.64 dB
- Phase = -arctan(3.142) = -72.3°