dc gain of the transfer function ?

[v9260019]

dc gain of transfer function

If G(S) is the forward transfer function, and

Limt(S->0)G(S) why called it as the dc gain of the forward transfer functon

THANKS A LOT

 

[leotim]

dc gain

"DC" equals zero frequency (0 Hz). and "0 Hz" is equal to s = 0. so if you put 0 instead of s in G(s), it gives value of G(s) at 0 Hz or DC.

 

[SkyHigh]

transfer function gain

Wrong! 0Hz does not mean s=0 since s=jw or 2Πfj. f=0Hz.
s->0 means s tends to zero in s-domain. This is also time tends to infinity.
In any linear system, time to infinity for a system is a stable system governed by final value theorem. For any system, it will encounter a short duration of transience. But over a long time (so-called time to infinity), it gets stable. When a system is stable in time, it is a DC condition.
Therefore G(s=0) or G(s->0) is DC gain or forward gain.

 

[LouisSheffield]

dc gain transfer function

leotim was close, albeit off by one:

For discrete LTI systems, most transfer functions may be expressed as a ratio of two polynomials in z.
The numerator polynomial has the zeroes of the transfer function as its roots, whereas the denominator has the poles.

The DC response exp(j0) may be readily solved by substituting z=1 into the polynomials.

Again ... this is for discrete LTI systems ...
Continuous systems solve differential equations, and, as such, are subject to boundary conditions for their complete solution.

 

[whynot910]

what is dc gain

SkyHigh: does time to infinity mean f=0Hz since f=1/T?

 

[leotim]

transfer function dc gain

For a stable system, the system output will be constant when time tends to infinity, aconstant value is a DC value or a 0Hz signal.