What is the difference between DC Gain and Gain Constant?

In summary, the conversation discusses learning about Butterworth filters and frequency scaling. The transfer function after scaling by Kf is found by dividing all 's' by Kf. In a homework problem, confusion arises when trying to find the new location of poles and the gain constant. The DC gain of the transfer function remains unchanged, but the answer suggests multiplying it by Knew=Kold*Kf^n. The conversation ends with the question of what the transfer function gain constant represents and the realization that it is different from the DC gain.
  • #1
Rib5
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I am learning about Butterworth filters right now, so we are also learning about frequency scaling. To find the new transfer function after you frequency scale something by Kf, you simply divide all 's' by Kf.

I am doing a homework problem where you have to find the new location of the poles and the gain constant. Here is where my confusion happened.

The DC gain of the transfer function does not change from what my calculations showed, but the answer was saying to multiply it by Knew=Kold*Kf^n where n is the order of the BW filter.

I am rambling on now. From what I get in my book, DC gain is different from the transfer function gain constant. DC gain is what happens to an actual signal when you put it through. What does the transfer function gain constant represent then? All my confusion started when I assumed they were the same thing.
 
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  • #2
You don't say what Kf is.

But to your basic question, of course they are different. Many filters completely block DC.
 

1. What is DC Gain?

DC Gain, also known as DC Open Loop Gain, is the ratio of the output voltage to the input voltage of a system when the input voltage is at a constant, or DC, level.

2. What is Gain Constant?

Gain Constant, also known as AC Gain or Gain, is the ratio of the output amplitude to the input amplitude of a system when the input is a varying, or AC, signal.

3. Are DC Gain and Gain Constant the same thing?

No, they are not the same thing. DC Gain is specifically for a constant input voltage, while Gain Constant is for an input signal with varying amplitude.

4. How are DC Gain and Gain Constant related?

DC Gain and Gain Constant are related by the overall gain of a system. In many systems, the DC Gain and Gain Constant are equal, but in some cases, they may be different due to non-linearities in the system.

5. Which is more important, DC Gain or Gain Constant?

The importance of DC Gain and Gain Constant depends on the specific application. In some cases, DC Gain may be more important for steady-state analysis, while in others, Gain Constant may be more important for analyzing the overall behavior of the system.

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