1st order transfer function from data

[havanna1]

Hello,

Im trying to model an RF attenuator for use in a control system. The control voltage is from 0-2.1V and I
applied a step function signal from 0-2.1V and measured the output. I was able to model it as a first
order system in the form Kdc / Xs + 1.

The issue I'm having is understanding how to represent the DC gain component in the numerator. I understand
that the DC gain is the value that the output settles at, but I feel like I need to normalize it to
a unit step function rather than a 2.1V step.


I input 0dBm of RF power and step the control voltage from 0-2.1V and the output swings from -27.6dBm to
-1.4dBm. How would the DC gain be normalized to a unit step function input for analysis and design of
the control loop.

Thanks.

 

[milesyoung]

I understand that the DC gain is the value that the output settles at, but I feel like I need to normalize it to a unit step function rather than a 2.1V step.

That's only true for a unit step response. In general, its DC gain is the steady-state gain to a constant input (if your system has a steady state), i.e. c_ss = K_DC*r ⇔ K_DC = c_ss/r, where c_ss is the steady-state output and r is the constant input.

In short, measure the ratio of the steady-state output to the constant input.