1st order model from Data

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.