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1st order transfer function from data

  1. Jun 6, 2013 #1

    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.

  2. jcsd
  3. Jun 6, 2013 #2
    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. css = KDC*r ⇔ KDC = css/r, where css 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.
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