HP 54753A - Page 226

Improving Time Domain Network Measurements
Removing Measurement Errors
10-20
(5)
The normalized response is the DUT frequency response multiplied by the
frequency response of an ideal impulse. Note that the error response has been
removed, and that N(f) is an impulse response.
When N(f) is converted to the time domain, the result is n
i
(t), a normalized
impulse response.
Because a step stimulus is used, a normalized step response, n
s
(t), is desired.
An ideal step can be defined in the time domain by convolving w(t), the ideal
impulse response, with u(t), the unit step function. Given this modification,
equation 6 further describes the effect of the filtering process.
(6)
The normalized response, n
s
(t), is the impulse response of the DUT convolved
with the ideal step defined by the convolution of w(t) with u(t). The result of
normalization is, therefore, the response of the DUT to an ideal step of risetime
determined by w(t). By varying the width, L, of W(f), normalization can predict
the response of the DUT at multiple risetimes based on a single-step response
measurement.
Mf() Df()=
Sf()Nf() Mf()Ff()=
Nf() Df()Sf()Ff()=
Nf() Df()Wf()Ef()
Wf()
Wf()Ef()
----------------------
=
Nf() Df()Wf()=
n
i
t() dt()wt()=
n
s
t() n
i
t()ut()=
n
s
t() dt()wt()ut()[]=