Obtaining A Good Model; Data Errors - HP 3563A Operating Manual

Curve Fit
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Obtaining Good Model

Obtaining a Good Model

The fundamental assumption in curve fitting is that the measured frequency response corresponds to
a finite-order rational-polynomial (linear) model. There are several challenges involved in making
accurate measurements which fulfill this assumption, and in utilizing measurements inevitably
subject to contamination and finite frequency span to obtain reasonable models.

Data Errors

There are four basic sources of data errors in frequency response measurements that prevent any
curve-fit algorithm from easily finding a linear model:
•
Nonlinearities
•
Noise
•
Quantization Errors
•
Digital Overflows
Nonlinearities
Frequency response measurements on systems that are either all-analog, or contain analog
subsystems (such as in sampled data systems), may be contaminated by distortion products
introduced by system nonlinearities.
search for sufficiently high system orders to compensate for these errors in the fit model. For
example, although a measured system may contain only
frequency response enough to look like a system with
no way in which the auto-order algorithm can differentiate between measurement errors and correct
data (user order will also do its best to fit measurement errors with the numerator order and
denominator order you set).
Measurements using the linear resolution mode and logarithmic resolution mode are based on the
Fast Fourier Transform (FFT). Broadband stimuli are used for FFT -based measurements. There
are two different types of broad band stimuli used in this analyzer:
•
Random noise
•
Periodic chirp.
If a truly random source is used (that is, RANDOM NOISE or BURST RANDOM), nonlinearities will
cause distortion products to randomly appear across the measurement span. Therefore, averaging
reduces the effects of nonlinearities on the frequency response measurement, and results in a linear
least-squares estimate of the system frequency response.
1 6-16
This
contamination can cause the auto-order algorithm to
poles and
4
poles and
10
3 zeros, errors may perturb the
In
zeros. other words, there is
10