Curve Fit Operating Modes - HP 3563A Operating Manual

Curve Fit Operating Modes

Each curve fitter (the s-domain curve fitter and the z-domain curve fitter) has two operating modes:
•
User Order
•
Auto Order
User Order
In user order, the curve-fit routine uses only the specified numerator and denominator order. A
model is developed, with these orders, that has a frequency response which comes as close as
possible to the frequency response data in a least-squares sense.
In user-order mode, there is no higher level curve-fit algorithm as in auto-order mode. Thus, user
order does not perform a search for the best fit by trying different numerator and denominator
orders. In user-order mode, the least-squares curve-fit technique is not iterative. Given the same
frequency response and coherence functions, the fit model
curve fit in user order (using the same data and set up parameters), you obtain the same answer.
User order does not search for pole and zero terms to cancel. 1bis allows you to find a system with
pole-zero pairs which might otherwise be cancelled during an auto-order curve fit (auto order looks
for pole and zero terms close enough together to cancel).
Auto Order
In auto-order mode, the auto-order algorithm operates the curve-fit routine with successively larger
system orders until it finds a good model, or until the maximum system order is reached. Both the
maximum numerator order (number of zeros) and the maximum denominator order (number of
poles) can be specified. For example, entering
auto-order algorithm to finding a model that has a maximum of three zeros.
The auto-order algorithm starts with a numerator/denominator order of
curve-fit routine given this order. The auto-order algorithm automatically performs a synthesis on
the fit model and compares this frequency response to the measured frequency response. If the fit is
poor, the orders are incremented to
continues until a good match
have t o be equal. The auto-order algorithm holds the order at the first upper bound reached, and
lets the other order climb to the higher order if the fits are poor. If both upper bounds are reached
before a good fit is found, the auto-order algorithm returns the fit which came closest to the
measured frequency response.
When a good fit is found, the auto-order algorithm tries to reduce the numerator order and
denominator order if it determines that this has the potential of creating a lower-order model that
still provides a close match to the measured frequency response. This order reduction usually results
in a numerator order lower than the denominator order. The s-domain curve-fit algorithm
automatically imposes the restriction that the numerator order can never be larger than the
denominator order (the z-domain curve-fit algorithm does not have this restriction).
3
for the numerator upper bound restricts the
2,2,
and another fit is done. This search upwards in order
is
found or the upper bounds are reached. The upper bounds do not
is
unique. Therefore, if you repeat a
1,1
and does a fit using the
Curve Fit
Curve Fit Overview
16-3