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Variable Frequency Step Determination

IP.com Disclosure Number: IPCOM000102161D
Original Publication Date: 1990-Oct-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 4 page(s) / 135K

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MacInnes, CS: AUTHOR


A method of choosing frequency points leading to accurate and efficient definition of frequency plots is provided.

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This is the abbreviated version, containing approximately 52% of the total text.

Variable Frequency Step Determination

       A method of choosing frequency points leading to accurate
and efficient definition of frequency plots is provided.

      One of the more often used ways of understanding the frequency
behavior of an electrical circuit is by means of a curve or graph
which shows the variation of some current or voltage in the circuit
as the frequency is varied over a given range.  It is important that
the points plotted on the graph give an accurate description of all
the peaks, troughs, and other features of the curve.  The method to
be described here produces an automatic, efficient selection of a
sequence of variably spaced frequency points, which not only give an
accurate graph of the curve, but do so with a minimum number of
points used.

      Let fbeg and fend denote the beginning and end, respectively,
of the frequency range to be considered.  Let the sequence of N
chosen frequencies be:
fbeg = f1, f2, ..., fN-1, Fn = fend (1)

      Let there be M magnitudes to be considered and let m, j = 1,
2, M denote the magnitude of the j - th circuit variable to be
graphed.  The magnitude of this variable over the entire range of
selected frequencies is then:
mj(f1), mj(f2), ..., mj(fN) (2)

      Conversely, all M magnitudes at a single specified frequency,
fr, would be denoted by:
m1(fr), ..., mM(fr) (3)

      Assume that the n - th frequency point has just been chosen.
In order to choose the next frequency point fn+1, a multiplier, Gj is
chosen for each of the magnitudes mj, j = 1, 2, ..., M.  A single
multiplier to actually be used is chosen as the minimum of all the
G = min Gj
j = 1, M (4)

      The next frequency will then be the product of G and the
current frequency, fn:
fn+1 = G x fn (5)

      The determination of the multipliers Gj, i = 1, ..., M will now
be discussed.  The strategy for choosing a frequency step size can be
simply stated:  smaller steps should be taken over regions where the
curve is changing rapidly.  The curve is changing rapidly whenever it
is falling or rising rapidly, i.e., when the slope is large (i.e.,
steep).  Another place where rapid change is taking place is where
there is a bend in the curve; this feature can be expressed
mathematically by noting that the curvature is large.

      Thus, if the slope and/or curvature is large, small steps
should be taken so that the curve will be accurately graphed.  On the
other hand, regions where the curve is fairly flat and horizontal
should not require too many points to accurately describe them.

      Consider the j - th magnitude, mj and th...