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CHAPTER 3: HF MODELLING STRATEGY
Re(Z)
Fitness Function
ref
f 1 f 2 f 3 f 4
sim
Figure 3.1: Example of error integration for impedance
Log(f)
The goodness of every individual is evaluated by the Fitness Function that associates a
numerical value to each of them; this function is the way to map how far each individ-
ual is from the desired goal. It can weight in different ways many aspects of the final
result, i.e. giving more importance to solutions generating a better match in a certain
range of frequencies or penalizing more the individuals that do not produce a desired
characteristic, such as a resonating frequency if the goal is to match an impedance with
that behaviour.
The Fitness Function used for the impedance matching in this work consists of the in-
tegral of the error between the measured reference impedance versus the frequency
and the relative simulated one with the parameters chosen by the GA, this is visually
represented by the area between the reference and the simulated impedance. Because
the impedance is a complex number, this area is calculated twice, once for the real and
once for the imaginary part, these two numbers are successively added to get the final
error. Fig. 3.1 shows the area so calculated, in this case just for the real part of the
impedance. The reference and the simulated impedance points might not be sampled
at the same frequency, so a process of interpolation takes place and subdivide the se-
ries of data at all the vertex of either of the two curves, to obtain eventually two set
of values sampled at the same frequencies. In this example the algorithm for the error
integration calculates the total area given by the five subsections shown in alternate
colors and patterns, every area can only be either a trapezium (third and fifth case) or
the double opposite triangle (first, second and fourth case); this is because it is defined
by 4 segments, two of witch have to be parallel, representing the frequency subdivision
in the impedances, that have been adjusted to be the same. To distinguish between the
two cases and pick the right formula, the algorithm simply checks if the reference and
the simulated impedance values cross each other or not.
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