We have verified that the efficiency of the resonators can
be improved using an IM circuit. Before automation can be
done, it is vital to know how the transmission and reflection ratios change as the matching parameters change so that
a suitable matching algorithm and hardware design can be
chosen. For example, in the event that local peaks exist, a
more sophisticated matching algorithm such as particle swarm
optimization will need to be implemented instead of simple 2-D
optimization algorithms such as the steepest gradient method.
The sharpness of the peak will also determine the precision
of the tuning parameters and optimization algorithm required.
Therefore, a simulation was conducted using MATLAB to
study the characteristics of S21 as capacitance used to set the
matching parameters (Cs and Cp) changes.
Fig. 13 shows the simulation results of S21 in the equivalent
circuit in Fig. 7(a) when the matching parameters (Cs and Cp)
are varied from 10 to 100 pF. The inductor Ls used in the
matching circuit is set to be 5000 nH, and the coupling coefficient
k is varied from 0.05 (large gap) to 0.25 (small gap).
Based on the figure, we can observe that there is only a
single peak with relatively gentle slopes at strong couplings and
steeper slopes at weaker coupling. This means that almost any
optimizing algorithm can be used to tune the system as long
as the precision of the tuning parameters is sufficiently high.
In this case, 1–2 pF for Cs and 5 pF for Cp will be sufficient
to tune the system. Another issue that has to be dealt with
is the parts where the gradient is too slight as the change in
signal-to-noise ratio of the directional coupler as the parameters
change becomes too small. One way to deal with this issue is
by measuring S11 from parameters further apart so that the S11
signal difference will be larger.