1, G is the re?¬‚ection coef?¬?cient of the load and its assumed lossless matching
network with respect to the source impedance RS, and R and C represent the resistance and
capacitance, respectively, in the parallel RC load (Figure 4.8).
Equation 4.1 places a maximum limit on the integral to p=RC. In order to completely use
the given limit of p=RC for a desired angular frequency bandwidth (Dv), jGj should be unity
along the entire band except for the bandwidth, Dv under consideration, thus implying a
complete mismatch outside Dv. Considering a minimum achievable mismatch over Dv and
thus aminimum bound on the re?¬‚ection coef?¬?cient of jGjDv over the bandwidth, Dv (refer to
Figure 4.14) yields Equation 4.2 which reveals that for a given RC load there is a compromise
between the maximum matching bandwidth and the maximum power transfer to the load:
G j jDv e 1
2DfRC: (4:2)
If matching is to be performed to satisfy a certain acceptable jGjDv (and hence, amount of
power transfer), the bandwidth may have to be reduced. On the other hand, if matching is
to be performed over a certain given bandwidth, the amount of power transfer to the load
may have to be compromised.
VS
RS
Lossless
matching
network
R C
FIGURE 4.13
Acircuit with a losslessmatching network and a parallel RC load. (From Ranasinghe,D.C., Leong,K.S.,Ng, M.L., and
Cole, P.
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