download searchable PDF of Circuit Design book - IEEE Global ...

92 Ladder Network Analysis
A
... •••
+
"" E,
+
'" E,
jX
Figure 4.15.
Series and parallel impedance forms.
shunt (see Figures 4.3b and 4.3c). Then the voltage and current are in the
complex linear update (Table 4.1), so that lines 9970-9985 are correct for
impedance calculation. If the next branch is odd, then line 9965 in Program
B4-l swaps the respective real and imaginary parts of the voltage and current;
otherwise, the calculation would have produced the admittance instead of the
impedance.
The parallel impedance form is often required when a lossless voltage
source exists and for various other reasons. The parallel-ohms form is much
more widely accepted than admittance mhos; the latter, when it is used
(primarily by microwave engineers), is often given in millimhos. The parallel
input impedance form is
(4.42)
where R p is the reciprocal conductance, and X p
is the negative of the
reciprocal susceptance (see Figure 4.15).
It is well known that power P may be computed as the real part of the
product of sinusoidal voltage and conjugated current:
P= Re(VI*).
Therefore, the power input to the network is
p! = V1rI 1r + ViiI Ii ,
(4.43)
(4.44)
where subscripts rand i denote real and imaginary parts, respectively.
It is assumed that power delivered to the load impedance was an arbitrary
independent variable the user specified. Therefore, efficiency in dB loss is
PI
'I = 1010glOpdB. (4.45)
L
Negative values of (4.45) imply an active network with power gam, I.e.,
PL>P I •
4.5.1. Scattering Parameters. Two-port network equations have been written
in terms of ABeD (chain) parameters in Section 3.3.2 and in terms of both