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70 Ladder Network AMlysis
nonadjacent nodes can be accommodated. Each branch of the basic ladder
network may contain a large variety of series-connected-element subsets
connected in parallel, and vice versa. A compact means for describing the
network topology is an important part of Chapter Four.
All branch voltages and currents are available by the ladder network
analysis method employed. Beyond direct applications, these provide exact
sensitivity (partial derivative) information about how network performance
changes with respect to each component value. This is an important part of
gradient optimization methods and plays a significant role in manual and
automatic network-tuning considerations.
A convenient, accurate, and familiar ladder network analysis program is
one of the most important tools an individual can have in the world of radio
frequency (rf) engineering.
4.1. Recursive Ladder Method
A definite form, nomenclature, and convention will be employed throughout
Cbapter Four. Various parts have been di3cussed in numerous references. The
ladder network structure is shown in Figure 4.1.
,
I
4././. Ladder Nomenclature. Series (even-numbered) currents and shunt
(odd-numbered) voltages are sbown in Figure 4.1, with numbering beginning
at the branch across the load impedance ZL and proceeding back to the input,
which may be either a series or a shunt branch. All voltages and currents will
be rms (root mean square) values. Voltages between nodes (across series
branches) may be obtained as the differences between the node voltages, and
currents in shunt branches may be obtained in a similar way. If a branch does
not exist physically, its immittance (impedance or admittance, as appropriate)
is set equal to zero.
Each branch might contain only a single lumped element; e.g., Y1=jwC
and Z, = jwL. If these occurred in reverse order, the immittances would be
YI = l/jwL and Z,=l/jwC for nonzero elements. The load branch ZL =R L +
jX L might be set to a very large real part (IEIO) and a zero imaginary part if
an open-circuit load is to be simulated. The load real part, R L
, must never be
zero, as explained below.
Vs V 3 V 1
...- z,--;--r-- z,~z, --;-r-z,
1 I 6 1 I 4 \2 I
Y s Y 3 Y I
••• ...L. .L L- -J
Figure 4.1.
The ladder structure with alternating shunt admittances and series impedances.