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Recursive Ladder Method 77
This last impedance sum is inverted, added to the admittance sum, and this is
then inveried to become the final branch-2 impedance. Only then is the
resistor processed; but it is branch 4, since the minus sign indicates a
null-branch 3.
Note that the resistor is introduced with a zero value; this is one of two
degenerate situations that may exist. The null resistor is needed to separate the
branch-2 description from the branch-5 description. The second degenerate
condition is covered by the following two rules: (I) level I can come before or
after level 2, or not at all; (2) multiple level-2 entries must be separated by
level I, even if by a null element. These dummy elements might be null C in
parallel or null R in series.
Depending on the mass storage capability of the small computer, it may be
possible for the program owner to have another program to prompt him for
input and arrange it in the proper form. However, the topological scheme just
described is easily mastered by sale users.
There are several ways to save memory in hand-held computers that are
register oriented. Referring to the topology data shown in Figure 4.4, one way
to save registers is to store each component type and its decrement (d = I/Q)
in one register to the left and right of the decimal point, respectively. For
example, the data in Figure 4.2 would be stored as -3.002,2.01, -1.0,2.004,
and - 3.0005. Unpacking is simplified by use of the integer and fractional
operators. Calls to the component-type subroutines are still easy, because most
calculators ignore the sign and the fractional part of the numbers. However,
any level-] and level-2 increases to the mantissa magnitude would need to be
removed; this usually occurs anyway in the test to see if levels I and 2 are
indicated. The unsealed component values would be paired with the registers;
this occurs naturally in the HP-67/97 calculators, where primary/secondary
register pairing is featured. In other programmable calculators, the pairing is
by a fixed register number difference, e.g., registers I and 21, 2 and 22, etc.
Packing the Nand K components and branch integers into one N.K format
also saves one register.
4.1.6, Recursive Ladder Analysis Sumtnary, The concept of working backward
in a ladder network, from what is arbitrarily assumed to have occurred
at the output end to what caused it at the input end, is well known. It is useful
because the network is assumed to be linear. The method is valuable for both
computations and algebraic formulations, as will be demonstrated in Section
8.3. There is only one complex functional form, which is solved repeatedly; it
requires just one multiplication and one addition. This operation is hest
programmed in assembly language for fast evaluation on machines providing
that opportunity along with a higher-level language, e.g., BASIC. The voltages
and currents obtained for shunt and series branches, respectively, are often of
direct interest; how they enable the exact calculation of component sensitivities
will be shown in Section 4.7.