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Recursive Ladder Method 73
This always indicates to the program that the preceding ladder branch
immittance was zero, i.e., a null prior branch. If the first - 3 in the type
column had been a positive 3, then the program would think that capacitor C 3
would have been in branch I (Figure 4.1). The value is in the units specified
separately, e.g., in microhenrys or picofarads. The Q column is the component
quality factor; it is meaningless for resistors, of course. A program feature
allows Q=O to indicate a lossless element (see Section 4.1.4). The two integer
pointers Nand K are used in the program to keep track of component
number and branch number, respectively. It is very important that the reader
understand this simple scheme. It puts some of the work on the user, but
programs employing this scheme are very efficient in both memory and speed,
The scheme can also be extended in many ways; for example, the column of
component values is often the set of variables that an optimizer can adjust for
improved performance. Subsequent sections in this chapter extend the topology
capability in many ways.
4,1.4. Ladder A1Ultysis Program Program B4-1 in Appendix B is written in
BASIC language. Some adaptation to make it more appropriate for hand-held
computers is discussed in Section 4.1.5. The program will be explained and
illustrated using the concepts previously discussed.
Program input begins with a request for the frequency, inductance, and
capacitance units; typically, this might be IE6, IE-6, and IE-12 for
megahertz, microhenry, and picofarad, respectively. Then the load resistance
and reactance values, in ohms, are requested. They are assumed to be
frequency independent in this program, but that can be changed without great
difficulty. The power delivered to the load is requested next; this enables
calculation of the load current according to (4.1). Referring to Program B4-1
in Appendix B, the main analysis loop at each frequency begins at line 1200,
where the frequency is input in the units previously specified. Radian frequency
is then calculated for subsequent use.
The recursion in Table 4.1 is implemented in the loop from lines 1300
through 1390. It is first initialized with load current magnitude (4.1) and phase
angle zero in code line 1220. Variable FI is a flag to indicate that a null
branch was processed in the previous complex linear update cycle. This is set
up in subroutine 9000, where a zero value is assigned to the null-branch
immittance. Otherwise, branch immittance is assigned by the calculated subroutine
call in line 1385, The variable MK had previously been assigned from
the component type array M(·); in line 1385, type MK= I would send the
program to subroutine 9100, MK=2 to subroutine 9200, etc. The actual
complex linear update (4.3) occurs in subroutine 9900, called at line 1370. A
little thought will show how elementary yet effective this ladder network
analysis scheme can be.
lt is important to understand the operation of the element-type suhroutines
9100, 9200, and 9300 in Program B4-1. There is a small amount of standard
overhead. If the branch number is odd (an admittance is anticipated), then the