[hp15c]

HP15c program: Parallel Impedance calculator


command         display

f LBL D        001-42,21,15
   1/x          002-      15
   x><y (swap)  003-      34
   1/x          004-      15
   + (add)      005-      40
   1/x          006-      15
g RTN          007-   43 32

Re-number program code starting with line number:

This program uses the following labels: LBL D
This program uses the following registers (STO/RCL): -none-

Using the program

I start every program with a label. This way you can have a number of programs in your 15c and you just select which one to run by pressing GSB LABELNAME (GSB D in this case, or GSB f D).

This program take to number (complex numbers if you want) from the X and Y registers of the stack and calculates the parallel impedance. It does not push any other numbers of the stack. The result is after the execution of the program in the X-register of the stack.

Enable complex number mode: g SF 8 (disable complex number mode would be: g CF 8).

Example 1)
What is "10K Ohm -j 20K Ohm" parallel to "4K Ohm + j 9K Ohm"?
You type:
10 EEX 3, Enter, 20 CHS EEX 3, f I
4 EEX 3, Enter, 9 EEX 3, f I
GSB D
The display shows "running" and then: 9.369 (more digits behind the decimal point), to see the imaginary part: f (i), 8.075 (more digits behind the decimal point)

Example 2)
A circuit with resistors only (no capacitors or coils): 10K Ohm parallel to 15K Ohm:
10 EEX 3, Enter
15 EEX 3,
GSB D
The display shows "running" and then: 6000
10K // 15K = 6K
(the // sign means parallel)


Example 3)
Calculate 10Ω + ( 4jΩ // -5jΩ )
(the // sign means parallel)
0 Enter 4 f I
0 Enter 5 CHS f I
GSB D
10 +
Result: 10 + 20j
Press f (i) to see the imaginary part of the number.

Algorithm

For two parallel impedances (complex number resistors):
      
              1          Z1 * Z2
Ztotal = ------------- = ---------
         1/Z1 + 1/Z2     Z1 + Z2

Z-values (impedance) of coil, capacitor, resistors

Coil: Z = jωL
Capacitor: Z = - j(1/ωC)
Resistor: Z = R

The unit of Z is Ohm (symbol Ω), C is to be given in F (Farad) and L is to be given in H (Henry).
ω = 2 π f

j is the imaginary part of the complex number also known as "i". We use j in the context of electic circuits to not confuse the symbol with the "i" symbol frequently used for current.


Example circuit:
       ----------------+------------+                    Calculate Ztotal for a sine frequency
                       |            |                    of 477.5Hz.
                       |            |
            C1=1μF    ---          ---  C2=2nF
                      ---          ---
                       |            |
                       |            |
Ztotal  ->             +-+          +-+
                      | |          | |
            R1=10KΩ   | |          | |  R2=6.8KΩ
                      | |          | |
                      +-+          +-+
                       |            |
                       |            |
       ----------------+------------+
Z1 = 10 *103 - j * 1/(2 * 3.1415 * 477.5 * 10-6) = 10000 Ohm -j 33.33 Ohm

Z2 = 6.8 *103 - j * 1/(2 * 3.1415 * 477.5 * 2 * 10-9) = 6800 Ohm -j 166654 Ohm

Now calculate the impedance of those two parallel elements:
10000, Enter, 33.33, CHS, f I,
6800, Enter, 166654, CHS, f I,
GSB D

Ztotal is: 9936.2 Ohm -j 626.8 Ohm
(not all digits behind the decimal point shown)

You press f (i) to view the imaginary part of the complex number.

You can press g ->P to convert this into the frequently used phasor form (9955 ∠ -3.6). Note that you must convert it back into rectangular coordinates if you want to use this number to do further complex number arithmetics on the calculator. STO/RCL do not store complete complex numbers on the HP15C. They store only the real part.
© Guido Socher