DM32 Progs - John's Vademecum

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====== DM32 Progs ======

** Description **

===== Return Loss & SWR from Complex Impedance =====

Input Rs and Xs to calculate |z|, |ρ|, VSWR and R.Loss

=== Complex numbers in DM32 ===

The DM32/HP31Sii handles complex numbers by treating stack-X as //Real//, stack-Y and //Imaginary// for one complex number, and stack-Z as //Real// and stack-T as //Imaginary// for a second complex number. 

This means the normal 4 level stack can hold 2 complex numbers. This is similar to the HP41 Advantage Pack's method.

To store a complex number in a register actually requires two to be used - one for Real part and one for Imaginary part. This is similar to the HP15C/DM15L.

Once the real and imaginary values are on the stack various "Complex" functions are accessed by <key>SHIFT</key><key>CMPLX</key><key>Function</key> for example to add

Z<sub>1</sub> = (10 + j20) 

and

Z<sub>2</sub> = (30 - j25)

gives

Z<sub>3</sub> = Z<sub>1</sub> + Z<sub>2</sub> = ( 10 + j20 ) + ( 30 - j25 )

<code>
20 ENTER 10 ENTER
25 CHS ENTER 30

</code>


The stack will show 
<code>
20.0000
10.0000
-25.0000
30.0000
</code>

Then carry out the addition

<code>

SHIFT CMPLX +
</code>

The display will show

<code>
20.0000
10.0000
-5.0000
40.0000
</code>


X has the real part of Z<sub>3</sub> (40) and Y has the imaginary part of Z<sub>3</sub> (-5)

Z<sub>3</sub> = ( 40 - j5 )


===== The program  =====

<code>

LBL Z
INPUT R
INPUT X
X<>Y       ; swap so Real is R and Imag is X
0
ENTER
50         ; enter Zo as 50 + j 0 
CMPLX +    ; complex addition Z + Zo
STO A      ; store intermediate value Re (Z + Zo)
R↓        
STO B      ; store intermediate value Im (Z + Zo)
R↓         ; X and Y stack now holds input Z real & imag again   
0
ENTER
50         ; enter Zo as 50 + j 0 (again)
CMPLX -    ; complex subtraction Z - Zo
RCL B      ; Im (Z + Zo)  
RCL A      ; Re (Z + Zo)
CMPLX ÷    ; complex divide (STACK z,t holds (Z - Zo) stack x,y holds (Z + Zo) (from reg. A & B) to calculate complex reflection coeff. ρ
STO E      ; save Re ρ
R↓
STO F      ; save Im ρ
RCL E
y,x -> θ, r ; convert complex rectangular ρ to mag/angle - X holds the magnitude |ρ| ( Y holds the angle, but we don't care)
STO P       ; save |ρ|
1
RCL+ P
1
RCL- P
÷
STO S       ; store VSWR ( 1 + |ρ| ) / ( 1 - |ρ| ) 
RCL P       
LOG
20
X
STO Y       ; store Return Loss = 20 LOG |ρ|
RCL X
RCL R
y,x -> θ, r
STO Z       ; store magnitude of impedance |z|
RCL P       ; |ρ|
RCL S       ; VSWR
RCL Y       ; Return Loss
RTN

</code>

=== Example ===

  * Z = 65.2 + j 17.7
  * R = 65.2
  * X = 17.7

  * Results on stack:

<code>
67.5598
0.2002
1.5006
-13.9718
</code>

  * |Z| = 67.6 ohms
  * |ρ| = 0.2
  * SWR = 1.5:1
  * Return Loss = 13.9dB


--- //John Pumford-Green 19/07/23 06:08//


===== Further Information =====


{{tag>calculator dm32}}

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