Description

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

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 SHIFTCMPLXFunction for example to add

Z₁ = (10 + j20)

and

Z₂ = (30 - j25)

gives

Z₃ = Z₁ + Z₂ = ( 10 + j20 ) + ( 30 - j25 )

20 ENTER 10 ENTER
25 CHS ENTER 30

The stack will show

20.0000
10.0000
-25.0000
30.0000

Then carry out the addition

SHIFT CMPLX +

The display will show

20.0000
10.0000
-5.0000
40.0000

X has the real part of Z₃ (40) and Y has the imaginary part of Z₃ (-5)

Z₃ = ( 40 - j5 )

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

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

• Results on stack:

67.5598
0.2002
1.5006
-13.9718

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

— John Pumford-Green 19/07/23 06:08