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--- public:calculator:progs:dm32_progs [24/07/23 16:32 BST] – [Return Loss & SWR from Complex Impedance] john
+++ public:calculator:progs:dm32_progs [06/03/25 06:49 GMT] (current) – external edit 127.0.0.1
@@ Line 12: / Line 12: @@
 === Complex numbers in DM32 ===
-The DM32 handles complex numbers by treating X as Real, Y and Imaginary for one complex number, and Z as Real and T as Imaginary for a second complex number.
+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.
-Then various "Complex" functions are access by <key>SHIFT</key><key>CMPLX</key><key>Function</key> for example to add
+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.
-Z<sub>1</sub> = (10 + j20) and Z<sub>2</sub> = (30 - j25) = Z<sub>3</sub>
+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>
 ENTER 10 ENTER
 CHS ENTER 30
+</code>
+The stack will show
+<code>
+.0000
+.0000
+-25.0000
+.0000
+</code>
+Then carry out the addition
+<code>
 SHIFT CMPLX +
 </code>
@@ Line 37: / Line 64: @@
 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 - j 5
+Z<sub>3</sub> = ( 40 - j5 )
-===== Section Two =====
+===== The program  =====
+<code>
+LBL Z
+INPUT R
+INPUT X
+X<>Y       ; swap so Real is R and Imag is X
+
+ENTER
+         ; 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
+
+ENTER
+         ; 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|
+
+RCL+ P
+
+RCL- P
+÷
+STO S       ; store VSWR ( 1 + |ρ| ) / ( 1 - |ρ| )
+RCL P
+LOG
+
+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>
+.5598
+.2002
+.5006
+-13.9718
+</code>
+  * |Z| = 67.6 ohms
+  * |ρ| = 0.2
+  * SWR = 1.5:1
+  * Return Loss = 13.9dB