**Casio fx-CG 50: Impedance Calculations**

**Introduction**
The program FX61IMP contains a suite of impedance calculations. Why the unusual name?

In the late 1980s, Casio had a fx-61F calculator. The fx-61F is a specialized programming scientific calculator, which is the only calculator, to my knowledge, to feature an Impedance mode. The impedance mode has specialized keys to calculate impedance of resistors, capacitors, and inductors (coils). The calculator also featured 29 specialized electrical formulas, a 30 step programming capability, base conversions, 1 variable statistics, and complex numbers.

**The main menu of FX61IMP:**
1. Impedance of a Coil (Inductor)

2. Impedance of a Capacitor

3. Impedance of two parallel resistors (Parallel)

4. Impedance of a Series Resistor

5. Analysis of total Impedance

6. Store results in X and Y

7. View Memory Registers

8. Clear Variables

9. Exit

Variables used:

Z = impedance of the current calculation

S = grand total impedance

X = user register

Y = user register

Note: In electronics, the symbol j is used in complex numbers. The fx-61F uses j. However, the fx-CG50 uses i in complex numbers. The program uses i and the user is notified of this when the program starts.

1. Impedance of a Coil (Inductor)

Provide the self-inductance (in H, Henrys) and frequency (in 1/s), the impedance is calculated as:

Z = 2 * π * f * L * i

The result is added to S.

2. Impedance of a Capacitor

Provide the capacitance (in F, Farads) and frequency (in 1/s), the impedance is calculated as:

Z = 1/(2 * π * f * C * i)

The result is added to S.

3. Impedance of two parallel resistors (Parallel)

This calculates the impedance of parallel resistors:

Z = 1/(1/a + 1/b) = (a * b) / (a + b)

The result is added to S.

4. Impedance of a Series Resistor

The impedance of the resistor is: R (in Ω, Ohms)

Z = R

The result is added to S.

5. Analysis of total Impedance

Takes the total impedance (S) and returns its total, magnitude, and phase angle (in degrees). You will have an opportunity to clear S (reset S to zero).

6. Store results in X and Y

You can store Z or S in the variables X and Y.

7. View Memory Registers

View the contents Z, S, X, and Y.

8. Clear Variables

Resets Z, S, X, and Y to 0.

9. Exit

Exits the program.

The program is listed in text form, which can be copied to the fx-CG 50.

**Program Text Listing:**
'ProgramMode:RUN
"2019-09-09 EWS"
Deg
a+bi
ClrText
Red Locate 1,3,"NOTICE"
Blue Locate 1,5,"J is represented"
Blue Locate 1,6,"by _Imaginary_. (_Sqrt__(-)_1)"
" "Disps0->S
0->Z
0->X
0->Y
Lbl 0
ClrText
Menu "IMPEDANCE","COIL",1,"CAPACITOR",2,"PARALLEL",3,"SERIES RESISTOR",4,"ANALYSIS",5,"STORE IN X OR Y",6,"VIEW MEMORY",7,"CLEAR VARS",8,"EXIT",E
Lbl 1
"FREQ: "?->F
"INDUCTANCE: "?->L
2piLFImaginary->ZDispsS+Z->S
Goto 0
Lbl 2
"FREQ: "?->F
"CAPACITY: "?->C
(2piFCImaginary)^<-1>->ZDispsS+Z->S
Goto 0
Lbl 3
"PARALLEL IMPEDANCE"
"A_#E6D7_B"
"A: "?->A
"B: "?->B
(AB)/(A+B)->ZDispsS+Z->S
Goto 0
Lbl 4
"RESISTANCE: "?->R
R->ZDispsS+Z->S
Goto 0
Lbl 5
"TOTAL IMPEDANCE:"
SDisps"MAGNITUDE: "
Abs SDisps"PHASE ANGLE: "
Arg SDispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl 6
Menu "WHAT TO STORE?","Z_->_X",M,"Z_->_Y",N,"S_->_X",O,"S_->_Y",P
Lbl M
Z->X
"DONE!"DispsGoto 0
Lbl N
Z->Y
"DONE!"DispsGoto 0
Lbl O
S->X
"DONE!"DispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl P
S->Y
"DONE!"DispsMenu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"DispsGoto 0
Lbl 7
ClrText
"Z: "
ZDisps"S: "
SDisps"X: "
XDisps"Y: "
YDispsGoto 0
Lbl 8
0->Z
0->S
0->X
0->Y
"DONE!"DispsGoto 0
Lbl E
ClrText
Red Locate 5,4,"FX61 IMPEDANCE"
Note: Disps: ◢, ⊿

Imaginary: i [SHIFT] [ 0 ]

**Program Calculator Listing:**
"2019-09-09 EWS"
Deg
a+bi
ClrText
Red Locate 1,3,"NOTICE"
Blue Locate 1,5,"J is represented"
Blue Locate 1,6,"by **i**. (√-1)"
" "⊿
0->S
0->Z
0->X
0->Y
Lbl 0
ClrText
Menu "IMPEDANCE","COIL",1,"CAPACITOR",2,"PARALLEL",3,"SERIES RESISTOR",4,"ANALYSIS",5,"STORE IN X OR Y",6,"VIEW MEMORY",7,"CLEAR VARS",8,"EXIT",E
Lbl 1
"FREQ: "?->F
"INDUCTANCE: "?->L
2πLF**i**->Z⊿
S+Z->S
Goto 0
Lbl 2
"FREQ: "?->F
"CAPACITY: "?->C
(2πFC**i**)⁻¹->Z⊿
S+Z->S
Goto 0
Lbl 3
"PARALLEL IMPEDANCE"
"A||B"
"A: "?->A
"B: "?->B
(AB)÷(A+B)->Z⊿
S+Z->S
Goto 0
Lbl 4
"RESISTANCE: "?->R
R->Z⊿
S+Z->S
Goto 0
Lbl 5
"TOTAL IMPEDANCE:"
S⊿
"MAGNITUDE: "
Abs S⊿
"PHASE ANGLE: "
Arg S⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl 6
Menu "WHAT TO STORE?","Z->X",M,"Z->Y",N,"S->X",O,"S->Y",P
Lbl M
Z->X
"DONE!"⊿
Goto 0
Lbl N
Z->Y
"DONE!"⊿
Goto 0
Lbl O
S->X
"DONE!"⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl P
S->Y
"DONE!"⊿
Menu "CLEAR TOTAL?","YES",Y,"NO",0
Lbl Y
0->S
"CLEARED!"⊿
Goto 0
Lbl 7
ClrText
"Z: "
Z⊿
"S: "
S⊿
"X: "
X⊿
"Y: "
Y⊿
Goto 0
Lbl 8
0->Z
0->S
0->X
0->Y
"DONE!"⊿
Goto 0
Lbl E
ClrText
Red Locate 5,4,"FX61 IMPEDANCE"
The || is found in (CHAR), (MATH).

**Examples:**
**Example 1**:

Two coils in a series with inductance of 0.1 H and 0.2 H, respectively. The frequency is 50 Hz.

Sequence:

Option 1: Enter 50 for frequency, 0.1 for inductance.

Option 1: Enter 50 for frequency, 0.2 for inductance.

Option 5: For analysis.

Total Impedance: 94.24777961

**i**
Magnitude: 94.24777961

Phase Angle: 90°

(Clear the total)

**Example 2:**
A capacitor of 30 μF, a resistor of 10 Ω, and coil of 0.3 H are in a series. Find the total impedance of the circuit if the frequency is 65 Hz.

Sequence:

Option 2: Enter 65 for frequency, 30E-6 for capacity

Option 4: Enter 10 for resistance

Option 1: Enter 65 for frequency, 0.3 for inductance

Option 5: For analysis

Total Impedance: 10 + 40.90419396

**i**
Magnitude: 42.10882429

Phase Angle: 76.26214952°

(Clear the total)

**Example 3:**
Three resistors in parallel with 100 Ω, 200 Ω, and 400 Ω, respectively. Find the total impedance.

Sequence:

Option 3: Enter 100 for A and 200 for B.

Option 6: Store S in X. Clear the total.

Option 3: Enter X for A and 400 for B.

Option 5: For analysis

Total Impedance: 57.14285714

Magnitude: 57.14285714

Phase Angle: 0°

Eddie

All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.