Meter Shunts and Multipliers
Written by Bryce Ringwood   

This program provides a means calculating the shunt or multiplier required to turn a meter movement into a Voltmeter or Ammeter. See article on multimeters.

Uses

Most of the time it would be used to calculate the shunts and/or multipliers needed to turn a microammeter into an indicating meter in an item of home-made equipment - such as a power supply. Also for educational use.

A collection of panel meters
Meter Shunt Meter Multiplier A Collection of Panel Meters

Data Entry Section

 

Enter Meter full scale  - Amps                 

Enter Meter Resistance Rm  - Ohms              

   Enter desired maximum voltage or current           

Meter multiplier or shunt required             

                         

 

 

 

Example - Multimeter

In the diagram opposite, if we assume a meter resistance of 1950 Ohms and a Full scale deflection of 50uA (Typical), then calculate (1) the shunt resistance required for a range of  0-10 Amperes.

Answer = 9.75 milliOhm

In practice you would use a small length of copper wire capable of taking the current. If you dismantle a multimeter, you will see how its done. You need to calculate the safe current for a particular wire gauge, then calculate the length of wire needed from wire tables. Not exactly for the faint-hearted. By the way, you should use a 10Amp fuse in series with the input lead for safety.

(2) Calculate the multiplier required to give a voltage range of 0- 10 Volts

Answer = 198.1 K

 In practice, a 200K 1% resistor would give results to within about 1%. This is good enough.

 

Theory

The theory follows from Ohm's, and Kirchoff''s laws. In the case of the multiplier, the same current flows through the meter and the multiplier resistance. The meter resistance can sometimes be ignored, because it is very small compared to the multiplier.

 In the case of the shunt, the same voltage is applied across the shunt and the meter resistance. The meter resistance can not be ignored. 

This theory does not work with digital panel meters because the input resistance is extremely high and is unknown. In addition, they are intrinsically voltmeters - not ammeters or microammeters like a mechanical meter with a d'Arsonval movement.  To calculate the shunt for a digital meter - just use Ohm's law to see what resistor (R) will give you the required V (2Volts or 200mV - depending) for the current (I) to be measured.

Digital meters and valve voltmeters use a potentiometer voltage divider - see potentiometer software next..

Formulae

 

For Shunt:
\textstyle I \times R_{shunt} = {\displaystyle {R_{m}} }\times {\displaystyle {FSD}} 
whence:
\textstyle {R_{shunt}}= {{{\displaystyle {R_{m}}}\times{\displaystyle {FSD}}} \over {\displaystyle {I}}}

For Multiplier:

\textstyle FSD \times ({\displaystyle {R_{mult}}} + {\displaystyle {R_m}} ) = {\displaystyle V}
and so:

\textstyle R_{mult} = {({{\displaystyle V} \over {\displaystyle FSD} })} - {\displaystyle R_m}

Where:

        FSD = Meter Full Scale Deflection
        I = Current Range
        V = Voltage Range
        Rshunt = Shunt Resistance
        Rmult = MultiplierResistance
        Rm = Meter Resistance

 


References

Ghirardi A.A  "Radio Physics Course " 2nd Edition - Murray Hill Books, 1933 pp 278 et seq.

He looks at the problem slightly differently. Maybe his treatment is a little easier to follow than mine.

Problems? - email me.

 
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