Shunt Resistor: What is it (And How Does it Work)?

Contents

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Key learnings:

Shunt Resistor Definition: A shunt resistor is a device with low resistance used to direct most of the circuit’s current through a specified path.
Connection Method: Shunt resistors are connected in parallel with measurement devices like ammeters to maintain equal voltage across them.
Using Ohm’s Law: To determine the current flowing through a shunt resistor, Ohm’s law is applied by measuring the voltage across the resistor.
Construction Tips: When building a shunt resistor, the type of wire and its length are crucial to achieving the desired resistance and functionality.
Applications: Shunt resistors are integral in applications such as current measurement, overvoltage protection, and bypassing faulty components in circuits.

What is a Shunt Resistor?

A current-sense shunt is a precisely known, low-value resistor placed in series with an electric current path. Current creates a small voltage drop across it, allowing a meter or control circuit to calculate current. Precision shunts often use a low-temperature-coefficient alloy so their resistance changes little with temperature.

In a traditional analogue ammeter, a shunt is connected in parallel with the sensitive meter movement and diverts most of the current around it. The complete ammeter remains connected in series with the circuit being measured.

How Does a Shunt Resistor Work?

For modern current sensing, the shunt sits in series with the load and the voltage-sensing input connects across the shunt. Its resistance stays low to limit burden voltage and power loss.

The measured voltage and calibrated resistance give current through Ohm’s law. Four-terminal, or Kelvin, shunts separate the high-current terminals from the voltage-sense terminals to reduce lead and contact errors.

Divide the voltage across the shunt by its resistance:

$I = \frac{V}{R}$

Using a Shunt Resistor to Measure Current

Consider an ammeter movement with resistance R_a and full-scale current I_a. To extend its current range, connect shunt resistor R_s in parallel with the movement. Some diagrams label the meter resistance R_m; the equations below use the a subscript.

The diagram shows the resulting current divider.

Total current I divides between the shunt and the meter movement.

Kirchhoff’s current law (KCL) gives:

$I = I_s + I_a$

where:

I_s is the current through shunt resistance R_s,

I_a is the current through meter resistance R_a.

$I_s = I - I_a$

Because R_s and R_a are in parallel, they have the same voltage drop.

$V_s = V_a$

$I_s R_s = I_a R_a$

$(I - I_a) R_s = I_a R_a$

$IR_s - I_a R_s = I_a R_a$

$IR_s = I_a R_a + I_a R_s$

$IR_s = I_a (R_a + R_s)$

$\frac{I}{I_a} = \frac{ R_a + R_s }{R_s}$

$N = 1 + \frac{R_a}{R_s}$

N is the shunt multiplying factor, or the ratio of total current to meter-movement current.

How to Build a Shunt Resistor

A calibrated commercial shunt is the safer choice for precision or high-current work. Its resistance, tolerance, temperature coefficient, power rating and overload limit are specified. A copper-wire shunt may serve as a rough low-voltage experiment, but its resistance changes with temperature and connection resistance can be substantial.

In a moving-coil ammeter, shunt resistance sets the extended current range. In an electronic measurement circuit, it sets the full-scale sense voltage and contributes power loss.

At 20°C, 10 AWG copper wire is about 2.59 mm in diameter and about 0.9989 ohms per 1000 feet. Actual resistance varies with temperature, material condition and the terminations.

Measure the finished resistance with a four-wire method. The protected legacy equation below mislabels its denominator: for its numerical example to work, convert the wire value to milliohms per foot before dividing.

$Length \, of \, wire = \frac{Required \, shunt \, resistance \, (m \Omega)}{Resistance \, per \, 1000 \, feet }$

For a rough 0.5 mΩ copper-wire example, 0.9989 ohms per 1000 feet converts to 0.9989 mΩ per foot:

$Length \, of \, wire = \frac{0.5}{0.9989}$

$Length \, of \, wire \approx 0.5 feet$

What Is the Purpose of Shunt Resistor (Applications)?

Shunt resistors are used for measurement, control and specialised bypass functions:

A resistor can form part of a shunt regulator or overvoltage-detection circuit, but the resistor does not provide overvoltage protection by itself.
Current-sense shunts produce a voltage for meters, amplifiers and control circuits.
A purpose-designed shunt can bypass a failed element in some series circuits. The circuit must be designed so the bypass can carry the resulting current safely.
A resistor and capacitor can form an RC snubber that damps switching-node ringing when its values and placement suit the circuit.
A current-sense shunt can feed an overload-protection circuit in equipment such as a power supply.

How to Size a Shunt Resistor

Size a current-sense shunt for the intended full-scale voltage, continuous current, short-duration overload and allowable power loss. Also check tolerance, temperature coefficient, mounting and the manufacturer’s thermal derating data.

Resistance equals the selected full-scale voltage drop divided by maximum current. The physical package and cooling must then keep the element within its power and temperature ratings.

Assume a maximum current of 100 A and a selected full-scale drop of 50 mV. Other designs may select 75 mV or 100 mV, subject to the measurement input, burden voltage and power budget.

Ohm’s law gives 0.5 mΩ. At 100 A, that resistance dissipates 5 W, so its rated power and thermal installation must include the required derating margin.

$V = I R$

$50 \times 10^{-3} = 100 R$

$R = 0.5 m \Omega$