August 18, 2010

How To Measure Current Using A Shunt Resistor

You have a digital multimeter. It’s rated at 10 A max, but you would like to measure a current at about 30 A. How is that possible? Good news is that by using Ohm’s Law you can circumvent such limitation! Ohm’s Law describes the relationship between voltage (V), current (I) and resistance (R) in the form: V = I x R
This article will talk about how we can perform such measurement and also how to verify that our instrument is capable of handling such a task by using real examples. Some good practices and precautions will also be mentioned here.
With just a slight manipulation of that equation, we can obtain I = V / R, which indicates to us that we can also derive the value of the current measurement if we know the voltage and resistance. From this, we observe that the current is inversely proportional to the resistance. So, if we could fix the resistance to some value using a resistor, we could then measure the voltage across that resistor to obtain the current. This resistor should be of a very small in order not to disrupt the circuit. This is termed as the shunt resistor and is placed in series with the circuit load as shown in Figure 1.
Figure 1 - Using a digital multimeter & shunt resistor to measure current

Let’s consider this real-life scenario - we are still interested to measure 30 A and the multimeter that you are using is for example, the Agilent U1253B 4.5 digit handheld digital multimeter, which has a maximum current rating of 10 A. Then consider some precision current shunts from Ohm-Labs. From the selection of shunt resistors, we identify one which is within the right range (rated greater than 30 A). Hence we select the CS-50 shunt resistor model with the following specs: 
Model
Amps
Ohms
Output
Accuracy
CS-20
20
0.05
1.0 V
0.1%
CS-50
50
0.01
0.5 V
0.01%
Table 1 - CS-50 shunt resistor specifications

Figure 2 - Image of CS-50 shunt resistor from Ohm-Labs.
CS-50 is a 0.01 Ohms shunt resistor with a 0.5 V output at maximum rated current of 50 A. Notice the fins in Figure 2? That's a heat sink to regulate the temperature on the resistor as things can get pretty heated up during operation.
Back to Ohm’s Law, if we are measuring current of 30 A with shunt resistance of 0.01 Ohm, we should obtain:
Vmeasure = 30 A x 0.01 A = 0.3 V

This 0.3 V is definitely within the safety rating of the Agilent U1253B which is 1000 V. This proves that by using shunt resistors, we can measure current (30 A) that are greater than the maximum rating (10 A) of the multimeter.

Although ensuring that our measurement stays within the instrument’s maximum ratings is crucial, we also need to ensure that we have sufficient resolution to measure the smallest step change that interests us. For example, to detect every 0.1 A of change in our measurement, our multimeter must be able to measure voltage as small as: 





Vmeasure = 0.1 A x 0.01 Ohm = 1 mV

As an illustration, Table 2 below shows some values of Vmeasure as we vary the Imeasure at a resolution of 0.1 A about our target current value of 30 A. Notice that with every 0.1 A step of change, the voltage also change with a step of 1 mV or 0.001 V. This table is also useful to help convert the voltage measured to the corresponding current value.
Vmeasure
Imeasure
Rshunt
0.295
29.5
0.01
0.296
29.6
0.01
0.297
29.7
0.01
0.298
29.8
0.01
0.299
29.9
0.01
0.300
30.0
0.01
0.301
30.1
0.01
0.302
30.2
0.01
0.303
30.3
0.01
0.304
30.4
0.01
0.305
30.5
0.01
Table 2 - Imeasure vs Vmeasure

Referring to the datasheet of the Agilent U1253B under ‘DC Specifications’ section (see Figure 3 below), we zoom in on the 500 mV or 0.5 V range as our measurement falls within this and find that the resolution is 0.01 mV. This means that the Agilent U1253B is more than sufficient to resolve a 1 mV change.
Figure 3 - DC voltage specifications of the Agilent U1253B