Series Resistance
6.3 Measuring Very Low Resistances
When calculating the number of squares, the most important
consideration is to use a consistent set of units for the length and the width. The number of squares is dimensionless.
Get in the habit of looking at the traces on your circuit board and quickly estimating the resistance of each trace. This will give you a feel for one of their electrical properties and what to expect for their performance.
To quickly estimate the resistance of a trace on your board, use the rules of thumb: for 1 oz copper, the series resistance of a 6 mil wide trace is 83 mohms/inch and, for a 20 mil
wide trace, it is 25 mohms/inch.
Watch this video and I will walk you through the concept of sheet resistance and why it is such a useful term to
characterize copper sheets and to estimate trace resistance.
6.3 Measuring Very Low Resistances 153
In some ohmmeters, it is possible to compensate the DMM for those offsets that are constant, such as the internal offset voltage or the lead resistance, but the contact resistance may vary from
measurement to measurement.
You can demonstrate this for yourself by taking your DMM, setting it to the lowest resistance scale and measuring the resistance with the leads shorted. Figure 6.4 shows examples of two different DMMs with two different types of shorted leads, showing a measured resistance of 0.21 ohms for short leads and 1.5 ohms for the standard clip leads.
Figure 6.4 Examples of the shorted resistance of two common DMM set as ohmmeters.
This means measuring resistances lower than 1 ohm will be difficult.
The way around these common problems is to use a technique developed in 1861 by William Thompson, also known as Lord Kelvin, referred to as the Kelvin 4-wire method.
The general method of measuring the resistance of a component is to force a current through it and measure the voltage across it, V, and the current through it, I. The resistance of the component is R = V/I.
In the conventional 2-wire method, there are two connections to the DUT. The current flows through the leads and the voltage is
measured at the ends of the leads. This voltage measurement includes the series resistance of the wire leads and the contact resistance of the leads to the DUT at each end.
The innovation Lord Kelvin introduced was to separate the leads and contacts that measured the voltage across the DUT from the forced current. The lead resistance and contact resistance is still present in the circuit with the forced current.
But the voltage measurement just includes the voltage drop across the DUT, not across the lead or contact resistances. Any lead
resistance or contact resistance in the voltage measurement path has no effect on the voltage measurement. These two measurement topologies are illustrated in Figure 6.5.
Figure 6.5 The measurement topology for the conventional 2-wire method (top) and the 4-wire method (bottom).
6.3 Measuring Very Low Resistances 155
To implement the 4-wire method, it is necessary to attach one set of leads to the DUT to force the current and a different set of
connections to measure the voltage induced across the DUT from the current. The resistance of the DUT independent of the contact resistance and lead resistance is just R = V/I.
For example, to measure the resistance of the vertical column in a solderless breadboard, we use one set of leads to force the current by connecting to a power supply. We add a series ammeter to
measure this current. Then we connect a separate pair of leads to the voltmeter, making separate connections to the vertical column strip.
This configuration is shown in Figure 6.6. In this case, we measure a voltage of 37.1 mV with a current of 1.000 A. This is a resistance of
V 37.1mV
R 37.1 mohms
I 1.000A
= = =
Figure 6.6 Measuring the resistance of half a vertical column in a solderless breadboard.
One pair of leads connects to a power supply and forces 1.000 A of current through the column. Another pair of leads connects the voltmeter and measures a voltage drop of
37.1 mV.
This is the resistance of half a vertical column in a solderless breadboard.
When I connected the voltmeter leads to the wires driving the current through the column, rather than making a separate
connection to the column, I measured a voltage of 90 mV. This extra voltage is the voltage drop across the contact resistance of the wire inserted into the hole of the solderless breadboard. The difference is about 50 mV, or 25 mV for each contact. This is a contact resistance of R = V/I = 25 mV/1 A = 25 mohms. This is a rough measure of the contact resistance of a wire plugged into a solderless breadboard.
Using the conventional 2-wire method, I measured a resistance of 1.9 ohms as the resistance of the column in the solderless breadboard.
We now see most of this resistance is artifact, the lead resistance of the DMM wires.
If we use a forcing current of 1 A and our DMM is capable of
measuring a voltage as low as 1 mV, we can measure a resistance as low as R = V/I = 1 mV/1 A = 1 mohm. By pushing the smallest voltage to 0.1 mV, we can routinely measure resistances as low as 100 uohms.
The kelvin 4-wire method is a very powerful technique to measure sub-mohm resistances. Whenever it is necessary to
measure a resistance below 1 ohm, the 4-wire method should be used.
Watch this video and I will show you how to measure a trace with the 4-wire method.