Choosing Between 2-Terminal and 4-Terminal Impedance Measurements

The MFIA is a high-precision impedance analyzer that can run measurements in either 2-terminal or 4-terminal mode. What is the right setting for your measurement? This blog post addresses this question and explains how to use the MFIA's full capability.

Theory

To calculate impedance, the Zurich Instruments MFIA Impedance Analyzer needs to determine current and voltage signals. According to the theory, a voltage should be measured with a large input impedance such that there is only a negligible current flow and no voltage drop occurs at any of the internal resistors of the measurement device or the measurement lines. For a current measurement, the voltage drop over a resistor with a precisely known resistance is measured, and that resistor should be small enough to not alter the characteristics of the whole electrical circuit. To resolve this contradiction, current and voltage measurements can be performed in two separate instances.

Reality

The main issue with the above approach, based on an ideal scenario, is that measuring current and voltage separately increases the complexity of the measurement device and introduces more sources of potential error. For example, 4-terminal (4T) measurements require four separate cables that are more likely to pick up inductive artifacts through mutual inductances or external magnetic fields. In this view, 2-terminal (2T) measurements offer a clear advantage and should be used whenever possible. But when is this actually possible? Let's take a closer look.

2T or 4T?

The general recommendation for when to use 2T or 4T measurements depends on the magnitude of the impedance of the device under test (DUT) as compared to the wiring and input/output resistances of the measurement device. Input/output resistances are high-precision resistors and their values are known precisely, hence their influence can be compensated for by factory internal calibration. Let us then look at the electrical wires used to connect the MFIA with the DUT. These wires are highly conductive, but even so it is difficult to design a setup where the series resistance of the wiring circuit - including terminals and connectors - accounts for less than 1 Ω. This contribution can be neglected if the measured impedance is larger than 10 kΩ (error < 0.01%). A 2-wire setup, where current and voltage are measured with the same leads, is suitable for this measurement task (see Figure 1). In general, it is also beneficial to keep the setup as simple as possible, because adding more wires to the setup increases the impact of inductive coupling. For impedance magnitudes below 1 kΩ, however, the influence of the wiring cannot be neglected: this is where the 4T mode should be used. By separating current and voltage branches, only a negligibly small current flows in the vertical voltage lines shown in Figure 1. In the current branch, in particular, the voltage drop is not an issue for measuring the current due to Kirchhoff’s law.

Other Scenarios

There are other reasons why the 4T mode is often required. DUTs can show large, undefined or poorly reproducible contact resistances. As discussed in this bioimpedance blog post, electrodes placed on the skin make use of a contact gel that typically shows a contact resistance above 100 kΩ: one can test this by gluing two such electrodes back-to-back. The 4T mode is then preferable here, because even for such large resistances the concept laid out above still holds: the negligible current in the voltage measurement branch avoids the voltage drop, and the voltage can thus be measured accurately. Importantly, additional resistances in the current branch do not affect the accuracy of the current measurement.

Other examples where the 4T mode is required are measurements on concrete or ion-conducting DUTs where the electrodes have another purpose apart from assuring connectivity: for example, they may act as charge transfer electrodes with large charge transfer resistances (instead of contact resistance). The transfer takes place from the electrical current in the wires to the ionic current in the DUT; lithium ion or oxygen ion conductors are prominent examples for such DUTs.

Input/Output Resistance of the MFIA

There is one peculiarity of the MFIA that needs to be mentioned here. The MFIA's current output and current input come with 50 Ω resistors. Even though this value appears much larger than an estimated 1 Ω for the wires, it does not cause any problem for impedance measurements because the internal compensation does consider these circumstances, whereas cable resistances are not taken into account. As such, the 1 kΩ resistor supplied with the MFIA and the MFITF Test Fixture can be measured in 2T and 4T modes: the MFIA will give you the correct resistance in both cases. However, when looking at the actual current and voltage signals in the LabOne^® Scope tool, it is clear that the current is not V_ampl / R_DUT, but V_ampl / (R_DUT + 100 Ω). In turn, this means that the voltage drop over the DUT is not equal to the applied V_ampl. This can also be checked in the Scope tool, where V_ampl is as expected in the Signal Output, whereas the Signal Input (which is the true voltage that drops over the DUT in the 4T mode) is slightly smaller for the considered example. For the 1 kΩ resistor, the difference is not large (10%); if you measure a DUT with significantly lower impedance and want to reach a certain excitation voltage over the DUT, however, these aspects have to be factored in – a certain fraction of the voltage will drop over the two internal 50 Ω resistors. It is important to note that this peculiarity in the device's architecture does not compromise measurement accuracy: it just splits the voltage drop over the two internal resistors and the DUT.

But why are the input and output resistors so large, given that potentiostats and DC measurement devices usually come with much smaller input/output resistances? This is where the origins of the MFIA are revealed: this instrument is based on the lock-in amplifier technology, where such values for resistors are standard. The large input/output resistances do offer an advantage for fast measurements. Indeed, the resistors simplify the control loop for setting the test signal, and enable fast and accurate application of the desired voltage without the danger of oscillations that can affect impedance analyzers based on auto-balanced bridge technology when trying to control the voltage over a DUT.

Conclusion

I hope that this blog post addressed some common questions regarding how to connect your DUT to the MFIA and what to consider for achieving the best possible measurement results.