Measurement Errors
When measuring small voltages and/or where voltages are to be accurately determined, measuring errors can quickly occur caused by interfering influences. This article discusses a number of causes that may affect the measurement of voltages and currents.
Ground Loops
Fig. 1: An experimental set-up where a ground loop is formed.
Measure and test equipment has in some cases the mass (or LO input) connected to the earth terminal, as usual with an oscilloscope. When two such instruments with such an inner connection are used in a test set-up, a ground loop will occur. This situation is shown in Figure 1. Because a voltage (Vg) can exist between different earth connections, will this cause unwanted currents (Ig). This situation will be worse if both instruments are not connected to the same junction box.
The resistance R in the circuit represents the connection and wiring resistances. This will be the order of tens of milli-ohms. Even small ground wire voltages will cause not negligible ground loop currents Ig. The voltage drop across this resistance Vr caused by the ground loop current causes a deviation of the measured voltage Vin and the source voltage Vs:
[equ. 1]
Isolation
Fig. 2: An experimental set-up with an open ground loop.
Earth currents can be prevented or reduced by interrupting the ground loop. This is possible by using equipment (power supplies, signal generators, etc.) whose inputs and/or outputs are isolated from the ground. But never disconnect the grounding itself.
Figure 2 shows a measurement set-up that uses a source which is isolated with respect to the grounding. But a full insulation is never possible: There is always some leakage resistance and parasitic capacitance here represented by the 1 MΩ resistor and 40 pF capacity.
The input voltage Vin is computed as follows:
[equ. 2]
Z is the impedance formed by the resistance and capacitance to the ground. The total resistance is much greater than with a closed ground loop. The current Ig is very small and has a minimal effect on the input voltage Vin. At high frequencies, the impedance Z is so small that its influence is no longer negligible.
Common mode voltages
Fig. 3: Common Mode Voltage can cause measurement errors.
Measuring instruments which input terminals are isolated from the earth have a differential input. These measure the voltage difference between the positive and negative input terminals, the differential voltage Vdiff. These instruments are also more or less sensitive to a common voltage between the two inputs and the earth, the common mode voltage Vcomm.
To what extent the common mode voltages are suppressed is indicated by a CMRR (Common Mode Rejection Ratio) value. This value is often expressed in dB and is always specified at a certain frequency.
When a voltage is superimposed on the measured power grid voltage (230 V, 50 Hz) and the given CMRR of the measuring instrument is "80dB @ 50 Hz", than the error voltage that the instrument displays is:
[equ. 3]
Magnetic Fields
Electrical equipment and the power grid generate alternating magnetic fields. A wire loop located in this changing magnetic field induces a voltage that is proportional to flux change per unit time:
[equ. 4]
Here E is the transient induced voltage, dB/dt the change of magnetic induction per unit time and A is the area of the loop. The larger the surface area of the loop, the greater the induced voltage.
Fig. 4: External alternating magnetic field induces voltages in a wide loop.
Fig. 5: Twisted leads reduce the disturbing effect of external magnetic fields.
The effect of induced currents can be reduced by making the surface of the loop as small as possible. This can be reached by bringing the test leads near as possible in a parallel way. In practice, therefore, the test leads will often be twisted as shown in Figure 5. Here is an AC voltage of 0 µV is measured, while the arrangement with the wide loop in figure 4 where 78 µV was measured.
Tribo-electric effect
Fig. 6: Tribo-electric effect is measured on a RG58 cable when abruptly impacted.
Cables who are subject to vibration or movements generate internally a charge difference. This charge will be translated into a current. If the cable at both ends is high-impedance terminated, significant voltage differences can be generated. This is called the tribo-electric effect and is most noticeable on coaxial cables.
The tribo-electric effect is caused by friction between the conductor and the insulator. Thereby electrons are rubbed free, creating so charge difference.
Figure 6 shows the tribo-electric effect of in a practical situation. An 1 meter free hanging end from a 2.5 meters long RG58A coaxial cable was subject to an impact. The only load was the 1 MΩ, 16 pF input of the oscilloscope. In this example, a peak voltage of 36 mV was generated.
In case where small voltages are measured, it is important that the cables can not move and are not subject to vibration. Using special cables with other types of insulation can reduce the tribo-electric effect.
Thermoelectric voltages
| Metal | S [µV/K] |
| Copper Oxide | 1400 |
| Te (Tellurium) | 570 |
| Si (Silicon) | 520 |
| Sb (Antimony) | 120 |
| Fe (Iron) | 88 |
| W (Tungsten) | 78 |
| Cu (Copper) | 77,5 |
| Au (Gold) | 77 |
| Ag (Silver) | 77 |
| Zn (Zinc) | 77 |
| Rh (Rhodium) | 76,5 |
| Ir (Iridium) | 76 |
| Manganine | 76 |
| Sn (Tin) | 74,5 |
| Pb (Lead) | 74,5 |
| Mg (Magnesium) | 74 |
| Al (Aluminium) | 74 |
| Hg (Mercury) | 70 |
| Pt (Platinum) | 70 |
| Ni (Nickel) | 55 |
| Co (Cobalt) | 54 |
| Constantan | 36 |
| Bi (Bismut) | 0 |
Fig. 7: Thermoelectric voltage across a junction of two different metals.
A connection (junction) of two different metals will always generate a thermoelectric voltage. How large this voltage is depends on the two types of metal connected together and is proportional to the absolute temperature of the junction. Only at absolute zero (0 K) is the voltage is 0 V. Figure 7 shows a junction of copper and aluminium at room temperature (293 K). This junction generates a thermal-electric voltage of 1026 µV. The size of the thermal voltage is calculated as follows:
[equ. 5]
Here S1 and S2 are the Seebeck coefficients of the two metals that are connected en make the junction, in this example, copper and aluminium. The Seebeck coefficients for various metals are listed in the table on the left. The metal that is highest on the list of the two metals is the positive one.
This given above is relevant for an open circuit consisting of two wires joined by a single weld. This can create a significant difference of potential, but this absolute thermoelectric voltage can hardly be measured in practice, and these voltages will mostly be eliminated in a closed circuit:
Thermo-voltages in a closed circuit.
An electric circuit, including a measuring circuit, will in practice be a closed loop. Figure 8 shows a measuring circuit where three different metals are used: constantan, copper and aluminium. Across the constantan wire stands a voltage Vb of (5 mV) which must be measured. This could for instance be a current shunt. The copper wire forms the connection to the instrument, and the instrument itself is made of an aluminium wire.
Fig. 8: Equalization of the thermoelectric voltages in a closed electrical circuit.
Each of the two junctions constantan/copper has a temperature of 60 °C (=333 K). Each junction will therefore generate a voltage of 13820 µV. But because the voltage of these junctions has an opposite polarity, they cancel each other out. Behind the junctions is therefor still the same potential difference of 5 mV as the voltage source. In the two copper/aluminium junctions is the same valid. Here the temperature is 293 K and the thermoelectric voltages are both 1026 µV, but here again the voltages are the opposite of each other. Therefor the instrument measures exactly the source voltage: 5 mV.
Fig. 9: Measurement errors caused by differences in thermal-electrical voltages caused by uneven temperatures.
Figure 9 shows the same situation, but one of the constantan/copper junctions has a higher temperature: 80 °C (=353 K). Hereby generates this junction a slightly higher thermoelectric voltage: 14650 µV instead of 13820 µV of the 60 °C junction. The difference in these two thermo-electric voltages is 829 µV and is noticeably behind the junctions. The voltage between the two copper wires is now 5829 µV instead of 5000 µV. The source voltage with the added fault voltage caused by the temperature difference is transmitted to the measuring instrument.
For accurate measurements and/or measuring small voltages, it's important that the measuring terminals are connected in places that have an equal temperature.
Electrochemical effects
Electrochemical potential differences occur in places where there is poor contact that is also polluted and humid. These induced voltages may amount to tens of millivolts. These voltages are greatest when the connection consists of two different metals. Always ensure that contacts are clean, free of oxidation and dry.
Also with two equal metals weak currents can be generated caused by chemicals. Eg by flux that stay behind on circuit boards after soldering. It's therefore important to remove the flux with freon or methanol.
Instrument limitations
It may be regarded as obvious that errors might occur if the measuring instruments are used outside their specifications. However, sometimes this happens unconsciously.
With graphic examples is shown where attention must be paid.
Overloading multimeters
Impulse voltages often cause overloading of the input circuit of measuring instruments. The peak voltage is much higher than the average or RMS voltage. Especially with multimeters, there is great risk of damaging the measurement and measuring errors because there is no indication of the amplitude. An example of such a waveform with the corresponding voltage values is shown below.
Fig. 10: Voltage measurement of an impulse.
The duty cycle of this signal is 10%. Although a low voltage is measured, the amplitude is 10 times higher than the average voltage and over three times higher than the RMS voltage. This situation occurs for example where a fly-back transformer is used. The input circuit of a conventional multimeter has a low-pass filter. This will cause the average voltage be measured correctly, but it's high pulse voltage can overload the input circuit. Parts can fail by voltage breakdown or burning.
Except damage, the change of measurement errors is much larger with True RMS meters. The RMS voltage is calculated using the momentary input voltages. If the instrument is set to a more sensitive range in response to a low displayed value, there is a possibility that the input amplifier will be overloaded. For better true-rms meters overdrive indicator is present. If not, you will need an oscilloscope to check whether the instrument is overloaded or not.
Frequency range
The average multimeter is unsuitable for high frequency signals to be measured. The frequency range is only a few thousand hertz. True RMS meters often have a slightly higher frequency range. The frequency range of multimeters is specified with the measurement accuracy within the specified tolerance.
The frequency range of an oscilloscope is usually given at the -3 dB point. Here is the amplitude approximately 0.7 times the original level.
Not only the measured fundamental frequency must taken into account with the given frequency range. Higher harmonics of non-sinusoidal signals are already weakened long before.
Fig. 11: 10 MHz square wave at 200 MHz bandwidth.
Alongside an image of a measurement of a 10 MHz square wave. The bandwidth of the oscilloscope is 200 MHz. The measured rise and fall times are well within the specified 8 ns of the original signal. Not only the fundamental frequency, but also the higher harmonics are virtually unimpaired passed.
Fig. 12: 10 MHz square wave at 25 MHz bandwidth.
Otherwise, this measurement. The bandwidth of the oscilloscope is now 25 MHz. Clear to see are the weakened steep slopes of the measured signal. The fundamental frequency is approximately unaffected passed through, but the higher harmonics are strongly attenuated. The result is a distorted image of the original waveform.
Fig. 13: Graphical representation of the attenuation at 25 MHz bandwidth.
The graph alongside shows the attenuation as a function of the frequency, displayed on the oscilloscope with a bandwidth of 25 MHz. Not only weakens the signal at higher frequencies, also phase shifts the signal components.
How the higher harmonics of non-sinusoidal signals affected bu this attenuation is explained below.
Fig. 14: The attenuation of the harmonics around the cut-off frequency.
A square wave consists of a large number of harmonics. Of the original 10 MHz square wave, these frequencies are shown as black bars to the 13th harmonic.
In this frequency range is the weakening by the 25 MHz low-pass filter shown as the thin red line. The blue bars show the resulting harmonic attenuation of the original harmonics. Clear visible is that higher harmonics disproportionately more attenuated than the lower ones.
Not only when measuring with oscilloscopes should consider the attenuation of harmonics, also multimeters will have difficulties in showing the correct value when measuring non-sinusoidal signals near the cut-off frequency.
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