# Low Frequency and DC Measurement Fundamentals

Publish Date: Oct 01, 2012 | 14 Ratings | 3.36 out of 5 |  PDF

## Overview

This tutorial is part of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic of common measurement applications, by explaining the theory and giving practical examples. This tutorial covers the basics of low frequency and DC measurements.

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page.

### 1. Low Frequency and DC Measurement Devices

In the early days of measurement, there were galvanometers, Wheatstone Bridges, and thermal AC meters. These were difficult to use and were very slow, manual measurements. Then along came the digital multimeter (DMM) and greatly simplified things. Now, we even see functions like Inductance and Capacitance being included, eliminating the need for a complex LCR meter in all but the most esoteric applications.

The DMM characteristics are:

• High Voltage measurement
• Isolated measurement—also to 100’s of volts
• Very high input resistance (GΩ, 10’s of pA)
• Built-in signal conditioning
• Returns calibrated fully processed results
• Robust protection (in contrast to traditional DAQ)
• Often combined with switching

### 2. Common-Mode Rejection Ratio (CMRR)

When taking low frequency measurements, you should consider using a floating device, such as a digital multimeter. The advantage of a floating instrument is that, at least for a band of frequency, the Common-Mode Rejection Ratio (CMRR) tends to be extremely high. Some instruments will specify 120-140 dB of CMRR. It is conventional to specify this rejection with a 1 kΩ resistor in the low lead as shown in figure 1. It doesn’t necessarily mean a resistor has to be present during the measurement. In some switching applications, it’s there because of the switch resistance.
Consider the following example: If you input 300 V into a DC measurement device, such as a digital multimeter, with 140 dB CMRR, the input error that results from this is less than 30 uV. Actually, most digital multimeters will deliver much more rejection if the 1 kΩ resistance is not in the circuit. AC common mode voltages are a challenge, especially if the measurement is made with the 1 kΩ resistor, because some stray capacitance, usually due to shielding and transformer capacitance, often exists in the “isolation barrier” of the measurement device.

Let’s consider an example of a thermocouple. If you want to measure the temperature of a device that is at line potential, say 250 V, a 120 dB common mode rejection appears as a 120 uV error on the digital multimeter. This is error is large considering thermocouples are <40 uV/C. Thankfully, most DMMs do much better—even 100x better (40 dB better) is not unusual. One of the reasons is that the 1 kΩ resistor is not actually part of the measurement circuit.

### 3. AC RMS Measurement Fundamentals

For high accuracy AC RMS measurements, users need to be careful because some measurement devices may offer only bridge rectifiers, not true RMS converters.
AC signals are typically characterized by their RMS amplitude, which is a measure of their
total energy. RMS stands for root-mean-square; to compute the RMS value of a waveform, you must take the square root of the mean value of the square of the signal level. Most
digital multimeters do this nonlinear signal processing in the analog domain, but the NI
Digital Multimeters use an onboard Digital Signal Processor (DSP) to compute the RMS value from digitized samples of the AC waveform. The result is quiet, accurate, and fast-settling

Also, make sure you know the frequency range of the signal you are trying to acquire. Some measurement devices may be only useful for 60 Hz – not for audio or complex signals. If you are measuring the RMS of a pulse train, for example, you need more bandwidth than just the fundamental frequency of the signal. You should allow for at least 10x the bandwidth of the fundamental frequency.

### 4. Understanding Crest Factor

Crest factor is an important parameter to understand when trying to take accurate low frequency signals. Crest factor is determined by the following formula:
Crest Factor = (Vpeak/Vrms)

For a sine wave, the crest factor is 1.414; for a 50% duty cycle square wave, the crest factor is 1. This specification is important because it indicates the maximum peak value of a waveform that the digital multimeter can handle without overloading or introducing additional error. For example, given a certain digital multimeter with an AC accuracy of 0.03 % (always specified for sine waves) with an additional error of 0.2 % for crest factors between 1.414 and 5, then the total error for measuring a triangular wave (crest factor = 1.73) is 0.03 % + 0.2 % = 0.23 %.

Historically, making AC measurements with digital multimeters has been very frustrating because many trade-offs exist. Traditional methods are derated for high crest factor signals. If you do not know the crest factor, it is difficult to predict the accuracy of the measurement. Also, high-frequency, low-level signals are measured poorly by most digital multimeters because of the analog techniques. These devices employ active diode rectifiers that cannot keep up effectively as frequency increases, unless they are driven very hard (for example, high amplitudes).

The method used by the NI Digital Multimeter is insensitive to crest factor error and capable of low-level measurements, limited primarily by noise. So while the specification allows for signal amplitudes of 1 % of range, in practice the useful measurement range extends at least a decade lower.

### 5. Resistance Measurements

There are three common resistance measurement configurations:
• 2-wire resistance measurement
• 4-Wire resistance measurement
• Offset Compensated Ohms

2-Wire Resistance Measurement
The 2-wire method is commonly used as it is the simplest and most straightforward method. In 2-wire, you can get accurate measurements above 100 kΩ relatively easily. For lower resistance (ohms) values, such as 100 Ω, the interconnecting cabling can add significant resistance (ohms) which can greatly affect your measurement. Copper is the most common and is the recommended cabling. Copper has a temperature coefficient in the 3,000 ppm/ºC range, which can add instability to the measurement.

Sometimes the leads can be locally shorted, a measurement made, and then this "offset" and its associated TC subtracted from the subsequent 2-wire resistance (ohms) measurement on the resistors under test. This technique works with careful experimental measurement practice. An outline of the methodology for this technique is as follows, in the context of an automated measurement system, with programmable switching available:

1. Short the leads as close to the resistance (ohms) under test as possible. If the measurement is part of an automated switching system, dedicate a switch channel to a zero value. During the measurement cycle, close the switch to the zero reference. Refer to the following figure:

2. Record the offset of this zero channel.
3. Switch to the resistance (ohms) channel you want to use.
4. Measure the resistance (ohms) value.
5. Subtract the offset value from the resistance (ohms) value on the selected channel.
6. The result is the resistance (ohms) reading you want.

This method is subject to the following caveats:

• If the zero relay has a different contact-resistance (ohms) than the rest of the relays, an error is introduced.
• If possible, you should terminate the zero channel with a cable very close in length to those cables leading to the resistance (ohms) under test, matching the path length as closely as possible.
• This method does not correct for the lead resistance (ohms) of the component you are testing.
• A time penalty occurs in the system and is associated with closing the zero relay and taking the additional measurement.
• The stability of the relay ON-resistance (ohms) may limit this method to a repeatability of about ±20 mΩ.

4-Wire Resistance Measurement
For precision measurements with resistances (ohms) below 100 kΩ, 4-wire works more reliably and conveniently than 2-wire. 4-wire requires 4-wire switching and more cabling; however, you may decide if the trade-off is acceptable, depending on the accuracy versus complexity requirements of your system.

Figure 3 below shows a 4-wire resistance (ohms) measurement, including lead and switching resistance: The Lead resistance in series with the Sense lines isn’t a problem either, because the DMM VM doesn’t draw any current. So, no measurement error is experienced. The 4-wire technique removes the effect of cable and switch resistance changes, as long as you select a sense point as close to the resistor you are measuring as possible.

Offset Compensated Ohms:
Offset Compensated Ohms takes out small voltages in series with the resistor under test. For simplicity sake, we consider the 2-wire method, although it works equally well with the 4-wire method.

The measurement involves 2 cycles. First, the measurement is made as normal. Then, the current source is switched off and the measurement is made again. This time, the only voltage in the circuit that can be measured is VTHERMAL. There is no voltage across Rx due to the current source, since it’s shut off.

If you subtract the results from the two cycles, you are left with the true resistance value. The value of VTHERMAL is there in both measurements, so it subtracts out, as shown in figure 4.

### 6. Current Measurement (Amps)

The trick behind measuring current is to do so without disrupting the circuit under test at all. This is done ideally if the current meter looks like a short circuit. In reality no current meter is ideal. All of them have a small amount of resistance. The voltage dropped across this resistance during the current measurement is called the Voltage Burden, which is described in figure 5. A large burden voltage can affect the circuit being measured, corrupting the measurement. For this reason, it is desirable for burden voltage to be kept as low as possible.

Common problem when taking current measurement is blowing the fuse by connecting voltages to the current input terminals. You can also blow fuses by hot wiring the DMM ammeter into a circuit with lots of capacitance. If the DMM acts as the “switch” to turn on the circuit, the current surge could damage the fuse.

Second, it’s not unusual to see long wires run to the DMM from the measurement circuit. What’s wrong with doing this? The higher the current, the more voltage you’re going to drop across the resistance of the cable and switching in the system. The best way to avoid this situation is to use external shunts and sense with the voltage terminals of the DMM.

### 7. Relevant NI products

Customers interested in this topic were also interested in the following NI products:
· LabVIEW Graphical Programming Environment
· SignalExpress Interactive Software Environment
· Digitizers
· Dynamic Signal Acquisition (DSA)
· Digital Multimeter (DMM)
· Data Acquisition (DAQ)

For the complete list of tutorials, return to the NI Measurement Fundamentals Main page.

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