# True RMS converter

Last updated

For the measurement of an alternating current the signal is often converted into a direct current of equivalent value, the root mean square (RMS). Simple instrumentation and signal converters carry out this conversion by filtering the signal into an average rectified value and applying a correction factor. The value of the correction factor applied is only correct if the input signal is sinusoidal.

## Contents

True RMS provides a more correct value that is proportional to the square root of the average of the square of the curve, and not to the average of the absolute value. For any given waveform, the ratio of these two averages is constant and, as most measurements are made on what are (nominally) sine waves, the correction factor assumes this waveform; but any distortion or offsets will lead to errors. To achieve this, a true RMS converter requires a more complex circuit.

## Digital RMS converters

If a waveform has been digitized, the correct RMS value may be calculated directly. Most digital and PC-based oscilloscopes include a function to give the RMS value of a waveform. The precision and the bandwidth of the conversion is entirely dependent on the analog to digital conversion. In most cases, true RMS measurements are made on repetitive waveforms, and under such conditions digital oscilloscopes (and a few sophisticated sampling multimeters) are able to achieve very high bandwidths as they sample at much higher sampling frequency than the signal frequency to obtain a stroboscopic effect.

## Thermal converters

The RMS value of an alternating current is also known as its heating value, as it is a voltage which is equivalent to the direct current value that would be required to get the same heating effect. For example, if 120 V AC RMS is applied to a resistive heating element it would heat up by exactly the same amount as if 120 V DC were applied.

This principle was exploited in early thermal converters. The AC signal would be applied to a small heating element that was matched with a thermistor, which could be used in a DC measuring circuit.

The technique is not very precise but it will measure any waveform at any frequency (except for extremely low frequencies, where the thermistor's thermal capacitance is too small so that its temperature is fluctuating too much). A big drawback is that it is low-impedance: that is, the power used to heat the thermistor comes from the circuit being measured. If the circuit being measured can support the heating current, then it is possible to make a post-measurement calculation to correct the effect, as the impedance of the heating element is known. If the signal is small then a pre-amplifier is necessary, and the measuring capabilities of the instrument will be limited by this pre-amplifier. In radio frequency (RF) work, the low impedance is not necessarily a drawback since 50 ohm driving and terminating impedances are widely used.

Thermal converters have become rare, but are still used by radio hams and hobbyists, who may remove the thermal element of an old unreliable instrument and incorporate it into a modern design of their own construction. Additionally, at very high frequencies (microwave), RF power meters still use thermal techniques to convert the RF energy to a voltage. Thermal-based power meters are the norm for millimeter wave (MMW) RF work.

## Analog electronic converters

Analog electronic circuits may use:

• an analog multiplier in a specific configuration which multiplies the input signal by itself (squares it), averages the result with a capacitor, and then calculates the square root of the value (via a multiplier/squarer circuit in the feedback loop of an operational amplifier), or
• a full-wave precision rectifier circuit to create the absolute value of the input signal, which is fed into a log amplifier, doubled and fed into an exponential amplifier as a means of deriving the square-law transfer function $x^{2}=e^{2\ln {|x|}}$ , and then the time-average and square root are performed, similarly to above,
• a log-domain precision detector (Blackmer RMS detector) also computes logarithm of absolute value of the input signal, however, time-averaging is performed on the logarithm, rather than square, of input. Output is logarithmic (decibel scale), with a fast attack but slow and linear decay. 
• a field-effect transistor may be used to directly create the square-law transfer function, before time-averaging.

Unlike thermal converters they are subject to bandwidth limitations which makes them unsuitable for most RF work. The circuitry before time averaging is particularly crucial for high-frequency performance. The slew rate limitation of the operational amplifier used to create the absolute value (especially at low input signal levels) tends to make the second method the poorest at high frequencies, while the FET method can work close to VHF. Specialist techniques are required to produce sufficiently accurate integrated circuits for complex analog calculations, and very often meters equipped with such circuits offer true RMS conversion as an optional extra with a significant price increase.

## Related Research Articles

In electronics, the figures of merit of an amplifier are numerical measures that characterize its properties and performance. Figures of merit can be given as a list of specifications that include properties such as gain, bandwidth, noise and linearity, among others listed in this article. Figures of merit are important for determining the suitability of a particular amplifier for an intended use. An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one. An operational amplifier is a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output. In this configuration, an op amp produces an output potential that is typically 100,000 times larger than the potential difference between its input terminals. Operational amplifiers had their origins in analog computers, where they were used to perform mathematical operations in linear, non-linear, and frequency-dependent circuits. A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.

The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude, which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. A multimeter is a measuring instrument that can measure multiple electrical properties. A typical multimeter can measure voltage, resistance, and current, in which case it is also known as a volt-ohm-milliammeter (VOM), as the unit is equipped with voltmeter, ammeter, and ohmmeter functionality. Some feature the measurement of additional properties such as temperature and volume. Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of reducing the average power delivered by an electrical signal, by effectively chopping it up into discrete parts. The average value of voltage fed to the load is controlled by turning the switch between supply and load on and off at a fast rate. The longer the switch is on compared to the off periods, the higher the total power supplied to the load. Along with maximum power point tracking (MPPT), it is one of the primary methods of reducing the output of solar panels to that which can be utilized by a battery. PWM is particularly suited for running inertial loads such as motors, which are not as easily affected by this discrete switching, because their inertia causes them to react slowly. The PWM switching frequency has to be high enough not to affect the load, which is to say that the resultant waveform perceived by the load must be as smooth as possible. In electronics, a digital-to-analog converter is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

Audio power is the electrical power transferred from an audio amplifier to a loudspeaker, measured in watts. The electrical power delivered to the loudspeaker, together with its efficiency, determines the sound power generated.

This is an index of articles relating to electronics and electricity or natural electricity and things that run on electricity and things that use or conduct electricity. A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.

In electronics, an analog multiplier is a device that takes two analog signals and produces an output which is their product. Such circuits can be used to implement related functions such as squares, and square roots.

Delta-sigma modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC). The wattmeter is an instrument for measuring the electric active power in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio frequency power; other types are required for radio frequency measurements.

A log amplifier is an amplifier for which the output voltage Vout is K times the natural log of the input voltage Vin. This can be expressed as, An oscilloscope is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetitive or single waveforms on the screen that would otherwise occur too briefly to be perceived by the human eye. The displayed waveform can then be analyzed for properties such as amplitude, frequency, rise time, time interval, distortion, and others. Originally, calculation of these values required manually measuring the waveform against the scales built into the screen of the instrument. Modern digital instruments may calculate and display these properties directly.

In electronics, power amplifier classes are letter symbols applied to different power amplifier types. The class gives a broad indication of an amplifier's characteristics and performance. The classes are related to the time period that the active amplifier device is passing current, expressed as a fraction of the period of a signal waveform applied to the input. A class A amplifier is conducting through all the period of the signal; Class B only for one-half the input period, class C for much less than half the input period. A Class D amplifier operates its output device in a switching manner; the fraction of the time that the device is conducting is adjusted so a pulse-width modulation output is obtained from the stage.

An RF chain is a cascade of electronic components and sub-units which may include amplifiers, filters, mixers, attenuators and detectors. It can take many forms, for example, as a wide-band receiver-detector for electronic warfare (EW) applications, as a tunable narrow-band receiver for communications purposes, as a repeater in signal distribution systems, or as an amplifier and up-converters for a transmitter-driver. In this article, the term RF covers the frequency range "Medium Frequencies" up to "Microwave Frequencies", i.e. from 100 kHz to 20 GHz.

The Blackmer RMS detector is an electronic true RMS converter invented by David E. Blackmer in 1971. The Blackmer detector, coupled with the Blackmer gain cell, forms the core of the dbx noise reduction system and various professional audio signal processors developed by dbx, Inc.

1. Tyler, Les; Kirkwood, Wayne (2008). "12.3.4 Dedicated Analog Integrated Circuits for Audio Applications". In Glen Ballou (ed.). Handbook for Sound Engineers. Fourth Edition. Focal/Elsevier. pp. 347–348. ISBN   978-0-240-80969-4.