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 The Blackmer gain cell is an audio frequency voltage-controlled amplifier (VCA) circuit with an exponential control law. It was invented and patented by David E. Blackmer between 1970 and 1973. The four-transistor core of the original Blackmer ce ...
, forms the core of the
dbx noise reduction system and various
professional audio
Professional audio, abbreviated as pro audio, refers to both an activity and a category of high quality, studio-grade audio equipment. Typically it encompasses sound recording, sound reinforcement system setup and audio mixing, and studio mu ...
signal processors developed by
dbx, Inc.
Unlike earlier RMS detectors that
time-averaged algebraic square of input signal, the Blackmer detector performs time-averaging on the
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
of the input, being the first successful, commercialized instance of
log-domain filter. The circuit, created by
trial and error
Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying.
According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (18 ...
, computes
root mean squared of various waveforms with high precision, although exact nature of its operation was not known to the inventor. First
mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...
of log-domain filtering and
mathematical proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proo ...
of Blackmer's invention were proposed by
Robert Adams in 1979; general log-domain filter synthesis theory was developed by
Douglas Frey in 1993.
Operation
Root mean square (RMS), defined as the
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
...
of the
mean square In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable.
It may also be defined as the arithmetic mean of the squares of the '' deviations'' betwee ...
of input signal over time, is a useful metric of
alternating current
Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
s. Unlike peak value or average value, RMS is directly related to
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
, being equivalent to the
direct current
Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or eve ...
that would be required to get the same heating effect. In audio applications, RMS is the only metric directly related to perceived
loudness
In acoustics, loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The relation of ph ...
, being insensitive to the phase of
harmonics in complex
waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
s.
Magnetic recording
Magnetic storage or magnetic recording is the storage of data on a magnetized medium. Magnetic storage uses different patterns of magnetisation in a magnetizable material to store data and is a form of non-volatile memory. The information is ac ...
and playback inevitably shifts
phases of harmonics; a
true RMS converter will not react to such phase shift. Simpler
peak detectors or
average detector
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
s, on the contrary, respond to changes in phase with changing output values, although energy level and loudness remain unchanged. For this reason David Blackmer, designer of
dbx noise reduction system, needed a cost-efficient precision RMS detector compatible with the
Blackmer gain cell The Blackmer gain cell is an audio frequency voltage-controlled amplifier (VCA) circuit with an exponential control law. It was invented and patented by David E. Blackmer between 1970 and 1973. The four-transistor core of the original Blackmer ce ...
. The latter had an exponential control characteristic, so a suitable detector had to have
logarithmic output.
Contemporary electronic RMS detectors had "normal", linear outputs, and were built exactly following the definition of RMS. The detector would compute square of the input signal, time-average the square using a
low-pass filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filt ...
or an
integrator, and then compute square root of that average to produce linear, not logarithmic, output. Analog computation of squares and square roots was performed using either expensive variable-transconductance
analog multiplier
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'' (apply same signal to both inputs), and '' ...
s (which remain expensive in the 21st century) or simpler and cheaper
logarithmic converters employing
exponential
current-voltage characteristic of a
bipolar transistor
A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar t ...
.
Thermal RMS conversion was too slow for audio purposes; electronic RMS detectors worked fine in measurement instruments, but their
dynamic range
Dynamic range (abbreviated DR, DNR, or DYR) is the ratio between the largest and smallest values that a certain quantity can assume. It is often used in the context of Signal (electrical engineering), signals, like sound and light. It is measured ...
was too narrow for professional audio - precisely because they operated on ''squares'' of input signal, taking up twice its dynamic range.
Blackmer reasoned that the log-antilog detector may be simplified by taking up processing to log domain, omitting physical squaring of input signals and thus retaining its full dynamic range. Squaring and taking square roots in log domain is very cheap, being simple scaling by a factor of 2 or 1/2. However, simple
linear filter
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using ...
s do not work in log domain, producing incorrect, irrelevant output. Correct time-averaging required
nonlinear filter
In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals ''R'' and ''S'' for two input signals ''r'' and ''s'' separately, but does not always o ...
s of yet unknown topology. Blackmer proposed simple replacement of a
resistor in
RC network with a silicon
diode biased with a fixed idle current. Since small-signal
impedance of such diode is controlled linearly by current, changing this current controls settling time of the detector. Cutoff frequency of this first order filter equals
:
,
where
is
thermal voltage (hence the frequency shifts with temperature). The equation is valid for a range of idle currents over , allowing wide tuning opportunity. The circuit has fast attack and slow decay, which are locked to each other and cannot be adjusted separately. Logarithmic output voltage is proportional to the mean of the square at a rate of around 3 mV/dB, and proportional to RMS at around 6 mV/dB.
When the crude test circuit was built, Blackmer and his associates did not expect it to work as a true RMS detector, but it did. According to Robert Adams, it "seemed to behave ideally", and rigorous tests with various waveforms confirmed ideal RMS performance. The circuit was absolutely insensitive to phase shifts in input signal. It was immediately patented and employed in
dbx, Inc. professional audio processors. No one in the company, including Blackmer, could explain why it works at all until 1977, when Robert Adams began work on proper
mathematical proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proo ...
of RMS compliance. Adams tried to extend log-domain concept to
Sallen–Key topology and failed. He published his thesis in 1979, and was later credited as the inventor of log-domain filter concept, but the idea remained unknown to general public until the 1993 pioneering work by
Douglas Frey.
References
Bibliography
*
*
*
{{refend
Analog circuits
Dynamics processing
Measuring instruments
American inventions
20th-century inventions
1970s in technology