A log amplifier, also known as logarithmic amplifier or logarithm amplifier or log amp, is an
amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost t ...
for which the output voltage ''V''
out is ''K'' times the
natural log
The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...
of the input voltage ''V''
in. This can be expressed as,
:
where ''V''
ref is the
normalization constant
The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics. The normalizing constant is used to reduce any probability function to a probability density function with total probability of one.
...
in volts and ''K'' is the scale factor.
The log amplifier gives an output voltage which is proportional to the logarithm of the applied input voltage.
To design a log amplifier circuit, high performance
op-amps like LM1458, LM771, LM714 are commonly used and a compensated log amplifier may include more than one. In some situations, especially in RF domain, monolithic log amplifiers are also used to reduce number of components and space used, as well improve bandwidth and noise performance.
The log amplifier's operation can be inverted by an ''exponentiator'', such as an
op-amp configured for exponential output.
Log amplifier applications
Log amplifiers are used in many ways, such as:
# To perform mathematical operations like multiplication, division and exponentiation. Multiplication is also sometimes called mixing. This is similar to operation of a
slide rule
The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically designed for addition or subtraction, which ...
, and is used in
analog computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...
s, audio synthesis methods, and some measurement instruments (i.e. power as multiplication of current and voltage).
# To calculate the dB value of a given quantity.
# As a
True RMS converter
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 i ...
.
# Extending dynamic range of other circuits, like
automatic gain control of transmit power in
RF circuits, or
analog-to-digital converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) 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 ...
s.
Drawbacks of basic log amplifier configuration
The reverse
saturation current The saturation current (or scale current), more accurately the reverse saturation current, is the part of the reverse current in a semiconductor diode caused by diffusion of minority carriers from the neutral regions to the depletion region. This ...
for the
diode doubles for every ten degree Celsius rise in temperature. Similarly the emitter saturation current varies significantly from one transistor to another and also with temperature. Hence, it is very difficult to set the reference voltage for the circuit.
RMS-to-DC Conversion Just Got Easy
Linear Technology, Design Note 288, 2002
Basic op-amp diode circuit
The relationship between the input voltage and the output voltage is given by:
:
where and are the saturation current and the thermal voltage of the diode respectively.
Transdiode configuration
A necessary condition for successful operation of a log amplifier is that the input voltage, ''V''in, is always positive. This may be ensured by using a rectifier and filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
to condition the input signal before applying it to the log amplifier's input. As ''V''in is positive, ''V''out is obliged to be negative (since the op amp
An operational amplifier (often op amp or opamp) 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 (relative to ...
is in the inverting configuration) and is large enough to forward bias
Forward is a relative direction, the opposite of backward.
Forward may also refer to:
People
*Forward (surname)
Sports
* Forward (association football)
* Forward (basketball), including:
** Point forward
** Power forward (basketball)
** Smal ...
the emitter-base junction of the BJT keeping it in the active mode of operation. Now,
:
where is the saturation current of the emitter-base diode and is the thermal voltage. Due to the virtual ground at the op amp differential input,
:, and
:
The output voltage is expressed as the natural log of the input voltage. Both the saturation current and the thermal voltage are temperature dependent, hence, temperature compensating circuits may be required.
See also
* Diode
* Operational amplifier applications § Logarithmic output
References
{{Reflist
External links
Integrated DC logarithmic amplifiers
from Maxim's AN 36211
Analog electronics with Op Amps
by A. J. Peyton, V. Walsh
Electronic amplifiers
de:Operationsverstärker#Logarithmus und Exponentialfunktion