A log

Logarithm

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 amplifier

Amplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

 (logarithmic converter) is one for which the output voltage V_out is K times the natural log of the input voltage V_in. This can be expressed as,


where V_ref is the normalization constant in volts and K is the scale factor.

Basic op-amp diode circuit

The relationship between the input voltage and the output voltage is given by:

where is the saturation current and is the thermal voltage.

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

Rectifier

A rectifier is an electrical device that converts alternating current , which periodically reverses direction, to direct current , which flows in only one direction. The process is known as rectification...

 and filter

Electronic filter

Electronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...

 to condition the input signal before applying to the log amp input. As V_in is positive, V_out is obliged to be negative (since the op amp is in the inverting configuration) and is large enough to forward bias 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

Virtual ground

Virtual ground is a node of the circuit that is maintained at a steady reference potential, without being connected directly to the reference potential...

 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

Logarithmic output

External links

Integrated DC logarithmic amplifiers from Maxim's AN 36211

Analog electronics with Op Amps by A. J. Peyton, V. Walsh