Log amplifier

A log amplifier is an amplifier for which the output voltage V_out is K times the natural log of the input voltage V_in. This can be expressed as, resistor on capacitor

V_{\text{out}}=K\ln \left({\frac {V_{\text{in}}}{V_{\text{ref}}}}\right)

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

Basic op-amp diode circuit

Basic op-amp diode log converter

The relationship between the input voltage $V_{{\text{in}}}$ and the output voltage $V_{{\text{out}}}$ is given by:

V_{\text{out}}=-V_{\text{T}}\ln \left({\frac {V_{\text{in}}}{I_{\text{S}}\,R}}\right)

where $I_{\text{S}}$ and $V_{\text{T}}$ are the saturation current and the thermal voltage of the diode respectively.

Transdiode configuration

A transdiode configuration with a BJT connected in the negative feedback loop.

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 to condition the input signal before applying it 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,

{\begin{aligned}V_{\text{BE}}&=-V_{\text{out}}\\I_{\text{C}}&=I_{\text{SO}}\left(e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}-1\right)\approx I_{\text{SO}}e^{\frac {V_{\text{BE}}}{V_{\text{T}}}}\\\Rightarrow V_{\text{BE}}&=V_{\text{T}}\ln \left({\frac {I_{\text{C}}}{I_{\text{SO}}}}\right)\end{aligned}}

where $I_{\text{SO}}\,$ is the saturation current of the emitter-base diode and $V_{\text{T}}\,$ is the thermal voltage. Due to the virtual ground at the op amp differential input,

I_{\text{C}}={\frac {V_{\text{in}}}{R_{1}}}

, and

V_{\text{out}}=-V_{\text{T}}\ln \left({\frac {V_{\text{in}}}{I_{\text{SO}}R_{1}}}\right)

The output voltage is expressed as the natural log of the input voltage. Both the saturation current $I_{\text{SO}}\,$ and the thermal voltage $V_{\text{T}}\,$ are temperature dependent, hence, temperature compensating circuits may be required.

External links

Integrated DC logarithmic amplifiers from Maxim's AN 36211
Analog electronics with Op Amps by A. J. Peyton, V. Walsh

This article is issued from Wikipedia - version of the 9/22/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.

Log amplifier

Basic op-amp diode circuit

Transdiode configuration

See also

External links