Log amplifier

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, resistor on capacitor

V_\mathrm{out} = K \ln\frac{V_\mathrm{in}}{V_\mathrm{ref}}

where Vref 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, Vin, 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 Vin is positive, Vout 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{align} V_\mathrm{BE} &= -V_\mathrm{out} \\ I_\mathrm{C} &= I_\mathrm{SO}\left(e^{V_\mathrm{BE} / V_\mathrm{T}} - 1\right) \approx I_\mathrm{SO} e^{V_\mathrm{BE} /V_\mathrm{T}} \\ \Rightarrow V_\mathrm{BE} &= V_\mathrm{T} \ln \frac{I_\mathrm{C}}{I_\mathrm{SO}} \end{align}

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

I_\mathrm C = \frac{V_\mathrm{in}}{R_1}, and
V_\mathrm{out} = -V_\mathrm T \ln \frac{V_\mathrm{in}}{I_\mathrm{SO} R_1}

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

See also

External links


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