Propagule pressure

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,

$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=K\ln \frac{V_{\mathrm{i}\mathrm{n}}}{V_{\mathrm{r}\mathrm{e}\mathrm{f}}}$

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 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,

$V_{\mathrm{B}\mathrm{E}}=-V_{\mathrm{o}\mathrm{u}\mathrm{t}}$

$I_{\mathrm{C}}=I_{\mathrm{S}\mathrm{O}}(e^{V_{\mathrm{B}\mathrm{E}}/V_{\mathrm{T}}}-1)\approx I_{\mathrm{S}\mathrm{O}}{e}^{V_{\mathrm{B}\mathrm{E}}/V_{\mathrm{T}}}$

$\Rightarrow V_{\mathrm{B}\mathrm{E}}=V_{\mathrm{T}}\ln \frac{I_{\mathrm{C}}}{I_{\mathrm{S}\mathrm{O}}}$

where $I_{\mathrm{S}\mathrm{O}}$ 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,

$I_{\mathrm{C}}=\frac{V_{\mathrm{i}\mathrm{n}}}{R_1}$, and

$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=-V_{\mathrm{T}}\ln \frac{V_{\mathrm{i}\mathrm{n}}}{I_{\mathrm{S}\mathrm{O}}{R}_1}$

The output voltage is expressed as the natural log of the input voltage. Both the saturation current $I_{\mathrm{S}\mathrm{O}}$ and the thermal voltage $V_{\mathrm{T}}$ 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

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