Log amplifier

Log Amplifier(Using OPAMP)

Introduction

A log amplifier is the one for which the output voltage V_out is K times the natural log of the input voltage V_in.

Numerically, $V\_\{out\}\; =\; K\; lnfrac\{V\_\{in\{V\_\{ref$

"V_ref is the normalization constant in volts, K is the scale factor"

Circuit diagram

The schematic circuit diagram is shown above, has Bipolar Junction Transistor in place of feedback resistor R_F.

Working

The condition that must be satisfied for successful working of a log amplifier is that the input voltage, V_in consists of only positive cycles(This may be accompanied by using rectifier & filters eliminating the negative cycles). Now, as V_in is positive, so V_out will be negative(because the Opamp is used in inverting configuration in the circuit diagram) & is large enough to forward bias the emitter base junction & hence keeping the BJT in active mode of operation.

Now,:$V\_\{BE\}\; =\; -V\_\{out\}$:$I\_C\; =\; I\_\{SO\}(e^v\_\{BE\}\; /\; V\_T\; -\; 1)\; approx\; I\_\{SO\}\; e^v\_\{BE\}\; /V\_T$:$Rightarrow\; V\_\{BE\}\; =\; V\_T\; ln\; frac\{I\_C\}\{I\_\{SO$

where $I\_\{SO\}$ is the saturation current of the emitter-base diode.Now, due to Virtual ground concept of an OPAMP, $I\_C\; =\; V\_\{in\}/R\_1$, so our final equation becomes: $V\_\{out\}\; =\; -V\_T\; ln\; frac\{V\_\{in\{I\_\{SO\}\; R\_1\}$

Clearly, the output voltage is expressed as the natural log of the input voltage. It must be noted that both the saturation current I_SO & the volt equivalent of temperature V_T are temperature dependent. Hence, proper compensating circuits may be employed.