Log amplifier

Log amplifier

Log Amplifier(Using OPAMP)

Introduction

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

Numerically, V_{out} = K lnfrac{V_{in{V_{ref

"Vref 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 RF.

Working

The condition that must be satisfied for successful working of a log amplifier is that the input voltage, Vin consists of only positive cycles(This may be accompanied by using rectifier & filters eliminating the negative cycles). Now, as Vin is positive, so Vout 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 ISO & the volt equivalent of temperature VT are temperature dependent. Hence, proper compensating circuits may be employed.


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