## Logarithmic amplifier

Definition

Logarithmic amplifier gives the output proportional to the logarithm of input signal.If Vi is the input signal applied to a differentiator then the output is Vo = K*ln(Vi)+l where K is gain of logarithmic amplifier,l is constant.

## Logarithmic amplifier operation

The circuit diagram of logarithmic amplifier is as shown below

logarithmic amplifier

It is obvious from the circuit shown above that negative feedback is provided from output to inverting terminal.Using the concept of virtual short between the input terminals of an opamp the voltage at inverting terminal will be zero volts.(Since the non inverting terminal of opamp is at ground potential). The logarithmic circuit can be redrawn as follows

The current equation of diode is given as Id = Ido*(exp (V/Vt)-1) where Ido is reverse saturation current,

V is voltage applied across diode; Vt is the voltage equivalent of temperature. Hence applying KCL at inverting terminal of opamp, we get

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(0-Vin)/R1 + Id = 0  implies Id = Vin/R1

Substituting the equation for current in the above equation we get Ido*(exp (V/Vt)-1) = Vin/R1. Assuming exp (V/Vt) >> 1 i.e. V>>Vt and V = – Vo, we get Ido*exp (-Vo / Vt) = Vin/R1. Applying Antilog on both sides we get

Vo = – Vt * ln (Vin/(R1*Ido)).

Gain of logarithmic amplifier

Gain of amplifier K = -Vt

Anti log amplifier

Definition

Anti log amplifier is one which provides output proportional to the anti log i.e. exponential to the input voltage.If Vi is the input signal applied to a Anti log amplifier then the output is Vo=K*exp(a*Vi) where K is proportionality constant, a is constant.

## Anti log amplifier operation

A simple Anti log amplifier is shown below

Anti logarithmic amplifier

It is obvious from the circuit shown above that negative feedback is provided from output to inverting terminal.Using the concept of virtual short between the input terminals of an opamp the voltage at inverting terminal will be zero volts.(Since the non inverting terminal of opamp is at ground potential). The anti log amplifier can be redrawn as follows

The current equation of diode is given as Id = Ido*(exp (V/Vt)-1) where Ido is reverse saturation current,V is voltage applied across diode; Vt is the voltage equivalent of temperature

Applying KCL at inverting node of opamp we get

Id = (0-Vo)/R = Io*(exp (Vin/Vt)) (assumed Vin /Vt >> 1)

Hence Vo = -Io*R*(exp (Vin/Vt)).

Gain of Anti log amplifier

Gain of Anti log amplifier K= -Io*R