Draw the circuit diagram of antilog amplifier using op-amp and diode as log element. Derive expression for output voltage.
Answers
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
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,
[/ezcol_2third_end]
V is voltage applied across diode; Vt is the voltage equivalent of temperature. Hence applying KCL at inverting terminal of opamp, we get
(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)).