AntiLog amplifier or anti–logarithmic amplifier is an electronic circuit that produces output that is proportional to the anti-logarithm of the applied input. Basically it performs mathematical operation of an anti-logarithm. In this article, we will see the different antilog amplifier circuits, its working and antilog amplifier applications. Basically two circuits are there to perform the anti-logarithmic function. First, using diode and op-amp and second, using BJT and op-amp.
Antilog amplifier using diode and op-amp

Diode, resistor and op-amp used in the antilog amplifier as shown in figure 1. The input Vi is applied through diode D at the inverting terminal. Vo is the output voltage. The non-inverting terminal of the op-amp is connected to the ground. This means that the voltage of the non-inverting terminal is zero volts.
Analysis
The analysis of the antilog amplifier is shown in figure 2. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V−) is equal to the voltage of the non-inverting terminal (V+ = 0V), according to the virtual short concept.
V− = V+ = 0V
The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

Let current I flows through the resistor R.
(1)
and diode current
(2)
where
Apply KCL at node P
(3)
and
Therefore, equation (2) becomes
(4)
From equation (1), (3) and (4), we have
Therefore, we have
Note: The negative sign in the output signifies that there is a 180° phase difference between output and the applied input.
Antilog amplifier using diode and transistor

Another circuit comprises of a BJT (PNP) T, resistor (R) and op-amp used as the antilog amplifier as shown in figure 3. The input Vi is applied through transistor T at the inverting terminal. Vo is the output voltage. The non-inverting terminal of the op-amp is connected to the ground. This means that the voltage of the non-inverting terminal is zero volts.
Analysis
The analysis of the antilog amplifier is shown in figure 4. Since the op-amp is ideal and negative feedback is present, the voltage of the inverting terminal (V−) is equal to the voltage of the non-inverting terminal (V+ = 0V), according to the virtual short concept.
V− = V+ = 0V
The currents entering both terminals of the op-amp are zero since the op-amp is ideal.

Let current I flows through the resistor R.
(5)
and collector current
(6)
where
and Is = Reverse saturation current of emitter-base junction
As we know that
since IB ≅ 0 A
Therefore
(7)
Apply KCL at node P
(8)
and
Therefore, equation (6) becomes
(9)
From equation (5), (7), (8) and (9), we have
Therefore, we have
Note: The negative sign in the output signifies that there is a 180° phase difference between output and the applied input.
Antilog Amplifier Applications
1. It is used in analog multiplier circuits.