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 
= forward bias voltage across diode D
Apply KCL at node P
(3) 
and
![\[V_{d} = V_{i}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-109bc13c7994420e293068c77c2a4468_l3.png "Rendered by QuickLaTeX.com")
Therefore, equation (2) becomes
(4) 
From equation (1), (3) and (4), we have
![\[-\frac{V_{o}}{R}=I_{o}e^{\frac{V_{i}}{\eta V_{T}}}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-73b8d1d24499a9241deee81a55439baa_l3.png "Rendered by QuickLaTeX.com")
Therefore, we have
![\[ \boxed{V_{o}=-I_{o}Re^{\frac{V_{i}}{\eta V_{T}}}} \]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-2ea5f6a95e94eb9a5026cae9b64d93cf_l3.png "Rendered by QuickLaTeX.com")
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
![\[V_{EB} = V_{i}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-d6fd42de77747fa63e0529601e5f009e_l3.png "Rendered by QuickLaTeX.com")
Therefore, equation (6) becomes
(9) 
From equation (5), (7), (8) and (9), we have
![\[-\frac{V_{o}}{R}=I_{s}e^{\frac{V_{i}}{\eta V_{T}}}\]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-6db8dc45766440b2a814a51e8a80ccc3_l3.png "Rendered by QuickLaTeX.com")
Therefore, we have
![\[ \boxed{V_{o}=-I_{s}Re^{\frac{V_{i}}{\eta V_{T}}}} \]](https://electricalvoice.com/wp-content/ql-cache/quicklatex.com-19b16e2a0974b6bbcd3a11d91f3fdf38_l3.png "Rendered by QuickLaTeX.com")
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.
