**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.

**Contents**show

## Antilog amplifier using diode and op-amp

Diode, resistor and op-amp used in the antilog amplifier as shown in figure 1. The input V_{i }is applied through diode D at the inverting terminal. V_{o} 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.

\begin{equation} \label{eq:poly}

I=\frac{0-V_{o}}{R}=-\frac{V_{o}}{R}

\end{equation}

and diode current $I_{d}$,

\begin{equation} \label{eq:poly}

I_{d}=I_{o}e^{\frac{V_{d}}{\eta V_{T}}}

\end{equation}

where $V_d$ = forward bias voltage across diode D

Apply KCL at node **P**

$I_{d} = 0 + I$

\begin{equation} \label{eq:poly}

I = I_{d}

\end{equation}

and

$V_{d} = V_{i}-0$

\[V_{d} = V_{i}\]

Therefore, equation (2) becomes

\begin{equation} \label{eq:poly}

I_{d}=I_{o}e^{\frac{V_{i}}{\eta V_{T}}}

\end{equation}

From equation (1), (3) and (4), we have

\[-\frac{V_{o}}{R}=I_{o}e^{\frac{V_{i}}{\eta V_{T}}}\]

Therefore, we have

\[

\quicklatex{color=”#000000″ size=20}

\boxed{V_{o}=-I_{o}Re^{\frac{V_{i}}{\eta V_{T}}}}

\]

**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 V_{i }is applied through transistor T at the inverting terminal. V_{o} 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.

\begin{equation} \label{eq:poly}

I=\frac{0-V_{o}}{R}=-\frac{V_{o}}{R}

\end{equation}

and collector current $I_{C}$,

\begin{equation} \label{eq:poly}

I_{C}=I_{s}e^{\frac{V_{EB}}{\eta V_{T}}}

\end{equation}

where $V_{EB} = V_E – V_B$

and I_{s} = Reverse saturation current of emitter-base junction

As we know that

$I_C + I_B = I_E$

since I_{B} ≅ 0 A

Therefore

\begin{equation} \label{eq:poly}

$I_C = I_E$

\end{equation}

Apply KCL at node **P**

$I_E = 0 + I$

\begin{equation} \label{eq:poly}

I = I_{E}

\end{equation}

and

$V_{EB} = V_{i}-0$

\[V_{EB} = V_{i}\]

Therefore, equation (6) becomes

\begin{equation} \label{eq:poly}

I_{C}=I_{s}e^{\frac{V_{i}}{\eta V_{T}}}

\end{equation}

From equation (5), (7), (8) and (9), we have

\[-\frac{V_{o}}{R}=I_{s}e^{\frac{V_{i}}{\eta V_{T}}}\]

Therefore, we have

\[

\quicklatex{color=”#000000″ size=20}

\boxed{V_{o}=-I_{s}Re^{\frac{V_{i}}{\eta V_{T}}}}

\]

**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.