Antilog Amplifier Circuit & Applications

AntiLog amplifier or antilogarithmic 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

Antilog amplifier circuit using diode and op-amp
Fig. 1 Antilog amplifier circuit using diode and op-amp

Diode, resistor and op-amp used in the antilog amplifier as shown in figure 1. The input Vis 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.

Fig. 2 Antilog amplifier analysis

Let current I flows through the resistor R.

(1)   \begin{equation*}  I=\frac{0-V_{o}}{R}=-\frac{V_{o}}{R} \end{equation*}

and diode current I_{d}

,

(2)   \begin{equation*}  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

(3)   \begin{equation*}  I = I_{d} \end{equation*}

and

V_{d} = V_{i}-0

    \[V_{d} = V_{i}\]

Therefore, equation (2) becomes

(4)   \begin{equation*}  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

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

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

Antilog amplifier circuit using transistor and op amp
Fig. 3 Antilog amplifier circuit using transistor and op-amp

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 Vis 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.

Fig. 4 Antilog amplifier analysis

Let current I flows through the resistor R.

(5)   \begin{equation*}  I=\frac{0-V_{o}}{R}=-\frac{V_{o}}{R} \end{equation*}

and collector current I_{C}

,

(6)   \begin{equation*}  I_{C}=I_{s}e^{\frac{V_{EB}}{\eta V_{T}}} \end{equation*}

where V_{EB} = V_E - V_B

and Is = Reverse saturation current of emitter-base junction

As we know that

I_C + I_B = I_E

since IB ≅ 0 A

Therefore

(7)   \begin{equation*}  $I_C = I_E$ \end{equation*}

Apply KCL at node P

I_E = 0 + I

(8)   \begin{equation*}  I = I_{E} \end{equation*}

and

V_{EB} = V_{i}-0

    \[V_{EB} = V_{i}\]

Therefore, equation (6) becomes

(9)   \begin{equation*}  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

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

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.

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