Antilog Amplifier using Op-amp

Antilog Amplifier

Dec.-14, 16

The log amplifier can easily be turned around to provide the antilog or exponential function which is called antilog amplifier. The basic antilog amplifier can be obtained by using a transistor.

1. Basic Antilog Amplifier using Transistor

The same circuit providing antilog of the input can be obtained by using a transistor instead of a diode. This is shown in the Fig. 3.3.1.

The node B is at virtual ground hence V_B = 0. Thus both collector and base of the transistor are at ground potential and V_CB = 0. Hence the voltage across the transistor is VBE and we can write the expression for its collector current as,

Now the current IC and current I are same as op-amp input current is zero.

Thus the output voltage is proportional to the exponential of V_in i.e. antilog of V_in Thus circuit works as basic antilog amplifier.

In both the above circuits, it can be seen that the terms Io, Is and VT are present in the output equation. All these are the function of temperature. Hence as temperature changes, these parameters also change and cause serious errors at the output. So the basic antilog circuits also face the same limitations as that of basic log amplifier circuits. And hence temperature compensation is must for the antilog amplifier circuits as well.

2. Temperature Compensated Antilog Amplifier

The circuit of transistor based antilog amplifier with temperature compensation is shown in the Fig. 3.3.2.

The two matched transistors Q₁ and Q₂ are used. The external voltage V_ref is connected to inverting terminal of op-amp A₂ through resistance R₁. The voltage divider receives the input voltage V_in. The thermistor R_T is used in the voltage divider.

As shown in the Fig. 3.3.2,

V_B2 = Voltage of base of Q₂

V_E2 = Voltage of emitter of Q₂ = V_x

Let us derive the expression for the output voltage V_o

For both the op-amps, as node A is grounded, node B is at virtual ground and hence V_B for both the op-amps is zero.

Referring to the equation (3.2.3) of section 3.2.1, we can write the equations for base-emitter voltages of Q₁ and Q₂ as,

Thus the output is proportional to the antilog (ln^-1) of the input. And the term R_T/V_T (R₂ + R_T ) is constant though temperature changes as RT also changes proportional to the changes in V_T . Thus a complete temperature compensation is achieved with this circuit.

Review Questions

1. Derive th expression for antilog amplifier with necessary diagram.

Dec.-14, Marks 5

2. Explain the circuit operation of temperature compensated antilog amplifier.

3. Write a note on antilog amplifier using op-amp.

Dec.-16, Marks 7