Basic Logarithmic Amplifier using Op-amp

Basic Logarithmic Amplifier

May-08,14, Dec.-08,14,16

The fundamental log amplifier is formed by placing a transistor as a diode in the negative feedback path of the op-amp.

1. Basic Log Amplifier using Transistor

The basic log amplifier can be obtained by using a transistor as a diode in the negative feedback path of an op-amp, as shown in the Fig. 3.2.1.

The node B is at virtual ground hence V_B = 0.

I = V_in – V_B / R = V_in / R  ….  (3.2.1)

As the op-amp input current is zero

I = I_C  = Collector current

The voltage V_CB = 0 as the collector is at virtual ground and base is grounded. Hence we can write the equation of I_C as,

The equation gives the output, proportional to the logarithm of the input voltage V_in

a. Disadvantages of Basic Circuit

The reverse saturation current Io for the diode changes with temperature. In fact it doubles for every ten degree celcius rise in the temperature.

Similarly the emitter saturation current varies significantly from one transistor to other and also with the temperature.

Hence it is very difficult to set the term V_ref for the circuit.

The term V_T which is kT also changes with temperature, which appears in both the equations.

Thus temperature affects the performance and accuracy of the basic logarithmic amplifier circuit. Hence it is must to provide some sort of temperature compensation to reduce the errors.

2. Temperature Compensated Log Amplifier

In this technique two log amplifiers are used. One of the log amplifiers is given as a reference voltage Vref while the other is given an input voltage V_in. The two transistors used in the two log amplifier circuits are integrated close together in the same silicon wafer. This ensures a close match of the saturation currents and provides good thermal tracking. The circuit is shown in the Fig. 3.2.2.

The transistors Q₁, Q₂ are fabricated on same chip. The op-amp A₁ and A₂ work as the basic transistor logarithmic amplifiers. For Q₁, Q₂ we can write,

 The op-amp A₃ acts as a difference amplifier with the unity gain.

The V_ref is decided by external battery and it is not temperature dependent.

The temperature dependent component I_s gets cancelled out.

Still the term V_T is present in V_x which depends on the temperature. This is compensated by the last stage of the op-amp A₄. It acts as a noninverting amplifier with gain of (1 + R₂ / R_T)  where R_T is the thermistor having positive temperature coefficient.

As temperature changes, V_T changes but at the same time R_T the ratio V_T (R₂ + R_T) / R_T remains constant.

Hence assuming this term as K, we can write,

V_o = Kln (V_in / V_ref) …. (3.2.16)

Thus properly matched coefficients and the resistance values provide a perfect temperature compensation for the circuit. The output is proportional to the logarithm of the input and temperature independent.

Review Questions

1. Explain the circuit operation of logarithmic amplifier using two op-amps with necessary diagrams.

2. Explain the basic log amplifier using transistor.

3. Derive the expression for the log amplifier with necessary diagram.