Logarithmic Amplifier

OBJECTIVE:

To design and study the logarithmic amplifier using opamp.

THOERY:

Many industrial applications measure physical quantities over a wide dynamic range. These applications use logarithmic amplifiers (log amps) to match a transmitter's dynamic output to the linear input range of a signal gauge. A log amplifier (logarithmic converter) is one for which the output voltage Vout is K times the natural log of the input voltage Vin. This can be expressed as,



where Vref is the normalization constant in volts and K is the scale factor.
Log amplifier can be mainly of two types:

1. Basic op-amp diode circuit(using diodes)
2. Transdiode configuration(using transistor)

Logarithmic Amplifier

When the output voltage V0 changes as the logarithm of the input voltage Vin we have logarithmic amplifier. A log amp makes use of the logarithmic relationship between the voltage and current of a forward-biased diode. Figure 1 shows the characteristic of the forward current, given by the exponential function.

-------------------------------(1)

Where VF and IF are the forward voltage and forward current of the diode, respectively; IS the theoretical reverse-saturation current; m is a correction factor; and VT is the temperature-equivalent voltage. Exchanging the x for the y axes and vice versa yields the forward voltage as a logarithmic function of the forward current. Mathematically, this corresponds to solving Equation 1 for VF:

-------------------------------(2)

For a forward-biased diode, the forward current is larger by far than the reverse current (IF >> IS). Thus, Equation 2 simplifies to

-------------------------------(3)

A simple log amp whose transfer function satisfies Equation 3 is shown in Figure 2. The op amp operates as an inverting amplifier with a feedback diode. With the diode being virtually anode-grounded, the op amp needs to generate a negative output voltage to forward bias the diode. For a given input current, IIN, the corresponding output voltage, VOUT, is




Fig.1 Diode characteristic in exponential and logarithmic form


Fig 2. Log amplifier with diode.