Log Amplifier using Operational Amplifier

 Log Amplifier:

There are several applications of log and antilog amplifiers.

Antilog computation may require functions such as ln x, log x or sin hx.

Uses:

Direct dB display on a digital Voltmeter and Spectrum analyzer.

Log-amp can also be used to compress the dynamic range of a signal.

A grounded base transistor is placed in the feedback path. Since the collector is placed in the feedback path. Since the collector is held at virtual ground and the base is also grounded, the transistor‘s= voltage[-current−1] relationship becomes that of a diode and is given by,

and since I_c =I_E for a grounded base transistor I_C  = I_s e ^kT

Is-emitter saturation current ≈10^-13A

k=Boltzmann‘s constant

T=absolute temperature (inºK)

where V_ref =R₁I_s

The output voltage is thus proportional to the logarithm of input voltage.

Although the circuit gives natural log (ln), one can find log10, by proper scaling

Log10X=0.4343 ln X

The circuit has one problem.

The emitter saturation current Is varies from transistor to transistor and with temperature. Thus a stable reference voltage V ref cannot be obtained. This is eliminated by the circuit given below

The input is applied to one log-amp, while a reference voltage is applied to one log-amp, while a reference voltage is applied to another log-amp. The two transistors are integrated close together in the same silicon wafer. This provides a close match of saturation currents and ensures good thermal tracking.

Assume  I_S1=I_S2=I_S

Thus the reference level is now set with a single external voltage source. Its dependence on device and temperature has been removed. The voltage Vo is still dependent upon temperature and is directly proportional to T. This is compensated by the last op-amp stage A4 which provides a non-inverting gain of (1+R₂/R_TC). Temperature compensated output voltage V_L

Where R_TC is a temperature-sensitive resistance with a positive coefficient of temperature (sensor) so that the slope of the equation becomes constant as the temperature changes.