Analog Circuits - Logarithmic Amplifier

There are various applications of op-amps. One of the important circuits using op-amp circuits is logarithmic amplifier. In logarithmic amplifier, the output is natural log of input signal.  the input signal can be a simple voltage. The basic equation that describes the logarithmic amplifier output is,

Vout = K * ln (Vin), K is gain of logarithmic amplifier

As we are saying logarithmic, this op-amp circuit is non-linear. So, a logarithmic amplifier converts linear voltage to non-linear. The main advantage of logarithmic amplifier is the dynamic range compression. So, if we have a very large dynamic range, it can be manipulated using a logarithmic amplifier.

The basic logarithmic amplifier circuit with diode is:

The basic electronic devices that help achieve logarithmic function are diodes and transistors. In a transistor, Vbe is related to Ic in a logarithmic way.

Output = -V_T ln(Input/I_s*R)

V_T  Thermal Voltage of the diode

 I_s    Saturation current in the diode

The reverse saturation current of the diode is temperature dependent.

Another logarithmic amplifier circuit with transistor is:

Some important points about logarithmic amplifier:

1. The gain of an ideal logarithmic amplifier approaches infinity as input approaches zero.

2. 

3. Change in output of logarithmic amplifier is the function of change in input voltage

3. Intercept voltage: The voltage at which the logarithmic value leads to zero. 

4. For smaller inputs, logarithmic amplifiers behave linear. The relation between input and output is linear.

Circuit by explanation: If i want to product of two analog signals, for suppose X and Y, we can do it using the below equation,

X * Y = Loginv(LOG(X)+Log(Y))

The above equation when represented in the form of block diagram, 

Application of logarithmic amplifiers:

1. Industrial circuits

     a. Process control

2. RF circuits

     a. Compression and decompression

     b. True RMS detection

Some vendors of logarithmic amplifiers used across different verticals of the industry are:

Texas Instruments - ADL5513 (Example of ic that is used in RF transmitter circuits)

Analog Devices - AD8307 (used in network and spectrum analyzers)

Maxim Integrated - MAX4206 (industrial applications)

Note: The reverse of logarithmic amplifier is anti-log amplifier where the non-linear signal is converted to linear signal.