where Vref is the normalization constant in volts and K is the scale factor.
The logarithm amplifier gives an output voltage which is proportional to the logarithm of applied input voltage. To design a logarithm amplifier circuit, high performance op-amps like LM1458, LM771, LM714 are commonly used and a compensated logarithm amplifier may include more than one.
Logarithmic amplifier applications
Logarithmic amplifiers are used in many ways, such as:
- To perform mathematical operations like multiplication, division and exponentiation.
- To calculate the dB value of a given quantity.
- As a True RMS converter.
Drawbacks of basic logarithmic amplifier configuration
The reverse saturation current for the diode doubles for every ten degree Celsius rise in temperature. Similarly the emitter saturation current varies significantly from one transistor to another and also with temperature. Hence, it is very difficult to set the reference voltage for the circuit.
Basic op-amp diode circuit
The relationship between the input voltage and the output voltage is given by:
where and are the saturation current and the thermal voltage of the diode respectively.
A necessary condition for successful operation of a log amplifier is that the input voltage, Vin, is always positive. This may be ensured by using a rectifier and filter to condition the input signal before applying it to the log amp input. As Vin is positive, Vout is obliged to be negative (since the op amp is in the inverting configuration) and is large enough to forward bias the emitter-base junction of the BJT keeping it in the active mode of operation. Now,
- , and
The output voltage is expressed as the natural log of the input voltage. Both the saturation current and the thermal voltage are temperature dependent, hence, temperature compensating circuits may be required.
- Integrated DC logarithmic amplifiers from Maxim's AN 36211
- Analog electronics with Op Amps by A. J. Peyton, V. Walsh
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