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. In some situations, especially in RF domain, monolithic logarithmic amplifiers are also used to reduce number of components and space used, as well improve bandwidth and noise performance.
Logarithmic amplifier applicationsEdit
Logarithmic amplifiers are used in many ways, such as:
- To perform mathematical operations like multiplication, division and exponentiation. Multiplication is also sometimes called mixing. This is similar to operation of a slide rule, and is used in analog computers, audio synthesis methods, and some measurement instruments (i.e. power as multiplication of current and voltage).
- To calculate the dB value of a given quantity.
- As a True RMS converter.
- Extending dynamic range of other circuits, like automatic gain control of transmit power in RF circuits, or analog-to-digital converters.
Drawbacks of basic logarithmic amplifier configurationEdit
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 circuitEdit
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.
- RMS-to-DC Conversion Just Got Easy Linear Technology, Design Note 288, 2002
- Integrated DC logarithmic amplifiers from Maxim's AN 36211
- Analog electronics with Op Amps by A. J. Peyton, V. Walsh