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Logarithmic Amplifiers

Sometimes we do not want a linear response from an op amp circuit. For example, what if we want the output voltage to represent the natural logarithm of the input voltage? What can we do for a feedback element to accomplish this?

An op amp using a diode to obtain a logarithmic response.

The answer is to use an electronic component that has a logarithmic relationship between the voltage applied to it and the current flowing through it. Such a component is the semiconductor diode, which can be used as a feedback element as shown to the right.

The semiconductor diode has the property that the current through it increases exponentially as the applied voltage increases linearly. In general use, this means that a silicon diode experiences an internal voltage drop of about 0.65 to 0.7 volt for a reasonable circuit current range. (For germanium diodes, it is about 0.3 volt.) However, it also means that the voltage will increase logarithmically if we control the applied current rather than the voltage. This is the normal behavior of the operational amplifier, so this is a highly practical method of generating a logarithm.

In the circuit shown, the applied input voltage must be positive, and the output voltage will be a negative logarithmic representation. Mathematically this is appropriate; you cannot find the logarithm of a negative number. However, sometimes you need a logarithmic response of either polarity. In such a case, you can connect a second diode in parallel with the one shown, but oriented in the opposite direction.

Using a transistor to reduce resistance effects.

A practical problem with a simple diode is the inherent internal resistance of any semiconductor material. This resistance is also subject to change with temperature, and may actually cause some internal heating in some applications. To reduce the problem, a transistor may be substituted for the diode as shown to the left.

In this circuit, the relatively high base resistance of the transistor is bypassed as most of the emitter current will flow through the collector region instead. Nevertheless, the logarithmic voltage/current characteristics of the emitter-base junction will still be in effect, so the circuit will perform quite well as a logarithmic amplifier. As with the diode circuit, you can get bipolar behavior if you connect a PNP transistor in parallel with the NPN transistor shown.

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