Logarithm and antilogarithm operations

1. Logarithmic operation circuit

Logarithmic operations can be realized by using the exponential volt-ampere characteristics of semiconductor PN junctions. In practice, the collector and base of BJT are often short-circuited. If connected in the form of a diode, there is a relatively accurate logarithmic relationship between the collector current IC and the emitter voltage VBE in a fairly wide range (such as IC from 10–9 to 10–3A). The relationship between iC and vBE of BJT is

This is because vBE>>VT (at room temperature 300K, VT»26mV).

The logarithmic operation circuit is shown in Figure XX_01. From , we can get

It can be seen that the output voltage is logarithmically related to the input voltage. The output voltage amplitude cannot exceed 0.7V, and vs>0 is required to ensure that the transistor is in the on state.

Since VT and IES are sensitive to temperature, the output voltage drifts seriously. Therefore, the actual logarithmic circuit adopts temperature compensation circuit. The circuit shown in Figure 2 can realize temperature compensation. The emitter junction voltages of T1 and T2 are

Since T1 and T2 are paired tubes, IES1 = IES2, we can get

Ignoring the base current of T2, , then

In the formula, VT is related to temperature. If the resistor Rt has a positive temperature coefficient, the temperature effect of VT can be compensated within a certain temperature range. In addition, adjusting the value of R3 can expand the output voltage to exceed 0.7V.

2. Antilogarithmic operation circuit

Figure 1

The resistor R and the BJT in the logarithmic circuit are swapped to form the antilogarithmic operation circuit shown in Figure 1. Since , using the relationship between the collector current and the emitter junction voltage of the BJT, we can get

It can be seen that the output voltage is in an antilogarithmic relationship with the input voltage, that is, antilogarithmic operation is realized. At this time, vs must be a positive value. Like the logarithmic operation circuit, temperature compensation is also required to eliminate the error caused by temperature to the operation circuit.