Log Converters:One of the most predictable non-linear elements commonly available is the bipolar transistor. The relationship between collector current and emitter base voltage is precisely logarithmic from currents below one picoamp to currents above one milliamp. Using a matched pair of transistors and integrated circuit operational amplifiers, it is relatively easy to construct a linear to logarithmic converter with a dynamic range in excess of five decades. The circuit in Figure 1 generates a logarithmic output voltage for a linear input current. Transistor Q1 is used as the non-linear feedback element around an LM108 operational amplifier. Negative feedback is applied to the emitter of Q1 through divider, R1 and R2, and the emitter base junction of Q2. This forces the collector current of Q1 to be exactly equal to the current through the input resistor. Transistor Q2 is used as the feedback element of an LM101A operational amplifier. Negative feedback forces the collector current of Q2 to equal the current through R3. For the values shown, this current is 10 mA. Since the collector current of Q2 remains constant, the emitter base voltage also remains constant. Therefore, only the VBE of Q1 varies with a change of input current. However, the output voltage is a function of the difference in emitter base voltages of Q1 and Q2: