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: