Jayashree Raghuraman
EDN
The novel logarithmic amplifier in Figure 1 relies on the exponential charging characteristics of a simple RC circuit. The expression for the time, T, required for a capacitor, C, to reach a voltage (V_{IN}–V_{K}) from 0 V, when charged through a resistor, R, with an applied voltage of V_{IN}, is
(1) 
where V_{K} is a fixed voltage. The expression for T reduces to
(2) 
clearly showing an inherent logarithmic characteristic. The circuit in Figure 1 demonstrates this characteristic, using a 556 timer. With the values shown, the first stage of the 556 timer is a standard astable circuit operating at a frequency of approximately 1 kHz. The output of this stage acts as the trigger for the second stage. The second stage operates as a modified monostable circuit. In this modified configuration, the RC combination, R_{1} and C_{1}, charges from an external voltage, V_{IN}, instead of V_{CC}. The controlvoltage pin, CV2, has the value V_{IN} minus one diode drop, V_{K}.
Figure 1.  A simple 556 timer depends on RC charging to form a logarithmic amplifier. 
Table 1.  Output versus input voltage  

The monostable pulse width, T, then depends on the time required for capacitor C_{1} to charge to V_{IN}–V_{K} through R_{1} with the applied voltage V_{IN}. The output of the second stage, filtered through R_{2 }and C_{2}, depends on the first stage's astable frequency; the supply voltage, V_{CC}; and the monostable pulse width, T. Because V_{CC} and the astable frequency are constant, V_{OUT} is proportional to T. Table 1 tabulates the experimental results, and Figure 2 shows graphical results. The circuit operation is limited to an input range of 2.5 to 13 V to satisfy the internal biasing requirements of the second stage of the 556. The diode drop, V_{K}, is not strictly constant, because it varies with current. In spite of these limitations, Table 1 and Figure 2 clearly show a distinct logarithmic characteristic.
Figure 2.  The circuit of Figure 1 produces a distinct logarithmic output. 
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