Log amp uses capacitor-charging law

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, R₁ and C₁, charges from an external voltage, V_IN, instead of V_CC. The control-voltage 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
Input voltage Output voltage Input voltage Output voltage 2.5 3.324 8 5.782 3 3.667 8.5 5.861 3.5 3.954 9 5.886 4 4.227 9.5 5.945 4.5 4.506 10 6.098 5 4.705 10.5 6.187 5.5 4.956 11 6.204 6 5.151 11.5 6.312 6.5 5.315 12 6.371 7 5.444 12.5 6.378 7.5 5.615 13 6.476

The monostable pulse width, T, then depends on the time required for capacitor C₁ to charge to V_IN–V_K through R₁ with the applied voltage V_IN. The output of the second stage, filtered through R₂ and C₂, 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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