A logarithmic (log) amplifier produces an output that is proportional to the logarithm of its input. Since the log function is nonlinear, it is clear that a log amplifier is not linear in the sense discussed in Chapter 3. A logarithmic transfer characteristic is shown in Figure 15-24. We see that the slope of the characteristic,and hence the voltage gain, is small for large values of and large for small values of Vin. Since the gain decreases with’ increasing input signal level, the amplifier is said to compress signals.

One important application of log amplifiers is in the amplification of signals having a wide dynamic range: signals that may be very small as well as very large. Suppose, for example, that a temperature sensor generates a few millivolts at very low,temperatures and a few volts at very high temperatures. To obtain good resolution, we would like the small signals to undergo significant amplification. The same amplification applied to the large signals, as would occur in a linear amplifier, would overdrive the amplifier and create clipping and distortion. The log amplifier eliminates this problem.

Of course, the nonlinear characteristic of the log amplifier creates output waveforms that are distorted versions of input waveforms. If necessary for a particular application. the distortion can be removed by an antilogarithmic (inverse log, or exponential) amplifier, which has a transfer characteristic that is exactly the opposite of the log amplifier. On the other hand, in some applications the antilog operation is not necessary, as, for example, when it is desired to create a display of signal magnitudes on a logarithmic scale. An example is a spectrum analyzer, in which the frequency content of a complex signal is displayed as a plot of decibel voltage levels versus frequency. Another application of log amplifiers is in analog computation, where signal voltages must be multiplied or divided. For example, if we wisned to generate the product voltage V,V2, we could sum the outputs of two log amplifiers to obtain loge, + loge, = logv,v2′ The output of an antilog amplifier whose input is logv,v2 would then be a voltage proportional to V,V2′

The logarithmic characteristic of a log amplifier stems from the relationship between the collector current and base-to-emitter voltage of a BJT, which is similar ro the diode equation (equation 2-13):

where Is Is the reverse saturation current of the base-emitter diode and V T is the thermal voltage, Vr = q/kT (as defined in equation 2-11). When Vb< is a few tenths of a volt, eV-‘v) p 1, and (15-15) becomes.

We see that Vo is a logarithmic function of Vin. Since the common logarithm (base 10) is related to the natural logarithm by lox = equation 15-18 can also be written in terms.

The practical difficulty of the configuration we have described is that the value of I, cannot usually be predicted accurately and is, in any event, highly sensitive to temperaure variations. To overcome this problem, a practical log amplifier is constructed as shown in Figure 15-26. The two transistors are closely matched in an integrated circuit, so their values of I, are essentially equal and change equally with temperature. Following the same procedure we used to obtain equation 15-20, we find.

Here we see that the output is no longer dependent on the value of Also, the external voltage VII can be adjusted to control the overall sensitivity of the amplifier (as can the gain of the output difference amplifier).

Note that values of must be negative. so that – Vin lVr is always positive. As in practical log .amplifiers. practical anti log amplifiers use two transistors and two operational amplifiers to compensate for the variability of Is » Examples of integrated-circuit log and antilog amplifiers are the lCL 8048 (log) and leL 8049 (antilog) amplifiers. manufactured by Intersi\. These devices can be used over a 60-dB (1000 to 1) dynamic voltage range, with output voltages up to 14 V. The 8048 does not incorporate a difference amplifier to compensate for Is> but arranges two matched transistors and two operational amplifiers in such a way that the output of the second amplifier is proportional to the logarithm of the input difference voltage. which accomplishes the same goal.