APPENDIX A --- THEORY OF OPERATION
In this appendix, we discuss some general principles relating to logarithmic amplification.
First of all, no amplifier can produce a logarithmic transfer function over a dynamic range
which includes an input signal level of zero, since log 0 = -8. All logarithmic amplifiers
must therefore specify a signal range over which they will "log". The classic log amp
discussed in most introductory texts exploits the I-V characteristics of a diode junction,
and consists of a diode feedback on an inverting operational amplifier. This approach
works well (over a dynamic range of >4 decades) at low speeds (less than 1 MHz), if the
circuit is properly temperature- compensated. At higher speeds the performance is
woeful, and other schemes
(1)
to approximate a logarithmic transfer are used.
The basic idea of the most common approach can be understood by examining the circuit
shown in Fig. A1, below.
Fig. A1
A1, A2 ... A
N
are identical linear amplifiers with gain G, which limit sharply for an input of
V
L
; and A
SUM
is a summing amplifier with a gain of G
0
.
Consider the transfer curve resulting from this amplifier combination for an input signal,
V
in
, whose size, V
in0
, is smaller than V
L
. The output signal, V
out
, is then given by:
N
(for V
in0
< V
L
)
V
OUT
= GG
0
X
V
INO
/5
J-1
J-1
If, in addition, V
L
> V
in0
> V
L
/5, an input of V
in
= 5V
in0
will give an output of:
-A1-
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