of Microprocessors

184 MUSICAL ApPLICATIONS OF MICROPROCESSORS
1.1
1.0
0.9
_ 0.8
2:
~ 0.7
;::
w2
0.5
Cl
0.4
IDEAL DIODE
WITH 0.05.rr
SERIES
RESISTANCE
'" \
IDEAL
EXPONENTIAL
AND IDEAL
DIOOE
.'"MEASURED
IN4001
0.3
0.2
0.1
IDEAL
DIODE
\
IDEAL
~ EXPONENTIAL
OL -=~~ ----::------:--____=_-____=_-_;-_;----
10-12 10-11 10-10 10-9 10- 8 10- 7 10- 6 10- 5 .10- 4 0.0011 0.01 I 0.1 0.3 1.0
DIODE CURRENT (AI 0.003 0.03
Fig. 6-3. Silicon junction diode characteristics
Exponential Converter
Before the widespread use of semiconductor technology, accurate nonlinear
transfer functions were very difficult to obtain. Those that could be
obtained were only approximations that were imperfect even with perfect
components. Silicon semiconductor junctions, however, are predicted by
theory to possess a current-voltage relationship that is exponential in nature.
The classical semiconductor diode equation relates current through the diode
with the voltage across it as I = Alse BT (e CV / T -1), where A, B, and Care
constants (combinations of fundamental physical constants), Is is another
constant related to the construction of the diode, T is the absolute temperature
in degrees Kelvin, and V is the applied voltage. Thus, it can be seen that
the current is an exponential function of voltage if ecvrris much greater than
unity.
Fortunately, available real diodes are ofsufficient quality to very closely
conform to theory. The graph in Fig. 6-3 shows the current-voltage relationship
of a 1N4001 diode, a very common lO-cent item. The graph is on
semilog coordinates to make exponential behavior readily apparent. Also
shown is a plot of an absolutely ideal exponential response, a theoretically
perfect diode, and a perfect diode with a fixed series resistance of0.05 ohms,
a typical value for the 1N4001. Note the extremely close correspondence
between the actual diode and the ideal diode with series resistor model over a
current range of better than 10 9 to 1. In fact, the range of close conformity