of Microprocessors

186 MUSICAL ApPLICATIONS OF MICROPROCESSORS
APPLIED
VOLTAGE
~
EXPONENTIAL
CURRENT fLOW
REfERENCE
CURRENT
REfERENCE
DIODE
CONVERSION
DIODE
Fig. 6--5. Temperature compensation with a second diode
Compensating Temperature Drift
Part of the solution to this problem lies in the use ofan additional diode
with characteristics identical to the first one and the circuit configuration of
Fig. 6-5. A constant reference current is applied to this added diode with a
magnitude about midway in the range of usable output currents from the
converter. The voltage to be converted is now applied between the two
diodes (in practice from an operational amplifier so that the reference current
is not upset), and the current flowing in the converter diode is the exponentially
converted current. Note that the input voltage must swing positive and
negative to get the full range of currents above and below the reference
current. This circuit completely compensates for the right shift of the diode
characteristic with increasing temperature because a similar shift occurs for
the voltage across the added compensation diode. The change in slope is not
corrected, but it is a much smaller effect than the horizontal shifting.
In a practical application, matched transistors are used for exponential
conversion partly because matched diodes are rare but mostly because the
three terminals on a transistor allow the circuit paths for voltage application
and current output to be separated. For good-quality transistors (constant,
high current gain), the collector current is proportional to the exponential of
the base to emitter voltage according to the equation,
Ie = AaleseBT (eIl627Vbe1T -1), where Ie is the collector current, a and I es are
transistor-construction-dependent constants (common base current gain and
emitter saturation current, respectively), and Vbe is the base-emitter voltage.
This equation is essentially identical to the diode equation given earlier.
Figure 6-{; shows a practical configuration with the input voltage
referenced to ground and an op-amp-regulated reference current source. The
op-amp maintains a constant reference current independent of changes in the
exponential output current by adjusting its own output voltage to carry away
the sum of the reference and output currents. The only real constraint on
reference current magnitude is that it not be so large as to cause internal
transistor resistances to come into play or be so small that leakages become
significant. Therefore, the reference current is ideally set to 1 /.LA, about
midway in the range of useful currents (1 nA to 1 rnA) but, due to finite