Logarithmic Currents - Keithley 6514 Instruction Manual

Logarithmic currents

The use of a diode junction in the external feedback path permits a logarithmic current-to-
voltage conversion. This relationship for a junction diode is given by the equation:
V = mkT/q ln(I/I
where; q = unit of charge (1.6022 x 10
The limitations in this equation center on the factors I
rent for V
conduction (recombination and diffusion mechanisms) within the junction, typically varying
between 1 and 2. Finally, RB constitutes the ohmic bulk resistance of the diode junction mate-
rial. I
O
The factor m introduces non-linearity's between those two extremes. Because of these limita-
tions, most diodes have a limited range of logarithmic behavior.
A solution to these constraints is to use a transistor configured as a "transdiode" in the feed-
back path, as shown in Figure 11-9. Analyzing the transistor in this configuration leads to the
relationship:
V = kT/q[ln(I/I
where; h
Figure 11-9
"Transdiode"
logarithmic current
configuration
Current
Input
From this equation, proper selection of Q1 would require a device with high current gain
(h ), which is maintained over a wide range of emitter currents. Suitable devices for this appli-
FE
cation include Analog Devices AD812 and Precision Monolithics MAT-01. Use the enclosure in
Figure 11-8 to shield the device.
Digital I/O, Analog Outputs, and External Feedback
) + I
O RB
k = Boltzmann's constant (1.3806 x 10
T = temperature (K).
. An empirical proportional constant, m, accounts for the different character current
O
and RB limit the usefulness of the junction diode at low and high currents respectively.
) - ln(h /(1 + h
O FE
is the current gain of the transistor.
FE
COM
Q1
Preamp
Out
-19
)
-23
)
, m, and RB. I
O
))]
FE
Model 6514
Input
10MΩ
HI
LO
<1Ω
S
(Chassis)
is the extrapolated cur-
O
Zero
Check
To Ranging
Op Amp
S
11-15
Amplifier