Method for extending transistor logarithmic conformance

The linear component appearing in the output of two logarithmic amplifiers connected for temperature compensation and having matched feedback semiconductor devices is cancelled in a resistor connected in series with a logarithmic device between the output and a point of reference potential so that a purely logarithmic voltage appears at their junction.

BACKGROUND OF THE INVENTION 
The detector of a chromatograph provides an analog signal corresponding to 
the concentrations of sample material flowing through it. Before the 
information is applied to an integrator, certain processing functions are 
generally carried out by a digital system. In most cases, the dynamic 
range of the signal is so great that the digital system would have to have 
an excessively large number of bits if a reasonable degree of resolution 
is to be attained, but only a reasonable number of bits are required if 
the signal is first translated into logarithmic form. This may be 
accomplished by applying the signal to an operational amplifier circuit in 
which the feedback is provided by a transistor. If the detector is a 
voltage source, such as a thermal conductivity detector, it is connected 
via a coupling resistor to the inverting input of the amplifier. The 
non-inverting input is connected to a point of reference potential, and 
the desired logarithmic signal appears at the output. It is essential that 
there be very little noise or other distortion at the output of the 
amplifier because any error will be multiplied many times when the antilog 
of the processed signal is taken. 
To compensate for variations in the temperature of the junction of the 
feedback transistor, a second operational amplifier and feedback 
transistor are provided. If the feedback transistors are a matched pair, 
the changes in the output of the operational amplifiers due to temperature 
variations can be substantially cancelled by subtracting one output from 
the other. 
As is well known, the current flowing through the feedback transistor 
associated with the first operational amplifier equals the input current 
applied to it. As the latter current approaches the maximum current for 
which the feedback transistor is designed, an error term in logarithmic 
operation due to the internal resistance of the device becomes 
significant. The error term appears as a linear component in the output of 
the first operational amplifier. When the value of the resistor coupling a 
TC detector to the inverting input of the operational amplifier is 
adjusted for the best compromise between current and voltage noise, it is 
found that the current can exceed the maximum operating current of the 
feedback transistor so as to introduce a linear component into the 
logarithmic output. It might seem at first that this could be eliminated 
by using feedback transistors having a sufficiently high maximum current 
rating, but the feedback transistors must be a matched pair, and the 
available matched transistors do not have high enough current ratings. 
BRIEF DESCRIPTION OF THE INVENTION 
In a circuit incorporating this invention, a series circuit comprised of a 
resistor and a logarithmic device is connected between a point of fixed 
potential and the output of the operational amplifier to which the input 
signal is applied. The logarithmic device may be a compensating transistor 
of large geometry so that its internal series resistance is negligible 
compared to the external series resistance. The voltage produced across 
the external series resistor is of such polarity as to oppose the linear 
component of voltage in the output of the operational amplifier. If the 
compensating transistor is ideal, i.e., if it has no internal resistance 
in series with its emitter, the resistance of the external series resistor 
will be the same as the internal resistance of the feedback transistor.

PREFERRED EMBODIMENT 
In the drawing, a source 2, which may be a thermal conductivity detector, 
is coupled by a resistor 4 to the input at the junction J of a logarithmic 
amplifier 6. The amplifier 6 is shown as being comprised of an operational 
amplifier U.sub.1 having its non-inverting input connected to a point of 
reference potential, its inverting input connected to the junction J, and 
its output connected to a junction J.sub.1. Also included is a feedback 
transistor Q.sub.1 with its emitter connected to J.sub.1, its base 
connected to a point of reference potential, and its collector connected 
to the junction J. A resistance r shown in dotted line represents the 
internal resistance of the transistor Q.sub.1 that is in series with the 
emitter-collector path. 
A resistor R and the emitter-to-collector path of a compensating transistor 
Q.sub.2 are connected in series between the output at J.sub.1 of the 
logarithmic amplifier 6 and a point of reference potential. The emitter of 
Q.sub.1 is connected to the resistor R, and its base and collector are 
connected to the resistor R, and its base and collector are connected to a 
point of reference potential so that Q.sub.2 operates as a diode. The 
junction J.sub.2 between the resistor R and the emitter of Q.sub.2 is 
connected to one input of a subtracting means 8. 
Temperature compensation is provided by another logarithmic amplifier 10 
that is comprised of an operational amplifier U.sub.2 and a feedback 
transistor Q.sub.3. The inverting input of U.sub.2 and the collector of 
Q.sub.3 are connected to the output of a fixed current source 12 at a 
junction J.sub.3, and the output of U.sub.2 and the emitter of Q.sub.3 are 
connected to an output junction J.sub.4. The junction J.sub.4 is connected 
to the inverting input of the subtracting means 8. In the particular 
circuit shown, the non-inverting input of U.sub.2 and the base of Q.sub.3 
are connected to a point of fixed potential, but if it is desired to set 
the threshold voltage at the output of the subtracting means 8 at some 
offset value, such voltage could be applied via a switch s.sub.1 to the 
non-inverting input of U.sub.2. In this case, the base of Q.sub.3 would be 
connected to its collector via a switch s.sub.2. 
In order to achieve temperature compensation, transistors Q.sub.1 and 
Q.sub.3 are a matched pair contained in a common structure indicated by 
the dotted rectangle 14. The output of the subtracting means 8 is 
connected to means 16 for processing the signals as desired. 
OPERATION 
Compensation for variation in the temperature of the junction of the 
feedback transistor Q.sub.1 is provided by adjusting the current from the 
constant current source 12 to a value equal to the current flowing from 
the input signal source 2 to the junction J when the data signal has zero 
value. Because Q.sub.1 and Q.sub.3 are a matched pair, the voltages and 
the temperature coefficient of the voltages at J.sub.1 and J.sub.4 are 
equal so that subtracting either one from the other in the subtracting 
means 8 causes its output to be effectively insensitive to the transistor 
junction temperature, as desired. 
The signal current I.sub.D must equal the collector current I.sub.c of 
Q.sub.1. When the value of the resistor 4 is set so that the minimum value 
of I.sub.D provides an adequate signal-to-noise ratio in the output signal 
at J.sub.1, larger values of the signal current I.sub.D and therefore 
I.sub.c exceed the maximum rated operating current of Q.sub.1 so that the 
internal resistance r will have sufficient magnitude to introduce a large 
undesired linear component in the output voltage at J.sub.1. 
Cancellation of this linear component is achieved as follows. The 
operational amplifier U.sub.1 will apply an output voltage to the emitter 
of Q.sub.1 of such nature that the collector current I.sub.c equals the 
signal current I.sub.D. Because the voltage V.sub.BE between the emitter 
and base of Q.sub.2 must be proportional to the logarithm of the collector 
current I.sub.c, the voltage at the junction J.sub.1 must also be 
logarithmic. It is to be noted that the presence of the internal 
resistance r requires that the voltage at the junction J.sub.1 have an 
added linear component equal to I.sub.c r. The voltage V.sub.J.sbsb.1 at 
the junction J.sub.1 can be expressed by the following equation in which K 
is Boltzmann's constant; T is the absolute temperature; q is the charge of 
an electron; and I.sub.s is the maximum current flowing through Q.sub.1 
when it is back-biased. 
##EQU1## 
The voltage V.sub.J.sbsb.1 will cause a current I.sub.A to flow through the 
resistor R and Q.sub.2. The voltage V.sub.J.sbsb.2 that is produced by 
this current at the junction J.sub.2 is represented by the following 
equation, wherein the constants are the same as in equation (1). 
##EQU2## 
The transistor Q.sub.2 is of such geometric proportion that its internal 
resistance can be neglected for the currents involved. If Q.sub.2 is 
ideal, this resistance is in fact zero. With the value of R set so that 
I.sub.A R=-I.sub.c r. the undesired linear component I.sub.c r at the 
output of the log amplifier 6 is cancelled in the resistor R. In most 
situations, I.sub.A /I.sub.s of Q.sub.2 will equal I.sub.c /I.sub.s of 
Q.sub.1, so that if the internal resistance of Q.sub.2 is zero, R will be 
equal to r. 
It will be understood that the polarity of the output voltage from the 
subtracting means 8 could be reversed by interchanging the connections of 
its positive and negative inputs. Diodes or other logarithmic devices 
could be substituted for the transistors as long as those substituted for 
Q.sub.1 and Q.sub.3 are a temperature matched pair.