US3612902A

US3612902A - Temperature-independent antilogarithm circuit

Info

Publication number: US3612902A
Application number: US767979A
Authority: US
Inventors: Richard L Moose
Original assignee: Bell Telephone Laboratories Inc
Current assignee: AT&T Corp
Priority date: 1968-10-16
Filing date: 1968-10-16
Publication date: 1971-10-12
Anticipated expiration: 1988-10-12

Abstract

A circuit for obtaining an output voltage proportional to the antilogarithm of an input voltage. The circuit is made insensitive to temperature variations by constructing its two transistors as an integrated structure on the same substrate so that they are made of the same materials, by the same process and with a very close thermal coupling. This construction insures that all the critical parameters of the transistors, particularly the ratio of the reverse saturation currents of the base-emitter junctions, are stabilized against temperature changes.

Description

United States Patent lnventor Richard L. Moose Burlington, N.C.

Appl. N0. 767,979

Filed Oct. 16, 1968 Patented Oct. 12, 1971 Assignee Bell Telephone Laboratories, Incorporated Murray Hill, NJ.

TEMPERATURE-INDEPENDENT ANTlLOGARITl-IM CIRCUIT 6 Claims, 2 Drawing Figs.

U.S. Cl 307/229, 307/310, 328/145, 307/303 Int. Cl 606g 7/24 Field of Search 307/310,

References Cited UNITED STATES PATENTS Platzer 3,308,271 3/1967 Fi'iiEibi 307/310 3,393,328 7/1968 Meadows.... 307/310 3,395,265 7/1968 Weir 307/310 3,444,362 5/1969 Pearlman 328/145 3,089,968 5/1963 Dunn 328/145 Primary Examiner-Donald D. Forrer Assistant Examiner-Harold A. Dixon Attorneys-R. J. Guenther and William L. Keefauver ABSTRACT: A circuit for obtaining an output voltage proportional to the antilogarithm of an input voltage. The circuit is made insensitive to temperature variations by constructing its two transistors as an integrated structure on the same substrate so that they are made of the same materials, by the same process and with a very close thermal coupling. This construction insures that all the critical parameters of the transistors, particularly the ratio of the reverse saturation currents of the base-emitter junctions, are stabilized against temperature changes.

PATENTEUUET 12 Ian wvuvron R. L. MOOSE BY "Z/Amb 14 My -AMP A T TOPNEY TEMPERATURE-INDEPENDENT AN'IILOGARITHM CIRCUIT GOVERNMENT CONTRACTS The invention herein claimed was made in the course of, or under contract with the Department of the Army.

BACKGROUND OF THE INVENTION This invention relates to the art of electrical calculation and more particularly to a temperature-independent antilogarithmic circuit.

While the characteristics of many solid-state devices are quite predictable, one of the defects inherent in most prior art antilogarithmic circuits using transistors is thermal drift which causes the output to vary as a function of temperature changes. This thermal drift usually created an intolerable error in the output circuit and was generally corrected by placing the transistors in thermally regulated ovens. This, of course, increases the size, weight and cost of the circuit, all of which are undesirable consequences of the need to eliminate the error due to thermal drift. The source of this drift error resides in the fact that the emitter current of a transistor is directly proportional to the saturation current through its base-emitter junction and since the saturation current can change by a ratio of 2:1 for each temperature change of 7 C., the emitter current will also change by the same ratio. Consequently, any circuit based on the absolute magnitude of the emitter current will be highly unstable with temperature.

SUMMARY OF THE INVENTION Stability against the effect of thermal drifts over a wide temperature range is achieved by this invention by means providing a close thermal coupling between two transistors of the same type which are closely matched both in materials and in their fabrication process. The base and collector of the first transistor are directly connected to the base of the second transistor and to one pole of a direct-voltage power source through a resistor while its emitter is connected to the other pole of the power source. A second resistor connects the collector of the second transistor to the power source. The input signal is supplied to the emitter of the second transistor from a low-impedance source while the antilogarithm output is taken from its collector. Because of the close thermal coupling and matching, the ratio of their base-emitter junction saturation currents will remain substantially constant, although these currents themselves vary greatly with temperature.

BRIEF DESCRIPTION OF THE DRAWINGS The invention may be better understood by a reference to the accompanying drawings in which:

FIG. I is a circuit diagram disclosing the essential features of a preferred embodiment of the invention; and

FIG. 2 shows the basic transistor circuit useful in explaining the operation of the invention.

DETAILED DESCRIPTION The circuits of a preferred embodiment of the invention are disclosed in FIG. 1 which shows a pair of transistors Q1 and Q2 of the same type which are thermally coupled through a thermal link 6. The two transistors should not only be of the same type but they should be closely matched as to the materials of which they are constructed and it is essential that they be closely coupled through the thermal path provided by the thermal link 6. Preferably, these two transistors are constructed of the same materials on a single, thermally conductive substrate which may comprise the thermal link 6. Under these circumstances, the materials of which the two transistors are constructed will be practically identical and they will be identically processed using integrated circuit techniques, thereby resulting in a very close material match. The emitter of transistor O1 is grounded while its base and collector are both ioined to one terminal of resistor R the other terminal of which is connected to a source of direct voltage +E. The bases of the two transistors are directly connected together while the collector of transistor O2 is connected to the direct voltage source through a resistor R, The emitter of transistor 02 is connected to ground through a very low impedance signal source provided by the output circuit of operational amplifier 3. The signal voltage e is applied between input terminal 1 and ground, input terminal 1 being connected to the input circuit of operational amplifier 3. Signal voltage e is preferably obtained from a commercially available logarithmic amplifier circuit 10 to which is applied an input voltage e The output circuit of operational amplifier 3 is connected to the emitter of transistor Q2 by way of conductor 5. The output terminal 2 of the circuit, from which the antilogarithm is obtained, is connected to the collector of transistor 02.

The operational amplifier 3 is of conventional construction having a high gain amplifier means 4 with feedback and input resistors R, and R respectively. The configuration is of conventional design and it is to be understood that its gain and feedback are such as to provide the amplifier circuit with a very low output circuit impedance. This is particularly true where resistor R is made very large, approaching infinity. In this case, the output impedance of the amplifier will closely approximate the impedance of its output stage divided by the forward gain of the amplifier means 4.

With the circuit as shown in FIG. I, a signal voltage e applied between input terminal 1 and ground will produce an output voltage 2,, between output terminal 2 and ground which is proportional to the antilogarithm of the signal voltage. Moreover, it can be shown that so long as the two transistors are of the same type and are closely matched both in materials and in their fabrication process and so long as they are very closely thermally coupled, the circuit will be virtually independent of temperature changes over a very wide temperature range.

The manner by which this circuit provides thennal stability may be more fully understood by reference to FIG. 2 which discloses the transistor circuits of FIG. I in which the operational amplifier 3 has been shown to comprise an output stage impedance R, in series with a generator voltage V, and an offset direct voltage V,. The generator voltage V, is actually a very close approximation of the input signal voltage e applied to input terminal 1. Currents I, and i,, flowing through their respective collector resistors R and R,, very closely approximate the emitter currents of their associated transistors 01 and Q2. The emitter-to-base voltage of transistor 01 is shown by the small arrow labeled V, while the emitter-to-base voltage of transistor 02 is similarly shown as V,,,. The voltage equation for the mesh comprising the two base-emitter junctions and the operational amplifier is:

b 3bl 9 i o l It remains to be shown that the emitter current of transistor Q2 is proportional to the antilogarithm of the voltage V,. This can best be shown by first considering the well known diode law which applies to the base-emitter junctions of both transistors. This law is expressed as follows:

where:

i= junction current I reverse saturation current e base of natural logarithms q electronic charge N constant of material K Boltzmann's constant T= temperature-degrees Kelvin V= voltage across junction Expression (2) may be solved for the junction voltage and may be expressed by the very close approximation given below, which is obtained from expression (2) by noting that the ratio of the junction current to the saturation current is very large compared with unity when the junction is in its forward conducting region.

U/M U/ Now by combining expressions (1 and (3) the following expression for the emitter current of transistor Q2 is obtained:

' i ..i*, tiff i i5; if)

where:

i,=(E0.7 )/R a constant,

e. 0.9 over a wide temperature range and f' z l where R, is made small. The initter current i of transistor O1 is essentially constant as is also the product of the two exponential functions included in the parenthesis in expression (4). The first exponential function closely approximates 0.9 for a very wide temperature range extending at least from C. to 100 C. The value of 0.9 is obtained when the material constant N is approximately 1.5, as is true for silicon junctions, and the offset voltage V approximates millivolts. The second exponential function closely approximates unity because the output impedance R, of the amplifier is made very small. The ratio of the saturation currents (I /I can be made constant provided that the transistors are of the same type, made of the same materials, fabricated by the same process and maintained at equal temperatures. In accordance with the present invention, this is preferably accomplished by forming the two transistors of the same materials on a single substrate. When this is done, the output current i may be expressed as follows:

i As:

where:

A the product of the constant emitter current i and the quantities contained in parentheses in expression (4).

Although the output current i is also a function of temperature because the expression for A contains a temperature parameter, the circuit is several orders of magnitude more stable than it would be if the two transistors were not constructed as described above and kept at equal temperatures. In a practical circuit, the logarithmic amplifier circuit is preferably of the type described in Fairchild Application Bulletin APP-124, Jan. 1966, FIG. 3 in which transistors and operational amplifiers are also used for deriving an output voltage which is the logarithm of its input signal voltage. Thus, in FIG. 1, the output voltage e from logarithmic amplifier 10 is proportional to the logarithm of the input signal voltage a, applied between input terminal 11 and ground. It will be evident to those skilled in this art that if two such logarithmic amplifiers are used and their outputs summed at terminal 1 of FIG. 1, the product (or quotient) of their two input signal voltages may be derived. Moreover, if the gain of logarithmic amplifier 10 is made other than unity, its output voltage e will vary as the logarithm of a power or root of the input signal voltage e For example, if the gain of logarithmic amplifier 10 is made 1/2, the output voltage e at terminal 2 will vary as the square root of the input signal voltage e, at terminal 11. Now, in accordance with the present invention, if the matched transistors in the logarithmic amplifier 10 are made in the same way as are transistors Q1 and Q2 of FIG. 1, and particularly if they are fabricated on the same substrate as are transistors Q1 and Q2, substantially complete temperature compensation is achieved. When this construction is used, the input voltage e for the linear case, which is substantially equal to voltage V can be written as:

where: k is an arbitrary constant determined by the component parameters of logarithmic amplifier 10.

Combining expressions (5) and (6) causes the A parameters to cancel so that:

i =A ke, (7)

Similar considerations will show that for the cases where powers, products or quotients are obtained, the A parameters still cancel to provide excellent temperature compensation without the need for a constant temperature oven.

While the invention has been described with reference to a specific embodiment, it will be apparent to those skilled in this art that various modifications may be made without departing from the scope of the invention.

What is claimed is: l. A temperature-independent antilogarithmlc circuit responsive to applied input signals comprising first and second closely matched transistors of the same type, each having a collector, a base and an emitter, said transistors being closely coupled through a thermal path, both the collector and the base of said first transistor being directly connected to the base of said second transistor; means for applying said input signals to the emitter of said second transistor, said input signals being applied with respect to a ground reference potential, said means for applying said input signals comprising a low-impedance signal source having first and second terminals, means for connecting the first of said terminals to the emitter of said second transistor, and means for maintaining the second of said terminals at said ground reference potential, said low impedance source comprising the output circuit of an operational amplifier having sufficient feedback to provide a very low output circuit impedance compared with its output circuit impedance without feedback; and means for maintaining the emitter of said first transistor at said ground reference potential so that output signals representative of the antilogarithm of said input signals appear at the collector of said second transistor.

2. The combination of claim 1 and a logarithmic amplifier having an output connected to supply a signal voltage to said operational amplifier.

3. A temperature-independent circuit for generating output signals representative of the antilogarithm of applied input signals comprising first and second closely matched transistors of the same type, each having a collector, a base and an emitter, means maintaining a close thermal coupling between said two transistors, means directly connecting both the collector and the base of the first transistor to the base of the second transistor, a source of direct voltage having first and second poles, means directly connecting the first of said poles to the emitter of said first transistor, first and second resistors respectively connecting the collectors of said first and second transistors to the second of said poles of said direct voltage source, means for applying said input signals between the emitter of said second transistor and the first of said poles of said direct voltage source, and an output terminal connected to the collector of said second transistor so that said output signals representative of the antilogarithm of said applied input signals appear at said output terminal.

4. The combination of claim 1 wherein said means maintaining a close thermal coupling comprises a single substrate upon which both of said transistors are formed into an integrated structure.

5. The combination of claim 1 wherein said means for applying said input signals comprises a low-impedance signal source connected between the emitter of said first transistor and the first of said poles of said direct voltage source, said low-impedance source comprising the output circuit of an operational amplifier having sufficient feedback to provide a very low output circuit impedance compared with its output circuit impedance without feedback.

6. The combination of claim 5 and a logarithmic amplifier having an output connected to supply a signal voltage to said operational amplifier.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 12,9 2 Dated October 12, 1971 lnv tofl Richard L. Moose It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below: K

H H a Column 2, line #8, change V to --V line 52, change Equation (1) from H V8132 V3101 V9 V R 1 to eb2 ebi o i 0 line 7'5, change Equation (3 from "v (1/7\)1n(i/I to Column 3, line 59, change Equation (6 from e V (1/7\)1n ke to Column LL, line 51, claim A change "1" to --3--; line 55, claim 5 change "1" to --3--.

Signed and sealed this 6th day of June 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GO'ITSCHALK Attesting Officer Commissioner of Patents )RM PO-IOBO (10-69) USCOMM DC some-p69 U 5 GOVERNMENT PRINYING OFFICF Q59 O.'HvB*1J4

Claims

1. A temperature-independent antilogarithmic circuit responsive to applied input signals comprising first and second closely matched transistors of the same type, each having a collector, a base and an emitter, said transistors being closely coupled through a thermal path, both the collector and the base of said first transistor being directly connected to the base of said second transistor; means for applying said input signals to the emitter of said second transistor, said input signals being applied with respect to a ground reference potential, said means for applying said input signals comprising a low-impedance signal source having first and second terminals, means for connecting the first of said terminals to the emitter of said second transistor, and means for maintaining the second of said terminals at said ground reference potential, said low impedance source comprising the output circuit of an operational amplifier having sufficient feedback to provide a very low output circuit impedance compared with its output circuit impedance without feedback; and means for maintaining the emitter of said first transistor at said ground reference potential so that output signals representative of the antilogarithm of said input signals appear at the collector of said second transistor.