NTH Order Function Converter

The present invention relates generally to analog electronic circuits and more particularly to a circuit for implementing nonlinear operators.

Various circuits are known in the prior art for performing Nth-order operations. One such device includes a log-converter, a gain stage (where the gain=k) and an antilog converter to provide the Kth-order function, such that the output V.sub.o is expressed as

In this case the gain K can be manipulated to yield either a power or a root. However, this method is very complex and requires a temperature compensating component in each converter. Typical circuits using this approach appear in a publication by National Semiconductor, Inc., entitled "Linear Applications", Vol. 1 (1973) at pages AN31-18,20. Another circuit at page AN31-15 of the above reference is a two quadrant multiplier wherein

However, this circuit is only useful for squaring and requires a thermistor for temperature compensation because it operates on the principle of modulating the r.sub.E term, which is equal to KT/qI.sub.E where I.sub.E is one of the inputs. Further, this circuit is not readily adaptable to yield the inverse function, i.e., the square root.

Yet another prior art approach utilizes the square-law characteristics of an MOS device to perform a squaring operation. This approach is extremely susceptible to temperature variation and the uniformity from device to device is generally poor because of the variation in threshold voltage V.sub.T. Again, the inverse function is not possible.

It is a principal object of this invention to provide a versatile Nth-order function converter that is readily programmable to operate as either an Nth-root extractor or an Nth-power operator. Another object of this invention is to provide a high speed analog function converter using bipolar devices in current mode operation. Still another object is to provide an inherently temperature stable converter requiring no external compensation.

In accordance with the present invention, an Nth-order analog function converter is provided that is readily programmable for either root or power operations. The converter is implemented using bipolar technology operating in the current mode to provide high speed operation.

In one embodiment of the invention, two current sources I.sub.1 and I.sub.2 are each coupled to the collector of a bipolar transistor, the bases of the transistors being coupled together. One or the other of the transistors is selectively configured to operate as a diode by coupling its base to its collector. Depending upon whether the I.sub.2 or the I.sub.1 transistor is so connected, the converter will function as either a "power" or a "root" operator, respectively. The emitter of the I.sub.2 transistor is coupled to a string of n transistors connected as diodes, each having its collector coupled to its base and its emitter coupled to the next transistor in the string. The emitter of the nth transistor is coupled to ground. The emitter of the I.sub.1 transistor is coupled to the inverting input and the output of a buffer having a low offset, for example a differential amplifier having a gain of k=1, the non-inverting input of which is coupled to a third current source I.sub.k. I.sub.k is also coupled to a second string of n transistors configured as described above, with the emitter of the nth transistor being coupled to ground. For n transistors in a string, and assuming a collector-base short on the I.sub.2 transistor, the output current I.sub.1 =I.sub.k.sup.-n I.sub.2.sup.n+1. With a collector-base short on the I.sub.1 transistor, the output current will be I.sub.2 =I.sub.k.sup.n/(n+1) I.sub.1.sup.1/(n+1). It is readily apparent that for n=1, i.e., one transistor in each string, the circuit will function as either a squaring converter or a square root extractor.

In the present configuration, the difference between the base-emitter voltage of I.sub.1 and I.sub.2 transistors is equal to the difference between the voltage across each string of transistors. Therefore, the thermal voltage component, KT/q, is cancelled out and the converter is inherently temperature stable.

The converter is useful, for example, in such applications as RMS measurement, auto-correlation, power measurement and gain compression/expansion.

The novel features believed characteristic of the invention are set forth in the appended claims. The invention itself, however, as well as further objects and advantages thereof, will be best understood by reference to the following detailed description when read in conjunction with the accompanying drawings, wherein:

FIG. 1 is a schematic diagram of an (n+1) order function converter according to the present invention;

FIG. 2 is a schematic diagram of a squaring circuit including the converter of FIG. 1; and

FIGS. 3a-3c are graphical representations illustrating the relationship of the input voltage to the output current in the circuit of FIG. 2.

Referring now to the drawings, there is shown in FIG. 1 a schematic diagram of the general case of a function coverter 10 according to the present invention. Details of the current sources and power supply have been omitted from FIG. 1 so as to not unduly burden the description thereof. Further, it will be readily apparent to those skilled in the art that although NPN transistors have been utilized, PNP transistors may be substituted therefor with appropriate modifications to the respective polarities. A first current source I.sub.1 is coupled to the collector of a transistor Q.sub.1 having its emitter coupled to the output of an amplifier 12 configured to have non-inverting unity gain. A second current source I.sub.2 is coupled to the collector of a transistor Q.sub.2 having its base coupled to the base of transistor Q.sub.1. The emitter of transistor Q.sub.2 is coupled to the collector of a transistor Q.sub.01 which is the first of a string of n series-connected transistors Q.sub.01 . . . Q.sub.n each having its collector coupled to the emitter of the preceding transistor. The emitter of Qn, the last transistor in the string, is coupled to ground. The base of each transistor Q.sub.01 . . . Qn is coupled to its respective collector. In effect, each transistor in the string functions as a diode and therefore the string Q.sub.01 . . . Qn may be replaced by a string of n series-connected diodes. It is preferred, however, to use transistors with a collector-base short as shown in FIG. 1 because they have operating characteristics that more closely approximate those of an ideal diode.

A third current source I.sub.k is coupled to a string of diode-connection transistors Q'.sub.01 . . . Q'.sub.n connected in the same configuration as the first string of transistors Q.sub.01 . . . Qn described above. The emitter of transistor Q'.sub.n is coupled to ground. This second diode string modulates the I.sub.k current source.

Amplifier 12, connected as a unity gain buffer, couples the voltage on the Q'.sub.01 collector-base terminal to bias the emitter of Q.sub.1, thus sinking the Q.sub.1 emitter current I.sub.1 without altering its voltage.

A pair of shorting means or jumpers J.sub.A and J.sub.B, shown as dashed lines in FIG. 1, selectively provide a collector-base short on either Q.sub.1 or Q.sub.2 depending upon the operational configuration desired for converter 10. When J.sub.A is connected, I.sub.1 is the output and the circuit operates as a power converter with I.sub.1 proportional to I.sub.2.sup.(n+1). Conversely, when J.sub.B is connected the circuit operates as a root extractor and I.sub.2 is the output proportional to I.sub.1.sup.1/(n+1). I.sub.K is used in both cases as a gain setting constant.

In operation, referring to FIG. 1, the voltage difference between points 14 and 16 is equivalent to the difference between the base-emitter voltages of transistors Q.sub.1 and Q.sub.2, i.e., V.sub.BE1 -V.sub.BE2. This is also the difference in the voltage drop across the respective strings of transistors Q.sub.01 . . . Qn and Q'.sub.01 . . . Q'.sub.n. Since the transistors in each string are identical, the respective voltage drops may be expressed as nV.sub.BE(Q01) and nV.sub.BE(Q'01), and the difference is n(V.sub.BEQ01 -v.sub.BEQ'01). The voltage difference at points 14 and 16 may then be expressed as

Using the thermal voltage equivalent expression for the base-emitter voltage in terms of the collector currents I.sub.1 and I.sub.2,

Similarly, the Q.sub.01 and Q'.sub.01 base-emitter voltage difference may be expressed in terms of I.sub.2 and I.sub.k as

Substituting into the first equation

Removing the common terms (KT/q),

or,

In terms of I.sub.1 this becomes ##EQU1## or, in terms of I.sub.2,

It should be noted that converter 10 is inherently insensitive to temperature since the last two equations are independent of the temperature term (KT/q) normally associated with diodes.

Assuming I.sub.k= 1, to obtain an output current I.sub.1 equal to the nth power of an input current I.sub.2, jumper J.sub.A must be connected and each string must contain (n-1) transistors, i.e., Q.sub.01 . . . Q.sub.n-1 and Q'.sub.01. . . Q'.sub.n-1. Converter 10 is programmed as an nth root extractor by merely disconnecting J.sub.A and connecting J.sub.B, whereupon the output current I.sub.2 now equals the nth root of the input current I.sub.1, again assuming I.sub.k =1.

The accuracy of the present converter is directly related to the common mode current gain, or beta, of transistors Q.sub.1 and Q.sub.2. That is, the higher the beta, the more accurate the conversion. If a particularly high conversion accuracy is required, an emitter-follower stage can be included to drive the bases of Q.sub.1 and Q.sub.2 over a wide range of betas. For example, the collector of Q.sub.2 can be connected to the base of an additional NPN transistor (not shown), whose emitter would be connected to the bases of Q.sub.1 and Q.sub.2, and whose collector would be connected to a V.sub.CC voltage supply.

Referring now to FIG. 2, converter 10 is configured as a squaring converter. That is, J.sub.A is connected, there is one transistor in each string (n=1), and output I.sub.1 is proportional to the square of input I.sub.2. An A.C. voltage source 18 having a ramp voltage V.sub.s is shown as a typical input for which the square function is required. An amplifier 20 and transistors Q.sub.3, Q.sub.4, Q.sub.5, Q.sub.6, and Q.sub.7 are used to convert the input voltage V.sub.s to a double-frequency absolute-valued current which is in turn coupled to input I.sub.2 of converter 10. The squared output is then obtained as a current I.sub.1.

By way of illustration, referring to FIG. 3a, a symmetrical sawtooth voltage signal V.sub.S applied to the input of the circuit of FIG. 2 has a positive voltage peak V.sub.SP and a negative voltage peak -V.sub.SP. Transistors Q.sub.3 -Q.sub.7 form a frequency doubling current source with Q.sub.5 and Q.sub.6 conducting on alternate half-cycles of the input signal V.sub.S. The Q.sub.4 collector current I.sub.2, shown in FIG. 3b, is also the input current to converter 10.

The input voltage V.sub.S, and the converter 10 input current I.sub.2, may be expressed by a linear equation. Since the output current I.sub.1 is related to the square of the input current I.sub.2 as explained above, the converter output waveform is in this example a series of parabolas as shown in FIG. 3c. The voltage at the output of converter 10 is thus:

In addition to the programmability of the converter of FIG. 1 for power or root functions by the connection of J.sub.A or J.sub.B, the circuit may also be programmed for any root or power up to n+1 by shorting the appropriate transistor in each string to ground. For example, if the cube root were desired, J.sub.B would be connected and a short to ground would be connected at the emitter of the second transistor in each string, i.e., Q.sub.02 and Q'.sub.02.

The present converter is readily adaptable to any number of applications. For example, the combination of a square and a square root converter could be utilized in an RMS or a power measuring application. Or, by applying the square-converted output current to a summing amplifier for integration a particular auto-correlation function could be achieved. Various other embodiments and modifications will be apparent to those skilled in the art in light of the above disclosure. Therefore, it is to be understood that modifications to the details thereof may be made without departing from the spirit and scope of the invention.