DC Current comparator circuit for generating an adjustable output proportional to an input signal

A DC current-comparator-based circuit generates an adjustable output proportional to an input signal, i.e. an input voltage or current. One use of the circuit is in the formation of a DC resistance bridge that can be controlled automatically by a microprocessor. The ends of a pair of test resistors (the resistances of which are to be compared) are connected to respective ratio windings of the current comparator. The same potential is applied across these resistors by a master power supply. A microprocessor is alternately supplied with two voltage signals, a first being proportional to the current in a variable one of the ratio windings of the comparator, and the second being proportional to any inequality between the current in the other ratio winding and the test resistor to which it is connected. The microprocessor controls a slave power supply that receives both the first signal and a third signal that is indicative of any unbalance in the bridge. Balance is achieved by adjusting the variable ratio winding. Another use of the basic circuit is in the formation of an improved digital-to-analog converter, in which case the digital input controls the number of turns on the variable winding and the third signal provides the equivalent analog output.

FIELD OF THE INVENTION 
This invention relates to a DC current comparator circuit for generating an 
adjustable output proportional to an input signal, e.g. an input voltage 
or current. 
In one aspect, the invention can take the form of a circuit that can be 
employed for resistance measurement in a current-comparator-based DC 
resistance bridge. In this case the input signal to the circuit can be a 
current through an unknown resistor, the resistance of which is to be 
measured, while the output becomes a value, i.e. the value of such 
resistance expressed as a ratio to a known resistance. 
In another aspect, the invention can take the form of a circuit that is 
employed as part of an improved digital to analog converter, hereinafter 
referred to as a DAC. In this case the input signal to the circuit can be 
a current or voltage, while the output is a DC analog signal (voltage or 
current) that is accurately proportional to a digital input and the input 
current or voltage. 
PRIOR ART 
In relation to the application of the present invention to use in a DC 
resistance bridge, it is convenient to refer initially to a publication of 
N.L. Kusters et al, "A Direct Current Comparator Bridge for High 
Resistance Measurements" that was published in IEEE Transactions and 
Measurement, Vol. 1M-22, No. 4, December 1973, pp. 382-386, and disclosed 
the use of a DC comparator as part of a bridge capable of measuring 
resistors to an accuracy of approximately one part per million. Similar 
technology had already been proposed by M. P. MacMartin et al in "A 
Direct-Current-Comparator Ratio Bridge for Four-Terminal Resistance 
Measurements" published in IEEE Transactions on Instrumentation and 
Measurement, Vol. 1M-15, No. 4, December 1966, pp. 212-220; and by N. L. 
Kusters et al in "Direct-Current Comparator Bridge for Resistance 
Thermometry" published in IEEE Transactions on Instrumentation and 
Measurement, Vol. 1M-19, No. 4, November 1970, pp. 291-297. U.S. Pat. Nos. 
3,490,038 issued Jan. 13, 1970 and 3,500,171 issued Mar. 10, 1970 to N. L. 
Kusters et al, and Canadian patent No. 769,229 issued Oct. 10, 1967 to M. 
P. MacMartin et al also relate to this technology and explain the basic 
structure and function of a current-comparator-based DC bridge. 
FIG. 1 of the present application, which is based on the circuit 
illustrated in FIG. 1 of the first of the Kusters et al articles referred 
to above, provides a typical example of the various prior art proposals. A 
self-balancing DC comparator CC is the central component of the bridge of 
FIG. 1. It has two cores C1 of high-permeability magnetic material that 
are driven into saturation twice per cycle by a magnetic modulator MM. 
When DC flows through a variable ratio winding N.sub.X, the signal at the 
input to a peak detector PD contains even harmonics of the modulation 
frequency. This signal is converted to DC by the peak detector PD and is 
amplified in a slave power supply SS, causing a current to flow through a 
second ratio winding N.sub.S with a fixed number of turns, to reduce the 
net combined ampere turns in the ratio windings. This self-balancing 
comparator thus performs like a current transformer that operates down to 
zero frequency, i.e., DC. 
The test resistors to be compared R.sub.X (unknown) and R.sub.S (standard), 
are connected so that current from a master power supply MS flows through 
the adjustable number of turns of the winding N.sub.X and through the 
resistor R.sub.X. Current from the slave power supply SS flows through the 
ratio winding N.sub.S and through the resistor R.sub.S. At balance, the 
ratio of the current in each side of the circuit is related to the inverse 
of the ratio of the number of turns in the corresponding winding, and is 
indicated by a null at an ampere-turn balance meter BM. Also, the ratio of 
the currents is related to the inverse of the ratio of the corresponding 
resistors, as indicated by a null at a galvanometer GA. The bridge is thus 
a double-balance bridge, the resistance ratio at balance being the same as 
the turns ratio, i.e., R.sub.X ==R.sub.S (N.sub.X /N.sub.S) For 
convenience the reference letters N.sub.X and N.sub.S that identify the 
windings are also used in the equations to indicate the number of turns in 
such windings. 
The ampere-turn balance is achieved, as follows. The closed loop control, 
consisting of the magnetic modulator MM and the peak detector PD, measures 
the ampere-turn unbalance and applies a signal to the slave supply SS to 
reduce the unbalance. A tracking circuit, which includes a high impedance 
amplifier A, makes the output voltage of the slave supply SS follow that 
of the master supply MS, to keep the net ampere turns on the N.sub.S side 
very nearly equal to those on the N.sub.X side. This reduces the range 
required of the closed loop control so that its error is nearly zero. The 
manner in which the tracking signal generator can be ganged with the 
slider on the winding N.sub.X is illustrated by way of example in an 
expanded version of this basic circuit illustrated in FIG. 2 of the second 
of the Kusters et al articles referred to above. 
In relation to the application of the present invention to use in a DAC, 
the nearest prior art to applicant's knowledge is his own U.S. Pat. No. 
4,638,302 issued Jan. 20, 1987. 
SUMMARY OF THE INVENTION 
In its broad aspect, the present invention consists of a new DC current 
comparator circuit comprising a current comparator having a pair of ratio 
windings, one of which windings has a variable number of turns, and means 
for generating a first signal proportional to an ampere-turn unbalance 
between said windings; means for connecting a first end of a resistor to a 
first end of the variable winding; master power supply means for applying 
a potential to the second end of said resistor; means for generating a 
second signal proportional to the current in the variable winding; and 
slave means having input means connected to receive said first and second 
signals and output means connected to one end of the other of said 
windings for supplying a current to such other windings. 
Means are connected to the other end of said other winding for generating a 
third signal that is functionally related to the number of turns on the 
variable winding and the current in the variable winding. When the circuit 
is employed as part of a bridge, this functional relationship is such that 
the third signal is proportional to the change to the number of turns on 
the variable winding needed to bring the bridge to balance. Thus, when 
this new circuit is employed as part of a DC bridge for comparing the 
resistances of a pair of test resistors, it represents an improvement over 
prior circuits of this type in that it is more readily adapted to the 
modern demands of automation. 
It is thus an object of the present invention to provide an improved 
current-comparator-based DC resistance bridge that can readily be 
automated for microprocessor control. 
The invention also includes a combination of such an improved bridge with a 
control circuit for achieving such automation. 
In addition, the preferred embodiments of resistance bridge according to 
the invention that are described below include the following further 
advantageous features: 
(a) a very sensitive galvanometer with a very high input impedance is not 
required; and 
(b) very high resolution can be obtained without the need for a very large 
number of turns on the adjustable ratio winding. Although the number of 
turns cannot be varied by a fraction of a turn, and ten thousand turns is 
about the structural limit for an adjustable ratio winding, a resolution 
far greater than one part per ten thousand is achievable. In fact, a 
resolution of the order of one part in 10.sup.8 can be achieved. 
When the new circuit is employed as part of a DAC, the functional 
relationship of the third signal is that it is proportional to the total 
number of turns on the variable winding (which number has been set by a 
digital input) and the current in the variable winding and hence provides 
the desired analog output corresponding to said digital input. When so 
employed, the invention provides improvements over prior circuits of this 
type in that it is simpler to operate and more flexible in respect of the 
resistance values that can be chosen for use in the circuit. 
It is thus a further object of the present invention to provide an improved 
DC current-comparator-based DAC that is simpler to construct and operate. 
The preferred embodiment of DAC according to the invention that is 
described below includes the following advantageous features: 
(c) in comparison with a prior circuit that required the use of a pair of 
resistors having an exact, comparatively high resistance ratio to each 
other, the embodiment permits the adoption of any resistance ratio between 
the two resistors used; 
(d) while the prior circuits have required a third resistor, the resistance 
value of which needed to be fixed compared to one of the main pair of 
resistors, the embodiment eliminates the need for a third resistor 
altogether; and 
(e) the embodiment has eliminated a need to adjust yet a fourth resistor 
that the prior circuits employed in accordance with the number of turns 
employed from time to time on the variable winding.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Use of the circuit in a bridge 
FIG. 2 shows a current comparator essentially the same as in FIG. 1, except 
that for simplicity the magnetic modulator and the peak detector are now 
shown combined into a single, ampere-turn balance detector BD. Also as in 
FIG. 1, a first end of the standard resistor R.sub.S is connected at point 
Y to a first end of the ratio winding N.sub.S, and a first end of the 
unknown resistor R.sub.X is connected at point X to a first end of the 
ratio winding N.sub.X. The master power supply MS is connected at point P 
to the second end of the resistor R.sub.X, and, through a unity gain 
amplifier A3, at point Q to the second end of the resistor R.sub.S. This 
arrangement serves to equalize the voltages of points P and Q, while 
presenting an almost infinite impedance to the flow of current between 
these points. Since, as explained more fully below, points Y and X are 
driven to ground potential by amplifiers A4 and A1, respectively, the 
result is a 4-terminal measurement circuit. If the resistances of the 
resistors R.sub.S and R.sub.X are large, a 3-terminal measurement circuit 
can be achieved by omitting the amplifier A3 and joining the points P and 
Q together directly, as shown by the broken line B. 
The point X between the resistor R.sub.X and the winding N.sub.X is 
connected to one input of an operational amplifier Al, the other input of 
which is grounded. The output of the amplifier A1 is connected through a 
sensing resistor R to the second end of the winding N.sub.X through which 
a current I.sub.NX flows. Thus, the resistor R is in effect in series with 
the winding N.sub.X. 
The voltage across the resistor R forms the inputs to a further amplifier 
A2, the output of which is passed as a voltage signal (subsequently 
referred to as a "second signal") on line K to a voltage divider VD that 
is ganged (connection D) to the slider of the variable winding N.sub.X. 
Instead of this mechanical ganging, the controls for these variable 
devices can be arranged to be adjustable simultaneously by an operator to 
achieve the same effect. The voltage divider VD feeds a proportional 
voltage to a voltage-to-current converter VC that also receives an 
out-of-balance voltage signal (subsequently referred to as a "first 
signal") on line F from the balance detector BD. The output of the 
converter VC is proportional to the sum of its input voltages. 
There will be seen to be three pieces of information that must be supplied 
to the slave supply SS that the divider VD and converter VC together 
constitute. This slave supply must know (a) the value of the current 
I.sub.NX in the winding N.sub.X (it receives this information as the 
second signal on line K); (b) the number of turns in use on the winding 
N.sub.X (it receives this information by the connection D); and (c) any 
unbalance in the comparator, which information it receives as the first 
signal on line F. The output of the converter VC is connected by line G to 
the second end of the winding N.sub.S. 
The point Y between the resistor R.sub.S and the winding N.sub.S is 
connected to one input of an operational amplifier A4, the other input of 
which is grounded. The output of the amplifier A4 is connected to an 
output terminal Ed which is also connected through a resistor Rd to the 
point Y. A voltmeter V can be connected by a line L between the terminal 
Ed and ground. 
The amplifiers Al and A4, together with their associated connections, each 
acts as means for driving the respective points X and Y to ground 
potential, from which it follows that the voltages across the resistors 
R.sub.S and R.sub.X must always be equal to each other, since the points P 
and Q are always at the same potential as each other. This feature is an 
important practical distinction over the prior art circuit of FIG. 1. In 
this latter circuit, the voltages across the resistors R.sub.S and R.sub.X 
become equalized as part of the balancing procedure, i.e. by adjustment of 
the currents in the resistors R.sub.S and R.sub.X to bring the 
galvanometer GA to a null reading. In contrast, in the FIG. 2 arrangement 
of the present invention the circuit connections ensure equality between 
the voltages across the respective resistors R.sub.S and R.sub.X at all 
times, while the balancing procedure furnishes a different balance, namely 
equalization of the currents I.sub.NS and I.sub.X in the winding N.sub.S 
and the resistor R.sub.X respectively. 
Another difference between the circuits of FIGS. 1 and 2 is that in FIG. 1 
the current in the resistor R.sub.X is supplied by the master power supply 
MS in series with the winding N.sub.X, and the current in the resistor 
R.sub.S is supplied by the slave power supply SS in series with the 
winding N.sub.S, whereas in FIG. 2 the currents in the resistors R.sub.S 
and R.sub.X are both supplied by the master supply MS. 
More specifically, since the winding N.sub.X is in the feedback of the 
amplifier A1, the current I.sub.X is equal to I.sub.NX and is independent 
of contact and winding resistances. Since the amplifiers A3, A1 and A4 
equalize the voltages across the resistors R.sub.X and R.sub.S in the 
four-terminal-resistor configuration, I.sub.X =E/R.sub.X and I.sub.S 
=E/R.sub.S, where E is the voltage across these resistors. With the 
current comparator operating in ampere-turn balance condition, 
EQU I.sub.NS =(N.sub.X /N.sub.S).I.sub.NX (1) 
Since I.sub.NX =I.sub.X, equation (1) can be rewritten as 
EQU I.sub.NS =(N.sub.X /N.sub.X).I.sub.x (2) 
Automatic balance of the net ampere turns is achieved by means of the slave 
supply SS which is, in effect, an ampere-turn tracking circuit providing 
the appropriate current I.sub.NS in the winding N.sub.S. The slave supply 
SS is driven by the output voltage of the amplifier A2, which is 
proportional to the current I.sub.NX, and hence proportional to the 
current I.sub.X in the resistor R.sub.X, and by the output of the 
ampere-turn balance detector BD. The polarity of the current I.sub.NS is 
such that it is opposite to that of the current I.sub.S in the reference 
resistor R.sub.S. When I.sub.NS =I.sub.S, the output voltage Ed 
(subsequently referred to as a "third signal") of the amplifier A4 is 
zero, indicating a bridge balance. Bridge balance is therefore achieved by 
adjusting the number of turns in the winding N.sub.X until a null is 
indicated at the output of the amplifier A4. Since at balance I.sub.NS 
=I.sub.S, equation (2) becomes 
EQU I.sub.S =(N.sub.X /N.sub.S).I.sub.X (3) 
Substituting I.sub.S =E/R.sub.S and I.sub.X =E/R.sub.X in equation (3) 
gives 
EQU R.sub.X .fwdarw.(N.sub.X /N.sub.S).R.sub.S (4) 
which is the same relationship as was obtained with the FIG. 1 circuit. The 
bridge is then direct reading in resistance. If the positions of the 
resistors R.sub.X and R.sub.X are interchanged so that the resistor 
R.sub.S is connected between points P and X and the resistor R.sub.X is 
connected between points Q and Y, then the bridge is direct reading in 
conductance, as shown in the following equation 
EQU G.sub.X =(N.sub.X /N.sub.S).G.sub.S (4a) 
The bridge balance can easily be automated using a microprocessor as in 
FIG. 3 which shows a control circuit that, together with the circuit of 
FIG. 2, provides a microprocessor-controlled current-comparator-based DC 
resistance bridge for 4-terminal measurement of resistors. 
As indicated above, due to practical limitations, the maximum total number 
of turns of the ratio windings is about 10,000. A practical example is for 
the ratio winding N.sub.X to have a 13-bit resolution with adjustable 
numbers of turns 4096, 2048, 1024, . . . , 2, 1, totalling 8191 or 
(2.sup.13 -1) turns, with the ratio winding N.sub.S having a fixed number 
of turns, say 800, providing a turns ratio (N.sub.X /N.sub.S)=10.24. This 
provides a resistance measuring range of 0 to 10.24 times the resistance 
of the reference resistor R.sub.S. Other ranges and ratios can, of course, 
be chosen. The total number of turns for the two ratio windings is 
therefore 8991. The 13-bit resolution (one part in 8192) is, however, 
insufficient for high accuracy measurements. Since the current comparator 
is capable of giving turns-ratio accuracies in the order of one part in 
10.sup.8, the resolution of the measurement should also be of the same 
order. To have a resolution of one part in 10.sup.8 (26-bit resolution), 
the primary winding N.sub.X would have to have a total number of turns of 
10.sup.8, which is impossible. 
Additional resolution (up to 26 bits or more) can be achieved by deriving 
fractional currents proportional to I.sub.X, through resistors R1 and R2, 
and driving these currents by means of operational amplifiers A5 and A6 
through additional primary ratio windings N.sub.XJ and N.sub.XK, 
respectively. For R1=256.G.R and R2=8192.G.R (G is the gain of the 
amplifier A2 and R is the resistance of the resistor R in series with the 
winding N.sub.X in the feedback of the amplifier A1), the winding N.sub.XJ 
has the numbers of turns (128, 64, 32, 16, 8, 4, 2, 1), thus providing an 
additional 8 bits, and the winding N.sub.XK has the numbers of turns (16, 
8, 4, 2, 1), thus providing the remaining 5 bits, for a total of 26 bits. 
A resolution of 26 bits can thus be obtained with no significant increase 
in the total number of adjustable turns of the ratio winding N.sub.X. The 
total number of turns of the ratio windings N.sub.X, N.sub.XJ and N.sub.XK 
together is only 2.sup.13 -1+2.sup.8 -1+2.sup.5 -1=8477. 
FIG. 4 shows the manner in which the winding N.sub.X can be divided into 13 
groups N1 . . . N13 of turns. Winding group N13 may have 1 turn, for 
example, with winding group N12 having 2 turns, and winding groups N11 to 
N1 having respectively 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048 and 
4096 turns. Each bit of the digital input to this arrangement will be 
applied to a respective terminal B1 . . . B13 and will operate a 
respective relay (not shown) having contacts W and Z. When a contact W is 
closed its corresponding contact Z is open, and vice versa. In the 
position shown with all the contacts Z closed and all the contacts W open, 
all thirteen groups N1 . . . N13 are in circuit. When any one of the 
contacts W is closed, with consequential opening of its associated contact 
Z, that particular group of turns is taken out of circuit. Windings 
N.sub.XJ and N.sub.XK can be similarly divided into 8 and 5 groups, 
respectively. Further details of this type of arrangement were disclosed 
in U.S. Pat. No. 4,638,302 issued to E. So, et al Jan. 20, 1987. It should 
be pointed out, however, that it is not essential to divide the turns into 
groups based on powers of 2 (binary). The numbers of turns can take 
another progressive relationship, such as the decimal system. 
The slave supply, now identified as SS1, becomes an adjustable current 
source driven by the output of the amplifier A2 and consisting of a 13-bit 
(or more) multiplying digital-to-analog converter MDAC1 that divides the 
voltage it receives from line K and drives the voltage-to-current L 
converter VC which, as before, receives the out-of-balance signal on line 
F and outputs the current I.sub.NS on line G. This arrangement provides 
ampere-turn tracking of the first 13-bits (or more) of the primary winding 
N.sub.X and adjusts the current in the secondary winding N.sub.S to keep 
the net ampere-turns approximately zero. The closed-loop control 
(feedback) from the ampere-turn balance detector BD (line F) through the 
voltage-to-current converter VC tends to keep the net ampere-turn 
unbalance at zero. The closed-loop gain is sufficiently high to correct 
for changes in the slave supply circuit due to temperature effects, and 
also to keep the net ampere-turn unbalance at zero, even through no 
ampere-turn tracking is provided for the remaining bits of the 26-bit 
winding N.sub.X. For zero net ampere-turns in the ratio windings, the 
current I.sub.NS is proportional to the current I.sub.X in the unknown 
resistor R.sub.X and to the digital input or the numbers of turns of the 
windings N.sub.X, N.sub.XJ, and N.sub.XK. Thus from equation (4) 
##EQU1## 
where 
N.sub.X =(2).sup.13-i turns for 1.ltoreq.i.ltoreq.13 
N.sub.XJ =(2).sup.21-j turns for 14.ltoreq.j.ltoreq.21 
N.sub.XK =(2).sup.26-k turns for 22.ltoreq.k.ltoreq.26. 
Alternatively, as shown by broken line H, the additional resolution of 13 
bits or more can be obtained by using the output of the amplifier A2 (line 
K) to drive a 13-bit (or more) multiplying digital-to-analog converter 
MDAC2. This 13-bit MDAC2 is used to provide adjustable fractional 
currents, proportional to I.sub.X, to a one-turn, auxiliary ratio winding 
N.sub.XD through a resistor Rm that has a resistance value of G.R, where G 
and R are as defined above, see equation (6) below. 
If the additional 13 bits (to obtain 26-bit resolution in the winding 
N.sub.X) are achieved through use of the 13-bit converter MDAC2 to provide 
adjustable fractional currents (proportional to I.sub.X) to the one-turn 
winding N.sub.XD through the resistor Rm with a resistance value of G.R 
then 
##EQU2## 
where Dm is the digital input of the 13-bit MDAC2 and is given by 
Dm=(2).sup.26-m for 14.ltoreq.m.ltoreq.26. 
The measurement process starts with the number of turns of the winding 
N.sub.X set at zero, i.e. N.sub.X =0. From equation (2), I.sub.NS =0. 
Currents I.sub.S and I.sub.X are then measured by the microprocessor MP. A 
switch S controlled by a switch controller SC alternately connects the 
outputs of the amplifier A4 (line L) and the amplifier A2 (line K) to an 
analog-to-digital converter AD. The microprocessor MP then calculates from 
equation (3) an initial setting for the winding N.sub.X to obtain an 
approximate balance of the bridge, and instructs the switch controller SC 
to switch the corresponding number of turns of winding N.sub.X 
accordingly. The balance condition of the bridge is then checked by 
measuring the unbalance output voltage on line L, which unbalance is given 
by 
EQU .DELTA.Ed=.DELTA.I.sub.NS.Rd (7) 
Where .DELTA.I.sub.NS is the required additional current in the winding 
N.sub.S to achieve a bridge balance, and Rd is the resistance of the 
feedback resistor Rd of the amplifier A4. The additional number of turns 
in the winding Nx needed to generate .DELTA.I.sub.NS can then be 
calculated by the microprocessor from equations (2) and (7), and is given 
by 
EQU .DELTA.N.sub.X =(N.sub.S /I.sub.X).(.DELTA.Ed/Rd) (8) 
where .DELTA.N.sub.X is the required additional number of turns in the 
winding N.sub.X to achieve a bridge balance. .DELTA.N.sub.X is then added 
to (or subtracted from) the initial calculated setting of N.sub.X by 
adjustment of the number of turns on windings N.sub.X, N.sub.XJ and 
N.sub.XK by the switch controller SC, depending on the magnitude and 
polarity of the voltage .DELTA.Ed. The process of measuring .DELTA.N.sub.X 
is then repeated by measuring .DELTA.Ed again, until a bridge balance is 
achieved. The bridge is in balance when the measured voltage .DELTA.Ed is 
zero or is less than the voltage change achievable by the least 
significant bit in the winding N.sub.XK. 
The unknown resistor R.sub.X can be measured without achieving a bridge 
balance. The bridge can be balanced for the first 12 to 15 bits or more. 
The remaining unbalance, as indicated by the voltage .DELTA.Ed, is then 
measured to obtain the value of .DELTA.N.sub.X required to achieve a 
balance. This calculated value of .DELTA.N.sub.X is, however, not used to 
adjust the previous setting of the number of turns of the winding N.sub.X 
to achieve balance. Instead, the microprocessor merely calculates the 
unknown resistor R.sub.X from the previous setting of N.sub.X and the 
calculated value of .DELTA.N.sub.X. The result is then displayed and/or 
printed. The accuracy of this measurement depends on the number of bits 
used for the initial balance. The more bits used for the initial balance, 
the less stringent is the accuracy requirement for measuring the remaining 
unbalance signal .DELTA.Ed, and the more accurate the measurement result 
of the resistor R.sub.X. 
To summarize the performance of the circuit of FIG. 2, it is to be noted 
that the third signal, which is the voltage Ed and appears on line L, 
senses the unbalance in the bridge by virtue of sensing the inequality 
between the current in the nonvariable winding N.sub.S and the current in 
the test resistor R.sub.S that is connected to such nonvariable winding. 
Since the point Y between the nonvariable winding and the test resistor 
connected to it is at ground potential by virtue of the amplifier A4, any 
inequality between the desirably equal and opposite currents I.sub.NS and 
I.sub.S must flow from the point Y through the resistor Rd whereby to 
generate a voltage (third signal) at the terminal Ed. When these equal and 
opposite currents are truly equal, the third signal will be zero and the 
unbalance in the bridge will have been eliminated. One way to achieve this 
balance in the basic circuit of FIG. 2 is to observe the voltmeter V, 
which is connected between the terminal Ed and ground, and use any reading 
observed to adjust the number of turns on the variable winding N.sub. X. 
In the automated embodiment of FIG. 3 this balance is achieved by the 
microprocessor MP, because the third signal which is received by the 
voltmeter V in FIG. 2 on line L is communicated via the switch S and the 
analog-to-digital converter AD to the microprocessor MP which repeatedly 
samples the third signal on line L and adjusts the number of turns on the 
windings to reduce this signal (also referred to as .DELTA.Ed) to zero. 
As explained above, it is not always essential to achieve a bridge balance, 
because any remaining unbalance, as represented by the voltage .DELTA.Ed 
can be measured and used to calculate an error that is then inserted into 
the reading of the value of the unknown resistor. 
Having regard to the fact that the unbalance in the bridge, as represented 
by the third signal, can thus be eliminated manually (FIG. 2), or 
automatically (FIG. 3) or only partially automatically, this third signal 
is said to enable adjustment of the number of turns of the variable 
winding to bring the unbalance to null, the term "enable" having been 
chosen to include the circumstance in which such adjustment is not made 
automatically (but is left to the operator), or, if made automatically, is 
not necessarily fully made. 
To return to a comparison between FIGS. 1 and 2, it has already been noted 
that the FIG. 2 circuit produces the same comparison between the test 
resistors, equation (4), as did the circuit of FIG. 1. But the circuit of 
FIG. 2 is more suitable for automatic control by a microprocessor for the 
following reasons: 
A. The potential that is indicative of unbalance in the bridge, i.e. the 
potential Ed, needs to be compared to ground potential for this 
indication. This comparison is easier to achieve accurately than the 
comparison between two varying potentials that the galvanometer GA was 
called upon to make in the FIG. 1 circuit. As a result, this comparison 
does not require a null detector that is as sensitive as the galvanometer 
GA and has as high an input impedance as did the galvanometer GA. 
B The circuit of FIG. 2 furnishes the microprocessor MP on line K with a 
voltage signal that is proportional to the current I.sub.NX in the 
variable winding N.sub.X which is equal to the current I.sub.X in the 
unknown resistor R.sub.X. This feature provides a means to automate the 
bridge more easily. It also provides a means to extend the resolution of 
the bridge without increasing significantly the number of turns in the 
N.sub.X winding (using either N.sub.XJ plus N.sub.XK or MDAC2). The 
circuit of FIG. 1 provides no equivalent to the signal on line K. 
Use of the circuit in a DAC 
Turning now to the DAC application of the invention with particular 
reference to the embodiment of the invention shown in FIG. 5, the DC 
current comparator CC is employed as before to generation a first signal 
on line F by means of the ampere-turn balance detector BD, such signal 
being supplied as one input to the voltage-to-current converter VC of the 
slave supply SS' of FIG. 3. The output of the slave supply SS' on line G 
passes a current I.sub.NS into one end of the fixed winding N.sub.S, the 
point Y at the other end of this winding being driven to ground potential 
by the amplifier A4, as before. Also unchanged from FIG. 2 are the 
resistor Rd and the output terminal Ed which continues to provide the 
third signal which, in this instance, is a voltage relative to ground 
potential that represents the desired analog output corresponding to the 
digital input. 
FIG. 5A shows an alternative arrangement in which the amplifier A4 is 
dispensed with, the end of the resistor Rd not connected to the winding 
N.sub.S being grounded, and the output Ed being the voltage across the 
resistor Rd. The amplifier A7 is optional. 
Alternatively, if an analog current output is required, the resistor Rd can 
be part of an external circuit that measures the current in the winding 
N.sub.S. 
FIG. 5 shows a complex winding N.sub.X consisting of three sections 
N.sub.XI, N.sub.XJ and N.sub.XK. To achieve the 26-bit overall winding 
N.sub.X referred to above in connection with equation (5), these winding 
sections can conveniently have 13, 8 and 5 groups of turns, i.e. bits, 
respectively. A master power supply MS, e.g. battery E1, supplies a 
current I.sub.X into one end of a resistor R.sub.X (this reference letter 
has been retained, since this resistor has the same location in the 
circuit as the resistor R.sub.X in FIG. 2, although it is no longer an 
unknown resistor, the resistance value of which is to be measured). The 
other end of the resistor R.sub.X is connected through point X to one end 
of part N.sub.XI of the complex winding N.sub.X. The amplifiers Al and A2 
and the sensing resistor R of the FIG. 2 circuit remain, the amplifier A1 
driving the point X to ground potential and the amplifier A2 generating 
the second signal on line K. This second signal is supplied to the 
multiplying digital-to-analog converter MDAC1 of the slave supply SS' and 
to the resistors R1 and R2 associated with the amplifiers A5 and A6 of the 
winding sections N.sub.XJ and N.sub.XK, these parts being essentially 
unchanged from FIG. 3. However, in this instance, i.e. use of the circuit 
to form a DAC, the third voltage signal at terminal Ed (or the current 
equivalent) is no longer applied to a microprocessor, no attempt being 
made to bring such signal to zero. While control of the number of turns on 
the variable winding N.sub.X is still exercised by the switch controller 
SC, this number of turns is based on a digital input signal DIS. 
Alternatively, this digital input can take the form of manual adjustment 
of the number of turns on the variable winding. 
The relationship in the FIG. 5 circuit between the values of Rd and R.sub.X 
is given by the equations 
##EQU3## 
These equations can be solved for Ed, the analog output signal, as 
##EQU4## 
Hence the absolute values of Rd and R.sub.X are unimportant, and the ratio 
of Rd to R.sub.X can be chosen at will. The only requirement is that it be 
known. Hence with E1, N.sub.S and the ratio Rd to R.sub.X all constant and 
known, the analog output signal Ed is proportional to the digital input 
(the number of turns on the winding N.sub.X). As in FIG. 3, the amplifiers 
A5, A6 and resistors R1, R2 can be replaced by the second multiplying 
digital-to-analog converter MDAC2, resistor Rm and auxiliary ratio winding 
N.sub.XD, connected to the line K by line H. 
Important differences between the new circuit of FIG. 5 and the prior 
circuit shown in U.S. Pat. No. 4,638,302 are as follows: 
(1) In the prior circuit it was essential that the resistances of the 
resistors R1 and R2 have an exact, predetermined ratio to each other, such 
ratio being fixed by the number of bits in the second winding section 
N.sub.j. In the example given in the patent, this number of bits was taken 
as 8, so that the ratio of R2 to R1 had to be equal to 2.sup.8 or 256. In 
the new circuit this requirement for a fixed, and in practice 
comparatively high ratio with respect to R1 is avoided. It is merely 
necessary to know the ratio of Rd to R.sub.X to calibrate the output, the 
only restrictions on the values of Rd and R.sub.X being that they must be 
compatible with the ratings of the amplifiers. 
(2) In the prior circuit there are two supplies, e.g. the batteries Er and 
Es. The new circuit needs only one supply, e.g. the battery E1. 
(3) In the prior circuit it is necessary to adjust the resistor Ri to 
correspond to the various positions of the switches 16, 17, so that its 
value corresponds at any given time to the number of turns in circuit in 
the first primary winding section Ni. In the new circuit there is no such 
need. A reason for this difference resides in the fact that, whereas the 
prior circuit contained elements that corresponded in function to the 
lines F (the "first" signal) and G of FIG. 5 and also an output Eo that 
corresponded to the output Ed (the "third" signal) of FIG. 5, it contained 
no equivalent to the line K that transmits the "second" signal. 
(4) The circuit of FIG. 5 thus shares with the circuit of FIG. 2 the 
generation of three signals that are absent from both prior resistance 
bridges and prior DAC's, and which are made use of in the present 
invention to enhance the performance of the bridge or DAC in which the 
circuit of the present invention is employed.