Technique for determining the values of circuit elements in a three terminal equivalent circuit

A technique which improves the accuracy of determining the circuit element values in a three terminal equivalent circuit is disclosed. The improvement results from the use of at least one ratio wherein the numerator and denominator of each ratio is a different function of at least one measurement of the three terminal equivalent circuit. Each ratio is representative of the true value of one preselected circuit element to another preselected circuit element value. This technique can be used for DC or AC analysis of the equivalent circuit and can be adapted for different sources of measurement errors.

TECHNICAL FIELD 
This invention relates to a technique for identifying circuit faults in a 
communications network by determining the values of circuit elements in a 
three terminal equivalent circuit and, more particularly, to an improved 
method and apparatus which more accurately determines these circuit 
element values. 
BACKGROUND OF THE INVENTION 
Telecommunications systems utilize numerous conductor pairs encompassed 
within a nonconductive sheath; the sheath also contains a continuous 
metallic shield so that cable may be grounded periodically to mitigate 
interference. The conductors of a pair are typically referred to as the 
tip and ring conductors. The tip and ring, together with circuit ground 
constitute a three-wire transmission line. Such a transmission line 
together with a variety of interconnected equipment provides a myriad of 
communications services. 
The identification of circuit faults in telecommunications systems is a 
difficult task due to the many different circuit arrangements. To 
facilitate the identification process, a three terminal equivalent or 
delta circuit is synthesized which is representative of the three-wire 
transmission line. The synthesized circuit has circuit elements which vary 
with the particular equipment connected to the three-wire transmission 
line. The values of these circuit elements are determined by performing 
different measurements of the three-wire transmission line. By determining 
the values of the circuit elements in the three terminal equivalent 
circuit using well-known techniques, faults in the actual circuit can 
often be identified. While this fault identification technique has long 
been used and provides satisfactory results, improper fault 
identifications do occur. Such errors typically arise when the value of 
one circuit element in the three terminal equivalent circuit is 
substantially different from the others. As a result of such improper 
fault identifications, incorrect selection of follow-up measurements, 
strategies or even false dispatches of repair forces can result. 
Accordingly, a technique which reduces errors in the determination of the 
circuit element values in a three terminal equivalent circuit would be 
highly desirable. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, the values of circuit elements in 
a three terminal equivalent circuit can be more accurately determined. 
This three terminal equivalent circuit is representative of an actual 
circuit. Pursuant to the present invention, predetermined signals are 
applied to the actual circuit being tested and measurements are performed. 
Using these measurements, at least one ratio is formed, the numerator and 
denominator of each ratio being a different function of at least one of 
the measurements. Each ratio is representative of a ratio of the value of 
one preselected circuit element to another preselected circuit element 
value in the three terminal equivalent circuit. Using the ratios formed 
and the measurements taken, the values of the circuit elements in the 
three terminal equivalent circuit are determined. 
An aspect of the present invention is that it is applicable to both AC or 
DC characterization of a three terminal equivalent circuit. Another aspect 
of the present invention is that it can be adapted to compensate for 
different sources of measurement error. Still another aspect of the 
present invention is that it can be used alone or in combination with 
prior art analysis of a three terminal equivalent circuit.

DETAILED DESCRIPTION 
A three-wire transmission line, comprising a tip conductor with terminal 
nodes 101 and 102, a ring conductor with terminal nodes 103 and 104 and a 
circuit ground with nodes 105 and 106, is shown in FIG. 1 connecting a 
test position 200 and a remotely-located termination position 100. The DC 
resistance of the tip conductor and ring conductor between positions 100 
and 200 is designated by resistors 121 and 122, respectively. In most 
situations, resistors 121 and 122 have substantially the same value. 
The illustrative circuit under the test having a termination position 100 
can be synthesized by a three terminal equivalent circuit 110. Circuit 110 
comprises tip-ring resistor 123, ring-ground resistor 124 in series with a 
DC source 125, and tip-ground resistor 126 in series with another DC 
source 127. Each DC source in FIG. 1 is represented by a battery. This DC 
three terminal equivalent circuit is representative of a class of 
telecommunications circuits which are tested. Moreover, if the DC sources 
125 and 127 are set to zero, then the three terminal equivalent circuit 
represents other passive networks, such as a coin telephone, which can be 
conducted to a three terminal transmission line. In addition, by 
substituting an impedance for each resistor, an AC three terminal 
equivalent circuit results, which also can be analyzed to determine 
circuit faults in a class of telecommunications circuits which are tested. 
Now, refer to FIG. 2. Using conventional techniques, the circuit element 
values for the three terminal equivalent circuit can be determined using 
measurements taken at test position 200 in a well-known fashion. In this 
analysis and those which follow, the tip and ring resistors 121 and 122 
are combined with the other resistors, 123, 124 and 126 to arrive at the 
three terminal equivalent circuit of FIGS. 2 and 3. This combination 
provides no limitation as the values of resistors 121 and 122 can be 
readily subtracted from the determined circuit element values to obtain 
the corresponding circuit element values of three terminal equivalent 
circuit 110. It should be noted that the determined values of R1=1021 ohms 
and R2=1020 ohms are close to the true value of 1011 ohms. However, the 
determined value of R12 is substantially different from its true value. 
This significant error arises whenever one circuit element value in the 
three terminal equivalent circuit is significantly different from the 
others. 
FIG. 3 shows the improved accuracy in the determined circuit element values 
resulting from the use of the present invention which utilizes at least 
one ratio, the numerator and denominator of each ratio being a different 
function of at least one of the measurements determined at test position 
200. This ratio is then used to determine the values of the circuit 
elements. Each ratio of the measurement functions is representative of the 
ratio of the true values of one selected circuit element to another in the 
three terminal equivalent circuit. The accuracy of the measurement 
function ratio to the ratio of the true values of the selected circuit 
elements varies with the internal resistance of the measuring equipment. 
Ideally, i.e., in the absence of such internal resistance and measurement 
error, each ratio of the measurement functions is equal to the ratio of 
selected circuit element values. 
Refer now to FIG. 4 which outlines the steps of the present invention. At 
the outset, a predetermined voltage source and a serially connected 
predetermined, source protection resistor is sequentially connected 
between first and second preselected pairs of terminals. For purposes of 
illustration, we will assume that the two preselected pairs of terminals 
are tip-to-ground and ring-to-ground, it, of course, being understood that 
any two pairs of terminals could be selected. The value of the source 
protection resistor should be large enough to limit the current flowing 
through the source to a safe level. The voltages measured are used to 
determined the appropriate values of the source protection resistor for 
signal source connection between each pair of terminals. The determined 
value of the source protection resistor for each pair of terminals is used 
when performing succeeding measurements since a more accurate 
determination of the resistor values in the three-terminal equivalent 
network can be made when the resistance of the source protection resistor 
is closely matched to the equivalent resistance between the selected 
terminal pairs and yet be large enough to prevent a damage to the 
measurement equipment. Similarly, the value of the voltage source should 
be large enough to get accurate measurements while not causing a current 
flow in the circuit under test which exceeds the maximum levels. The 
appropriately valued source protection resistor corresponding to each of 
the preselected pairs of terminals is used in all of the measurement steps 
shown in FIG. 4. 
As shown in step 1, signal source apparatus comprising a voltage source 
having a first predetermined level, V.sub.rs1, and a serially connected 
protection resistor, R.sub.p1, is applied across the ring and ground 
terminals and a voltage measurement between the ring and tip terminals is 
made, designated as V.sub.ra1. Next, as shown by step 2, the signal source 
apparatus of step 1 is left unchanged and a voltage measurement between 
the tip and ground terminals, designated as V.sub.rb1, is made. In steps 3 
and 4, the signal source apparatus is left unchanged but set to another 
source level, V.sub.rs2, and voltage measurements across ring to tip, 
V.sub.ra2, and tip to ground, V.sub.rb2, are made. Source levels V.sub.rs1 
and V.sub.rs2 are selected so as to provide the maximum possible voltage 
swing between these levels. With these 4 measurements, the total 
resistance of the three terminal equivalent circuit viewed between the 
ring to ground terminals, R.sub.x1, can be determined in accordance with 
the following relationship: 
##EQU1## 
and a ratio K.sub.2 can be formed in accordance with the following 
expression: 
##EQU2## 
With the signal source apparatus connected between the ring and ground 
terminals, the current through resistors R2 and R12 is the same and 
K.sub.2 is equal to the ratio of resistors R2/R12 in the absence of 
measurement error and the effect of the measurement meter's internal 
resistance. Since measurement error and internal resistance of a meter are 
always present to some extent, it can be said that the ratio K.sub.2 is 
representative or is an estimate of the ratio of the values of resistors 
R2/R12. 
In measurement steps 5 through 8, the signal source apparatus and serially 
connected source protection resistor, R.sub.p2, are connected between the 
tip and ground terminals. In steps 5 and 6, a source level designated as 
V.sub.ts1 is applied. The measurement meter is respectively connected 
between the tip and ring and ring and ground terminals to provide 
measurements V.sub.ts1 and V.sub.tb1. Finally, the procedure of steps 5 
and 6 is respectively repeated in measurement steps 7 and 8 using an 
associated source level V.sub.ts2 to determine the measurements V.sub.ta2 
and V.sub.tb2. Source levels V.sub.ts1 and V.sub.ts2 are selected with the 
same guidelines used for V.sub.rs1 and V.sub.rs2. Using the measurements 
of steps 5-8, the total resistance, R.sub.x2, of the three terminal 
equivalent network viewed between the tip and ground terminals and the 
ratio K1 can be determined, where 
##EQU3## 
Again, with the signal source apparatus connected between tip and ground, 
the current through resistors R1 and R12 is the same and K.sub.1 is an 
estimate of the ratio of resistors R1/R12. Furthermore, K.sub.1 is equal 
to this resistor value ratio in the absence of measurement errors and the 
effect of the meter's internal resistance. 
Using the derived quantities K.sub.1, K.sub.2, R.sub.x1 and R.sub.x2, the 
values of resistors R1, R2 and R12 can be readily determined. 
Specifically, 
##EQU4## 
Resistor R.sub.12 in the illustrative three terminal equivalent circuit can 
be determined in accordance with equation 7 or 8. Preferably, the equation 
used should be the one wherein the ratio K.sub.1 or K.sub.2 in the second 
term of the equation, i.e., 
##EQU5## 
has the smallest error. The error for the ratio K.sub.1 or K.sub.2 can be 
determined, in well-known fashion, from the known or estimated error 
associated with each measurement used to form the ratio. This ratio error 
determination is even simpler for certain three terminal equivalent 
circuits where the ratio with the smallest error is the ratio closest to 
one. Such is the case for a three terminal equivalent circuit including 
only resistors between the tip, ring and ground terminals. 
With the values of R.sub.1, R.sub.2 and R.sub.12 determined, the values of 
E.sub.1 and E.sub.2 can be readily determined from a number of different 
mathematical expressions. In one such expression, 
##EQU6## 
It should be noted that the presence of the meter's internal resistance 
during a measurement alters the element values of the three terminal 
equivalent circuit viewed from the test position. Furthermore, this 
alteration varies as the meter connections change from one pair of 
terminals to another. To avoid this meter effect, one or more compensating 
resistors, each having a value equal to that of the meter's internal 
resistance, is advantageously connected between one or more pairs of 
terminals so as to maintain the same equivalent circuit element values as 
the meter connections are changed. The effect of the compensating 
resistor, designated as R.sub.m, can then be readily subtracted from the 
determinations of R.sub.1, R.sub.2 and R.sub.12. In general, the values of 
any resistor corrected to the effect of R.sub.m can be expressed by 
EQU R.sub.n '=(R.sub.n.sup.-1 -R.sub.m.sup.-1).sup.-1 ; (11) 
where 
R.sub.n =R.sub.1,R.sub.2 or R.sub.12 ; and 
R.sub.n ' is the corresponding resistor value corrected for the addition of 
compensating resistor R.sub.m. Similarly, the values of E.sub.1 and 
E.sub.2 can be corrected for the presence of R.sub.m by the expression. 
##EQU7## 
n=1 or 2; and 
E.sub.n ' is the corresponding battery value corrected for the presence of 
R.sub.m. 
The present invention can be adapted to compensate for different sources of 
measurement error. For example, in certain applications the value of 
resistor R.sub.12 is very much greater than the values of the resistors 
R.sub.1 and R.sub.2 and the values of E.sub.1 and E.sub.2 exceed a 
predetermined threshold value. In such an event, a measurement error has 
occurred due to the bias effect of a battery element in the three terminal 
equivalent circuit. This error can be reduced by employing a bias 
compensation technique which utilizes additional measurements to improve 
the accuracy of the determined value of resistor R.sub.12. Pursuant to 
this technique, the ratio K.sub.1 and K.sub.2 having the largest value is 
selected, and certain measurements used in calculating the selected ratio 
are repeated using a biasing voltage. The repeated measurements are those 
which were made between a pair of terminals whose directly interconnecting 
equivalent circuit path includes a battery element. Specifically, if ratio 
K.sub.1 is selected, measurement steps 6 and 8 are repeated with a biasing 
voltage in series with the measurement meter. The value of the biasing 
voltage is equal to the determined value of element E.sub.1 or the average 
value of V.sub.tb1 and V.sub.tb2. 
If ratio K.sub.2 is selected, measurement steps 2 and 4 are repeated with a 
biasing voltage equal to the determined value of element E.sub.2 or the 
average of V.sub.rb1 and V.sub.rb2 serially connected to the measurement 
meter. Using these two additional measurements, the value of the selected 
ratio is recalculated and then the value of element R.sub.12 is calculated 
using the equation in which the selected ratio appears in the denominator 
of the second term. 
Another situation in which the accuracy of the determined circuit element 
values can be further improved arises when R.sub.12 is very much less than 
R.sub.1 and R.sub.2 and ratios K.sub.1 and K.sub.2 each have an 
unacceptable error. Then, it is advantageous to utilize a ratio reduction 
technique. In this technique, one of the ratios K.sub.1 or K.sub.2 is 
arbitrarily selected and the measurement steps used to form the selected 
ratio are repeated. These measurements are preferbly repeated with a 
source protection resistor having a revised value to reflect the addition 
of the external resistor. Specifically, for ratio K.sub.1, measurement 
steps 5 through 8 are repeated with an external resistor coupled between 
the ring and ground terminals. Similarly, for ratio K.sub.2, measurement 
steps 1 through 4 are repeated with an external resistor coupled between 
the tip and ground terminals. In either case, the value of the external 
resistor should be small enough to reduce the value of the selected ratio 
below a preselected maximum value. 
The above-described bias compensation and ratio reduction technique can be 
incorporated together into the present invention or, in certain 
applications, either one alone may be so incorporated. 
FIG. 5 shows a block-schematic diagram of apparatus which performs the 
measurement methodology described hereinabove for a three terminal 
equivalent circuit. At the beginning of testing, controller 507 directs 
switch 501, via bus 508, to connect measurement meter 509 across the ring 
to ground and tip to ground terminals to provide a pair of voltage 
measurements. Then, a predetermined DC voltage is provided by source 506 
across leads 503 and 516 and a predetermined resistor from source 
protection resistor selector 505 is inserted between leads 502 and 516. 
Switch 501, controlled by controller 507 via bus 508, respectively 
connects leads 502 and 503 to the ring and ground terminals and then to 
the tip and ground terminals. In addition, switch 501 sequentially 
connects leads 510 and 511 of measurement meter 509 to these terminal 
pairs to provide a pair of voltage measurements. For these four 
measurements and for those to be described, switch 504 advantageously 
connects one or more compensating resistors from compensating resistor 
selector 515. Each resistor having a value equal to the internal 
resistance of the measurement meter, is connected between selected pairs 
of terminals so as to maintain the same equivalent circuit element values 
as the meter connections are changed. 
The four voltage measurements provided by meter 509 are coupled via bus 512 
to processor 513 which determines the total resistance of the three 
terminal equivalent circuit between the ring and ground terminals and 
between the tip and ground terminals. Processor 513 then selects a 
resistor having the closest value to each determined total resistance from 
a plurality of preselected resistors in selector 505. The selections made 
and the appropriate levels for source 506 are communicated to controller 
507 via bus 514. Controller 507 directs selector 505 to insert a selected 
resistor between leads 502 and 516 when the source is coupled between a 
corresponding pair of circuit terminals. 
With the appropriate source protection resistor inserted, controller 507 
via bus 508 sequentially directs switch 501 to provide the source and 
measurement meter connections as set for in measurement steps 1-8 of FIG. 
4. Controller 507 also controls the voltage level of source 506 and the 
operation of meter 509 for these steps via bus 508. In addition, 
controller 507 advantageously controls the operation of switch 504 so as 
to provide compensating resistors across the terminals during the 
measurement steps which maintain the same equivalent circuit element 
values as the meter connections are changed. 
Processor 513 determines the values of R.sub.x1, R.sub.x2, K.sub.1 and 
K.sub.2 and thence the circuit element values. The determined values are 
then examined by processor 513, and if they don't fall within 
predetermined categories, the determined values are coupled via bus 518 to 
output device 517. If however, the determined values fall within these 
categories, then either the bias compensation or the ratio reduction 
technique is instituted to further improve the accuracy of the determined 
value of R.sub.12. The appropriate technique to use along with the source 
levels, necessary biasing voltage external resistor value, source 
protection resistor value, and source and meter connections are 
communicated to controller 507 via bus 514. The required biasing voltage 
is provided within meter 509 under the control of controller 507. In 
addition, compensating resistor selector 515 provides the 
approximately-valued external resistor for the ratio reduction via signals 
on bus 508 from controller 507. 
FIGS. 6 and 7 set forth the operations of processor 513. As shown by 
operations 601-603, the four tip to ground and ring to ground voltages are 
stored and the values of the source protection resistors for ring to 
ground and tip to ground source connections are calculated. A selection of 
the closest one of a plurality predetermined resistors in selector 505 and 
the appropriate signal source levels are then made and communicated to 
controller 507 via bus 514. The measurements made during steps 1-8 are 
supplied by bus 512 to processor 513 and stored therein as shown by 
operation 604. These stored measurements are then selectively used, as 
shown by operation 605, to calculate the equivalent resistances R.sub.x1 
and R.sub.x2 and the ratios K.sub.1 and K.sub.2 as previously described. 
These four quantities, as depicted by operation 606, are used to determine 
the values of all the circuit elements. 
Operation 607 designates the examination of the relative values of the 
circuit element values to determine whether the bias compensation or ratio 
reduction technique should be applied. If not, the determined results are 
coupled, as illustrated by operation 608 to the output device. If the bias 
compensation technique should be applied, operations 701-705 illustrate 
the sequentially steps provided by processor 513. Similarly, operations 
706-710 illustrate the sequential procedures performed by processor 513 
when the ratio reduction technique is used. 
The present invention can also be applied after conventional techniques 
have been used to determine the described circuit element values and one 
or more of said values is inaccurate. In one possible application, only 
one resistor value is incorrect and the present invention can be used to 
correct this value. In such case, only one ratio need be formed from the 
associated measurements. The inaccurate circuit element value is then 
corrected using this ratio. 
It should, of course, be understood that while the present invention has 
been disclosed in reference to a particular embodiment which determines 
the circuit element values of an illustrative three terminal equivalent 
circuit, numerous variations should be apparent to those skilled in the 
art. First, while the illustrative equivalent circuit comprises resistors 
and batteries, the invention is also applicable to an equivalent circuit 
comprising only resistors and for which measurement steps 3, 4, 7 and 8 
can be deleted and the corresponding measured results set to zero. Second, 
while a voltage source is applied and corresponding measurements are 
taken, a current source could be applied and corresponding mesurements 
could be made. Finally, while the present invention has been described in 
reference to the DC characterization of a three terminal equivalent 
circuit, an AC characterization can also be provided. In an AC 
characterization, the circuit elements are impedances having a real and 
imaginary part. The signal applied to the three terminal equivalent 
circuit is from an AC source and the measurements taken involve the use of 
a demodulator and equipment which determines the magnitude and phase of 
the AC signal between the described circuit terminals. The computations in 
an AC characterization are the same as those disclosed except that for an 
AC characterization complex numbers are involved instead of the real 
numbers manipulated in a DC characterization.