Method and system for determining a number of load coils in a transmission line

A method and system for determining a number of load coils in a transmission line are provided. An impulse response of the transmission line is calculated from a characteristic impedance of the transmission line. A number of complex conjugate pole pairs of a transfer function of the impulse response is then determined. Thereby, the number of load coils in the transmission line, which is equal to the number of complex conjugate pole pairs, is determined.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to detecting load coils in a transmission line. More particularly, the present invention relates to determining the number of load coils in a transmission line by using the characteristic impedance of the transmission line.

BACKGROUND OF THE INVENTION

A load coil is an inductor that is inserted into a circuit to increase its inductance. Load coils are often inserted into a transmission line, e.g., a loop, to reduce amplitude and phase distortions of signals transmitted over the transmission line. As a result of their relatively high inductance, load coils generate poles in the transfer function representing the characteristic impedance of the transmission line.

With reference toFIG. 1, in the past, load coils110were inserted periodically, e.g., at a spacing on the order of kilometers, into a twisted-pair transmission line100used for plain old telephone service (POTS) to improve the quality of voice signals transmitted over the transmission line100. Typically, each load coil110includes two windings111, each connected in series with one wire101of the twisted-pair transmission line100.

However, the insertion of load coils into the transmission line leads to a rapid increase in attenuation above a cut-off frequency that depends on the spacing of the load coils. Typically, transmission lines including load coils at a spacing suitable for POTS have a cut-off frequency just above the upper voice frequency limit of 3.4 kHz. Therefore, in order to use these loaded transmission lines for services, e.g., digital subscriber line (DSL) services, operating at higher frequencies, e.g., above 10 kHz, the load coils must be detected and removed.

One prior-art technique for determining the number of load coils in a transmission line involves finding, e.g., by taking a derivative, and counting local maxima in the characteristic impedance of the transmission line. Variations of this technique are disclosed in U.S. Pat. No. 7,778,317 to Jin, issued on Aug. 17, 2010, in U.S. Pat. No. 7,395,162 to Fertner et al., issued on Jul. 1, 2008, in U.S. Pat. No. 5,881,130 to Zhang, issued on Mar. 9, 1999, in U.S. Pat. No. 5,404,388 to Eu, issued on Apr. 4, 1995, and in U.S. Pat. No. 4,087,657 to Peoples, issued on May 2, 1978, for example. Unfortunately, when the local maxima are close to one another or overlapping, it is often difficult to correctly determine the number of local maxima.

SUMMARY OF THE INVENTION

Accordingly, one aspect of the present invention relates to a method of determining a number of load coils in a transmission line having a characteristic impedance, the method comprising: calculating an impulse response of the transmission line from the characteristic impedance of the transmission line; and determining a number of complex conjugate pole pairs of a transfer function of the impulse response to thereby determine the number of load coils in the transmission line, wherein the number of complex conjugate pole pairs is equal to the number of load coils.

Another aspect of the present invention relates to a system for determining a number of load coils in a transmission line having a characteristic impedance, the system comprising: a processing unit for calculating an impulse response of the transmission line from the characteristic impedance of the transmission line; and for determining a number of complex conjugate pole pairs of a transfer function of the impulse response to thereby determine the number of load coils in the transmission line, wherein the number of complex conjugate pole pairs is equal to the number of load coils.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a method and system for determining the number of load coils in a transmission line. Advantageously, the present invention allows the number of load coils in the transmission line to be determined in a simple and straightforward manner by using the characteristic impedance of the transmission line.

The characteristic impedance of the transmission line is the impedance of the transmission line as a function of frequency, i.e., the frequency response of the transmission line. The characteristic impedance is a property of the transmission line and is independent of the method and apparatus used to measure the characteristic impedance. Several suitable measurement methods and apparatus are available, any of which may be used by the present invention.

With reference toFIG. 2A, an exemplary measurement circuit200for measuring the characteristic impedance of a transmission line includes a digital-to-analog converter (DAC)210, resistors220-225, capacitors230-232, and an analog-to-digital converter (ADC)240. The DAC210is used to generate sine waves of different frequencies, e.g., 64 different frequencies up to about 6 kHz. The different frequencies are, preferably, evenly spaced to facilitate the subsequent calculation of an inverse Fourier transform.

The sine waves are sent to the ADC240via the resistors220-225and capacitors230-232as illustrated inFIG. 2A. The measurement circuit200is connected to the tip and ring of the loop, i.e., the two wires of the transmission line. The impedance of the transmission line at the different frequencies will change the voltage Vinat the input of the ADC240. These changes in voltage at the different frequencies are used to determine the characteristic impedance Z0of the transmission line.

The output impedance of the DAC210and the input impedance of the ADC240are very close to zero, so the measurement circuit200may simplified as illustrated inFIG. 2B, where Z1-Z4are impedances of the measurement circuit200. Since the output impedance of the DAC210is very close to zero, the output voltage Voutis substantially the same whether or not the transmission line is connected. Therefore, the input voltage Vinis measured at different frequencies and is stored in memory as calibration data, e.g., in a calibration file. This calibration data is used to calculate the output voltage Voutaccording to Equation (1):

To calculate the characteristic impedance Z0of the transmission line, we notice that the voltage VABbetween points A and B may be expressed according to Equation (2):

Z0=((Vout-Vin)⁢Z3-Vin⁢Z2-Vin⁢Z1)⁢Z4-Vin⁢Z1⁢Z3-Vin⁢Z1⁢Z2(Vout-Vin)⁢Z3-Vin⁢Z2-Vin⁢Z1.(4)
To simplify, two variables T1 and T2 are assigned according to Equations (5) and (6):
T1=VinZ1;  (5)
T2=(Vout−Vin)Z3−VinZ2−VinZ1.  (6)

Using these variables, Equation (4) reduces to Equation (7):

Therefore, by measuring the input voltage Vinat different frequencies, the characteristic impedance Z0of the transmission line may be determined by applying Equation (7). With reference toFIG. 3, the characteristic impedance310measured according to this method for a standard transmission line including four load coils is in good agreement with the characteristic impedance320calculated according to a mathematical model for the same transmission line. The large capacitors at the input are responsible for the angle mismatch at low frequencies.

In general, the characteristic impedance of a transmission line may be represented as a transfer function H(z) in polynomial form, having Q coefficients biand P coefficients aj, according to Equation (8):

H⁡(z)=∑i=0Q⁢⁢bi⁢z-i1+∑j=1P⁢⁢aj⁢z-j.(8)
Equation (8) may be rewritten in factored form to give Equation (9):

For load coil detection, we are interested in the poles of the transfer function H(z) in factored form of Equation (9), because the number of complex conjugate pole pairs is equal to the number of load coils in the transmission line. Rather than attempting to find local maxima in the characteristic impedance, the present invention calculates the impulse response, i.e., the time response, of the transmission line from the characteristic impedance and determines the number of complex conjugate poles pairs from the impulse response.

As is commonly known, the impulse response of a system is the output signal when the input signal is an impulse. The transfer function of the impulse response describes the relation between the input and output signals.

According to the present invention, the impulse response of the transmission line is, typically, calculated by performing an inverse Fourier transform, e.g., an inverse fast Fourier transform (FFT), on the characteristic impedance. The number of complex conjugate pole pairs of the transfer function of the impulse response is then determined.

Typically, the transfer function of the impulse response is found by applying a parametric modeling technique to the impulse response. As is commonly known, a parametric modeling technique finds the parameters for a mathematical model describing a system, by using known information about the system. Several suitable parametric modeling techniques are available for use in the present invention, such as the Prony method, the Levinson-Durbin method, the Yule-Walker method, etc. The Prony method is presently preferred as the parametric modeling technique.

In general, the parametric modeling technique finds the coefficients biand ajof the transfer function H(z) in polynomial form of Equation (8) by using the impulse response. Once the transfer function has been found, a root-finding algorithm finds the poles and the zeros, i.e., the roots piand qi, of the transfer function H(z) in factored form of Equation (9).

Typically, the parametric modeling technique requires initial guess values for the number of poles P and the number of zeros Q, i.e., the number of coefficients, of the transfer function H(z). The guess values for the numbers of poles and zeros are selected to be greater than the expected numbers of poles and zeros. Typically, the guess values for the numbers of poles and zeros are the same and are greater than the expected number of poles, which is two times the expected number of load coils in the transmission line. The expected number of load coils in the transmission line, in turn, may be determined from the length of the transmission line, by considering standard spacings of load coils, e.g., a spacing of 6000 ft between load coils, and a spacing of 3000 ft before and after the first and last load coils.

Typically, the guess values for the numbers of poles and zeros are selected to be at least two times greater than the expected numbers of poles and zeros, i.e., at least four times greater than the expected number of load coils. For example, if the expected number of load coils in a transmission line is three, the expected number of poles is six, i.e., three complex conjugate pole pairs, and the guess values for the numbers of poles and zeros are each selected to be at least 12.

The transfer function found by the parametric modeling technique has poles equal in number to the guess value for the number of poles. Once the poles of the transfer function have been found by the root-finding algorithm, it is necessary to determine which of the poles are valid. Valid poles occur as complex conjugate pole pairs. Therefore, the number of complex conjugate pairs indicates the number of load coils in the transmission line.

Accordingly, complex conjugate pole pairs are identified among the poles found by the root-finding algorithm. Poles having an imaginary part b with an absolute magnitude of less than a first threshold, e.g., |b|<0.08, are not considered further. The remaining poles are identified as complex poles. Complex conjugate pole pairs are then identified among the complex poles by calculating distances between the complex poles and conjugates of the complex poles. If the absolute distance between a first complex pole z1and the conjugatez2of a second complex pole is less than a second threshold, e.g., |z1−z2<0.15, the first complex pole z1and the second complex pole z2are identified as a complex conjugate pole pair. Ideally, the absolute distance should be zero, but in practice it is usually small because of noise and limited hardware accuracy.

The first and second thresholds are selected by taking practical limitations into consideration. Typically, the first and second thresholds are determined empirically through experimentation.

The complex conjugate pole pairs identified in this manner are considered to be valid poles. The complex conjugate pole pairs are then counted to determine the number of load coils in the transmission line, which is equal to the number of complex conjugate pole pairs.

Several examples are provided hereafter to further illustrate the present invention. With reference toFIG. 4, in a first example, the present invention was applied to a 15 000 ft transmission line not including any load coils. The characteristic impedance, i.e., the frequency response, of the transmission line, which is plotted inFIG. 4A, was measured by using the measurement circuit200ofFIG. 2. The impulse response of the transmission line, which is plotted inFIG. 4B, was calculated by applying an inverse Fourier transform to the characteristic impedance. The transfer function of the impulse response was found by applying the Prony method to the impulse response. 10 poles of the transfer function, which are plotted inFIG. 4C, were found by using a root-finding algorithm. However, all of the poles were determined to be invalid because they did not belong to valid complex conjugate pole pairs. Therefore, the number of load coils in the transmission line was correctly determined to be zero. It should be noted that the direct current (DC) and very low-frequency response could not be detected by the alternating current (AC) coupled hardware and was approximated by extrapolation. Consequently, one pair of poles is close to a valid complex conjugate pole pair, but the absolute distance |z1−z2| is greater than the second threshold.

With reference toFIG. 5, in a second example, the present invention was applied to a transmission line including one load coil (LC) at the following spacing: 3000 ft, LC, 3000 ft. The characteristic impedance, i.e., the frequency response, of the transmission line, which is plotted inFIG. 5A, was measured by using the measurement circuit200ofFIG. 2. The impulse response of the transmission line, which is plotted inFIG. 5B, was calculated by applying an inverse Fourier transform to the characteristic impedance. The transfer function of the impulse response was found by applying the Prony method to the impulse response. 10 poles of the transfer function, which are plotted inFIG. 5C, were found by using a root-finding algorithm. Of these, one pair of poles was determined to be a valid complex conjugate pole pair. Therefore, the number of load coils in the transmission line was correctly determined to be one.

With reference toFIG. 6, in a third example, the present invention was applied to a transmission line including two load coils (LCs) at the following spacing: 3000 ft, LC, 6000 ft, LC, 3000 ft. The characteristic impedance, i.e., the frequency response, of the transmission line, which is plotted inFIG. 6A, was measured by using the measurement circuit200ofFIG. 2. The impulse response of the transmission line, which is plotted inFIG. 6B, was calculated by applying an inverse Fourier transform to the characteristic impedance. The transfer function of the impulse response was found by applying the Prony method to the impulse response. 14 poles of the transfer function, which are plotted inFIG. 6C, were found by using a root-finding algorithm. Of these, two pairs of poles were determined to be valid complex conjugate pole pairs. Therefore, the number of load coils in the transmission line was correctly determined to be two.

With reference toFIG. 7, in a fourth example, the present invention was applied to a transmission line including three load coils (LCs) at the following spacing: 3000 ft, LC, 15 000 ft, LC, 6000 ft, LC, 3000 ft. The characteristic impedance, i.e., the frequency response, of the transmission line, which is plotted inFIG. 7A, was measured by using the measurement circuit200ofFIG. 2. The impulse response of the transmission line, which is plotted inFIG. 7B, was calculated by applying an inverse Fourier transform to the characteristic impedance. The transfer function of the impulse response was found by applying the Prony method to the impulse response. 14 poles of the transfer function, which are plotted inFIG. 7C, were found by using a root-finding algorithm. Of these, three pairs of poles were determined to be valid complex conjugate pole pairs. Therefore, the number of load coils in the transmission line was correctly determined to be three.

With reference toFIG. 8, in a fifth example, the present invention was applied to a transmission line including four load coils (LCs) at the following spacing: 3000 ft, LC, 6000 ft, LC, 6000 ft, LC, 6000 ft, LC, 3000 ft. The characteristic impedance, i.e., the frequency response, of the transmission line, which is plotted inFIG. 8A, was measured by using the measurement circuit200ofFIG. 2. The impulse response of the transmission line, which is plotted inFIG. 8B, was calculated by applying an inverse Fourier transform to the characteristic impedance. The transfer function of the impulse response was found by applying the Prony method to the impulse response. 14 poles of the transfer function, which are plotted inFIG. 8C, were found by using a root-finding algorithm. Of these, four pairs of poles were determined to be valid complex conjugate pole pairs. Therefore, the number of load coils in the transmission line was correctly determined to be four.

The present invention may be implemented in hardware, software, or a combination thereof. When implemented in software, instructions for carrying out the actions described heretofore are stored in a non-transitory computer-readable storage medium, e.g., memory, and are executed by a processor of a hardware device, e.g., a general purpose computer or a test device.

With reference toFIG. 9, an exemplary system900for determining the number of load coils in a transmission line includes a measurement unit910and a processing unit920. In a preferred embodiment, the system900is embodied as a test device, e.g., a portable or fixed test device, in which the measurement unit910and the processing unit920are supported by a common housing. In other embodiments, the measurement unit910may be embodied as a test device, e.g., a portable or fixed test device, and the processing unit920may be embodied as a separate hardware device or as software stored and executed by a separate hardware device, e.g., a general purpose computer.

The measurement unit910measures the characteristic impedance of the transmission line, typically, by means of a measurement circuit, such as the measurement circuit200ofFIG. 2described heretofore. The processing unit920calculates the impulse response of the transmission line from the characteristic impedance and determines the number of complex conjugate pole pairs of the transfer function of the impulse response, as described heretofore. Thereby, the processing unit920determines the number of load coils in the transmission line, which is equal to the number of complex conjugate pole pairs. Typically, the number of load coils is reported by the system900, e.g., on a display.

It should be noted that other embodiments of the system may omit the measurement unit, which is optional. Embodiments omitting the measurement unit are suitably configured to receive the characteristic impedance, i.e., frequency-dependent impedance data, as input.

Of course, numerous other embodiments may be envisaged without departing from the spirit and scope of the invention.