Time-domain reflectometer

[0001] This application claims priority to GB 0805407.4, filed on Mar. 25, 2008 and entitled “Time-Domain Reflectometer,” the disclosure of which is incorporated herein by reference in its entirety.

[0002] This invention relates to a time-domain reflectometer and to a method of time-domain reflectometry, for testing electrical cables that may be faulty or have faulty terminations.

[0003] Whenever a signal travelling along a transmission line encounters some change, i.e., discontinuity, in the line characteristic, a portion of the signal is reflected back towards the sending end of the line. The nature of the reflection signal is determined by the discontinuity characteristic, which might be anywhere between a short circuit and an open circuit.

[0004] Time domain reflectometers provide a means to determine the characteristics of faulty and normal electrical transmission lines, by sending an excitation signal, receiving a reflected response and analysing the response.

[0005] FIG. 1 (Prior Art) shows schematically the external appearance of a portable time domain reflectometer, TDR. Other forms are possible, for instance a fixed installation wherein the TDR is automatically controlled and does not require any user keypad or visual display.

[0006] FIG. 2 (Prior Art) shows the typical blocks that make up a TDR. These are:

[0007] Power Supply—which provides the necessary power to the various circuits;

[0008] Processor/Memory—which, as in many examples of modern instrumentation, provides overall operational control, processing of user actions, control of information provided to the user, management for the generation of test signals, management for the acquisition of measured signals, mathematical analysis of measurements and the application of signal processing algorithms.

[0009] In this context, the term “user” might also mean a separate piece of linked system control equipment as well as a human operator;

[0010] User Interface(s)—in a portable TDR these would typically be a keypad for entering commands/data and a screen for the display of measured signal responses, derived measurements and system information. In a fixed installation, the user interface might consist of a serial communication port such as a RS232 or USB port;

[0011] Test Signal Generator—provides a test signal for application to the transmission line (cable) under test. In practice it might be in the form of a voltage source or a current source. It might also be presented in either a single-ended (unbalanced) or balanced form.

[0012] Line Feed Resistor(s)—this or these provide the correct matching impedance for the line being tested. As previously mentioned, when a signal travelling along a transmission line encounters a change in characteristic, a reflection occurs. This is also true for a reflected wave returning to the TDR instrument. The instrument should therefore present an impedance characteristic sensibly close to the impedance characteristic of the line under test, if it is to avoid causing further unwanted signal reflections. The line feed resistor(s) is or are therefore provided to give the correct matching characteristic for the line under test. Multiple selections may be provided to cater for various line types.

[0013] In practical realisations, the test signal generator may consist of a voltage generator which is then arranged in series with the line feed resistor(s) or a current generator arranged in parallel with the line feed resistor(s). These are equivalent as per the well known Thevenin and Norton equivalent forms. Also the signals might be provided, and the responses measured, as either a single-ended or a balanced form which are well known in measurement systems. The later analysis is presented in the single-ended (unbalanced) form although this is easily extended to the balanced form, as is well known.

[0014] Additionally, some form of dc isolation might be provided between the TDR instrument circuitry and the connectors providing the access to the line (cable) under test. Typically this is done by the use of capacitors whose value is chosen to have minimal effect on the signals generated to and received from the line (cable) under test. If these capacitors do have a significant effect, it can be compensated for by the use of traditional analogue or digital filter techniques.

[0015] Signal Measurements—This block provides the ability to capture the electrical signals appearing on the TDR line (cable) under test, access point. It can therefore acquire signals with or without the cable actually connected. Typically an input amplifier of suitable impedance when considered in conjunction with the line feed resistor(s) will pass the signal to an analogue to digital converter (ADC) which is used to capture signal values on a point by point basis in time, which are then passed via the processor to a memory store for later evaluation.

[0016] In a practical TDR, the effect on the measured signal due to any dc isolation may again be compensated for by use of traditional analogue or digital filter techniques. Also, the input amplifier/ADC circuit may be presented in either single-ended (unbalanced) or balanced configurations.

[0017] Access Point—provides the terminal connections such that the cable under test can be connected to the instrument's test and measurement circuitry.

[0018] Traditional TDRs use a substantially rectangular pulse, or pulses that are smoother in nature such as a half-sine shape or a raised cosine shape. Other TDRs use a step waveform, which does not return to zero over the duration of the measurement.

[0019] One characteristic of an electrical transmission line is the rise/fall charge transients that can be seen when signals are applied to its input. This effect can hinder the observation and analysis of weak reflection signals in TDR responses. It is thus of fundamental interest to substantially remove this unwanted characteristic.

[0020] A variety of hardware and software techniques exist to reduce the unwanted effect. These techniques may be referred to as compensation, correction, balance or signal processing, amongst others.

[0021] One technique is to make measurements (baseline reference results) on a known good line of the same type being tested and then to subtract this reference signal from the subsequent line test response. The resulting response then primarily consists of only the desired reflection response. This method has the disadvantage of requiring access to known good lines, which may not be convenient or even possible.

[0022] Another technique provides an adjustable hardware balance network, which attempts to provide an approximation of the unwanted effect, which can be subtracted from the overall response. In practice, the unwanted characteristic, which is described by a combination of Bessel functions and exponential decays, is not easily characterised by simple hardware circuits and the balance effectiveness is of only limited value. In any case it is desirable to replace hardware solutions with software solutions, where possible. This principle is illustrated in FIG. 3.

[0023] Other techniques based on signal processing software alone may be applied.

[0024] Embodiments of the present invention advantageously improves time domain reflectometry with regard to its readability and its range of measured responses.

[0025] Accordingly, embodiments of the present invention provide a time domain reflectometer for testing an electrical cable, comprising a test signal generator; at least one line feed resistor connected between the test signal generator and a pair of terminals for connection to the ends of the electrical cable under test; and a signal processor connected to the terminals to receive a line signal including a reflection of a test signal transmitted into the cable under test; the signal processor being programmed to filter the line signal to enhance a portion of the signal indicative of any fault on the cable by balancing the signal according to the electrical characteristics of a normal cable of the same type as the cable under test, by applying a filter function: 1+Rf.Y(s) to the reflected signal, where Rf is the resistance of the feed resistor, and Y(s) is an estimate of the input admittance of the transmission line, s being the Laplace variable, and acquiring at least one estimate of Y(s) from known or estimated electrical characteristics of the cable under test selected from the variables: C, the distributed line capacitance per unit length, L, the distributed line inductance per unit length, R, the distributed line resistance per unit length and G, the distributed line conductance per unit length or functions of these variables, in the equation for input admittance in the Laplace domain: Y(s)=√((sC+G)/(sL+R)).

[0026] Embodiments of the present invention also provide a method of time domain reflectometry comprising transmitting a test signal through at least one line feed resistor to the ends of an electrical cable under test, receiving a line signal from the cable at those ends, and filtering the line signal to enhance a portion of the signal indicative of any fault on the cable by balancing the signal according to the electrical characteristics of a normal cable of the same type as the cable under test, by applying a filter function, to generate and output a filtered signal.

[0027] Time domain reflectometers embodying the present invention can implement software-based filtration substantially removing the input transient effect from TDR responses. This requires minimal prior knowledge of the cable electrical characteristics. It is capable of performing sufficiently well that it allows very small reflections to be separated from input transients. Further, there is no requirement for special loading conditions, i.e. for hardware-based balancing at the terminals of the cable under test.

[0028] The techniques of the present invention can of course be applied not only to faulty cables but also to normal or non-faulty cables.

Glossary of Terms

[0042]

Standard Engineering Terms
	TDR	Time Domain Reflectometer
	RS232	A serial data exchange standard
	USB	Universal Serial Bus, a serial data exchange standard
	ADC	Analogue to Digital Converter

[0043]

Standard Mathematical Terms
	s	The Laplace variable, familiar to circuit and signals
		specialists
	I0 and I1	The zeroth and first order modified Bessel function as
		defined in standard mathematical texts
	δ(t)	the dirac delta function, familiar to signals specialists
	f	frequency in Hertz
	w	frequency in radians per second = 2 πf
	L−1	the inverse Laplace Transform operation
	Z−1	delay of 1 sample, in a sampled data system

[0044]

Standard Transmission Line Terms
	R	is the distributed line resistance per unit length
	L	is the distributed line inductance per unit length
	G	is the distributed line conductance per unit length
	C	is the distributed line capacitance per unit length
	Y(s)	is the line input admittance in Laplace
		form = √((sC + G)/(sL + R))
	Z(s)	is the line input impedance in Laplace form = 1/Y(s)
	Y(t)	is the time domain convolution admittance = L−1 Y(s)
	Z0	is the characteristic line impedance = √(L/C)
	Y0	=1/Z0

[0045]

Terms Defined Herein
	Rf	is the Feed Resistor and its Resistance
	VS(s)	is a voltage signal for application to the feed resistor,
		represented in the Laplace domain
	VS(t)	is a voltage signal equivalent to VS(s), but
		represented in the time domain
	VL(s)	is a voltage signal appearing on the line,
		represented in the Laplace domain
	VL(t)	is a voltage signal appearing on the line, equivalent to
		VL(s) but represented in the time domain
	VL(n)	is a voltage signal appearing on the line, equivalent to
		VL(s) but represented as a series of time samples
	VP(s)	is a voltage signal resulting from some filtering
		function applied to VL(s), represented in the Laplace
		domain
	VP(t)	is a voltage signal equivalent to VP(s), but represented
		in the time domain,
	VP(n)	is a voltage signal equivalent to VP(s) but represented
		as a series of time samples,
	v	=((G/C) − (R/L))/2
	u	=((G/C) + (R/L))/2
	Vpu	voltage at top of test pulse leading edge,
		with no cable under test connected
	Vpl	voltage at top of test pulse leading edge with
		cable under test connected
	bk	the kth coefficient of a traversal digital filter,
		where k is an integer 0, 1, 2, 3 . . .

[0046] The preferred embodiments of the invention make use of transmission line equations, filters derived from them in time or frequency domains and the automated tuning of the filters to produce an optimal reduction in the input transient effect.

[0047] The well known transmission line equations provide the transmission line input admittance Y(s) as:
Y(s)=√((sC+G)/(sL+R))  (1)

[0048] It is the characteristics of equation (1) that determine the response at the input of a transmission line, including the unwanted input transient effects.

[0049] FIG. 4 shows the essential elements of a TDR from the block diagram of FIG. 2, in a form familiar for circuit/signal analysis. For simplicity, the principles are developed for the single-ended (unbalanced) case, but this can be routinely extended to the balanced case if desired.

[0050] FIG. 4 shows a simplified representation of the signals applied in a time-domain reflectometer, whereby a test signal VS(s) is applied via a feed resistor Rf to the transmission line under test.

[0051] Using standard notation, the signal at the input to the transmission line VL(s) is described as:
VL(s)=VS(s)/(1+Rf.Y(s))  (2)

[0052] For the purposes of this analysis, any reflected signals, that might add on to the applied signal, are ignored. Although the principles that follow are valid for any test signal, for the purposes of clarity, the examples are for the case where the test signal is a single pulse. In practice, the line signal VL(s) when considered in the time domain VL(t) includes some degree of unwanted transient response, as illustrated in FIG. 5.

[0053] In accordance with the invention, a filtering function:
1+Rf.Y(s)  (3)
is created by software, which acts on the signal VL(s), as shown in FIG. 6, to produce a processed signal VP(s).

[0054] The signal VP(s) is now simply equal to the original applied signal VS(s) and the effects of the cable characteristic Y(s) will have been removed. Any reflections appearing after the completion of the applied test pulse VS(s) will now be visible without the unwanted cable input transient effect.

[0055] In the general case, the values of R, L, G and C, which make up the quantity Y(s), are unknown. However, it is possible to simplify matters as follows:

[0056] Equation (1) can be dealt with either in the time domain or in the frequency domain.

Time Domain Approach

[0057] By using the standard Laplace transform tables, the time domain solution Y(t) is:
Y(t)=Y₀[v(I₁(vt)+I₀(vt))e^−ut+δ(t)]  (4)

[0058] This is the input admittance impulse response and represents a time function that can be convolved with an input signal, to produce the appropriate output signal.

[0059] For many practical applications the value of the cable parallel conductance G can be considered as 0, which results in v=−u, allowing equation (3) to be simplified to:
Y(t)=Y₀[v(I₁(vt)+I₀(vt))e^vt+δ(t)]  (5)
which now has only two unknowns, Y₀ and v.

[0060] Y₀ is the reciprocal of the line characteristic impedance Z₀, which may well be known from cable data sheets. If not, Z₀ can be estimated as follows:

[0061] With reference to FIG. 4, the cable under test can be disconnected, to generate VS(t) as a pulse signal. As the TDR is now unloaded, the measured signal VL(t) will be equal to VS(t). Therefore the signal VS(t) can be measured.

[0062] Now, the cable under test can be connected (loaded condition) and the application of the pulse signal can be repeated. This time, the signal VL(t) gives the loaded response on the line.

[0063] It is well known that pulse edges contain the highest frequency components of a signal, so by examining the levels attained by the pulse edges in the unloaded condition=VS(t) and the loaded condition=VL(t) and by the use of Ohm's law, the high frequency value of the cable impedance=Z₀ can be found by computing:
(level of pulse edge,loaded)=(level of pulse edge,unloaded)×Z₀/(Z₀+Rf)  (6)
Z₀ and hence Y₀ can thus be found.

[0064] FIG. 7 shows an example of unloaded and loaded waveforms, U and L respectively. In this example:

• • [0065] Rf=125 ohms,
  • [0066] Level of pulse edge, unloaded=Vpu=4 volts, and
  • [0067] Level of pulse edge, loaded=Vpl=1.734 volts.
    From equation (6), Z₀=(Rf(Vpl/Vpu))/(1−(Vpl/Vpu)), so
  • [0068] Z₀=(125(1.734/4))/(1−(1.734/4))=125(0.4335/0.5665)=95.65 ohms and
  • [0069] Y₀=1/95.65=0.01045.

[0070] The filter of equation (3) can thus now be realised in block diagram form as shown in FIG. 8. The part of the filter represented by the equation
Rf.Y₀[v(I₁(vt)+I₀(vt))e^vt]  (7)
can be realised in practice by taking the filter input in samples and applying it to a transversal FIR filter whose coefficients are set with the values of equation (7) as t varies from 0 to a suitably long settling time. The action of this well known arrangement implements the required convolution process.

[0071] The detail of a suitable realisation of the filter of equation (3) is shown in FIG. 9.

[0072] An auto-balance mechanism can now be described as:

• • [0073] 1. Use data sheet value for Y₀ or estimate it using the method described above.
  • [0074] 2. Start with some estimate value for v based on a reasonable value of R and L.
  • [0075] 3. Apply the filter to a sample response containing an unwanted input transient.
  • [0076] 4. Assess the flatness of the resulting TDR pulse by inspection of the trace after the first vertical transition and/or the trace after the second vertical transition.
  • [0077] 5. Modify the value of v and repeat the process until the trace(s) after the transition reach optimum flatness.
  • [0078] 6. If desired, modify the value of Y₀ around the original value and repeat steps 2 to 5 above to obtain an optimum response as a function of both v and Y₀.

[0079] FIG. 10 shows this process in flow chart form.

[0080] This is essentially the task of optimising a measure of goodness as a function of two variables.

[0081] In this case, it is desired to minimise the amount of transient response seen on the transmission line (cable) after the application of the first test pulse. In other words, the filtered transient response should decay to zero at the earliest opportunity and remain there, thus allowing subsequent fault reflections to be most easily detected.

[0082] A variety of measures exist to carry out this optimisation. These include:

• • [0083] (a) Take the integral of the magnitude of the deviation from zero, between a point shortly after the end of the applied test signal VS(t) and the earliest expected reflection signal.
  • [0084] (b) Take the integral of the square of the deviation from zero, between a point shortly after the end of the applied test signal VS(t) and the earliest expected reflection signal.
  • [0085] (c) Take time-weighted versions of either of (a) and (b) above to allow greater initial deviations in favour of smaller deviations at a later time.

[0086] It is anticipated that the “best” measure for a particular situation may be any of the above or indeed other measures that those skilled in the art will be familiar with.

[0087] Likewise, many methods exist to find the values of the variables (in this case v and Y₀) that result in the optimal condition. In the simplest case the condition to be optimised can simply be measured for all combinations of a set range of v values and a set range of Y₀ values, stored e.g. in a table. Once all measurements are done, that combination of values of v and Y₀ resulting in the best result can be used. Other standard methods exist to enable the optimum values of v and Y₀ to be located efficiently.

[0088] The optimisation is preferably implemented by a computer program. In the example of FIG. 10, the method iteratively modifies values of v and Y₀ and chooses the pair of values for best flatness. If Y₀ were known, the only v would be iteratively modified.

[0089] In real cables, the values of R, L, G and C and hence u and v may be frequency dependent. This variation is not represented in the time domain solution. In practice, however, the filter action provided by the arrangement described above quickly converges after a short period to substantially balance out the great majority of the unwanted cable input transient.

[0090] FIG. 11 shows the response of a sample cable with a high resistance fault. The upper curve is the unprocessed response comprising of both the unwanted cable input transient and the fault reflection signal at around 20 μs, the portion of the signal indicative of the fault. The lower curve shows the signal after processing by the arrangement described above. The substantial removal of the unwanted transient and the subsequent enhancement of the fault reflection signal is apparent.

Frequency Domain Approach

[0091] If suitable processing is available, the filtering may alternatively be done in the frequency domain. From Equation (1), the equation for the transmission line admittance in the frequency domain can be written:
Y(s)=Y₀√((s+u+v)/(s+u−v))  (8)
If G=0 as is usual, then:
Y(s)=Y₀√(s/(s+2u))  (9)

[0092] There are several options in forming a frequency domain filter, which can be applied to signals by means of the Fast Fourier Transform (FFT).

[0093] In this approach, the required convolution of the signal to be processed with the filter function is carried out in the frequency domain, by the well known technique of multiplying together the Fourier Transforms of the signal and the filter function and then taking the inverse Fourier transform to calculate the final result, for viewing in the time domain.

[0094] FIG. 12 shows the general arrangement of the frequency domain approach for the filter.

Option a)

[0095] As with the time domain method, a first option is to approximate Y₀ as the inverse of the hf cable impedance and then tune u for maximum flatness. The actual components of the filter at each frequency can be calculated as: Real part (1+Rf.Y₀√(jw/(jw+2u))) and Imaginary part (1+RfY₀√(jw/(jw+2u))), where j=√(−1) and w=the frequency of interest in radians per second.

Option b)

[0096] If the values of R, L, C and G are known, then the filter may be constructed using: Real part (1+Rf√((jwC+G)/(jwL+R))) and Imaginary part (1+Rf√((jwC+G)/(jwL+R))). In this case, if R, L, G and C are frequency dependant, this can be included to create a more accurate balance filter.

Option c)

[0097] If the characteristic Z(s) can be measured explicitly, e.g. by inspection of a cable test signal and the corresponding current, the Y(s)=1/Z(s) can be used to create a near perfect balance filter constructed using: Real part (1+RfY(jw)) and Imaginary part (1+RfY(jw)). Option a) is basically a technique in the frequency domain which provides a similar result to the time domain method. It is however more efficient, as the FFT method requires substantially less computation when compared to the time domain convolution filters.

[0098] As shown in FIG. 13a, the process of Option a) is shown in flow chart form. It involves the steps:

• • [0099] 1. Use a data sheet value for Y₀ or estimate it using the method described above.
  • [0100] 2. Start with some estimate value for u based on a reasonable value of R and L.
  • [0101] 3. Apply the filter to sample response containing an unwanted input transient.
  • [0102] 4. Assess the flatness of the resulting TDR pulse by inspection of the trace after the first vertical transition and/or the trace after the second vertical transition.
  • [0103] 5. Modify the value of u and repeat the process until the trace(s) after the transitions reach optimum flatness.
  • [0104] 6. If desired, modify the value of Y₀ around the original value and repeat steps 2 to 5 above to obtain an optimum response as a function of both u and Y₀.

[0105] Option b) is shown in FIG. 13b and avoids searching for a best fit by using cable data if they are known.

[0106] Option c) is shown in FIG. 13c and can provide the best balance filter if the cable input impedance characteristic can be obtained by measurement.

[0107] FIG. 14a shows the unprocessed response for a sample cable including the unwanted input transient signal.

[0108] FIG. 14b shows the response after processing in the frequency domain by means of method option a) described above. As with the previously described time domain arrangement, the substantial removal of the unwanted transient and the subsequent enhancement of the fault reflection signal is again apparent.

[0109] FIG. 14c shows the response after processing in the frequency domain by means of method option c) described above. In this case the removal of the input transient signal features further significant improvement.

[0110] The many features and advantages of the invention are apparent from the detailed specification, and, thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and variations will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and, accordingly, all suitable modifications and equivalents may be resorted to that fall within the scope of the invention.