10th WSEAS Int. Conf. on MATHEMATICAL METHODS AND COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING (MMACTEE'08),
Sofia, Bulgaria, May 2-4, 2008
A Novel Correlation Pulse Echo Methodology for
Transmission Line Fault Identification and Location
using Pseudorandom Binary Sequences
Richard A. Guinee , MIEEE
Cork Institute of Technology, Cork, IRELAND
Abstract- A novel pulse echo test methodology, using pseudorandom binary sequence (PRBS) excitation, is presented in this paper as
an alternative to Time Domain Reflectometry (TDR) for transmission line fault location and identification. The essential feature of
this scheme is the cross correlation (CCR) of the fault response echo with the PRBS test input stimulus input which results in a
unique signature for identification of the fault type, if any, or load termination present as well as its distance from the point of test
stimulus injection. This fault identification method can used in a number of key industrial applications incorporating printed circuit
boards, overhead transmission lines and underground cables in inaccessible locations which rely on a pathway for power transfer or
signal propagation. As an improved method PRBS fault identification can be performed over several cycles at low amplitude levels
online to reject normal signal traffic and extraneous noise pickup for the purpose of multiple fault coverage, resolution and
identification. In this paper a high frequency co-axial transmission line model is presented for transmission line behavioural
simulation with PRBS stimulus injection under known load terminations to mimic fault conditions encountered in practice for proof
of concept. Simulation results, for known resistive fault terminations, with measured CCR response demonstrate the effectiveness of
the PRBS test method in fault type identification and location. Key experimental test results are also presented for a co-axial cable,
under laboratory controlled conditions, which substantiates the accuracy of PRBS diagnostic CCR method of fault recognition and
location using a range of resistive fault terminations. The accuracy of the method is further validated through theoretical calculation
via known co-axial cable parameters, fault resistance terminations and link distances in transmission line experimental testing.
I.
correlation of the input PRBS stimulus with the fault echo
response, over several PRBS cycles in averaging out noise
pickup and normal signal traffic in the online mode, to
identify the nature or characteristic signature of the fault.
Based on the distinct spike-like attribute of the PRBS
autocorrelation (ACR) function, fault location measurement
relies on the time displacement of the transmission link
conditioned PRBS cross-correlated echo response from the
ACR peak for accurate (CCR) fault/load positioning and
identification. This measured time translation of the
correlation peaks can be subsequently used to determine the
propagation delay of the reflected response from the
fault/load-termination of the unit under test (UUT). This
procedure not only results in fault/load parameter
identification but also of the reflection transit time from the
fault interface and thus the distance of the fault from the
point of stimulus insertion.
In this paper the novel application with experimental
validation of the PRBS perturbation method of transmission
line testing for fault identification with location is
presented. A simplified distributed model is employed to
simulate transmission line behaviour [10,11] for a range of
known load terminations mimicking fault conditions
encountered in practice for comparison purposes with
experimental results. Essential test results, which were not
available for [10], are presented here for the first time for
experimental verification of the accuracy of the PRBS
diagnostic method of fault identification and location in co-
INTRODUCTION
Transmission line testing and fault finding is a mature
and well established test and measurement trouble-shooting
strategy deployed in the telecommunications and electrical
power utilities industries to guarantee quality of service to
telephone subscribers and a stable electrical energy supply
to consumers. Time domain reflectometry (TDR) as a test
strategy [1,2] has been at the forefront of this discipline for
many years in the development of high frequency test and
measurement network analysers for a range of HF
industrial applications encompassing IC [3] and PCB
design layout [4] for minimization of track parasitics.
However if has the disadvantage [1,2] of relying on a single
pulse echo for transmission link fault finding that is
susceptible to measurement inaccuracy resulting from link
attenuation with fault distance and phase change distortion
with frequency as well as resolution error in the presence of
noise pickup.
The alternative improved strategy proposed in this paper
is the application of a bipolar PRBS stimulus, which
consists of a random time arrangement of pulses, resulting
in a sustained pulse echo sequence with an accumulated
CCR response build-up, which overcomes the difficulty of
uncorrelated link noise, at low pulse energy-to-noise ratio
conditions, in fault location measurement. This stochastic
method, which is a well known system identification tool
[5,6,7] in optimal control, can also be used via cross
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10th WSEAS Int. Conf. on MATHEMATICAL METHODS AND COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING (MMACTEE'08),
Sofia, Bulgaria, May 2-4, 2008
A transmission line can be modelled by a lumped
parameter ‘T-section’ unit equivalent circuit in Fig. 1 at
low frequencies (LF) [12,13] with a uniformly distributed
series inductance L, resistance R and a shunt capacitance C
in parallel with a conductance G over elemental distance
dx. The T-section can be suitably scaled to the required
dimensions
axial cable testing under laboratory controlled conditions
using a range of known resistive fault terminations. Further
validation and substantiation of accuracy of the method is
provided through theoretical calculation via known co-axial
cable parameters, fault resistance terminations and link
distances in transmission line experimental testing.
II. OVERVIEW OF TDR AND PRBS TESTING
R dx
2
TDR is based on single pulse propagation down a cable
UUT such that when it reaches the cable fault some of the
pulse energy is reflected back to the TDR test instrument.
Since the propagation velocity is assumed constant for
UUT the pulse transit time is a measure of the fault
distance. TDR displays the fault information as a waveform
and distance reading. This test technique is not a perfect
fault location method because the transmitted pulse is
progressively broadened and made less sharp as it
propagated down the line as a result of pulse distortion due
to phase change.
Pulse resolution is essential in TDR where narrow pulses
give rise to very sharp trace features that are ideal for
measurement. Narrow pulses are easily attenuated with
signal path frequency response rolloff, due to reciprocity of
pulsewidth with bandwidth [2], which causes reflected
pulse amplitude definition loss and as such narrow pulse
TDR is useful over short distances only.
Alternative TDR wide pulse usage produces wider and
more rounded echo trace features with leading edge
transitions that are difficult to gauge and lead to inaccurate
fault distance resolution. These wide pulse stimuli are,
however, not so quickly attenuated which make them
suitable for long distance measurements. The TDR
technique is susceptible to link noise interference, which
can mask out weak long distance fault reflections [1], with
resulting pulse definition loss for accurate fault location
measurement. Pulse stimuli can be sent repeatedly but they
are uncorrelated and the fault information is contained in
unconnected pulse echoes which renders repeated pulse
injection unproductive in noisy link fault measurements.
The alternative PRBS line fault location method employs
a random series of bipolar pulses that are reflected by the
impedance mismatch as a correlated response build-up over
the entire test sequence. CCR evaluation of the fault
response with the incident PRBS and comparison of its
time displaced peak with that for the ACR peak can
identify the fault location. The echo CCR amplitude profile
yields a characteristic signature, which identifies the type of
fault present. Link noise can be averaged out through CCR
evaluation over multiple PRBS cycles [6,7]
which
accentuates the fault signature. This ‘magnified’ fault
characteristic can be built up over a number of PRBS
lengths, dramatically reducing the impact of noise.
L dx
2
R dx
2
L dx
2
G dx
2
C dx
2
dx
Fig.1: Full Model Lumped Parameter ‘T’ - Section
for overhead line and underground cable modelling and
PCB operation at high frequency (HF). The T-section can
be simplified for transmission line operation at high
frequency ω with the elimination of the distributed
resistance and conductance in accordance with the
condition [12]
ωL>>R and ωC>>G
(1)
This reduced ‘T’ model is simulated below and compared
with experimental results for HF co-axial cable operation
for various types of line faults, known apriori, with PRBS
injection in order to gauge the accuracy of the CCR process
in identifying the type of fault and its location.
A. Full Model Example for Low Frequency Line Operation
The T-section model in Fig.1 is first exercised with
lumped parameter values per-loop-km of R = 10.15Ω, L =
3.93mH, G = 0.29uS, C = 0.00797uF at a line frequency of
5000rad/sec. Longer line lengths can be obtained by
chaining several sections in tandem. The model
characteristic impedance Zo and complex propagation
coefficient γ are given by [12]
Z0 =
( R + j ωL )
( G + j ωC )
(2)
γ = ( R + jωL)(G + jωC ) = α + jβ
(3)
The
propagation
coefficient
for this line is
with
attenuation
coefficient α in Nepers/km and phase-change coefficient β
in rads/km. The propagation velocity is determined from
the line frequency 5000 rads/sec and phase-change
coefficient as
vp = f ⋅(2π/β) = (ω/β) =173611 km/s
γ = α + jβ = 0.00712 + j 0.0288
III. TRANSMISSION LINE ‘T-SECTION’ MODELLING FOR
FAULT SIMULATION MEASUREMENT
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Sofia, Bulgaria, May 2-4, 2008
The pseudonoise (pN) stimulus has a unique delta
function like ACR defined for a time shift τ = kΔt with 0 ≤
k ≤ (L-1) over one period T, as per Fig.3, by
1.0
0.8
0.6
PRBS_ACR =1
B. Reduced Model Example for High Frequency Line
Operation
PRBS_ACR Stimulus
Reference Peak
ACR =0.5
0.4
0.2
Repeat PRBS
ACR Peak
Transit
Delay ττl
0.0
0.2
V. FAULT FINDING WITH PSEUDONOISE SEQUENCES
PRBS Period
T = 6.25μs
When a transmission line is mis-terminated in a load
impedance ZL ≠Z0 an echo reflection Y(t) will be present on
the line at any point along with the incident wave X(t). The
worst cases of line fault mismatch occur for (i) a short
circuit fault with ZL = 0 and (ii) an open circuit fault with
ZL=∞. Besides these well known line faults other types of
partial line discontinuities result in reflections caused by [1]
joints, splits and waterlogged zones, which are all
characterised as minor mismatches. The degree of
reflection at the load termination ZL ≠Z0 can be determined
from the incident wave by the reflection coefficient ρ [12]
as
Time μs
0.26
0.24
0.28
Fig.2: Open Circuit Line – CCR Fault Signature
For HF ‘lossless line’ operation in (1) with α=0 the real
characteristic impedance Z0 and propagation coefficientγ,
as the phase change coefficient β, are given respectively by
Z0 =
L
C
(4)
γ = jβ = jω LC
(5)
If for example, a 100m HF line operating at 20MHz
based on the pSpice distributed ‘lossless’ model [11] with
transmission wavelength λ=5.1862m and Z0 = 30Ω is
simulated for open circuit conditions with a PRBS stimulus
the CCR echo response along with the PRBS ACR are
shown in Fig.2. The propagation velocity is calculated from
vp = λ×f as 103724 km/s.
1.2
Z − Zo
ρ= L
Z L + Zo
(7)
The resulting voltage standing wave ratio (VSWR) s is
determined from ρ, with −1 ≤ ρ ≤ 1 , as
s=
V2
0.8
0.6
0.4
- V2/L
T = LΔt
Delay
τ = kΔt
0.2
0
-4
-2
0
-0.2
2
4
6
8
10
Δt
Fig. 3: PN Autocorrelation Function (ACR)
IV. TRANSMISSION LINE TESTING USING PRBS
PRBS stimuli x(t), employed in transmission line testing,
change logic state pseudo randomly between prescribed
voltage levels +V and –V at discrete time intervals Δt. The
bipolar test signal is generated from a specially configured
n stage linear feedback shift register [8,14] and has a
maximum sequence length L =2n-1 with period T=LΔt.
ISBN: 978-960-6766-60-2
1+ ρ
1− ρ
(8)
Four general cases of line termination can arise to
influence the values [12,13] of ρ and s which will provide
an indication of the type of line fault present:
(i) Matched load conditions with Zo = ZL:
⇒ ρ = 0 with no reflection and s =1.
(ii) Open-circuit line ZL = ∞: complete incident wave
reflection occurs without phase reversal
⇒ ρ = 1 as per Fig.2
(iii) Short-circuit line ZL = 0: complete incident wave
reflection occurs with phase reversal
⇒ ρ = - 1 as per Fig.4
(iv) Mismatch termination ZL ≠ Z0: incident wave
reflection occurs with or without phase reversal
depending on the relative sizes of ZL and Z0.
(1) If ZL < Z0 ⇒ ρ < 0 and s = Z0/ZL.
(2) If ZL > Z0 ⇒ ρ > 0 and s = ZL /Z0.
The phase relationship between the reflection echo
response and the incident PRBS, determined through ρ in
the PRBS-CCR process along with the VSWR, indicates
the type of load termination present.
For PRBS X(t) = {x(1), x(2), …, x(L)} injection into a
faulty line a conditioned echo response will result as Y(t) =
PRBS Autocorrelation
Function (ACR)
RXX(τ)
1
⎧⎪+ V 2
1 L
for k = 0
∑ x( j ) x( j + k ) = ⎨ 2
L j =1
⎪⎩− V L for k ≠ 0
(6)
The PRBS ACR along with the CCR fault response is
used to determine the transit time delay τl and thus the fault
distance l.
Repeat Echo
CCR Peak
Reflected PRBS Echo
Correlation Peak
O/C Echo
Response CCR
0.22
R xx (k ) =
157
ISSN: 1790-5117
10th WSEAS Int. Conf. on MATHEMATICAL METHODS AND COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING (MMACTEE'08),
Sofia, Bulgaria, May 2-4, 2008
{y(1), y(2), …, y(L)} which can be cross correlated with the
incident disturbance X(t) as
R xy (k ) =
1
Alternatively if the 100m HF line has a s/c fault the pN
input test signal will undergo phase reversal upon reflection
as evidenced by the negative CCR echo response in Fig.4.
Again simple calculation reveals that the relative time
displacement τl of the ACR and CCR peaks provide an
accurate estimate lˆ of the ‘known’ fault location l, which
is identical to the o/c position in Fig.2, and its identity.
Lossy line simulation demonstrates the effects of PRBS
stimulus attenuation as it is propagated down the line under
test. However if multi PRBS injection is used the effect of
pN pulse attenuation, unlike TDR, is surmounted with
multiple cycle correlation [7]. If the lossy line in § III-B is
simulated for an o/c fault, at a distance l =100km, pN fault
diagnosis similar to that for Fig.2 results in an ACR to CCR
peak displacement or round trip propagation delay τl =
1.1507ms. Thus the fault location estimate is easily
estimated, via (10), with vp= 173611km/s, as lˆ = (173611
km/s)⋅(1.151ms/2) ≈ 100km which is identical to the known
value l used in simulation and as such validates the PRBS
test methodology for fault detection on lossy lines. Further
pN testing [10] for a range of lossy line fault impedance
terminations yield estimates which are practically identical
to those used in line simulation which further establishes
concept validation.
Lossy line simulation demonstrates the effects of PRBS
stimulus attenuation as it is propagated down the line under
test. However if multi PRBS injection is used the effect of
pN pulse attenuation, unlike TDR, is surmounted with
multiple cycle correlation [7]. If the LF lossy line in § III(b) is simulated for an o/c fault, at a distance l =100km, pN
fault diagnosis similar to that for Fig.2 results in an ACR to
CCR peak displacement or round trip propagation delay τl
= 1.1507ms. Thus the fault location estimate lˆ is easily
estimated, via (10), with vp= 173611km/s, as lˆ = (173611
km/s)⋅(1.151ms/2) ≈ 100km which is identical to the known
value l used in simulation and as such validates the PRBS
test methodology for fault detection on lossy lines. Further
pN testing [10] for a range of lossy line fault impedance
terminations yield estimates which are practically identical
to those used in line simulation which further establishes
concept validation
L
∑ x(i) y (i + k )
L i =1
(9)
to yield a characteristic CCR signature of the line fault
present. The CCR process yields a correlation peak at some
shift time τl, as per Fig.2 for an open circuit fault, which is
indicative of the line fault distance l from the test stimulus
input X(t). The time displacement τl of CCR peak is
measured from incident PRBS reference ACR peak as per
Fig.2 which when divided by two and multiplied by the line
propagation velocity vp will give the fault distance l to the
source of reflection as
l = vp⋅τl /2
(10)
VI. SIMULATED HF AND LF LINE FAULT DIAGNOSIS
The HF model simulation in §III–B for open circuit (o/c)
and short circuit (s/c) termination faults employed a 127 bit
PRBS input with frequency f PRBS =1/Δt=20Mhz, as the
reciprocal of the chip time Δt, and period T = L/fPRBS = LΔt
= 6.35μs. The ACR reference peaks with period T, as
shown in Figs.2, 3 & 4, are generated via the
autocorrelation of the incident PRBS at the stimulus source.
For an o/c line fault the incident PRBS stimulus is reflected
back to the source without phase reversal. If the combined
incident and reflected components are cross-correlated with
the incident PRBS the resultant non inverted CCR peak
indicates the presence of a open circuit fault ‘echo’ via (9)
as the line fault signature along with the reference ACR in
Fig.2. The relative displacement τl ≈ 1.9μs of the CCR and
ACR peaks results in the propagation delay for the PRBS
stimulus to traverse the line from the input to the fault and
back with a total distance 2l. For the 100m open circuit HF
line, known apriori, the measured ACR-CCR displacement
τl in Fig.2 along with the known phase velocity vp in § III –
(b) provides an accurate gauge of the fault location l and its
identity as l = (τl/2)*vp = 0.96μs*103724km/s = 100m.
Hence knowledge of the CCR peak displacement τl and link
propagation velocity vp is all that is needed for accurate
estimation of the fault location l.
VII. EXPERIMENTAL HF LINE FAULT DIAGNOSIS
A 50m roll and 500m drum of URM-43 HF co-axial
cable with Z0 = 50Ω and distributed capacitance C =
100pF/m was tested using PRBS stimuli for various
‘known’ discontinuities apriori in order to experimentally
validate the fault location and identification capability of
the PRBS CCR technique. Assuming lossless HF line
behaviour, at the pN test frequency fPRBS =100MHz, the
other line parameters can be derived for fault location
estimation during test. Using (4) for HF line operation the
distributed inductance L can be determined as L=CZ02 =
0.25 μH/m along with the line propagation velocity as
v p = 1 LC = 1 Z 0C =2×108m/s. This value of vp can be
used with the echo fault response transit time τl /2, back to
PRBS Autocorrelation
PRBS – ACR =1
1.0
0.5
ACR Reference Peak due to
Incident PRBS
ACR = 0.5
τl =1.9282us
0.0
Cross Correlation Peak due
to Fault Reflected PRBS
S/C Response CCR
-0.5
0.25
0.26
0.27
Time (μs)
0.28
Fig.4: Short Circuit Line – CCR Fault Signature
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Sofia, Bulgaria, May 2-4, 2008
line input test point, to determine the fault location distance
as per (10).
A. PRBS Stimulus Characteristics and Fault Distance
Resolution
1.00E+00
Experimental PRBS - CCR Fault Diagnosis
8.00E-01
Incident PRBS
ACR Reference Peak
50 m HF Co-Axial Cable
Z0 = 50Ω
6.00E-01
4.00E-01
63 Bit Bipolar PRBS Stimulus Injection X(t)
S/C CCR Response
2.00E-01
τl =506.5 ns
PRBS Amplitude (Volts)
0.00E+00
1
76 151 226 301 376 451 526 601 676 751 826 901 976 1051 1126 1201 1276 1351
-2.00E-01
PRBS S/C Fault CCR Peak
Time (× 0.5 ns)
-4.00E-01
Fig.7: Experimentally derived S/C Fault Signature
HP Test Pattern Generator O/P: 100 MBPS
⇒ Chip Time Δt = 10ns
A 50m reel of co-axial cable was initially terminated
under o/c and s/c conditions to gauge the accuracy of the
PRBS CCR method of fault identification and location as
depicted in Figs. 6 & 7 respectively. The location l of o/c
and s/c faults can ascertained from the relative
displacement τl =506.5ns of the CCR fault response from
the ACR reference peak via (10) as l = vp⋅τl /2 = (2×108
m/s)⋅(506.5×10-9s/2) =50.65m which is the same as the
measured line length used. Additional testing with resistive
fault terminations in 10Ω steps beginning at 10Ω up to 100
Ω and thereafter in 100Ω steps, with little observed
difference from o/c conditions, further validated the
accuracy of pN–CCR method as per Figs.8 & 9 which
enhances confidence in this trouble-shooting technique of
fault identification. The importance of the CCR fault
observations in Figs.6 & 7 is that the existence of correlated
echo peaks and their polarity provides an indication of the
type of line fault present. The first observation that should
be made is whether or not a CCR fault peak is present other
than the reference ACR spikes.
Time (Secs)
Fig.5: Observed Bipolar PRBS Stimulus Injection
A 63 bit PRBS test pattern, shown in Fig.5, was
employed at various polarities (unipolar and bipolar) and
voltage levels for test stimulus injection with a 10ns bit
duration Δt which coincides with the co-axial cable
specified operational frequency of 100 MHz and also
within HP IC Test Generator (TPG) limits. Using the bit
duration Δt = 10ns with the line propagation velocity vp=
2×108 m/s the fault distance resolution accuracy Δd can be
determined as Δd = vpΔt = 2m.
An 8-channel Agilent mixed storage oscilloscope with
sampling frequency 2GHz was used at the line i/p end for
simultaneous data capture of the i/p test stimulus along with
the delayed fault echo response for later post test data
analysis and cross correlation signal processing. The higher
sampling frequency results in an improved fault distance
resolution accuracy of Δd = vpΔt/20 = 0.1m.
1.00E+00
Experimental pN - CCR Fault Analysis: ZL≠Z0
8.00E-01
B. Co-Axial Cable Test Fault Results
1.00E+00
Experimental PRBS - CCR Fault Diagnosis
8.00E-01
Incident PRBS
ACR Reference Peak
6.00E-01
4.00E-01
50 m HF Co-Axial Cable
Z0 = 50Ω
CCR Responses: ZL> Z0
0.00E+00
1
-2.00E-01
4.00E-01
-4.00E-01
2.00E-01
τl =507.5 ns
79
157
235 313 391
469 547
625 703
781 859 937 1015 1093 1171 1249 1327
CCR Responses: ZL< Z0
Time (× 0.5 ns)
Fig.8: Experimentally Determined ACR and CCR Fault Responses for
Termination Conditions ZL≠Z0
0.00E+00
1
τl =506.5 ns
2.00E-01
PRBS O/C Fault CCR Peak
-2.00E-01
Repeat pN – ACR
Reference Peak
Incident pN - ACR
Reference Peak
6.00E-01
76 151 226 301 376 451 526 601 676 751 826 901 976 1051 1126 1201 1276 1351
O/C CCR Response
Time (× 0.5 ns)
Fig.6: Experimentally derived O/C Fault Signature
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4.00E-01
3.00E-01
0.6
O/C
2.00E-01
Z L > Z0
1.00E-01
0.00E+00
300Ω
200Ω
99Ω
82Ω
68Ω
30Ω
Z L < Z0
-2.00E-01
-3.00E-01
Fault Termination
Response CCR ZL≠Z0
-4.00E-01
150Ω
91Ω
62Ω
0
-0.2
> max R xy
50
100
150
200
250
300
350
-0.6
40Ω
20Ω
Theoretical Reflection Coefficient ρ
Estimated Reflection Coefficient ρ̂
-0.8
-1
10Ω
-1.2
S/C
Fig 10: Reflection Coefficient Experimental Estimates
Relative Time (× 0.5 ns)
PRBS fault diagnosis can also be used to estimate the
reflection coefficient ρ for a given RL as
ρˆ =
max R xy
CCR
max R xx
ACR
(12)
from the ratio comparison of ‘reflected’ CCR to the
incident ACR peaks in (12) for each of the resistive fault RL
cases in Fig.9. This information can then be used to
estimate the actual resistive fault manifestation RL [13]
from the expression
(1+ ρˆ )
Rˆ L =
Z0
(1− ρˆ )
(13)
and the VSWR s, from (8), as
1 + ρˆ
sˆ =
1 − ρˆ
(14)
Comparison of the reflection coefficient estimates ρ̂ ,
scaled shifted by 2.5, with those values ρ from theoretical
considerations using (12) show a good fit when plotted in
Fig.10 for various line fault terminations which validates
the PRBS test strategy.
Similar pN test fault results, which are ongoing, have
been successfully obtained for a drum of HF co-axial cable
of nominal length 500m. These results have returned a
consistent fault location estimate lˆ =529m for various
resistive terminations in 10Ω steps beginning at 10Ω up to
100 Ω using PRBS lengths L = 1023 bits at test frequencies
of 100 MHz.
VIII.
Z L1
CONCLUSIONS
In this paper the PRBS strategy of fault finding and
identification on HF co-axial transmission lines has been
experimentally validated for accuracy and examined as a
competitive alternative to the industrial TDR standard. This
novel trouble-shooting mechanism relies on the unique
randomness attributes of maximal length pN sequences and
their distinctive delta/spike-like autocorrelation function for
faultfinding. Hence it can be deployed in the impulse
response estimation of a faulty transmission line, in order to
identify the fault type and its location, through cross
correlation of the reflected response with input pN test
(11)
for RL2>RL1. Similar conclusions prevail for the converse
case in Fig.9, which depicts a negative polarity change with
RL<Z0 and increased absolute CCR value with reduced fault
termination resistance.
ISBN: 978-960-6766-60-2
0
-0.4
Fig 9: Enlarged View of pN Echo CCR Responses in Fig.8
Z L2
Fault Termination Resistance RL
0.2
If no CCR peak is present then matched conditions prevail
with no line reflections for ZL=Z0. If, however, a positive
peak exists then ZL>Z0 and a possible open circuit or high
impedance fault is present as in Fig.8. Conversely, if a
negative peak is present then ZL<Z0 and a possible short
circuit or low impedance fault exists on the line as shown in
Fig.8. The presence of high or low fault impedances
besides o/c or s/c types, can also be deduced from the CCR
of the pN echo response experimentally as in Figs.6 to 9 for
a range of load terminations ZL≠Z0. Co-axial cable
termination with fault impedance values from 10Ω to
100Ω, in steps of 10 Ω, and cross correlation of line fault
response reveal the existence of CCR echos with peak
magnitudes and polarities commensurate with the
termination values as per Figs.8 & 9. All CCR peaks occur
as expected at the same time shift in Figs.8 & 9, because
the impedance faults are located the same distance l = 50m
away from the pN source stimulus.
The CCR peak amplitude varies with ZL and the degree
of mismatch with Z0 in terms of the reflection coefficient ρ
in (7), which is proportionally passed to the correlation
peaks. If fault resistance terminations (RL1,RL2)>Z0 are
employed for example with RL2>RL1 then the polarities of
the CCR peaks are positive in both instances. Also a
comparison of the CCR peak amplitudes illustrate
increasing CCR values with fault termination RL, as per
Figs.8 & 9, resulting in increased reflected echo coefficient
ρ, that is,
max R xy
Ref. Coef. ρ
0.4
1 18 35 52 69 86 103120 137 154 171188205 222 239 256 273 290 307324 341 358 375
-1.00E-01
Reflection Coefficient ρ Vs Termination Resistance
0.8
Fault CCR for 50m Co-Axial Cable with Z0 = 50Ω
160
ISSN: 1790-5117
10th WSEAS Int. Conf. on MATHEMATICAL METHODS AND COMPUTATIONAL TECHNIQUES IN ELECTRICAL ENGINEERING (MMACTEE'08),
Sofia, Bulgaria, May 2-4, 2008
stimulus. The line fault echo signature is the magnified
collective response to a time arranged pN sequence of
random pulse stimuli, propagated down the line towards the
fault termination, and as such is the main advantage of
using PRBS testing in preference to the single pulse method
in TDR.
This novel test strategy, which is incorporated as a BIST
feature for CPU and digital IC ‘health’ conditioning
monitoring and functionality in complex integrated
systems, has been validated experimentally for HF co-axial
transmission lines for a range of fault impedance
terminations ranging from open to short circuit types.
Further confidence enhancement of the method has been
provided by the success in the identification of a range
mismatched fault impedance terminations.
ACKNOWLEDGMENT
The author wishes to acknowledge research funding from
the Science Foundation Ireland (SFI) - National Access
Program for test equipment usage and technical support at
the Tyndall Research Institute, Cork for experimental
validation of the PRBS test strategy.
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ISSN: 1790-5117