A time domain reflectometer (TDR) is an electronic test instrument measuring reflections along a cable or transmission line. It works like radar by sending energy pulses down a cable, measures the time it takes to return, and pinpoints the distance and type of faults or impedance changes.
[1] A TDR for cable fault detection
[2] [D1]
A pulse generator is a circuit circuit that generates and sends the low-voltage pulsed signal down the transmission line.
Shield
Core
A pulse generator is a circuit circuit that generates and sends the low-voltage pulsed signal down the transmission line.
Shield
Core
The distance of a TDR's transmission line is generally defined mathematically as: d = vp * t/2.
vp = propagation velocity (m/s)
t = transmit time
But the standard TDR transmission distance formula uses a velocity factor (VF) value and light speed, and doesn't use a velocity value: d = *(c*VF*t)/2.
This standard is really used if the cable manufacturer provides the cable's specification velocity factor percentage IO raw speed.
E.g., if the total round-trip time the TDR measures is 2 μs and the cable's has a VF of 0.66.
The transmission line length would be:
light speed unit conversion: 3e8 m2/s = 3e8/1e6 = 300 m2/μs
(300*0.66*2)/2 = 198 m long
E.g., for a twisted pair copper cable of 100 m via signal propagation speed of 2e8 m/s and a VF of 0.66, then the round-trip time (in seconds) for a signal to travel across the cable would be calculated as following:
t = d*2/(c*VF) = (100*2)/(2e8*.66) = 1.52e-6 = 1.52 μs
E.g., a fiber-optic TDR (OTDR) sends a light pulse down a fiber cable. The propagation light speed in the glass core is 204,000 km/s. The reflection returns 120 μs after transmission.
The distance to the fiber break in kilometers would be calculated as:
120 μs = 120e-6 s
d = (204e3*120e-6)/2 = 12.24 km
In imperial measurements units If the a TDR measures a round-trip delay time 450 μs, the cable datasheet specifies a VF of 0.66, the distance, in feet units, would be:
light speed unit conversion to imperial: 3e8 m2/s = 984e6 ft2/s = 984 ft2/μs
d = (984 * 0.66*450)/2 = 146,124 ft
Impedance mismatch occurs if, mathematically defined as:
[2] [D1]
ρ = reflection coefficient (range from -1 to 1)
Ei = incident (input) pulse voltage
Er = reflected pulse voltage
Z0 = transmission line's characteristic impedance
ZL = load/fault impedance
E.g., a TDR with a characteristic impedance of 50 sends a 5 V incident pulse down a coaxial cable. The cable a complete break, the reflection coefficient and the reflected pulse's voltage level is calculated as follows:
Note that an open circuit's has infinite impedance, thus the coefficient is: ρ = (∞-50)/(∞+50) = 1.
This calculation involves using calculus limits:
limx→∞ (∞-50)/(∞+50) = (x-50)/(x+50) = (x/x - 50)/(x/x +50) = (1 - 50/x)/(1 + 50/x) = (1-0)/(1+0) = 1
The reflected pulse voltage is: Er = ρ*Ei = 1*5V = 5 V
The velocity factor (VF) is the speed of a wave in a material divided by the light speed in a vacuum, generally defined as VF = v/c
v = wave speed in the medium
c = light speed
It's also calculated via material's dielectric constant: 1/√εr
εr = insulating material's relative permittivity/dielectric constant around conductor, assuming relative permeability (μr =1)
E.g., for a coaxial cable using solid polyethylene insulation with a relative permittivity of 2.25, a TDR sends a signal down the cable and detects a fault reflection after a round-trip time of 1.2 μs, the velocity factory can and the distance can be calculated as follows:
VF = 1/√2.25 = 0.66
d = (1.2*300*0.66)/2 = 118.8 m
The following graphs are the possible impedance responses that can occur along a TDR transmission line when sending an energy pulse depending on the different conditions and configuration of the impedance.
[D3] Open end: pulse travels down cable til it hits open air, so ZL = ∞ and with a physical break, no current can flow
Short at cable end: center and grounding wire connect at the end, causing a short and V = ZL = 0, also causing inverted pulse
Matched impedance: connected load's internal impedance matches exactly cable’s characteristic impedance. The load absorbs the incident pulse's energy. Without boundary mismatch to cause reflection, TDR receives nothing back.
Joint: transmission line divides into cable A and B whose respective center and outer wires connect which caused tiny reflection (ripple), which is an attempt of matching impedance but imperfect, causing some to reflect back.
[2] [D1]
[D3] Short core to core: core and shield are shorted together somewhere along line, causing inverted pulse, like TDR b)
Parallel resistance core to core: fault where accidental resistance path between core and shield, causing part of voltage to flow to ground (sudden voltage drop) which bounces small invertred reflection back to TDR.
Interrupt: fault where both or either core and shield are cut, causing signal to drop to zero and bounce back
Serial resistance: cable not fully broken, but has an unwanted obstacle in core wire, often corroded connector/loose terminal screw/badly soldered joint
[2] [D1]
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[1] Wikipedia
[2] everythingRF