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5. Conclusions
The fact that every cable has a velocity of propagation obviously means that it takes time for a signal to go down a cable. That time is called delay, normally measured in nanoseconds (Dn). Vp can easily be converted into delay. Since Vp is directly related to dielectric constant (DC), they are all directly related as shown in Eq. 6.8 and determine the delay in nanoseconds-per-foot (ns/ft).
Dn V
While these equations will give you a reasonable approximate value, the actual equations should be:
Delay
Delay becomes a factor in broadcasting when multiple cables carry a single signal. This commonly occurs in RGB or other component video delivery systems. Delay also appears in high-data rate UTP, such a 1000Base-T (1GBase-T) and beyond where data is split between the four pairs and combined at the destination device.
Coaxial Cable Signal Loss (Attenuation) in dB/100 ft
Frequency
Characteristic impedance— 50.0 50.0 50.0 52.0 50.0 75.0 75.0 75.0
Velocity of propagation—% 66 66% 80% 66% 84% 66% 82% 78%
Capacitance pF/ft, pF/m 30.8/101.0 29.9/98.1 25.3/83.0 29.2/96.8 24.6/80.7 20.5/67.3 16.2/53.1 17.3/56.7 Table 6.29
Loading coil connected in a balanced transmission line.
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Where signals are split up and recombined, the different cables supplying the components will each have a measurable delay. The trick is for all the component cables to have the same delay to deliver their portions at the same time. The de facto maximum timing variation in delay for RGB analog is delivery of all components within 40 ns. Measuring and adjusting cable delivery is often called timing. By coin-cidence, the maximum delay difference in the data world is 45 ns, amazingly close. In the data world, this is called skew or delay skew, where delivery does not line up.
In the RGB world, where separate coax cables are used, they have to be cut to the same electrical length.
This is not necessarily the same physical length. Most often, the individual cables are compared by a Vectorscope, which can show the relationship between components, or a TDR (time domain reflectom-eter) that can establish the electrical length (delay) of any cable.
Any difference in physical versus electrical length can be accounted for by the velocity of propagation of the individual coaxes, and, therefore, the consistency of manufacture. If the manufacturing consist-ency is excellent, then the velocity of all coaxes would be the same, and the physical length would be the same as the electrical length. Where cables are purchased with different color jackets, to easily iden-tify the components, they are obviously made at different times in the factory. It is then a real test of quality and consistency to see how close the electrical length matches the physical length.
Where cables are bundled together, the installer then has a much more difficult time in reducing any timing errors. Certainly in UTP data cables, there is no way to adjust the length of any particular pair.
In all these bundled cables, the installer must cut and connectorize.
This becomes a consideration when four-pair UTP data cables (category cables) are used to deliver RGB, VGA, and other nondata component delivery systems. The distance possible on these cables is therefore based on the attenuation of the cables at the frequency of operation, and on the delay skew of the pairs. Therefore, the manufacturers measurement and guarantee (if any) of delay skew should be sought if nondata component delivery is the intended application.
aTTenuaTIon
All cable has attenuation and the attenuation varies with frequency. Attenuation can be found with the equation:
A R
Zt pf
o
4.35 2.78 ε
(6.10) where,
A is the attenuation in dB/100 ft,
Rt is the total DC line resistance in /100 ft,
ε is the dielectric constant of the transmission line insulation, p is the power factor of the dielectric medium,
f is the frequency,
Zo is the impedance of the cable.
Table 6.29 gives the attenuation for various 50 , 52 , and 75 cables. The difference in attenuation is due to either the dielectric of the cable or center conductor diameter.
cHaracTerISTIc ImPedance
The characteristic impedance of a cable is the measured impedance of a cable of infinite length. This impedance is an AC measurement, and cannot be measured with an ohmmeter. It is frequency-depend-ent, as can be seen in Figure 6.19. This shows the impedance of a coaxial cable from 10 Hz to 100 MHz.
At low frequencies, where resistance is a major factor, the impedance is changing from a high value (approximately 4000 at 10 Hz) down to a lower impedance. This is due to skin effect, where the signal
193 is moving from the whole conductor at low frequencies to just the skin at high frequencies. Therefore,
when only the skin is carrying the signal, the resistance of the conductor is of no importance. This can be clearly seen in the equations for impedance; Eq. 6.13, for low frequencies, shows R, the resist-ance, as a major component. For high frequencies, Eq. 6.14, there is no R, no resistresist-ance, even in the equation.
Once we enter that high-frequency area where resistance has no effect, around 100 kHz as shown in Figure 6.19, we enter the area where the impedance will not change. This area is called the characteristic impedance of the cable.
The characteristic impedance of an infinitely long cable does not change if the far end is open or shorted. Of course, it would be impossible to test this as it is impossible to short something at infinity.
It is important to terminate coaxial cable with its rated impedance or a portion of the signal can reflect back to the input, reducing the efficiency of the transmission. Reflections can be caused by an improper load, using a wrong connector—i.e., using a 50 video BNC connector at high frequencies rather than a 75 connector—a flattened cable, or too tight a bend radius, which changes the spacing between the conductors. Anything that affects the dimensions of the cable will affect the impedance and create reflective losses. It would just be a question of how much reflection is caused. Reflections thus caused are termed return loss.
The characteristic impedance of common coaxial cable can be between 30 and 200 . The most common values are 50 and 75 . The characteristic Zo is the average impedance of the cable equal to:
Z D
o 138 d
ε log (6.11)
where,
is the dielectric constant,
D is the diameter of the inner surface of the outer coaxial conductor (shield) in inches, d is the diameter of the center conductor in inches.
The true characteristic impedance, at any frequency, of a coaxial cable is found with the equation:
Z R j fL
Impedance of coaxial cable from 10 Hz to 100 MHz.
194
where,
R is the series resistance of the conductor in ohms per unit length, f is the frequency in hertz,
L is the inductance in henrys,
G is the shunt conductance in mhos per unit length, C is the capacitance in farads.
At low frequencies, generally below 100 kHz, the equation for coaxial cable simplifies to:
Z R
j C
o
2ρπ (6.13)
At high frequencies, generally above 100 kHz, the equation for coaxial cable simplifies to:
Z L
o C (6.14)
cHaracTerISTIc ImPedance
The characteristic impedance of a transmission line is equal to the impedance that must be used to ter-minate the line in order to make the input impedance equal to the terminating impedance. For a line that is longer than a quarter-wavelength at the frequency of operation, the input impedance will equal the characteristic impedance of the line, irrespective of the terminating impedance.
This means that low-frequency applications often have quarter-wavelength distance way beyond com-mon practical applications. Table 6.30 shows comcom-mon signals, with the wavelength of that signal and the quarter-wavelength. To be accurate, given a specific cable type, these numbers would be multiplied by the velocity of propagation.
The question is very simple: Will you be going as far as the quarter-wavelength, or farther? If so, then the characteristic impedance becomes important. As that distance gets shorter and shorter, this distance
Characteristics of Various Signals
Signal Type Bandwidth Wavelength
Quarter-Wavelength Quarter-Wavelength
Analog audio 20 kHz 15 km 3.75 km 12,300 ft
AES 3—44.1 kHz 5.6448 MHz 53.15 m 13.29 m 44 ft
AES 3—48 kHz 6.144 MHz 48.83 m 12.21 m 40 ft
AES 3—96 kHz 12.288 MHz 24.41 m 6.1 m 20 ft
AES 3—192 kHz 24.576 MHz 12.21 m 3.05 m 10 ft
Analog video (U.S.) 4.2 MHz 71.43 m 17.86 m 59 ft
Analog video (PAL) 5 MHz 60 m 15 m 49.2 ft
SD-SDI 135 MHz clock 2.22 m 55.5 cm 1 ft 10 in
SD-SDI 405 MHz third harmonic 74 cm 18.5 cm 7.28 in
HD-SDI 750 MHz clock 40 cm 10 cm 4 in
HD-SDI 2.25 GHz third harmonic 13 cm 3.25 cm 1.28 in
1080P/50-60 1.5 GHz clock 20 cm 5 cm 1.64 in
1080P/50-60 4.5 GHz third harmonic 66 mm 16.5 mm 0.65 in
Table 6.30 Table 6.30
195 becomes critical. With smaller distances, patch cords, patch panels, and eventually the connectors
themselves become just as critical as the cable. The impedance of these parts, especially when measured over the desired bandwidth, becomes a serious question. To be truly accurate, the quarter-wavelength numbers in Table 6.28 need to be multiplied by the velocity of propagation of each cable. So, in fact, the distances would be even shorter than what is shown.
It is quite possible that a cable can work fine with lower-bandwidth applications and fail when used for higher-frequency applications. The characteristic impedance will also depend on the parameters of the pair or coax cable at the applied frequency. The resistive component of the characteristic imped-ance is generally high at the low frequencies as compared to the reactive component, falling off with an increase of frequency, as shown in Figure 6.19. The reactive component is high at the low frequencies and falls off as the frequency is increased.
The impedance of a uniform line is the impedance obtained for a long line (of infinite length). It is appar-ent, for a long line, that the current in the line is little affected by the value of the terminating impedance at the far end of the line. If the line has an attenuation of 20 dB and the far end is shortcircuited, the char-acteristic impedance as measured at the sending end will not be affected by more than 2%.
TWISTed-PaIr ImPedance
For shielded and unshielded twisted pairs, the characteristic impedance is:
Zo 101670C VP ( )
(6.15)
where,
Zo is the average impedance of the line, C is found with Eqs. 6.16 and 6.17, Vp is the velocity of propagation.
For unshielded pairs:
ODi is the outside diameter of the insulation, DC is the conductor diameter,
Fs is the conductor stranding factor (solid 1, 7 strand 0.939, 19 strand 0.97.
The impedance for higher-frequency twisted-pair data cables is:
Z VP h
196
where,
h is the center to center conductor spacing,
Fb is very near 0. Neglecting Fb will not introduce appreciable error.