Component Video Cables - The Definitive Guide - page 2
2.2 Electromagnetic Interference (EMI)
Electromagnetic Interference (EMI) is around us at all times. It comes from radio towers, sun spots, cell phones, modems, remote controls, computers and a number of other signals that are generated from most electronics used in every day life. EMI transmissions exist in wide ranges of frequencies including Radio Frequency range (RF noise). EMI exists within the range of video signal frequencies and at frequencies that are harmonically related to video signals. It is possible for stray signals from EMI to find their way into a video cable and therefore, create a false signal or internal noise within the component video cable. The result can range from very minor to significant depending on the noise origination and strength. A quality 75-ohm shielded video cable implements several methods to minimize EMI from entering into the cable. These methods include the use of braided grounding shields and nonmagnetic foils as explained in the sub-Sections of 3.0.
2.3 Mismatched Impedance
Mismatched impedance is one of the most common and most frequently experienced sources of signal degradation. This phenomenon occurs when a high frequency bandwidth signal, designed to be matched to a characteristic impedance of 75-ohms, encounters different impedances through its signal path (IE. Transmission Line), usually on the order of 35-ohm or 50-ohm for Home Theater applications. It can occur in long runs of video cables ( > 1/10th the wavelength) that do not use true 75-ohm cables, or it can occur from the DVD player or the TV monitor, depending on the nature of their internal impedances. This mismatch can create a bounce back effect or reflection that results in a delay and/or loss of signal level for certain frequencies. Thus for component video cable, transmission line effects of any cable lengths beyond 3 meters (remember 1/10 of 30 meters) must be considered.
When the characteristic impedance changes in a cable, part of the signal (incident wave) is reflected. The reflection coefficient can be calculated as:
Where Vi and Zo are the incident voltage and characteristic impedance of the first media. Vr and Zr represent the reflected voltage and characteristic impedance of the media that caused the reflection.
An open circuit implies that Zr = ∞ or ρ = 1, and a short circuit implies that Z R = 0 or ρ = -1. A perfect reflection coefficient is when Zr = Zo or ρ = 0.
The decibel loss due to reflection is given by:
Power from reflected signals are reflected back to the source (DVD player) so that phase addition and subtraction of the incident and reflected waves create a voltage standing wave pattern on the cable. The ratio of the maximum to minimum voltage is know as Voltage Standing Wave Ratio (VSWR) and can be defined as:
VSWR = Emax/Emin = (Ei+Er)/(Ei-Er)
E max = maximum voltage on the standing wave
E min = minimum voltage on the standing wave
E i = incident voltage wave amplitude
E r = reflected voltage wave amplitude
In the case where the conductor line is properly terminated into its characteristic impedance (75-ohm for component video cables), VSWR = 1 and there is no reflected wave.
The reflection coefficient (r) is defined as E r /E i and in general, it will be a complex number.
|Additionally we define:||r = (Zi - Zo) / (Zi + Zo)|
The refection coefficient (r) , is the absolute value of the magnitude of G .
If the equation for VSWR is solved for the reflection coefficient, it is found that:
|Reflection Coefficient = ρ = |r| = (VSWR -1) / (VSWR + 1)|
VSWR = (1 + p) / (1-p)
The return loss is related through the following equations:
Return Loss = 10 log [Pi/Pr] = -20 log [ (VSWR -1) / (VSWR + 1) ] = -20 log ρ
Return loss is a measure in db of the ratio of power in the incident wave to that in the reflected wave, and as defined above, always has a positive value. For example if a load has a return loss of 10 db, then 1/10 of the incident power is reflected. The higher the return loss, the less power is actually lost.
Impedance mismatch can occur when a cable with internal impedance less than 75-ohm is connected to a true 75-ohm load, such as a video line driver in a Projector to DVD player. In this situation, some of the frequencies that make up the signal will be reflected back to the source. Since the source is a 75-ohm impedance, this reflected signal is sent directly back to it creating a delay effect at certain frequencies. This delay, for example, can show up as a ghost in the picture. Multiple ghosts resulting from multiple frequency reflections can look like ringing around the original image. These reflections can also cause partial signal cancellations at various frequencies corresponding to a partial signal loss resulting in a loss of picture detail or color.
Other examples of mismatched impedance include any mismatches between the source's output impedance (DVD player), the cable's characteristic impedance (using audio cables or a poorly made 75-ohm cable), and the load's input impedance (the TV monitor). One possible scenario is if damage to a component video cable from crushing or kinking has occurred, or if the connectors are improperly installed, the internal impedance of the cable is changed resulting in reflection and power or signal loss.
2.4 Skin Effect
Skin effect is sound engineering phenomenon that can be defined mathematically, however as outlined in the following examples, it is not detrimental to low frequencies within the range of audio and video cables. Skin Effect is dependent on a number of factors including conductor diameter, the permeability / conductivity of the cable, and the frequency of the transmitted signal.
For the purposes of understanding skin effect, the following discussion presents a general outline and example. To begin with, an electromagnetic wave traveling in a coaxial cable produces both, an electric and a magnetic field between the inner conductor and the outer return (ground). The electric field (E) is radial and varies in time. As an alternating current flows along the inner conductor, an oscillating magnetic field (H) circles that conductor.
Electric field (E) and magnetic field (H) belong to the principal mode in a coaxial line.
At high frequencies, resistance increases on a conductor due to skin effect. The strength of a magnetic field (H) at these higher frequencies is enough to cause the alternating current on a conductor to spread unevenly throughout the conductor. Instead, it is strongest at the outer surface and decays exponentially at points further into the conductor. The field is opposite for the ground as the force from the magnetic field causes the current inward. This phenomenon is called the skin effect. Skin effect causes 95% of the current to be carried within about three skin depths of the surface of the conductor. As a result, the current only flows on the outer surface of the inner conductor and the inner surface of the outer return. The material beyond several skin depths has little effect on the wave therefore the signal is transmitted down a decreased area of conductor. The decreased area carrying the signal results in an increase in resistance within the cable resulting in a potential for loss of signal. For audio and video frequencies, this change in area and increase in resistance is not significant enough to create a measurable loss in signal. This can be verified through basic, fundamental engineering calculations as shown in the following example. In fact, if you continue with these calculations you will find that it doesnât even become an issue until over 1GHz which is significantly higher then audio, component video and HDTV signals.
As explained above, the current density varies exponentially inward from the surface of the conductor by 1 / e (current density ratio = J), where e ℮ = 2.718. The distance in which the current density decreases to 1 / e ℮ of its surface value is called the Înominal dept of penetration.â
The current density ration listed above J = 1/ e ℮ = 1 / 2.718 = .368 amperes / meter
For reference purposes, the formula for approximating the actual skin depth is:
√ Square root of 2 / (2 x л x ° x permeability of the cable x conductivity of the cable)
This equation can be simplified for a copper conductor coaxial cable found in most component video cables, by applying the applicable constants. When simplified, the formula for calculating the nominal depth of penetration is:
- Nominal depth of penetration for copper = δ = 6.64 / square root of √ f
- Depth of penetration at 60 Hz, δ = .857cm;
- Depth of penetration at 10 KHz, δ=.066cm;
- Depth of penetration at 10 MHz, δ=.0021cm = 21 microns
As discussed above, 95% of the current is carried within about three skin depths of the surface of the conductor. At 10MHz the current density for one skin depth (.857cm) is defined as J = .368 or 36.8% of the surface value. This means that 63.2% (100% ö 36.8%) of the signal is at one skin depth. At two skin depths the current density is 1/℮ e^ 2 = .135 or 13.5% of its surface value. This means that 86.5% (100% - 13.5%) of the signal within two skin depths. At three skin depths the current density is 1/℮ e^ 3 = .05 or 5% of the surface value. This confirms that 95% (100% - 5%) of the signal is within three skin depths.
Once the depth of penetration is determined, the area of the conductor can be found and used for calculating the resistance in the cable. As discussed, the increased resistance due to decreased area will result in a signal loss.
For solid, round copper conductors the AC and DC resistances are approximately related by the following expression (ITT 1968):
RAC = (0.096*d* f ^1/2 + 0.26) x RDC
where d is the conductor diameter in inches and f is the frequency in Hz (hertz).
For d* f ^1/2 > 10, this equation is accurate within a few percent. For d* f ^1/2 < 10, the actual AC resistance is greater than given by this equation. If the material is something other than copper, the first term in this equation must be multiplied by a factor of (µr / ρ r)^1/2 where µr is the permeability of the conductor material and ρ r is the relative resistivity of the material compared to copper.
AC resistance for conductor:
d = (perimeter of cross section) / pi
Quick Facts on Skin Effect
- Hollow Tube and Solid Core with same diameter and same material have same resistance
- Depth of Skin Layer decreases by a factor of 10x for every 100x increase in frequency.
- RF resistance is often much higher than DC resistance.
- Rough estimate of fc (cutoff frequency) where nonferrous wire show skin effect:
- Frequency (MHz) = 124 / (d^2 ), where d is diameter in mils.
- Above cutoff frequency, resistance increases by 10x for every 2 decades of frequency. Roughly 3.2 for every decade.
The following example determines the power loss due to skin effect on a typical 6-foot (2-meter) 18-AWG cable with a 10MHz signal (max range of component video).
First, it is important to calculate the power loss of a 6 feet length 18-AWG solid copper conductor (0.04ä = 40.2-mils diameter) @ 10MHz with a DC resistance of 6.386-ohm / 1000ft (Table data on copper wire).
DC resistance = (6 ft)*(6.386-ohm / 1000ft) = 38-mohm.
The equation where Skin Effect starts is defined as:
fc = 124 / (d^2 )
For our example:
fc = 124 / ((40.2-mils)^2) / (1000^2 ) = 75-kHz
10MHz is approximately x decades above 75-kHz; solve for x by:
Frequency Ratio = fx / fc= 10*10^6 / 75*10^3 = 133.3333
Therefore, 10MHz is 2.12 decades (log 133.333) above 75kHz
Zloss = (38-mohm)*(10)*(2.12) = 0.81-ohm Resistance
The following ratio can be obtained with this equation:
Zratio = Zo/ (Zo + Zloss) where Zo is 75-ohm (defined by cable)
Zratio = .989
To calculate the decibels of power loss use the following equation.
10 x Log (Zratio ) = 10 x Log (.989) = -0.047 db
In a solid conductor of 18-AWG with a 10MHz signal, there is only 0.047 db power loss of signal due to the DCR of the cable and the AC resistance resulting from skin effect.
For more information on Skin Effect and its insignificant effects on audio cables, check out the following article: Skin Effect Relevance For Speaker Cables.
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