Fundamentals of Digital Television Transmission phần 6 potx

Reference to Figures 6-1 and 6-2 shows that the responsetilt of coaxial lines is dependent on frequency and the length of line.. CORRUGATED COAXIAL CABLES 131Line length feet Group delay

The frequency response of coaxial lines is simply the slope of the attenuationversus frequency curve Reference to Figures 6-1 and 6-2 shows that the responsetilt of coaxial lines is dependent on frequency and the length of line In general,the response tilt is small In mathematical terms, the slope of the frequencyresponse is the first derivative of the formula for attenuation with respect tofrequency, or

ft run would exhibit only 0.09 dB over 6 MHz Thus for all practical purposes,frequency-response tilt may be ignored in rigid coaxial lines For those who wish

to do so, this amount of tilt could be preequalized This could be accomplishedusing either analog IF equalizers or programmable digital equalizers using theequation above and the appropriate frequency, line size, and line length.Phase nonlinearity and group delay variations do not occur in matched coaxiallines Since the operating mode is TEM, the phase is linear with frequencyand there is uniform group delay If the line is mismatched, however, phasenonlinearity and group delay is present, depending on the antenna reflectioncoefficient and the line length Eilers has published an analysis of this effect.10The group delay for a constant antenna VSWR of 1.05:1 ( D 0.025) and losslesstransmission line are shown in Figure 6-5 The group delay is periodic with ripplefrequency and magnitude directly proportional to line length For this example,

a maximum group delay of 100 ns is computed for a 2000-ft line length Theripple frequency increases to 24 ripples across a 6-MHz band for a line length

of the reflection

In the practical case, antenna VSWR is not constant with frequency, andneither the phase ripple, group delay, or amplitude ripple can easily be predicted

as a function of frequency To some extent, the effect of antenna VSWR will

be reduced due to the transmission line losses Thus, these linear distortions aredifficult to determine without measurement and thus are difficult to preequalize.The best approach is to specify and maintain antenna VSWR as low as possible

10Carl G Eilers, “The In-Band Characteristics of the VSB Signal for ATV,” IEEE Trans Broadcast.,

Vol 42, No 4, December 1996, p 298.

CORRUGATED COAXIAL CABLES 131

Line length (feet) Group delay Ripple frequency

Figure 6-5 Group delay and ripple frequency.

STANDARD LENGTHS

Rigid coaxial lines are manufactured in standard section lengths for television

of 19.5, 19.75, and 20 ft The optimum section length for a particular channel

is based on the need to minimize the accumulated reflections from the flangeconnections for a long length of line It is well known that identical reflectionsspaced an odd number of quarter-wavelengths apart will cancel, so that the totalreflection coefficient is zero Since the bandwidth of the digital television signal

is at least 6 MHz, this condition cannot be achieved precisely for all frequencieswithin the band However, by proper selection of the section length, the effect

of accumulated reflections can be minimized within the channel bandwidth.The proper section length for each channel is available in tabular form fromtransmission line suppliers

CORRUGATED COAXIAL CABLES

Installation time and cost are yet other major factors in transmission lineselection Continuous runs of semiflexible air-dielectric corrugated coaxialcables are available to reduce these costs As with rigid lines, there arevariations among the various manufacturers’ offerings However, these cablesshare some characteristics Inner and outer conductors are usually corrugated

copper, although at least one manufacturer11 offers a 9-in diameter line with acorrugated aluminum outer conductor Inner conductors are supported by spirals

of polyethylene, polypropylene, or Teflon Under normal conditions, the dielectricmaterial may be considered to be almost equivalent to dry air The velocity

of propagation is more than 90% that of free space, somewhat lower thanrigid coaxial lines These cables are also covered with a black polyethylene

or fluoropolymer jacket

Acquisition cost of corrugated cables is usually lower than for rigid lines.Corrugated cables are often easier to install than rigid lines since the continuoussections are longer A longer continuous run reduces the concern for performance

at a specific channel, since there are fewer flanges Cable sizes of 3-, 4-, 5-,

618-, 8-, and 9-in diameter are available The standard characteristic impedance

is 50 $

In general, efficiency is somewhat lower than the corresponding-size rigid line.This a consequence of the 50-$ characteristic impedance and the requirementfor more dielectric material to support the inner conductor properly Althoughthe expression for attenuation is of the same form as for rigid line, the constants,

A and B, are different For example, consider 618-in corrugated cable At

800 MHz, one manufacturer’s graph shows this cable to have attenuation of0.18 dB per 100 ft12 compared to 0.154 dB per 100 ft for rigid 618-in line Themanufacturer’s graph fits closely if A and B are chosen as 0.00472 and 0.0000632,respectively

Charts and graphs of attenuation and maximum average power for corrugatedcoaxial cables are shown in Tables 6-4, 6-5, 6-6, and 6-7 and Figures 6-6 and6-7 for 5-, 618-, 8-, and 9-in lines, respectively These are based on the formulasabove using the same derating factor for attenuation as for rigid lines Theaverage power rating is determined using maximum dissipations of 1.58, 1.82,2.4, and 3.23 kW per 100 ft for each respective cable The dissipation ratingsfor these cables are higher than for the rigid lines, as a consequence of thelarger inner conductor needed for the 50-$ characteristic impedance and higherheat transfer coefficient.13 Except for lines exposed to direct solar radiation,14the derating factors used and the assumptions made with regard to dissipationare considered adequate Consequently, these charts and curves are considered

to be conservative and may be used to estimate the operating specifications formost digital television system designs However, the data presented should beconsidered representative and not used for cables supplied by all manufacturers.The reader may apply the computational technique to the cables being consideredfor a specific installation

11 Radio Frequency Systems, Inc., Catalog 720C, pp 44–45.

12 Ibid., p 40.

13 Cozad, op cit.

14 Consult manufacturers’ data for derating factors for solar radiation Additional derating at temperate latitudes of 8% may be need for cables using Teflon supports; 15% for those using polyethylene Even higher derating may be needed at tropical latitudes.

CORRUGATED COAXIAL CABLES 133 TABLE 6-4 Power Rating and Attenuation of 5-in 50-Z Corrugated Coaxial Cable

is greater than 30 If the line length is 500 ft, AERP of 900 kW can be achievedwith a gain of 30 up to U.S channel 25 Alternatively, AERP of 1000 kW may

TABLE 6-5 Power Rating and Attenuation of 6 1 8 -in 50-Z Corrugated Coaxial Cable

be supported with 8-in cable and antenna gain of 25 for U.S channels through

39 if the line length is 1000 ft or less

The cutoff frequency of corrugated cables is generally lower than that of rigidlines by virtue of their lower characteristic impedance The larger inner conductorcoupled with the usual reduction by 5% to allow for the effects of manufacturingtolerances, transitions, and connections at flanges results in 8-in cable beingusable through U.S channel 39; 9-in cable is usable through U.S channel 27.Smaller corrugated cables are usable throughout the UHF broadcast band

WIND LOAD 135 TABLE 6-6 Power Rating and Attenuation of 8-in 50-Z Corrugated Coaxial Cable

TABLE 6-7 Power Rating and Attenuation of 9 16 3 -in 50-Z Corrugated Coaxial Cable

to line efficiency by using waveguide

The effect of line efficiency on TPO and the choice of final amplifier is illustrated

in Figure 6-11 Recognizing that UHF power tubes come in average DTV powerratings of 10, 12.5, 17.5, and 25 kW, it is seen that a variety of system designoptions are available For a transmitter power output between 25 and 50 kW, apossible configuration could be a pair of 17.5- or 25-kW final amplifier Either ofthese might be a good choice, assuming the use of any one of the rigid coaxiallines For a TPO below 25 kW, a pair of 12.5-kW finals could be used withany one of the waveguide types Because the line efficiency has an impact on

Figure 6-7 Power rating, corrugated cable.

2000′ 1000′ 500′

Figure 6-8 Maximum AERP.

6 1/8" corrugated cable, gain = 30

Figure 6-9 Maximum AERP.

Figure 6-10 Maximum AERP.

TABLE 6-8 Attenuation of UHF Transmission Lines (U.S Channel 14)

% D2a

Transmission line efficiency (%)

Figure 6-11 TPO versus line efficiency.

where ai is the wide inside dimension of the waveguide In practice, the actualoperating frequency is set approximately 25% above the cutoff frequency toassure minimum attenuation and phase nonlinearity

Like coaxial lines, the upper-frequency limit of rectangular waveguide isdetermined by the cutoff frequency of the first higher-order mode There are twomodes with the same cutoff frequency, the TE11 and TM11 modes For standardwaveguides for which the height, bi, is half the width, the cutoff wavelength is

%cD0.894ai

The upper frequency of operation is usually reduced below the first mode cutoff frequency by 17 to 19% to allow for the effects of manufacturingtolerances and moding at elbows, transitions, and connections at flanges.The maximum bandwidth ratio, BW, of rectangular waveguide is the ratio ofthe cutoff wavelength for the TE10 and TE11 modes, or

0.894 D2.237Accounting for the allowances made for operation above the dominant modeand below the first higher-order-mode cutoff frequencies, the actual operatingbandwidth ratio of a rectangular waveguide is approximately 1.5:1

BANDWIDTH 141

Due to the rectangular cross section, there is a preferred direction for thefield orientation in rectangular waveguide There is therefore no need for specialdesign techniques to maintain polarization, as in circular waveguide

For circular waveguide, the dominant or fundamental mode is the TE11, forwhich the cutoff wavelength is

%cD1.706Di

where Di is the inside diameter of the guide In practice, the actual operatingfrequency is set at least 19% above the cutoff frequency to assure minimumattenuation and phase nonlinearity

The first higher-order mode for unmodified circular waveguide is the TM01mode, for which the cutoff wavelength is given by

%cD1.307Di

The ideal bandwidth ratio, BW, of unmodified circular waveguide is, therefore,the ratio of the cutoff wavelength for the TE11 and TM01 modes, or

BW D 1.7061.307 D1.305This is considerably less than the bandwidth ratio of rectangular waveguide.Accounting for the allowances made to operate above the dominant modeand below the first higher-order-mode cutoff frequencies, the actual operatingbandwidth ratio of unmodified circular waveguide would be less than 1.09:1 Ifsome means were not devised to increase the bandwidth ratio, circular waveguidewould find very little application

When care is taken to avoid discontinuities that can generate order modes, circular waveguide may be manufactured with greater operatingbandwidth This involves precise manufacturing and installation techniques tominimize deformations from true circular cross section and discontinuities atflange junctions, as well as avoidance of elbows Because of circular symmetry,there is no preferred field direction in an unmodified circular waveguide Toassure that the TE11 mode is properly oriented at the output to couple the RFenergy properly to the antenna, it is necessary to control the polarization of thedominant mode Recognizing that the electric field must always go to zero inthe presence of a tangential conducting boundary, it is apparent that a preferredorientation of the electric field may be established by inserting a conductingboundary in the guide in a direction orthogonal to the TE11 field lines Such aboundary would have no appreciable effect on propagation of the TE11 mode.This boundary can be constructed with metallic pins at appropriate intervals,introducing only minimal mismatch to the transmission line These pins alsoserve to stabilize the precise circular shape of the guide, thereby helping tosuppress higher-order modes

higher-If the TM01 mode is suppressed, the next-higher-order mode in circularwaveguide is the TE21 This mode has a cutoff wavelength given by

%cD1.0285Di

The bandwidth ratio for the cutoff frequencies of the TE11 and TE21 modes is

BW D 1.706

1.0285 D1.659Now accounting for the allowances made to operate above the dominantmode and below the second-higher-order mode cutoff frequencies, the actualoperating bandwidth ratio of modified circular waveguide may be increased to asmuch as 1.36:1 Circular waveguide manufacturers provide charts indicating therecommended operating frequencies for each waveguide size To operate overthis much bandwidth requires that input and output connections and elbows beconstructed in rectangular waveguide If dimensions are measured in inches, thecutoff frequency of the modes in both rectangular and circular guide is given by



The results of calculations based on these formulas is shown graphically forrectangular waveguide in Figure 6-12 and for circular waveguide in Figure 6-13.Aside from having lower attenuation than coaxial lines, waveguides are unique

in that the attenuation for any specific-sized waveguide actually decreases withincreasing frequency The attenuation of circular waveguide is generally lowerthan the corresponding rectangular waveguide For multiple stations using acommon waveguide, the operating bandwidth must cover all channels of interest

POWER RATING

For all practical purposes, the average power rating of waveguide may beconsidered “unlimited” for digital television applications Obviously, this is notliterally true But at least one manufacturer gives the average power rating as

360 kW or more for all waveguides, independent of frequency.15 This is abovethe TPO of all currently available digital television transmitters Thus, waveguidemay be selected on the basis of channel and desired transmission line efficiencywithout regard for power-handling limitations

where %g is the guide wavelength of the line

For air-dielectric coaxial lines, the free-space wavelength is equal to thewaveguide wavelength However, for hollow waveguides, the guide wavelength

of guide is also plotted For long lines, the group delay due to the waveguidecannot be neglected

There is also small but usually negligible amplitude tilt in the frequencyresponse of waveguide The worst case is for WR1150 operating at U.S channel

42, for which the tilt is 0.00259 dB per 6 MHz per 100 ft Even for a 2000-ft run,this amounts to a response tilt of only 0.05 dB Since both the phase nonlinearityand the amplitude tilt are predictable, they may be preequalized in the exciter in

a manner similar to that indicated for coaxial lines

Antenna VSWR produces phase and amplitude ripple in the transmission lineresponse just as it does for coaxial lines In practice, this effect is somewhatmore noticeable for waveguide because the line efficiency is higher As indicatedbefore, the need to minimize the antenna VSWR is extremely important

15 Andrew Corporation, Catalog 36, p 288.