Fundamentals of Digital Television Transmission phần 5 pot

This is done by subtracting thetransmitter output emissions from the applicable emissions mask see Chapter 4.From these data the required attenuation versus frequency may be plotted in t

filters may be mounted on the floor or ceiling, often with welded frames forsupport In any case, performance requirements must be met while minimizingsize, weight, and cost.

In practice, some compromise must be made to the ideal The transitionfrom passband to stopband is gradual in practical filters Thus, perfectly flatin-band amplitude response cannot be achieved Steep transitions from passband

to stopband are associated with rapid changes in phase with respect to frequency.Thus perfectly flat in-band phase response is not feasible In fact, a smallamount of amplitude and phase ripple must be tolerated throughout the passband

The quality factor, Q , of practical cavities is finite, so that a small amount of

ohmic loss must be accepted Power rating is also related to losses Out-of-bandattenuation is also limited In the transition between passband and stopbands,the filter cannot provide the ideal attenuation curve The transmitter must besufficiently linear to provide adequate IP suppression in this region

Since the purpose of the filter is to reduce out-of-band emissions to acceptablelevels, this requirement must be defined first This is done by subtracting thetransmitter output emissions from the applicable emissions mask (see Chapter 4).From these data the required attenuation versus frequency may be plotted in theform of a filter response mask The interdependence of the filter and transmitterreinforces the need to procure both items from the same source to assure goodsystem performance

A typical response mask for an ATSC UHF DTV output filter is shown

in Figure 5-3 In-band ripple is specified to be less than š0.05 dB over a

minimum bandwidth of 6 MHz The transition from passband to stopband extendsfrom š3 to š9 MHz The maximum stopband attenuation of 64 dB extends toš40 MHz Beyond these frequencies the attenuation varies in accordance withFCC requirements, which includes attenuation of harmonics to required levelsand protection of other services.

To illustrate the adequacy of the stopband response, the unfiltered anduncorrected IP output of a typical solid-state transmitter of 40 dB (seeChapter 4) may be added to the filter response at š9 MHz This yields totalout-of-band suppression of 104 dB At 90 MHz, the filter response is 44 dB;the transmitter’s unfiltered response is down more than 60 dB Again, the totalout-of-band suppression is 104 dB

The in-band amplitude response is specified to be flat enough that no additionalequalization is required Substantial amounts of group delay may be tolerated,however, with the assumption that sufficient equalization is available in thetransmitter Typical measured group delay response for a filter of this type isshown in Figure 5-4 There is nearly a 120-ns delay variation at š3 MHz fromband center

Figure 5-4 Group delay of filter for digital television (Data courtesy of Scott Durgin of

Passive Power Products, Gray, Marine.)

The cutoff slope is a key design parameter and is defined as

SdBD AsbApb

fsb/fpb1 dB/MHzwhere Asb and Apb are the attenuation at the stopband and passband edgefrequencies, fsb and fpb, respectively For the mask shown in Figure 5-3 at

US channel 14,

SdBD 64  0.05479/473  1 D7568 dB/MHzThe number of filter sections is related directly to the cutoff slope as well as theripple in the passband and attenuation in the stopband For a specified passbandripple and stopband attenuation, the greater the cutoff slope, the more sectionsare required

ELLIPTIC FUNCTION FILTERS

To achieve the required level of performance demands advanced, complexfilter designs Minimum in-band ripple, steep skirts in the passband-to-stopbandtransition region and high stopband attenuation, high power-handling capability,and minimum cost necessitate all the filter designer’s skills This has led tothe nearly universal use of designs based on lumped-element prototypes usingthe early work of Cauer and Darlington on elliptic functions and modernnetwork filter theory These functions provide poles of attenuation near the cutofffrequencies so that the slope in the transition region may be extremely large with

a reasonable number of filter sections

Elliptic function filters are characterized by equiripple response in both thepassband and stopbands This means that the peak-to-peak ripple in the passband

is of low magnitude and constant; similarly, the peak-to-peak attenuation in thestopband is constant, although very high These filters are optimum in the sensethat they provide the maximum slope between the passband and stopbands forspecified ripple in the passband and stopbands and for a given number of filtersections This is in contrast to Butterworth or even Chebyshev designs, in which alarge number of sections would be required for similar performance For example,

an elliptic function design may be less than half the length of a correspondingChebyshev design.1An elliptic function design may also have less insertion lossand group delay variation than the Chebyshev design with equivalent rejection.The normalized response or transmission power function, tf2, of a filter isdefined in terms of the ratio of the power delivered by the transmitter, Pt, to the

1William A Decormier, “Filter Technology for Advanced Television Requirements,” IEEE

Broad-cast Technology Society Symposium Proceedings, September 21, 1995.

power delivered to the load, Pl; that is,

tf2 D Pt

PlThe filter attenuation is simply 10 logtf2 Since in the ideal or lossless case,the filter consists only of reactive elements, any power not delivered to the load

is reflected Thus the output power must be the difference between the powerdelivered by the transmitter and the reflected power The lossless filter maytherefore be fully characterized by the transmission and reflection coefficientfunctions, that is,

tf2 D1 C 2where  is the reflection coefficient function To achieve attenuation of less than0.05 dB in an ideal filter, the reflection coefficient must be less than about 0.1

In practice, resistive losses are always present This requires that the reflectioncoefficient be reduced to make allowance for internal circuit losses

For elliptical function filters, tf2 is given by

tf2D 1

1 C ε2R2 nwhere ε is the passband ripple ApbD20 log ε, Rn is the ratio of a pair ofpolynomials defining the filter poles and zeros, and n is the number of poles orfilter order.2Transmission zeros occurring when the frequency is on the imaginaryaxis of the complex frequency plane result in high attenuation; transmission zerosoccurring when the frequency is on the real axis result in group delay self-equalization By combining transmission zeros on the real and imaginary axes,filters with the desired rejection and acceptable group delay may be designed

It is has not been possible to apply the necessary degree of phase correction

to high-power elliptical function filters.3 This has led to the use of a similar class

of filters with cross couplings between nonadjacent resonators These filters arereferred to as cross-coupled or pseudoelliptic filters These may be implemented

in a variety of ways, including interdigital structures for low-power applications

or in-line or single-mode TE101 or TE102 resonators in rectangular waveguide.Either of the latter are suitable for high-power applications

In-line single-mode resonators can provide the levels of performanceapproaching those required However, overall filter size can become an issuedue to the extreme amount of rejection required by the emissions masks Eachresonator contributes only one resonance, so that the minimum filter length must

2Albert E Williams, “A Four-Cavity Elliptic Waveguide Filter,” IEEE Trans Microwave Theory

Tech., Vol 18, No 12, December 1970, pp 1109–1114.

3Graham Broad and Robin Blair, “Adjacent Channel Combining in Digital TV,” NAB Broadcast

Engineering Conference Proceedings, 1998, p 13.

equal the number of resonators times one-half the waveguide wavelength For a10-resonator filter operating at 470 MHz, this may amount to a length exceeding

20 ft If the TE102 mode is required to achieve sufficient Q, the resonator is afull wavelength long and the filter length is double

Use of in-line, dual-mode resonators or cavities in a square or circularwaveguide permit construction of filters with approximately half the size of thesingle-mode filters In this structure, illustrated in Figure 5-5, each resonatorsupports a pair of orthogonal modes or polarizations These modes are depicted

by mutually perpendicular vectors Since there are two electrical resonances, eachresonator functions as the equivalent of a pair of resonators.4 The equivalentcircuit of a waveguide pseudoelliptic function filter is shown in Figure 5-6 A

Coupling apertures

M56 Probes

1

4

M14 M01

total of n coupled resonators are employed to produce the desired transmissionzeros at the desired frequencies Each resonator is a single resonant circuit withmultiple couplings to the other resonators.5 The value of the coupling factors,

Mmn, determine the degree to which the cavities are coupled The resonatorsproduce transmission zeros at the edges of the stopband and at f D 1 Inpractice, R1 DRn, so that the filter is matched to the system characteristicimpedance

CAVITIES

An ideal cavity is a lossless dielectric region completely enclosed by perfectlyconducting walls The operation of a cavity is based on the properties of a short-circuited transmission line At certain frequencies, the cavity is resonant just like

a shorted line The input impedance, Zsc, of a short-circuited lossless transmissionline as a function of frequency is

ZscDjZ0tan f

2f0where f0 is the frequency at which the transmission line is 14 wavelength long.This is just the product of the characteristic impedance, Z0, and a complexfrequency variable, S, given by

S D jtan f

2f0

so that Zsc is directly proportional to this complex frequency, that is,

ZscDZ0SWhen used as a series element, a shorted stub produces a transmission zero when

f D f0 Since S is periodic in 2f0, the response of the line section repeats atthis interval

A cavity may be visualized as a pair of short-circuited transmission linesconnected at their inputs as shown in Figure 5-7 It supports the appropriatetransmission line mode and is an integer number of half-wavelengths long atthe resonant frequency Key design parameters include the resonant frequencyand quality factor A cavity may be constructed of either waveguide or coax,depending primarily on the frequency of operation, allowable losses, and power-handling requirements

To minimize insertion loss, the cavities used in filters for digital televisionoperating at UHF are constructed of air-dielectric circular waveguide operating

5A.E Atia and A.E Williams, “Narrow-Bandpass Waveguide Filters,” IEEE Trans Microwave

Theory Tech., Vol 20, No 4, April 1972, pp 258–265.

Short circuit Short circuit

.

Input

Figure 5-7 Cavity equivalent circuit.

in the TE11 mode For this, the lowest-order mode, resonance occurs when thetotal length of the cavity, 2hc, is equal to one-half the guide wavelength, g Theguide wavelength is

[εr/c2]1/2where c is the cutoff wavelength of the guide In an air-dielectric cavity, εr,the relative dielectric constant, is approximately unity From these relationships

it can be shown that the resonant wavelength of a circular cavity operating in thedominant mode6 is given by

[1/hc2C1.17/a2]1/2The mode designation, TE111, indicates that the cylindrical waveguide isoperating in the TE11 mode and the cavity length is one-half guide wave-length

Means must be provided for coupling the input cavity to the transmitter output,the cavities to each other, and the output cavity to the transmission line andantenna This involves removal of sections of the cavity walls and the introduction

of coupling apertures, such as inductive slots or irises These apertures, illustrated

in Figure 5-5, must be shaped, located, and oriented to excite the proper modeand in such a way as to minimize the perturbation of the field configuration andresonant frequency of the cavity By proper selection of the point and degree

of coupling, the cavity input impedance at resonance and the loaded Q are

determined

The pair of modes within each cavity are coupled to each other by a tuningplunger or probe oriented at 45° with respect to the desired mode polarization.The probe introduces asymmetry to the cavity, giving rise to two identicalbut orthogonal modes which are polarized parallel to one coupling iris andperpendicular to the other The degree of coupling between the orthogonalmodes is determined by the probe depth This type of coupling is represented inFigure 5-5 by M12, M34, and M56

Coupling between successive cavities and nonadjacent resonances is inductiveand frequency dependent It is achieved by apertures or irises in the end wall

of each resonator For example, M14 provides coupling between nonadjacent

6Reference Data for Radio Engineers, 6th ed., Howard W Sams, Indianapolis, Ind., 1977, p 25–19.

resonances 1 and 4 The sign of the coupling factors between adjacent modes,M01, M12, and M23 must be positive; the cross or nonadjacent coupling factorsmust be negative The cross or reverse coupling produces a pseudoellipticalresponse with two poles of attenuation per cross-coupled cavity Group delaycompensation may be designed in by adding cavities with positive couplingsbetween cross-coupled modes The effect of the reactance of the probes andirises is to increase the electrical length of the cavities; this requires the cavity

to be shortened to compensate

The cavity Q is defined as 2 times the ratio of the energy stored to the

energy dissipated per cycle and is closely related to the bandwidth and loss of

the cavity Unloaded Q , which accounts only for losses internal to the cavity, is

designated Qu Loaded Q accounts for the added effects of coupling to external

circuits and is designated Ql The effects of all sources of dissipation are thusincluded

The relationship between loaded and unloaded Q may be derived by reference

to Figure 5-8, which shows the equivalent circuit of a cavity with single input andoutput couplings to external circuits The cavity is modeled as a shunt resonantcircuit with shunt conductance Gc Similarly, the coupling to input and outputcircuits are modeled as shunt conductances, Gin and Gout, plus shunt suceptance

At resonance, the combination of all susceptances appears as an open circuit; allthat remains is the shunt conductances In the absence of coupling, the energydissipated is proportional to V2Gc The coupling results in additional dissipation,

V2GinCGout In both cases, the stored energy is the same Thus the ratio of

the unloaded Q to the loaded Q is

Figure 5-8 Equivalent circuit of cavity with input and output coupling.

7Carol G Montgomery, Techniques of Microwave Measurements, Boston Technical Publishers,

Lexington, Mass., 1963, p 290.

corresponding conductances normalized to the cavity conductance8:

Min D Gin

Gcand

ω D ω0/Qlwhere ω is the radian frequency difference between half-power points and ω0

is the radian resonant frequency

The unloaded Q is related to the size of the cavity; the larger the cavity, the

higher the value of Qu and the lower the insertion loss In theory, unloaded Qu

of 35,000 to over 40,000 can be achieved with half-wavelength circular cavitiesoperating in the TE111 mode, depending on cavity dimensions, material, andfrequency The theoretical Quvalue of aluminum and copper cavities operating at

800 MHz as a function of the length-to-radius ratio, hc/a, is shown in Figure 5-9.Maximum Qu occurs for hc/aof approximately 0.76 The Qu of copper cavities

is approximately 23% greater than aluminum cavities

The variation of Qu with frequency is shown in Figure 5-10 The surfaceresistance of the metal walls increases with increasing frequency due to the skineffect Consequently, Qu is highest at the lower frequencies In practice, Qu

is limited to about 75% of these values, due to limitations in fabrication andassembly.9

Insertion loss is inversely proportional to Qu,10 that is,

Qu D 

˛cgwhere ˛cis the cavity attenuation in nepers per unit length For half-wave cavitieswith Qu of 35,000, this expression implies that attenuation is on the order of

8Williams, op cit.; Darko Kaifez, “Q-Factor Measurement Techniques,” RF Design, August 1999,

p 60.

9 Small, op cit., p 1.

10William Sinnema, Electronic Transmission Technology, Prentice Hall, Upper Saddle River, NJ,

p 75, 1988, 2nd Edition.

TE111 cylindrical cavities

Figure 5-9 Unloaded Q versus h/a.

TE111 Cylindrical cavities, h/a = 0.67

0.002 dB per cavity Since the size of the cavities is related to the insertionloss, it follows that average power handling is also determined by the cavitydimensions Insertion loss of 0.002 dB represents dissipation of about 0.5 W perkilowatt of input It is estimated that up to 10 sections will be required to meetthe rejection specification of the FCC mask This would imply ohmic losses inthe filter of about 0.02 dB.

At the input and output, the slots must properly couple to the main transmissionline A long thin slot is used for this coupler The coupling coefficient isdetermined by the magnetic polarizability of the slot, which is related to thelength of the slot with appropriate correction for slot thickness

The rejection specification determines the minimum number of resonators toachieve a given passband ripple The number of cavities and the size of eachdetermine the overall size of the filter Thus, even with the use of dual-modecavities, the space required for the filter is related directly to the key electricalspecifications

The resonant frequency of a cavity changes because of expansion andcontraction of the cavity due to temperature changes Thus, it is important

to select cavity materials to minimize losses while minimizing the effects oftemperature variations If the cavity is made of a single type of metal, the change

in resonant frequency will be very nearly directly proportional to the linearcoefficient of expansion of the metal and the absolute temperature This is becausethe resonant frequency is inversely proportional to the linear dimensions of thecavity For copper, the linear coefficient of expansion at a temperature of 25°C is16.8 ð 106 °C1 A 25°C change in temperature will produce a 0.044% change

in dimensions and a corresponding resonant frequency change At 800 MHz,this amounts to 0.35 MHz, a significant change For aluminum cavities, thecoefficient of expansion and change in resonant frequency is 38% greater Inpractice, combinations of materials may be used Aluminum waveguide may beused for the body of the filter with either aluminum or copper irises

The resonant frequency also changes as a function of temperature and humiditydue to changes in dielectric constant of the atmosphere The relative dielectricconstant of standard atmospheric air at sea level is approximated by

of mercury, respectively, and Ta is the absolute temperature in Kelvins For dryair, Pa is the same as atmospheric pressure (¾760 mmHg) and Pw D0 Forsaturated air, Pa ranges from ¾755 to 667 mmHg and Pw ranges from 5 to

93 mmHg, as temperature ranges from 0 to 50°C The relative dielectric constant

of both dry and saturated air is plotted in Figure 5-11 Even when the air isdry, the dielectric constant is slightly greater than unity If a cavity is tuned

at a temperature of 25°C and a humidity of 60%, a change in temperature

to 50°C with a relative humidity increase to 100% results in a change in the

15% humidity saturated

Figure 5.11 Dielectric constant of air.

dielectric constant of air from 1.0007 to 1.0014 This results in a change inresonant frequency of 0.035% At 800 MHz, this amounts to 0.28 MHz Thecombination of frequency shifts due to cavity expansion and changes in thedielectric constant of air impose additional constraints on the trade-off betweenpassband and stopband characteristics

These considerations also indicate possible strategies for mitigating resonantfrequency changes due to temperature and humidity The maximum use of coppermay be worth the extra weight and cost The use of air conditioning in thespace occupied by the filter would prevent large temperature variations Airconditioning will also serve to reduce humidity Evidently, when the relativehumidity is in the neighborhood of 20%, the dielectric constant of air is nearlyconstant over a wide temperature range The importance of testing the transmitter,cooling system, and filter as a system is also reinforced by these considerations;this assures that the filter performance is known at the typical ambient temperaturealong with the effects of heating due to ohmic losses

The resonant frequency may also depend on the load and transmitterimpedances, especially if those impedances are reactive Fortunately, digitalbroadcast systems are normally well matched to maintain maximum powertransfer For convenience of design and measurement, system impedances arealso resistive Unless severe mismatches occur due to antenna icing or otheremergency condition, filter response should not be affected

CHANNEL COMBINERS

Finding suitable tower space for a new digital television antenna and transmissionline while continuing to operate the analog system is one of the major hurdlesthat a broadcaster must overcome during the transition period Co-location of thedigital transmitter with the analog and using a common antenna and transmissionline for both is a possible solution This give rise to the need for suitable channelcombining techniques

To provide sufficient spectrum to accommodate the required number of DTVallocations in the United States, upper N C 1 and lower N  1 adjacentchannel assignments were necessary, especially in major markets This has givenrise to the potential for severe adjacent channel interference from the signaltransmitted by the NTSC station to the transmitted DTV signal Even if thepaired signals are not in adjacent channels, there is potential for interference,although to a lesser degree For these reasons, it is important to provide adequateisolation when combining the two signals

The average power of a DTV signal at the transmitter is nominally 12 dBbelow the NTSC peak of sync At these relative levels, any signal outside theNTSC channel has the potential for creating interference to the DTV signal.This is especially true if the DTV channel is below the NTSC The relationshipbetween the desired and undesired signals is illustrated in Figure 5-12 Thepotential for interference is apparent The specification for the NTSC lowersideband is only 20 dB below the peak sync level Although this specification

is usually met with some margin in well-maintained transmitters, significantinterference is still possible For pulsed UHF systems, the level of the reinsertedlower sideband may be up to 10 dB higher than shown, further increasing thepotential for interference Even without the effects of unequal antenna patternsand propagation, the lower sideband might be only 8 dB below the average DTVpower in the absence of additional filtering

Several factors must be considered when determining the level and effect ofthe interference as well as strategies to minimize its effect Obviously, combining

to a common antenna is feasible only if the stations are co-located.11 Thetransmission line loss and antenna gain will generally be approximately equal forboth channels The coverage for both stations should also be nearly equivalent,assuming comparable AERP Assuming that the antenna and transmission linehave sufficient pattern and impedance bandwidth to accommodate both channels,the signals may be combined without the use of a separate channel combiner Thismay involve the use of a hybrid combiner with a turnstile antenna, similar to themethod used for combining visual and aural signals in VHF batwing antennas.Isolation between inputs is obtained by virtue of the isolation inherent in thehybrid less the effect of the return loss of the antenna This approach may be

11 In this context, co-located means to be physically co-sited The FCC rules define co-location as being located within a 10-mile separation Obviously, this definition does not apply when considering channel combining of any type.

NTSC

N

NTSC

Figure 5-12 Adjacent channel signals (From R.J Plonka, “Planning Your Digital

Tele-vision Transmission System,” NAB Broadcast Engineering, 1997; used with permission.)

used for either N C 1 or N  1 combining The power rating of the antenna andtransmission line must be adequate to support both signals simultaneously.Channel combining can also be done with separate collinear antennas Forexample, the antenna for analog could be mounted above the antenna for digital

TV In this case the antennas and transmission lines must be capable of providingthe bandwidth and power-handling capability for only one channel each Isolation

is achieved by virtue of element phasing if radiation of both antennas toward the