1、 Rec. ITU-R SM.1138-2 1 RECOMMENDATION ITU-R SM.1138-2 Determination of necessary bandwidths including examples for their calculation and associated examples for the designation of emissions (1995-2007-2008) Scope This Recommendation serves as a basis for the determination of necessary bandwidths of
2、 emissions under amplitude, frequency and pulse modulation by various types of signals. Sample calculations and designation of emissions are also provided. The ITU Radiocommunication Assembly, considering a) that the assignment of frequencies requires the determination of the necessary bandwidth of
3、emissions; b) that necessary bandwidth is a key data element of all automated spectrum-management systems, recommends 1 that the formulae given in Annex 1 shall be used to calculate the necessary bandwidth when required by the Radio Regulations (RR). Annex 1 Determination of necessary bandwidths, in
4、cluding examples for their calculation and associated examples for the designation of emissions 1 The necessary bandwidth is not the only characteristic of an emission to be considered in evaluating the interference that may be caused by that emission. 2 In the formulation of the table, the followin
5、g terms have been employed: Bn: necessary bandwidth (Hz) B: modulation rate (Bd) N: maximum possible number of black plus white elements to be transmitted per second, in facsimile M: maximum modulation frequency (Hz) C: sub-carrier frequency (Hz) D: peak deviation, i.e. half the difference between t
6、he maximum and minimum values of the instantaneous frequency. The instantaneous frequency (Hz) is the time rate of change in phase (rad) divided by 2 t: pulse duration (s) at half-amplitude 2 Rec. ITU-R SM.1138-2 tr: pulse rise time (s) between 10% and 90% amplitude K: an overall numerical factor wh
7、ich varies according to the emission and which depends upon the allowable signal distortion. In the case of orthogonal frequency division multiplexed multi-carrier signal, K is the number of active sub-carriers as defined by equation (52) in Recommendation ITU-R SM.328 Nc: number of baseband channel
8、s in radio systems employing multichannel multiplexing fp: continuity pilot sub-carrier frequency (Hz) (continuous signal utilized to verify performance of frequency-division multiplex systems) Ns: frequency separation between two sub-carriers (kHz). Necessary bandwidth Description of emission Formu
9、la Sample calculation Designation of emission I. NO MODULATING SIGNAL Continuous wave emission NONE II. AMPLITUDE MODULATION 1. Signal with quantized or digital information Continuous wave telegraphy, Morse code Bn= BK K = 5 for fading circuits K = 3 for non-fading circuits 25 words per minute B = 2
10、0, K = 5 Bandwidth: 100 Hz 100HA1AAN Telegraphy by on-off keying of a tone modulated carrier, Morse code Bn= BK + 2M K = 5 for fading circuits K = 3 for non-fading circuits 25 words per minute B = 20, M = 1 000, K = 5 Bandwidth: 2 100 Hz = 2.1 kHz 2K10A2AAN Selective calling signal using sequential
11、single frequency code, single-sideband full carrier Bn= M Maximum code frequency is: 2 110 Hz M = 2 110 Bandwidth: 2 110 Hz = 2.11 kHz 2K11H2BFN Direct-printing telegraphy using a frequency shifted modulating sub-carrier, with error-correction, single-sideband, suppressed carrier (single channel) Bn
12、= 2M + 2DK 2BM = B = 50 D = 35 Hz (70 Hz shift) K = 1.2 Bandwidth: 134 Hz 134HJ2BCN Telegraphy, multichannel with voice frequency, error-correction, some channels are time-division multiplexed, single-sideband, reduced carrier Bn= highest central frequency + M + DK 2BM = 15 channels; highest central
13、 frequency is: 2 805 Hz B = 100 D = 42.5 Hz (85 Hz shift) K = 0.7 Bandwidth: 2 885 Hz = 2.885 kHz 2K89R7BCW 2. Telephony (commercial quality) Telephony, double-sideband (single channel) Bn= 2M M = 3 000 Bandwidth: 6 000 Hz = 6 kHz 6K00A3EJN Telephony, single-sideband, full carrier (single channel) B
14、n= M M = 3 000 Bandwidth: 3 000 Hz = 3 kHz 3K00H3EJN Telephony, single-sideband, suppressed carrier (single channel) Bn= M lowest modulation frequency M = 3 000 lowest modulation frequency = 300 Hz Bandwidth: 2 700 Hz = 2.7 kHz 2K70J3EJN Rec. ITU-R SM.1138-2 3 Necessary bandwidth Description of emis
15、sion Formula Sample calculation Designation of emission 2. Telephony (commercial quality) (cont.) Telephony with separate frequency modulated signal to control the level of demodulated speech signal, single-sideband, reduced carrier (Lincompex) (single channel) Bn= M Maximum control frequency = 2 99
16、0 Hz M = 2 990 Bandwidth: 2 990 Hz = 2.99 kHz 2K99R3ELN Telephony with privacy, single-sideband, suppressed carrier (two or more channels) Bn= NcM lowest modulation frequency in the lowest channel Nc= 2 M = 3 000 lowest modulation frequency = 250 Hz Bandwidth: 5 750 Hz = 5.75 kHz 5K75J8EKF Telephony
17、, independent sideband (two or more channels) Bn= sum of M for each sideband 2 channels M = 3 000 Bandwidth: 6 000 Hz = 6 kHz 6K00B8EJN 3. Sound broadcasting Sound broadcasting, double-sideband Bn= 2M M may vary between 4 000 and 10 000 depending on the quality desired Speech and music M = 4 000 Ban
18、dwidth: 8 000 Hz = 8 kHz 8K00A3EGN Sound broadcasting, single-sideband, reduced carrier (single channel) Bn= M M may vary between 4 000 and 10 000 depending on the quality desired Speech and music M = 4 000 Bandwidth: 4 000 Hz = 4 kHz 4K00R3EGN Sound broadcasting, single-sideband, suppressed carrier
19、 Bn= M lowest modulation frequency Speech and music M = 4 500 lowest modulation frequency = 50 Hz Bandwidth: 4 450 Hz = 4.45 kHz 4K45J3EGN 4. Television Television, vision and sound Refer to relevant ITU-R documents for the bandwidths of the commonly used television systems Number of lines: 625 Nomi
20、nal video bandwidth = 5 MHz Sound carrier relative to video carrier: 5.5 MHz Total vision Bandwidth: 6.25 MHz FM sound bandwidth including guardbands: 750 kHz RF channel Bandwidth: 7 MHz 6M25C3F - 750KF3EGN 5. Facsimile Analogue facsimile by sub-carrier frequency modulation of a single-sideband emis
21、sion with reduced carrier, monochrome Bn= C + 2N+ DK K = 1.1 (typically) N = 1 100 corresponding to an index of cooperation of 352 and a cycler rotation speed of 60 rpm. Index of cooperation is the product of the drum diameter and number of lines per unit length. C = 1 900 D = 400 Hz Bandwidth: 2 89
22、0 Hz = 2.89 kHz 2K89R3CMN Analogue facsimile; frequency modulation of an audio frequency sub-carrier which modulates the main carrier, single-sideband suppressed carrier Bn= 2M + 2DK M = 2NK = 1.1 (typically) N = 1 100 D = 400 Hz Bandwidth: 1 980 Hz = 1.98 kHz 1K98J3C - 4 Rec. ITU-R SM.1138-2 Necess
23、ary bandwidth Description of emission Formula Sample calculation Designation of emission 6. Composite emissions Double-sideband, television relay Bn= 2C + 2M + 2D Video limited to 5 MHz, audio on 6.5 MHz, frequency modulated sub-carrier, sub-carrier deviation = 50 kHz: C = 6.5 106D = 50 103Hz M = 15
24、 000 Bandwidth: 13.13 106Hz = 13.13 MHz 13M1A8W - Double-sideband radio-relay system, frequency division multiplex Bn= 2M 10 voice channels occupying baseband between 1 kHz and 164 kHz M = 164 000 Bandwidth: 328 000 Hz = 328 kHz 328KA8E - Double-sideband emission of VOR with voice (VOR: VHF omnidire
25、ctional radio range) Bn= 2Cmax+ 2M + 2DK K = 1 (typically) The main carrier is modulated by: a 30 Hz sub-carrier a carrier resulting from a 9 960 Hz tone a telephone channel a 1 020 Hz keyed tone for continual Morse identification Cmax= 9 960 M = 30 D = 480 Hz Bandwidth: 20 940 Hz = 20.94 kHz 20K9A9
26、WWF Independent sidebands; several telegraph channels with error-correction together with several telephone channels with privacy; frequency division multiplex Bn= sum of M for each sideband Normally composite systems are operated in accordance with standardized channel arrangements (e.g. Rec. ITU-R
27、 F.348). 3 telephone channels and 15 telegraphy channels require the bandwidth: 12 000 Hz = 12 kHz 12K0B9WWF 7. Standard frequency and time signals 7.1 High frequency (voice) Voice announcements, double-sideband Bn= 2M Speech M = 4 000 Bandwidth: 8 000 Hz = 8 kHz 8K00A3XGN 7.2. High frequency (time
28、code) Time code as telegraphy Bn= BK + 2M B = 1/s M = 1 K = 5 Bandwidth: 7 Hz 7H00A2XAN 7.3. Low frequency (time code) Time code as telegraphy Bn= BK + 2M B = 1/s M = 1 K = 3 Bandwidth: 5 Hz 5H00A2XAN Rec. ITU-R SM.1138-2 5 Necessary bandwidth Description of emission Formula Sample calculation Desig
29、nation of emission III-A. FREQUENCY MODULATION 1. Signal with quantized or digital information Telegraphy without error-correction (single channel) Bn= 2M + 2DK 2BM = K = 1.2 (typically) B = 100 D = 85 Hz (170 Hz shift) Bandwidth: 304 Hz 304HF1BBN Telegraphy, narrow-band direct-printing with error-c
30、orrection (single channel) Bn= 2M + 2DK 2BM = K = 1.2 (typically) B = 100 D = 85 Hz (170 Hz shift) Bandwidth: 304 Hz 304HF1BCN Selective calling signal Bn= 2M + 2DK 2BM = K = 1.2 (typically) B = 100 D = 85 Hz (170 Hz shift) Bandwidth: 304 Hz 304HF1BCN Four-frequency duplex telegraphy Bn= 2M + 2DK B:
31、 modulation rate (Bd) of the faster channel. If the channels are synchronized: 2BM = (otherwise, M = 2B)K = 1.1 (typically) Spacing between adjacent frequencies = 400 Hz Synchronized channels B = 100 M = 50 D = 600 Hz Bandwidth: 1 420 Hz = 1.42 kHz 1K42F7BDX 2. Telephony (commercial quality) Commerc
32、ial telephony Bn= 2M + 2DK K = 1 (typically, but under certain conditions a higher value of K may be necessary) For an average case of commercial telephony, D = 5 000 Hz M = 3 000 Bandwidth: 16 000 Hz = 16 kHz 16K0F3EJN 3. Sound broadcasting Sound broadcasting Bn= 2M + 2DK K = 1 (typically) Monaural
33、 D = 75 000 Hz M = 15 000 Bandwidth: 180 000 Hz = 180 kHz 180KF3EGN 4. Facsimile Facsimile by direct frequency modulation of the carrier; black and white Bn= 2M + 2DK 2NM = K = 1.1 (typically) N = 1 100 elements/s D = 400 Hz Bandwidth: 1 980 Hz = 1.98 kHz 1K98F1C - Analogue facsimile Bn= 2M + 2DK 2N
34、M = K = 1.1 (typically) N = 1 100 elements/s D = 400 Hz Bandwidth: 1 980 Hz = 1.98 kHz 1K98F3C - 6 Rec. ITU-R SM.1138-2 Necessary bandwidth Description of emission Formula Sample calculation Designation of emission 5. Composite emissions (see Table III-B) Radio-relay system, frequency division multi
35、plex Bn= 2fp+ 2DK K = 1 (typically) 60 telephone channels occupying baseband between 60 kHz and 300 kHz; rms per-channel deviation: 200 kHz; continuity pilot at 331 kHz produces 100 kHz rms deviation of main carrier. D = 200 103 3.76 2.02 = 1.52 106Hz fp= 0.331 106Hz Bandwidth: 3.702 106Hz = 3.702 M
36、Hz 3M70F8EJF Radio-relay system, frequency division multiplex Bn= 2M + 2DK K = 1 (typically) 960 telephone channels occupying baseband between 60 kHz and 4 028 kHz; rms per-channel deviation: 200 kHz; continuity pilot at 4 715 kHz produces 140 kHz rms deviation of main carrier. D = 200 103 3.76 5.5
37、= 4.13 106Hz M = 4.028 106fp= 4.715 106(2M + 2DK) 2 fpBandwidth: 16.32 106Hz = 16.32 MHz 16M3F8EJF Radio-relay system, frequency division multiplex Bn= 2fp600 telephone channels occupying baseband between 60 kHz and 2 540 kHz; rms per-channel deviation: 200 kHz; continuity pilot at 8 500 kHz produce
38、s 140 kHz rms deviation of main carrier. D = 200 103 3.76 4.36 = 3.28 106Hz M = 2.54 106K = 1 fp= 8.5 106(2M + 2DK) 2 fpBandwidth: 17 106Hz = 17 MHz 17M0F8EJF Stereophonic sound broadcasting with multiplexed subsidiary telephony sub-carrier Bn= 2M + 2DK K = 1 (typically) Pilot tone system; M = 75 00
39、0 D = 75 000 Hz Bandwidth: 300 000 Hz = 300 kHz 300KF8EHF Rec. ITU-R SM.1138-2 7 III-B. MULTIPLYING FACTORS FOR USE IN COMPUTING D, PEAK FREQUENCY DEVIATION, IN FM FREQUENCY DIVISION MULTIPLEX (FM-FDM) MULTI-CHANNEL EMISSSIONS For FM-FDM systems the necessary bandwidth is: Bn= 2M + 2DK The value of
40、D, or peak frequency deviation, in these formulae for Bnis calculated by multiplying the rms value of per-channel deviation by the appropriate “multiplying factor” shown below. In the case where a continuity pilot of frequency fp exists above the maximum modulation frequency M, the general formula b
41、ecomes: Bn= 2fp+ 2DK In the case where the modulation index of the main carrier produced by the pilot is less than 0.25, and the rms frequency deviation of the main carrier produced by the pilot is less than or equal to 70% of the rms value of per-channel deviation, the general formula becomes eithe
42、r: Bn= 2fpor Bn= 2M + 2DK whichever if greater. Multiplying factor(1)Number of telephone channels Nc20levelreferencemodulationabovedBinvalueantilog)factorPeak( 3 Nc 12 20approvaltionadministratosubject licensee,stationorermanufacturequipmentthebyspecifieddBinvalueaantilog47.4 12 Nc 60 +20log22.6anti
43、log76.3cNMultiplying factor(2)Number of telephone channels Nc20levelreferencemodulationabovedBinvalueantilog)factorPeak( 60 Nc 240 +20log41antilog76.3cNNc 240 +20log0115antilog76.3cN(1)In the above chart, the multipliers 3.76 and 4.47 correspond to peak factors of 11.5 and 13.0 dB, respectively. (2)
44、In the above chart, the multipliers 3.76 correspond to peak factors of 11.5 dB. 8 Rec. ITU-R SM.1138-2 Necessary bandwidth Description of emission Formula Sample calculation Designation of emission IV. PULSE MODULATION 1. Radar Unmodulated pulse emission tKBn2= K depends upon the ratio of pulse dura
45、tion to pulse rise time. Its value usually falls between 1 and 10 and in many cases it does not need to exceed 6 Primary radar range resolution = 150 m K = 1.5 (triangular pulse where t tr, only components down to 27 dB from the strongest are considered) Then: =lightofvelocity)resolution(range2t 810
46、 3150 2= = 1 106s Bandwidth: 3 106Hz = 3 MHz 3M00P0NAN 2. Composite emissions Radio-relay system tKBn2= K = 1.6 Pulse position modulated by 36 voice channel baseband; pulse width at half amplitude = 0.4 s Bandwidth: 8 106Hz = 8 MHz (Bandwidth independent of the number of voice channels) 8M00M7EJT 3.
47、 Standard frequency and time signals 3.1 High frequency (tone bursts) Ticks used for epoch measurement Bn= 2/trtr= 1 ms Bandwidth: 2 000 Hz = 2 kHz 2K00K2XAN 3.2 Low frequency (time code) Time code leading edge used for epoch measurement Bn= 2/trtr= 1 ms Bandwidth = 2 000 Hz = 2 kHz 2K00K2XAN V. MISCELLANEOUS Orthogonal frequency division multiplexing (OFDM) or coded OFDM (COFDM) Bn= NsK 53 active sub-carriers are used, each spaced 312.5 kHz apart (K = 53 and Ns= 312.5 kHz). Data sub-carriers can be BPSK, QPSK, QAM modulated Bn= 312.5 kHz 53 = 16.6 MHz 16M6W7D
