RECOMMENDATION  ITU-R SM.1138*

 

DETERMINATION OF NECESSARY BANDWIDTHS INCLUDING EXAMPLES FOR THEIR CALCULATION AND ASSOCIATED
EXAMPLES FOR THE DESIGNATION OF EMISSIONS

(1995)

The ITU Radiocommunication Assembly,

   considering

a)    the Final Report and recommendations of the Voluntary Group of Experts (VGE) to study allocation and improved use of the radio-frequency spectrum and simplification of the Radio Regulations (RR) was established in accordance with Resolution No. 8 of the Plenipotentiary Conference (Nice, 1989) and continued its work in accordance with Resolution No. 8 of the Additional Plenipotentiary Conference (Geneva, 1992);

b)    that the 1995 World Radiocommunication Conference (WRC-95) will consider and adopt, as appropriate, proposals for the Simplified RR,

   recommends

1     that the formulae given in Annex 1 shall be used to calculate the necessary bandwidth when required by the RR.

_______________

* Reference has been made to this Recommendation in the Radio Regulations (RR) as revised by the World Radiocommunication

Conference 1995 (WRC-95). This will come into force on 1 June 1998.

 

ANNEX  1

Determination of necessary bandwidths including examples
for their calculation and associated examples
for the designation of emissions

 

For the full designation of an emission, the necessary bandwidth, indicated in four characters, shall be added just before the classification symbols. When used, the necessary bandwidth shall be determined by one of the following methods:

1) use of the formulae included in the following table which also gives examples of necessary bandwidths and designation of corresponding emissions;

2) computation in accordance with ITU-R Recommendations1 ;

3) measurement, in cases not covered by 1) or 2) above.

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 following terms have been employed:    

Bn = Necessary bandwidth in hertz
B = Modulation rate in bauds
N = Maximum possible number of black plus white elements to be transmitted per second, in facsimile
M = Maximum modulation frequency in hertz
C = Sub-carrier frequency in hertz
D = Peak deviation, i.e., half the difference between the maximum and minimum values of the instantaneous frequency. The instantaneous frequency in hertz is the time rate of change in phase in radians divided by 2 pi
t = Pulse duration in seconds at half-amplitude
tr = Pulse rise time in seconds between 10% and 90% amplitude
K = An overall numerical factor which varies according to the emission and which depends upon the allowable signal  distortion
Nc = Number of baseband channels in radio systems employing multi-channel multiplexing
fp = Continuity pilot sub-carrier frequency (Hz) (continuous signal utilized to verify performance of frequency-division multiplex systems).   

Description of Emission Necessary Bandwidth Designation of Emission
Formula Sample Calculation
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 non­fading circuits
25 words per minute;
B = 20, 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 non­fading 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
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 = 2M + 2DK
M=B/2
B = 50
D = 35 Hz (70 Hz shift)
K = 1.2
Bandwidth:
134 Hz
134HJ2BCN
Telegraphy, multi­channel with voice frequency, error­correction,
some channels are time­division multiplexed, single­sideband,
reduced carrier
Bn = highest central frequency + M + DK
M=B/2
15 channels;
highest central 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, double­sideband
(single channel)
Bn = 2M M = 3 000
Bandwidth:
6 000 Hz
= 6 kHz
6K00A3EJN
Telephony, single­sideband,
full carrier
(single channel)
Bn = M M = 3 000
Bandwidth:
3 000 Hz
= 3 kHz
3K00H3EJN
Telephony, single­sideband,
suppressed carrier (single channel)
Bn = M -
lowest modulation frequency
M = 3 000
lowest modulation frequency is 300 Hz
Bandwidth:
2 700 Hz
= 2.7 kHz
2K70J3EJN
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 is 2 990 Hz
M = 2 990
Bandwidth:
2 990 Hz
= 2.99 kHz
2K99R3ELN
Telephony with privacy, single-sideband, suppressed carrier
(two or more channels)
Bn = Nc M -
lowest modulation frequency
in the lowest channel
Nc = 2
M = 3 000
lowest modulation frequency is 250 Hz
Bandwidth:
5 750 Hz
= 5.75 kHz
5K75J8EKF
Telephony, 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
Description of Emission Necessary Bandwidth Designation of Emission
Formula Sample Calculation
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
Bandwidth:
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 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;
Nominal 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 emission with reduced carrier, monochrome
Bn =
C + N/2 + 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:
2 890 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
=N/2
K = 1.1 (typically)
N = 1 100
D = 400 Hz
Bandwidth:
1 980 Hz
= 1.98 kHz
1K98J3C --
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 × 106
D = 50 × 103 Hz
M = 15 000
Bandwidth:
13.13 × 106 Hz
= 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 omnidirectional
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 frequency modulated by a 30 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
20K9A9WWF
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. CCIR Rec. 348-2).
3 telephone channels and 15 telegraphy channels require the bandwidth
12 000 Hz
= 12 kHz
12K0B9WWF
Description of Emission Necessary Bandwidth Designation of Emission
Formula Sample Calculation
III-A. FREQUENCY MODULATION
1. Signal with Quantized or Digital Information
Telegraphy without error-correction
(single channel)

Bn
= 2M + 2DK

M = B/2

K = 1.2 (typically)

B = 100
D = 85 Hz
(170 Hz shift)
Bandwidth:
304 Hz
304HF1BBN
Telegraphy,
narrow-band direct­printing with error-correction
(single channel)

Bn
= 2M + 2DK

M = B/2

K = 1.2 (typically)

B = 100
D = 85 Hz
(170 Hz shift)
Bandwidth:
304 Hz
304HF1BCN
Selective calling
signal

Bn
= 2M + 2DK

M = B/2

K = 1.2 (typically)

B = 100
D = 85 Hz
(170 Hz shift)
Bandwidth:
304 Hz
304HF1BCN
Four-frequency duplex telegraphy
Bn
= 2M + 2DK
B
= Modulation rate in bauds of the faster channel.
If the channels are synchronized:

M = B/2

(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)
Commercial
telephony
Bn = 2M + 2DK
K
= 1
(typically, but under certain conditions a higher value 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
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

M = N/2

K = 1.1 (typically)

N = 1 100 elements/sec;
D = 400 Hz
Bandwidth:
1 980 Hz
= 1.98 kHz
1K98F1C --
Analogue facsimile
Bn
= 2M + 2DK

M = N/2

K = 1.1 (typically)

N = 1 100 elements/sec;
D = 400 Hz
Bandwidth:
1 980 Hz
= 1.98 kHz
1K98F3C --
5. Composite Emissions (see Table III-B)
Radio-relay system, frequency division multiplex 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 × 106 Hz;

fp = 0.331 × 106 Hz;

Bandwidth:
3.702 × 106 Hz
= 3.702 MHz

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 per­channel deviation:
200 kHz;
continuity pilot at 4 715 kHz produces 140 kHz rms deviation
of main carrier.
D = 200 × 103 × 3.76
× 5.5 = 4.13 × 106 Hz;
M = 4.028 × 106;

fp = 4.715 × 106;
(2M + 2DK) > 2 fp

Bandwidth:
16.32 × 106 Hz
= 16.32 MHz

16M3F8EJF
Radio-relay system, frequency division multiplex Bn = 2fp 600 telephone channels occupying baseband between 60 kHz and
2 540 kHz;
rms per-channel deviation: 200 kHz;
continuity pilot at 8 500 kHz produces 140 kHz rms deviation
of main carrier.
D = 200 × 103 × 3.76
× 4.36 = 3.28 × 106 Hz;
M = 2.54 × 106;
K = 1;

fp = 8.5 × 106;
(2M + 2DK) < 2 fp

Bandwidth:
17 × 106 Hz = 17 MHz

17M0F8EJF
Stereophonic sound broadcasting with multiplexed subsidiary telephony sub-carrier Bn = 2M + 2DK

K
= 1 (typically)
Pilot tone system;
M = 75 000
D = 75 000 Hz
Bandwidth:
300 000 Hz = 300 kHz
300KF8EHF


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 D, or peak frequency deviation, in these formulae for Bn is 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 becomes:

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 either

Bn = 2fp or Bn = 2M + 2DK

whichever is greater.

Number of
telephone channels
Nc
Multiplying factor 1
(peak factor) × antilog
value in dB above modulation reference level
________________________________
20
3 < Nc < 12 4.47 × antilog
value in dB specified by the equipment manufacturer or station license, subject to administration approval
________________________________
20
12< Nc < 60 3.76 × antilog
2.6 + 2 log Nc
____________________
20

_______________

1 In the above chart, the multipliers 3.76 and 4.47 correspond to peak factors of 11.5 dB and 13.0 dB, respectively.

 

Number of
telephone channels
Nc
Multiplying factor 1
(peak factor) × antilog
value in dB above modulation reference level
_______________________________
20
60 < Nc < 240 3.76 × antilog
-1 + 4 log Nc
___________________
20
Nc < 240 3.76 × antilog
-15 + 10 log Nc
____________________
20

_______________

1 In the above chart, the multiplier 3.76 corresponds to a peak factor of 11.5 dB.

 

Description of Emission Necessary Bandwidth Designation of Emission
Formula Sample Calculation
IV. PULSE MODULATION
1. Radar
Unmodulated pulse emission Bn = 2K / t

K depends upon the ratio of pulse duration to pulse rise time. Its value usually
falls between 1and 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:

Bandwidth:
3 × 106 Hz
= 3 MHz

3M00P0NAN
2. Composite Emissions
Radio-relay system Bn = 2K / t
K = 1.6
Pulse position modulated by 36 voice channel baseband; pulse width at half amplitude = 0.4 ms
Bandwidth:
8 × 106 Hz
= 8 MHz
(Bandwidth independent of the number of voice channels)
8M00M7EJT

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