Title 47
SECTION 2.202
2.202 Bandwidths.
§ 2.202 Bandwidths.(a) Occupied bandwidth. The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission. In some cases, for example multichannel frequency-division systems, the percentage of 0.5 percent may lead to certain difficulties in the practical application of the definitions of occupied and necessary bandwidth; in such cases a different percentage may prove useful.
(b) Necessary bandwidth. For a given class of emission, the minimum value of the occupied bandwidth sufficient to ensure the transmission of information at the rate and with the quality required for the system employed, under specified conditions. Emissions useful for the good functioning of the receiving equipment as, for example, the emission corresponding to the carrier of reduced carrier systems, shall be included in the necessary bandwidth.
(1) The necessary bandwidth shall be expressed by three numerals and one letter. The letter occupies the position of the decimal point and represents the unit of bandwidth. The first character shall be neither zero nor K, M or G.
(2) Necessary bandwidths:
between 0.001 and 999 Hz shall be expressed in Hz (letter H); between 1.00 and 999 kHz shall be expressed in kHz (letter K); between 1.00 and 999 MHz shall be expressed in MHz (letter M); between 1.00 and 999 GHz shall be expressed in GHz (letter G).(3) Examples:
- 0.002 Hz - H002
- 0.1 Hz - H100
- 25.3 Hz - 25H3
- 400 Hz - 400H
- 2.4 kHz - 2K40
- 6 kHz - 6K00
- 12.5 kHz - 12K5
- 180.4 kHz - 180K
- 180.5 kHz - 181K
- 180.7 kHz - 181K
- 1.25 MHz - 1M25
- 2 MHz - 2M00
- 10 MHz - 10M0
- 202 MHz - 202M
- 5.65 GHz - 5G65
(c) The necessary bandwidth may be determined by one of the following methods:
(1) Use of the formulas included in the table, in paragraph (g) of this section, which also gives examples of necessary bandwidths and designation of corresponding emissions;
(2) For frequency modulated radio systems which have a substantially linear relationship between the value of input voltage to the modulator and the resulting frequency deviation of the carrier and which carry either single sideband suppressed carrier frequency division multiplex speech channels or television, computation in accordance with provisions of paragraph (f) of this section and formulas and methods indicated in the table, in paragraph (g) of this section;
(3) Computation in accordance with Recommendations of the International Radio Consultative Committee (C.C.I.R.);
(4) Measurement in cases not covered by paragraph (c) (1), (2), or (3) of this section.
(d) The value so determined should be used when the full designation of an emission is required. However, the necessary bandwidth so determined is not the only characteristic of an emission to be considered in evaluating the interference that may be caused by that emission.
(e) In the formulation of the table in paragraph (g) of this section, the following terms are 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 frequency 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 t = Pulse duration in seconds at half-amplitude tr = Pulse rise time in seconds between 10% and 90% of maximum amplitude K = An overall numerical factor which varies according to the emission and which depends upon the allowable signal distortion. Nc = Number of baseband telephone channels in radio systems employing multichannel multiplexing P = Continuity pilot sub-carrier frequency (Hz) (continuous signal utilized to verify performance of frequency-division multiplex systems).(f) Determination of values of D and Bn for systems specified in paragraph (c)(2) of this section:
(1) Determination of D in systems for multichannel telephony:
(i) The rms value of the per-channel deviation for the system shall be specified. (In the case of systems employing preemphasis or phase modulation, this value of per-channel deviation shall be specified at the characteristic baseband frequency.)
(ii) The value of D is then calculated by multiplying the rms value of the per-channel deviation by the appropriate factors, as follows:
| Number of message circuits | Multiplying factors | Limits of X (Pavg (dBmO)) |
|---|---|---|
| More than 3, but less than 12 | 4.47 × [a factor specified by the equipment manufacturer or station licensee, subject to Commission approval] | |
| 3.76 antilog (X + 2 log10 Nc) | ||
| At least 12, but less than 60 | - - - - - - - - - - - - - | X: −2 to + 2.6. |
| 20 | ||
| 3.76 antilog (X + 4 log10 Nc) | ||
| At least 60, but less than 240 | - - - - - - - - - - - - - | X: −5.6 to −1.0. |
| 20 | ||
| 3.76 antilog (X + 10 log10 Nc) | ||
| 240 or more | - - - - - - - - - - - - - | X: −19.6 to −15.0. |
| 20 |
Where X represents the average power in a message circuit in dBmO; Nc is the number of circuits in the multiplexed message load; 3.76 corresponds to a peak load factor of 11.5 dB.
(2) The necessary bandwidth (Bn) normally is considered to be numerically equal to:
(i) 2M + 2DK, for systems having no continuity pilot subcarrier or having a continuity pilot subcarrier whose frequency is not the highest modulating the main carrier;
(ii) 2P + 2DK, for systems having a continuity pilot subcarrier whose frequency exceeds that of any other signal modulating the main carrier, unless the conditions set forth in paragraph (f)(3) of this section are met.
(3) As an exception to paragraph (f)(2)(ii) of this section, the necessary bandwidth (Bn) for such systems is numerically equal to 2P or 2M + 2DK, whichever is greater, provided the following conditions are met:
(i) The modulation index of the main carrier due to the continuity pilot subcarrier does not exceed 0.25, and
(ii) In a radio system of multichannel telephony, the rms frequency deviation of the main carrier due to the continuity pilot subcarrier does not exceed 70 percent of the rms value of the per-channel deviation, or, in a radio system for television, the rms deviation of the main carrier due to the pilot does not exceed 3.55 percent of the peak deviation of the main carrier.
(g) Table of necessary bandwidths:
| Description of emission | Necessary bandwidth | Designation of emission | |
|---|---|---|---|
| Formula | Sample calculation | ||
| I. NO MODULATING SIGNAL | |||
| Continuous wave emission | N0N (zero) | ||
| II. AMPLITUDE MODULATION | |||
| 1. Signal With Quantized or Digital Information | |||
| Continuous wave telegraphy | Bn = BK, K = 5 for fading circuits, K = 3 for non-fading circuits | 25 words per minute; B = 20, K = 5, Bandwidth: 100 Hz | 100HA1A |
| Telegraphy by on-off keying of a tone modulated carrier | Bn = BK + 2M, K = 5 for fading circuits, K = 3 for non-fading circuits | 25 words per minute; B = 20, M = 1000, K = 5, Bandwidth: 2100 Hz = 2.1 kHz | 2K10A2A |
| Selective calling signal, single-sideband full carrier | Bn = M | Maximum code frequency is: 2110 Hz, M = 2110, Bandwidth: 2110 Hz = 2.11 kHz | 2K11H2B |
| Direct-printing telegraphy using a frequency shifted modulating sub-carrier single-sideband suppressed carrier | Bn = 2M + 2DK, M = B ÷ 2 | B = 50, D = 35 Hz (70 Hz shift), K = 1.2, Bandwidth: 134 Hz | 134HJ2B |
| Telegraphy, single sideband reduced carrier | Bn = central frequency + M + DK, M = B ÷ 2 | 15 channels; highest central frequency is: 2805 Hz, B = 100, D = 42.5 Hz (85 Hz shift), K = 0.7 Bandwidth: 2.885 Hz = 2.885 kHz | 2K89R7B |
| 2. Telephony (Commercial Quality) | |||
| Telephony double-sideband | Bn = 2M | M = 3000, Bandwidth = 6000 Hz = 6 kHz | 6K00A3E |
| Telephony, single-sideband, full carrier | Bn = 2M | M = 3000, Bandwidth: 3000 Hz = 3 kHz | 3K00H3E |
| Telephony, single-sideband suppressed carrier | Bn = M−lowest modulation frequency | M = 3000, lowest modulation frequency is 3000 Hz, 2700 Hz Bandwidth: 2700Hz = 2.7 kHz | 2K70J3E |
| Telephony with separate frequency modulated signal to control the level of demodulated speech signal, single-sideband, reduced carrier | Bn = M | Maximum control frequency is 2990 Hz, M = 2990, Bandwidth: 2990 Hz = 2.99 kHz | 2K99R3E |
| Telephony with privacy, single-sideband, suppressed carrier (two or more channels) | Bn = Nc M−lowest modulation frequency in the lowest channel | Nc = 2, M = 3000 lowest modulation frequency is 250 Hz, Bandwidth: 5750 Hz = 5.75 kHz | 5K75J8E |
| Telephony, independent sideband (two or more channels) | Bn = sum of M for each sideband | 2 channels, M = 3000, Bandwidth: 6000 Hz = 6 kHz | 6K00B8E |
| 3. Sound Broadcasting | |||
| Sound broadcasting, double-sideband | Bn = 2M, M may vary between 4000 and 10000 depending on the quality desired | Speech and music, M = 4000, Bandwidth: 8000 Hz= 8 kHz | 8K00A3E |
| Sound broadcasting, single-sideband reduced carrier (single channel) | Bn = M, M may vary between 4000 and 10000 depending on the quality desired | Speech and music, M = 4000, Bandwidth: 4000 Hz= 4 kHz | 4K00R3E |
| Sound broadcasting, single-sideband, suppressed carrier | Bn = M−lowest modulation frequency | Speech and music, M = 4500, lowest modulation frequency = 50 Hz, Bandwidth: 4450 Hz = 4.45 kHz | 4K45J3E |
| 4. Television | |||
| Television, vision and sound | Refer to CCIR documents for the bandwidths of the commonly used television systems | Number of lines = 525; Nominal video bandwidth: 4.2 MHz, Sound carrier relative to video carrier = 4.5 MHz | 5M75C3F |
| Total vision bandwidth: 5.75 MHz; FM aural bandwidth including guardbands: 250,000 Hz | 250KF3E | ||
| Total bandwidth: 6 MHz | 6M25C3F | ||
| 5. Facsimile | |||
| Analogue facsimile by sub-carrier frequency modulation of a single-sideband emission with reduced carrier | Bn = C−N ÷ 2 + DK, K = 1.1 (typically) | N = 1100, 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 = 1900, D = 400 Hz, Bandwidth = 2.890 Hz = 2.89 kHz | 2K89R3C |
| 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 = 1100, D = 400 Hz, Bandwidth: 1980 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 subcarrier deviation = 50 kHz: C = 6.5 × 10 6 D = 50 × 10 3 Hz, M = 15,000, Bandwidth: 13.13 × 10 6 Hz = 13.13 MHz | 13M2A8W |
| Double-sideband radio relay system | Bn = 2M | 10 voice channels occupying baseband between 1 kHz and 164 kHz; M = 164,000 bandwith = 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 9960 Hz tone frequency modulated by a 30 Hz tone - a telephone channel - a 1020 Hz keyed tone for continual Morse identification. Cmax = 9960, M = 30, D = 480 Hz, Bandwidth: 20,940 Hz = 20.94 kHz | 20K9A9W |
| Independent sidebands; several telegraph channels together with several telephone channels | 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 | 12K0B9W |
| 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 | 304HF1B |
| Four-frequency duplex telegraphy | Bn2M + 2DK, B = Modulation rate in bands 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: 1420 Hz = 1.42 kHz | 1K42F7B |
| 2. Telephony (Commercial Quality) | |||
| Commercial telephony | Bn = 2M + 2DK, K = 1 (typically, but under conditions a higher value may be necessary | For an average case of commercial telephony, M = 3,000, Bandwidth: 16,000 Hz = 16 kHz | 16K0F3E |
| 3. Sound Broadcasting | |||
| Sound broadcasting | Bn = 2M + 2DK, K = 1 (typically) | Monaural, D = 75,000 Hz, M = 15,000, Bandwidth: 18,000 Hz = 180 kHz | 180KF3E |
| 4. Facsimile | |||
| Facsimile by direct frequency modulation of the carrier; black and white | Bn = 2M + 2DK, M = N ÷ 2, K = 1.1 (typically) | N = 1100 elements/sec; D = 400 Hz, Bandwidth: 1980 Hz = 1.98 kHZ | 1K98F1C |
| Analogue facsimile | Bn = 2M + 2DK, M = N ÷ 2, K = 1.1 (typically) | N = 1100 elements/sec; D = 400 Hz, Bandwidth: 1980 Hz = 1.98 kHz | 1K98F3C |
| 5. Composite Emissions (See Table III-B) | |||
| Radio-relay system, frequency division multiplex | Bn = 2P + 2DK, K = 1 | Microwave radio relay system specifications: 60 telephone channels occupying baseband between 60 and 300 kHz; rms per-channel deviation 200 kHz; pilot at 331 kHz produces 200 kHz rms deviation of main carrier. Computation of Bn:D = (200 × 10 33 × 3.76 × 1.19), Hz = 0.895 × 10 6, P = 0.331 × 10 6 Hz; Bandwidth: 2.452 × 10 6 Hz | 2M45F8E |
| Radio-relay system frequency division multiple | Bn = 2M + 2DK, K = 1 | Microwave radio relay relay systems specifications: 1200 telephone channels occupying baseband between 60 and 5564 kHz; rms per channel deviation 200 kHz; continunity pilot at 6199 kHz produces 140 kHz rms deviation of main carrier. Computation of Bn:D = (20 0 × 10 3 × 3.76 × 3.63) = 2.73 × 10 6; M = 5.64 × 10 6 Hz; P = 6.2 × 10 6 Hz; (2M + 2DK<2P; Bandwidth 16.59 × 10 6 Hz | 16M6F8E |
| Radio-relay system, frequency division multiplex | Bn = 2P | Microwave radio relay system specifications: Multiplex 600 telephone channels occupying baseband between 60 and 2540 kHz; continuity pilot at 8500 kHz produces 140 kHz rms deviation of main carrier. Computation of Bn:D = (200 × 10 3 × 3.76 × 2.565) = 1.93 × 10 6 Hz; M = 2.54 × 10 6 Hz; 2DK)≤2P Bandwidth: 17 × 10 6 Hz | 17M0F8E |
| Unmodulated pulse emission | Bn = 2K ÷ t, K depends upon the ratio of 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 t = 2 × range resolution ÷ velocity of light = 2 × 150 ÷ 3 × 10 8 = 1 × 10−6 seconds, Bandwidth: 3 × 10 6 Hz = 3 MHz | 3M00P0N |
| 6. 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 us, Bandwidth: 8 × 10 6 Hz = 8 MHz (Bandwidth independent of the number of voice channels) | 8M00M7E |
| Radio-relay system | Bn = 2K/t K = 1.6 |
Pulse position modulated by 36 voice channel baseband: pulse width at half amplitude 0.4 μS; Bn = 8 × 10 6 Hz = 8 MHz (Bandwidth independent of the number of voice channels) | 8M00M7E |
| Composite transmission digital modulation using DSB-AM (Microwave radio relay system) | Bn = 2RK/log2S | Digital modulation used to
send 5 megabits per second by use of amplitude modulation of the
main carrier with 4 signaling states R = 5 × 10 6 bits per second; K = 1; S = 4; Bn = 5 MHz |
5M00K7 |
| Binary Frequency Shift Keying | (0.03 <2D/R <1.0); Bn = 3.86D + 0.27R (1.0 <2D/R <2) Bn = 2.4D + 1.0R |
Digital modulation used to
send 1 megabit per second by frequency shift keying with 2
signaling states and 0.75 MHz peak deviation of the carrier R = 1 × 10 6 bps; D = 0.75 × 10 6 Hz; Bn = 2.8 MHz |
2M80F1D |
| Multilevel Frequency Shift Keying | Bn = (R/log2S) + 2DK | Digital modulation to send 10
megabits per second by use of frequency shift keying with four
signaling states and 2 MHz peak deviation of the main carrier R = 10 × 10 6 bps; D = 2 MHz; K = 1; S = 4; Bn = 9 MHz |
9M00F7D |
| Phase Shift Keying | Bn = 2RK/log2S | Digital modulation used to
send 10 megabits per second by use of phase shift keying with 4
signaling states R = 10 × 10 6 bps; K = 1; S = 4; Bn = 10 MHz |
10M0G7D |
| Quadrature Amplitude Modulation (QAM) | Bn = 2R/log2S | 64 QAM used to send 135 Mbps
has the same necessary bandwidth as 64-PSK used to send 135
Mbps; R = 135 × 10 6 bps; S = 64; Bn = 45 MHz |
45M0W |
| Minimum Shift Keying | 2-ary: Bn = R(1.18) 4-ary: Bn = R(2.34) |
Digital modulation used to
send 2 megabits per second using 2-ary minimum shift keying R = 2.36 × 10 6 bps; Bn = 2.36 MHz |
2M36G1D |