Radio Frequency by Steve Winder and Joe Carr - HTML preview

2.2 Decibels referred to absolute values

While the decibel scale expresses ratios only, if a reference value is added to the statement as a suffix it can be used to refer to absolute values. For example, a loss of 10 dB means a reduction in power to a level equal to one tenth of the original and if the statement is −10 dBm the level referred to is 1/10 of a milliwatt. Commonly used suffixes and, where applicable, their absolute reference levels are as follows. Table 2.2 shows the relative levels in decibels at 50 ohms impedance.

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Table 2.1 The decibel figures are in the centre column: figures to the left represent decibel loss, and those to the right decibel gain. The voltage and current figures are given on the assumption that there is no change in impedance

Voltage or Power dB current ratio ←− ratio +→

Voltage or Power current ratio ratio

1.000 1.000 0
0.989 0.977 0.1
0.977 0.955 0.2
0.966 0.933 0.3
0.955 0.912 0.4
0.944 0.891 0.5
0.933 0.871 0.6
0.912 0.832 0.8
0.891 0.794 1.0
0.841 0.708 1.5
0.794 0.631 2.0
0.750 0.562 2.5
0.708 0.501 3.0
0.668 0.447 3.5
0.631 0.398 4.0
0.596 0.355 4.5
0.562 0.316 5.0
0.501 0.251 6.0
0.447 0.200 7.0
0.398 0.159 8.0
0.355 0.126 9.0
0.316 0.100 10
0.282 0.0794 11
0.251 0.0631 12
0.224 0.0501 13
0.200 0.0398 14
0.178 0.0316 15
0.159 0.0251 16
0.126 0.0159 18
0.100 0.0100 20
3.16× 10⁻² 10⁻³ 30
10⁻² 10⁻⁴ 40
3.16× 10⁻³ 10⁻⁵ 50
10⁻³ 10⁻⁶ 60
3.16× 10⁻⁴ 10⁻⁷ 70
10⁻⁴ 10⁻⁸ 80
3.16× 10⁻⁵ 10⁻⁹ 90
10⁻⁵ 10⁻¹⁰ 100
3.16× 10⁻⁶ 10⁻¹¹ 110
10⁻⁶ 10⁻¹² 120 Table 2.2 Relative levels in decibels at 50 ohms impedance

1.000 1.000
1.012 1.023
1.023 1.047
1.035 1.072
1.047 1.096
1.059 1.122
1.072 1.148
1.096 1.202
1.122 1.259
1.189 1.413
1.259 1.585
1.334 1.778
1.413 1.995
1.496 2.239
1.585 2.512
1.679 2.818
1.778 3.162
1.995 3.981
2.239 5.012
2.512 6.310
2.818 7.943
3.162 10.00
3.55 12.6
3.98 15.9
4.47 20.0
5.01 25.1
5.62 31.6
6.31 39.8
7.94 63.1 10.00 100.0
3.16× 10 10³ 10² 10⁴
3.16× 10² 10⁵ 10³ 10⁶
3.16× 10³ 10⁷ 10⁴ 10⁸
3.16× 10⁴ 10⁹ 10⁵ 10¹⁰
3.16× 10⁵ 10¹¹ 10⁶ 10¹²

dB µV Voltage dBV dBm dBW Power −20 100 nV −140 −127 −157 200 aW −19 115 −139 −126 −156 250 −18 125 −138 −125 −155 315 −17 140 −137 −124 −154 400 ₋16 160₋136₋123₋153 500 −15 180 −135 −122 −152 630 ₋14 200₋134₋121₋151 800 −13 225 −133 −120 −150 1 fW −12 250 −132 −119 −149 1.25 −11 280 −131 −118 −148 1.6 −10 315 −130 −117 −147 2.0 −9 355 −129 −116 −146 2.5 −8 400 −128 −115 −145 3.15 −7 450 −127 −114 −144 4.0 −6 500 −126 −113 −143 5.0 −5 565 −125 −112 −142 6.3 −4 630 −124 −111 −141 8.0 ₋3 710₋123₋110₋140 10 −2 800 −122 −109 −139 12.5 ₋1 900₋121₋108₋138 16 01µV −120 −107 −137 20 11.15 −119 −106 −136 25 21.25 −118 −105 −135 31.5 31.4 −117 −104 −134 40 41.6 −116 −103 −133 50 51.8 −115 −102 −132 63 62.0 −114 −101 −131 80 72.25 −113 −100 −130 100 82.5 −112 −99 −129 125 92.8 −111 −98 −128 160 10 3.15₋110₋97₋127 200 11 3.55 −109 −96 −126 250 12 4.0₋108₋95₋125 315 13 4.5 −107 −94 −124 400 14 5.0 −106 −93 −123 500 15 5.65 −105 −92 −122 630 16 6.3 −104 −91 −121 800 17 7.1 −103 −90 −120 1 pW 18 8.0 −102 −89 −119 1.25 19 9.0 −101 −88 −118 1.6 20 10.0 −100 −87 −117 2.0 21 11.5 −99 −86 −116 2.5 22 12.5 −98 −85 −115 3.15 23 14 −97 −84 −114 4.0 24 16 −96 −83 −113 5.0 25 18₋95₋82₋112 6.3
dB µV Voltage dBV dBm dBW Power 26 20 −94 −81 −111 8.0 27 22.5 −93 −80 −110 10 28 25 −92 −79 −109 12.5 29 28 −91 −78 −108 16 30 31.5₋90₋77₋107 20 31 35.5 −89 −76 −106 25 32 40₋88₋75₋105 31.5 33 45 −87 −74 −104 40 34 50 −86 −73 −103 50 35 56.5 −85 −72 −102 63 36 63 −84 −71 −101 80 37 71 −83 −70 −100 100 38 80 −82 −69 −99 125 39 90 −81 −68 −98 160 40 100 −80 −67 −97 200 41 115 −79 −66 −96 250 42 125 −78 −65 −95 315 43 140 −77 −64 −94 400 44 160 −76 −63 −93 500 45 180₋75₋62₋92 630 46 200 −74 −61 −91 800 47 225₋73₋60₋90 1 nW 48 250 −72 −59 −89 1.25 49 280 −71 −58 −88 1.6 50 315 −70 −57 −87 2.0 51 355 −69 −56 −86 2.5 52 400 −68 −55 −85 3.15 53 450 −67 −54 −84 4.0 54 500 −66 −53 −83 5.0 55 565 −65 −52 −82 6.3 56 630 −64 −51 −81 8.0 57 710 −63 −50 −80 10 58 800₋62₋49₋79 12.5 59 900 −61 −48 −78 16 60 1 mV₋60₋47₋77 20 61 1.15 −59 −46 −76 25 62 1.25 −58 −45 −75 31.5 63 1.4 −57 −44 −74 40 64 1.6 −56 −43 −73 50 65 1.8 −55 −42 −72 63 66 2.0 −54 −41 −71 80 67 2.25 −53 −40 −70 100 68 2.5 −52 −39 −69 125 69 2.8 −51 −38 −68 160 70 3.15 −50 −37 −67 200 71 3.55 −49 −36 −66 250 72 4.0 −48 −35 −65 315
dB µV Voltage dBV dBm dBW Power

73 4.5 −47 −34 −64 400
74 5.0 −46 −33 −63 500
75 5.65 −45 −32 −62 630
76 6.3 −44 −31 −61 800
77 7.1₋43₋30₋60 1_µW
78 8.0 −42 −29 −59 1.25
79 9.0₋41₋28₋58 1.6
80 10 mV −40 −27 −57 2.0
81 11.5 −39 −26 −56 2.5
82 12.5 −38 −25 −55 3.15
83 14 −37 −24 −54 4.0
84 16 −36 −23 −53 5.0
85 18 −35 −22 −52 6.3
86 20 −34 −21 −51 8.0
87 22.5 −33 −20 −50 10
88 25 −32 −19 −49 12.5
89 28 −31 −18 −48 16
90 31.5 −30 −17 −47 20
91 35.5 −29 −16 −46 25
92 40₋28₋15₋45 31.5
93 45 −27 −14 −44 40
94 50₋26₋13₋43 50
95 56.5 −25 −12 −42 63
96 63 −24 −11 −41 80
97 71 −23 −10 −40 100
98 80 −22 −9 −39 125
99 90 −21 −8 −38 160
100 100 −20 −7 −37 200
101 115 −19 −6 −36 250
102 125 −18 −5 −35 315
103 140 −17 −4 −34 400
104 160 −16 −3 −33 500
105 180₋15₋2₋32 630
106 200 −14 −1 −31 800
107 225₋13 0₋30 1 mW 108 250 −12 1 −29 1.25 109 280 −11 2 −28 1.6 110 315 −10 3 −27 2.0 111 355 −94 −26 2.5 112 400 −85 −25 3.15 113 450 −76 −24 4.0 114 500 −67 −23 5.0 115 565 −58 −22 6.3 116 630 −49 −21 8.0 117 710 −310 −20 10
118 800 −211 −19 12.5

dB µV Voltage dBV dBm dBW Power

119 900 −112 −18 16
120 1 V 0 13 −17 20
121 1.15 1 14 −16 25
122 1.25 2 15 −15 31.5
123 1.4 3 16₋14 40
124 1.6 4 17 −13 50
125 1.8 5 18₋12 63
126 2.0 6 19 −11 80
127 2.25 7 20 −10 100
128 2.5 8 21 −9 125
129 2.8 9 22 −8 160
130 3.15 10 23 −7 200
131 3.55 11 24 −6 250
132 4.0 12 25 −5 315
133 4.5 13 26 −4 400
134 5.0 14 27 −3 500
135 5.65 15 28 −2 630
136 6.3 16 29 −1 800
137 7.1 17 30 0 1 W
138 8.0 18 31 1 1.25
139 9.0 19 32 2 1.6
140 10 20 33 3 2.0
141 11.5 21 34 4 2.5
142 12.5 22 35 5 3.15
143 14 23 36 6 4.0
144 16 24 37 7 5.0
145 18 25 38 8 6.3
146 20 26 39 9 8.0
147 22.5 27 40 10 10
148 25 28 41 11 12.5
149 28 29 42 12 16
150 31.5 30 43 13 20
151 35.5 31 44 14 25
152 40 32 45 15 31.5
153 45 33 46 16 40
154 50 34 47 17 50
155 56.5 35 48 18 63
156 63 36 49 19 80
157 71 37 50 20 100
158 80 38 51 21 125
159 90 39 52 22 160
160 100 40 53 23 200
161 115 41 54 24 250
162 125 42 55 25 315
163 140 43 56 26 400
164 160 44 57 27 500
165 180 45 58 28 630

dB µV Voltage dBV dBm dBW Power

166 200 46 59 29 800
167 225 47 60 30 1 kW
168 250 48 61 31 1.25
169 280 49 62 32 1.6
170 315 50 63 33 2.0
171 355 51 64 34 2.5
172 400 52 65 35 3.15
173 450 53 66 36 4.0
174 500 54 67 37 5.0
175 565 55 68 38 6.3
176 630 56 69 39 8.0
177 710 57 70 40 10
178 800 58 71 41 12.5
179 900 59 72 42 16
180 1 kV 60 73 43 20

Decibel glossary

dBa stands for dB ‘adjusted’. This is a weighted circuit noise power referred to −85 dBm, which is 0 dBa. (Historically measured with a noise meter at the receiving end of a line. The meter is calibrated on a 1000 Hz tone such that 1 mW (0 dBm) gives a reading of +85 dBm. If the 1 mW is spread over the band 300–3400 Hz as random white noise, the meter will read +82 dBa.)

dBa0 circuit noise power in dBa referred to, or measured at, a point of zero relative transmission level (0 dBr). (A point of zero relative transmission level is a point arbitrarily established in a transmission circuit. All other levels are stated relative to this point.) It is preferable to convert circuit noise measurement values from dBa to dBa0 as this makes it unnecessary to know or to state the relative transmission level at the point of measurement.

dBd used for expressing the gain of an antenna referred to a dipole. dBi used for expressing the gain of an antenna referred to an isotropic radiator.

dB µV decibels relative to 1 microvolt.
dbm decibels relative to 1 milliwatt. The term dBm was originally used for telephone and audio work and, when used in that context, implies an impedance of 600 , the nominal impedance
of a telephone line. When it is desired to define a relative
transmission level in a circuit, dBr is preferred.

Table 2.3 Binary decibel values Bits Max. value Decibels (dB)

12 6.02
24 12.04
38 18.06
416 24.08
532 30.10
664 36.12
7 128 42.14
8 256 48.16
9 512 54.19
10 1024 60.21
11 2048 66.23
12 4096 72.25
13 8192 78.27
14 16 384 84.29
15 32 768 90.31
16 65 536 96.33
17 131 072 102.35
18 262 144 108.37
19 524 288 114.39
20 1 048 576 120.41
21 2 097 152 126.43
22 4 194 304 132.45
23 8 388 608 138.47
24 16 777 216 144.49
25 33 554 432 150.51
26 67 108 864 156.54
27 134 217 728 162.56
28 268 435 456 168.58
29 536 870 912 174.60
30 1 073 741 824 180.62
31 2 147 483 648 186.64
32 4 294 967 296 192.66

dBm0 dBm referred to, or measured at, a point of zero transmission level.
dBmp a unit of noise power in dBm, measured with psophometric weighting. dBmp= 10 log₁₀ pWp− 90= dBa− 84= dBm− 2.5 (for flat noise 300–3400 Hz).
pWp= picowatts psophometrically weighted.
dBm0p the abbreviation for absolute noise power in dBm referred to or measured at a point of zero relative transmission level, psophometrically weighted.
dBr means dB ‘relative level’. Used to define transmission level at various points in a circuit or system referenced to the zero transmission level point.
dBrn a weighted circuit noise power unit in dB referenced to 1 pW (−90 dBm) which is 0 dBrn.
dBrnc weighted noise power in dBrn, measured by a noise measuring set with ‘C-message’ weighting.
dBrnc0 noise measured in dBrnc referred to zero transmission level point.
dBu decibels relative to 0.775 V, the voltage developed by 1 mW when applied to 600 . dBu is used in audio work when the impedance is not 600 and no specific impedance is implied.
dbV decibels relative to 1 volt.
dbW decibels relative to 1 watt.

Note: To convert dBm to dBµV add 107 (e.g. −20 dBm=−20+ 107= 87 dBµV.

The beauty of decibel notation is that system gains and losses can be computed using addition and subtraction rather than multiplication and division. For example, suppose a system consists of an antenna that delivers a −4.7 dBm signal at its terminals (we conveniently neglect the antenna gain by this ploy). The antenna is connected to a 40 dB low-noise amplifier (A1) at the head end, and then through a 370 metre long coaxial cable to a 20 dB gain amplifier (A2), with aloss(L1) of −48 dB. The amplifier is followed by a bandpass filter with a−2.8 dB insertion loss (L2), and a−10 dB attenuator (L3). How does the signal exist at the end of this cascade chain?

S1 −4.7 dBm A1 40.0 dB A2 20.0 dB L1 −48.0 dB L2 −2.8 dB L3 −10.0 dB Total: −5.5 dBm

Converting dBm to watts

P

 

=

 

10dBm/10 1000

Converting any dB to ratio

Power levels:

 

^P1 _{= 10}dB/10

 

P2

 

Voltage levels:

 

^V1 _{= 10}dB/20

 

V2

 

^I1 = 10^dB/20Current levels:_I2

Binary decibel values

Binary numbers are used in computer systems. With the digitization of RF systems it is necessary to understand the decibel values of binary numbers. These binary numbers might be from an analogue-to-digital converter (ADC or A/D) that digitizes the IF amplifier output, or a digital-to-analogue converter (DAC or D/A) used to generate the analogue signal in a direct digital synthesis (DDS) signal generator.