Conversion of dBm, dBmV and dBµV in CATV
Abstract: Cable TV systems are generally based on a 75Ω interface, but the impedance of most RF test equipment is 50Ω. This article describes some necessary conversions between power and level between these two environments. Two tables are provided to quickly find the appropriate conversion parameters.
More information:
The CATV system works in a 75Ω environment. Most of the standard test instruments equipped in RF laboratories use 50Ω as the standard interface impedance.
dBmV and dBµVMost CATV measurements are based on voltage and measured in dBmV or dBµV. According to the standard definition, dBmV is referenced to 1mVrms, and the output voltage (Vout) is measured in units of mVrms (EQN1). Since EQN1 obtains a voltage ratio, it can also be measured in units of mVpp when taking 1mVpp as a reference value; or it can be expressed in other voltage units, as long as they use the same units.
It can be seen from EQN1 that dBmV has nothing to do with impedance.
In the standard definition, dBµV is referenced to 1µVrms, and the output voltage (Vout) is measured in µVrms (EQN2). Because EQN2 obtains a voltage ratio, it can also be measured in units of µVpp when taking 1µVpp as a reference; or it can be expressed in other voltage units, as long as they use the same units.
It can be seen from EQN2 that dBµV has nothing to do with impedance.
Conversion between dBm and dBmVEQN3 gives the definition of dBm.
The unit of measurement for Pout is mW, and dBm is referenced to 1mW. EQN3 is related to load impedance, as shown in EQN4. Most RF equipment has a 50Ω load and input impedance. EQN3 is correct for any load impedance, including 75Ω loads.
The power depends on the load impedance. EQN4 establishes the relationship between power and output voltage and load impedance.
Organize all available:
Solve EQN3 and get Pout,
Solve for EQN1 and get Vout,
Substitute EQN3.1 and EQN1.1 into EQN4.1,
Express dBmV in dBm,
When R = 50Ω,
EQN5.2 is suitable for measuring devices with an impedance of 50Ω.
When R = 75Ω, solving EQN5.1 gives:
EQN5.3 is suitable for measuring equipment with an impedance of 75Ω.
Using the same method, the relationship between dBµV and dBmV can be obtained as follows,
Table 1 and Table 2 show the conversion relationship between dBmV, dBµV and dBm under the conditions of 50Ω and 75Ω respectively.
Table 1. Power conversion at 50Ω impedance
| dBmV | dBµV | dBm 50Ω | mVrms | mW 50Ω |
| 8 | 68 | -38.99 | 2.51 | 1.3E-04 |
| 9 | 69 | -37.99 | 2.82 | 1.6E-04 |
| 10 | 70 | -36.99 | 3.16 | 2.0E-04 |
| 11 | 71 | -35.99 | 3.55 | 2.5E-04 |
| 12 | 72 | -34.99 | 3.98 | 3.2E-04 |
| 13 | 73 | -33.99 | 4.47 | 4.0E-04 |
| 14 | 74 | -32.99 | 5.01 | 5.0E-04 |
| 15 | 75 | -31.99 | 5.62 | 6.3E-04 |
| 16 | 76 | -30.99 | 6.31 | 8.0E-04 |
| 17 | 77 | -29.99 | 7.08 | 1.0E-03 |
| 18 | 78 | -28.99 | 7.94 | 1.3E-03 |
| 19 | 79 | -27.99 | 8.91 | 1.6E-03 |
| 20 | 80 | -26.99 | 10.00 | 2.0E-03 |
| twenty one | 81 | -25.99 | 11.22 | 2.5E-03 |
| twenty two | 82 | -24.99 | 12.59 | 3.2E-03 |
| twenty three | 83 | -23.99 | 14.13 | 4.0E-03 |
| twenty four | 84 | -22.99 | 15.85 | 5.0E-03 |
| 25 | 85 | -21.99 | 17.78 | 6.3E-03 |
| 26 | 86 | -20.99 | 19.95 | 8.0E-03 |
| 27 | 87 | -19.99 | 22.39 | 0.010 |
| 28 | 88 | -18.99 | 25.12 | 0.013 |
| 29 | 89 | -17.99 | 28.18 | 0.016 |
| 30 | 90 | -16.99 | 31.62 | 0.020 |
| 31 | 91 | -15.99 | 35.48 | 0.025 |
| 32 | 92 | -14.99 | 39.81 | 0.032 |
| 33 | 93 | -13.99 | 44.67 | 0.040 |
| 34 | 94 | -12.99 | 50.12 | 0.050 |
| 35 | 95 | -11.99 | 56.23 | 0.063 |
| 36 | 96 | -10.99 | 63.10 | 0.080 |
| 37 | 97 | -9.99 | 70.79 | 0.100 |
| 38 | 98 | -8.99 | 79.43 | 0.126 |
| 39 | 99 | -7.99 | 89.13 | 0.159 |
| 40 | 100 | -6.99 | 100.00 | 0.200 |
| 41 | 101 | -5.99 | 112.20 | 0.252 |
| 42 | 102 | -4.99 | 125.89 | 0.317 |
| 43 | 103 | -3.99 | 141.25 | 0.399 |
| 44 | 104 | -2.99 | 158.49 | 0.502 |
| 45 | 105 | -1.99 | 177.83 | 0.632 |
| 46 | 106 | -0.99 | 199.53 | 0.796 |
| 47 | 107 | 0.01 | 223.87 | 1.002 |
| 48 | 108 | 1.01 | 251.19 | 1.262 |
| 49 | 109 | 2.01 | 281.84 | 1.589 |
| 50 | 110 | 3.01 | 316.23 | 2.000 |
| 51 | 111 | 4.01 | 354.81 | 2.518 |
| 52 | 112 | 5.01 | 398.11 | 3.170 |
| 53 | 113 | 6.01 | 446.68 | 3.991 |
| 54 | 114 | 7.01 | 501.19 | 5.024 |
| 55 | 115 | 8.01 | 562.34 | 6.325 |
| 56 | 116 | 9.01 | 630.96 | 7.962 |
| 57 | 117 | 10.01 | 707.95 | 10.024 |
| 58 | 118 | 11.01 | 794.33 | 12.619 |
| 59 | 119 | 12.01 | 891.25 | 15.887 |
| 60 | 120 | 13.01 | 1000.00 | 20.000 |
| 61 | 121 | 14.01 | 1122.02 | 25.179 |
| 62 | 122 | 15.01 | 1258.93 | 31.698 |
| 63 | 123 | 16.01 | 1412.54 | 39.905 |
| 64 | 124 | 17.01 | 1584.89 | 50.238 |
| 65 | 125 | 18.01 | 1778.28 | 63.246 |
| 66 | 126 | 19.01 | 1995.26 | 79.621 |
| 67 | 127 | 20.01 | 2,238.72 | 100.237 |
| 68 | 128 | 21.01 | 2511.89 | 126.191 |
Table 2. Power conversion at 75Ω impedance
| dBmV | dBµV | dBm 75Ω | mVrms | mW 75Ω |
| 8 | 68 | -40.75 | 2.51 | 8.4E-05 |
| 9 | 69 | -39.75 | 2.82 | 1.1E-04 |
| 10 | 70 | -38.75 | 3.16 | 1.3E-04 |
| 11 | 71 | -37.75 | 3.55 | 1.7E-04 |
| 12 | 72 | -36.75 | 3.98 | 2.1E-04 |
| 13 | 73 | -35.75 | 4.47 | 2.7E-04 |
| 14 | 74 | -34.75 | 5.01 | 3.3E-04 |
| 15 | 75 | -33.75 | 5.62 | 4.2E-04 |
| 16 | 76 | -32.75 | 6.31 | 5.3E-04 |
| 17 | 77 | -31.75 | 7.08 | 6.7E-04 |
| 18 | 78 | -30.75 | 7.94 | 8.4E-04 |
| 19 | 79 | -29.75 | 8.91 | 1.1E-03 |
| 20 | 80 | -28.75 | 10.00 | 1.3E-03 |
| twenty one | 81 | -27.75 | 11.22 | 1.7E-03 |
| twenty two | 82 | -26.75 | 12.59 | 2.1E-03 |
| twenty three | 83 | -25.75 | 14.13 | 2.7E-03 |
| twenty four | 84 | -24.75 | 15.85 | 3.3E-03 |
| 25 | 85 | -23.75 | 17.78 | 4.2E-03 |
| 26 | 86 | -22.75 | 19.95 | 5.3E-03 |
| 27 | 87 | -21.75 | 22.39 | 6.7E-03 |
| 28 | 88 | -20.75 | 25.12 | 8.4E-03 |
| 29 | 89 | -19.75 | 28.18 | 0.011 |
| 30 | 90 | -18.75 | 31.62 | 0.013 |
| 31 | 91 | -17.75 | 35.48 | 0.017 |
| 32 | 92 | -16.75 | 39.81 | 0.021 |
| 33 | 93 | -15.75 | 44.67 | 0.027 |
| 34 | 94 | -14.75 | 50.12 | 0.033 |
| 35 | 95 | -13.75 | 56.23 | 0.042 |
| 36 | 96 | -12.75 | 63.10 | 0.053 |
| 37 | 97 | -11.75 | 70.79 | 0.067 |
| 38 | 98 | -10.75 | 79.43 | 0.084 |
| 39 | 99 | -9.75 | 89.13 | 0.106 |
| 40 | 100 | -8.75 | 100.00 | 0.133 |
| 41 | 101 | -7.75 | 112.20 | 0.168 |
| 42 | 102 | -6.75 | 125.89 | 0.211 |
| 43 | 103 | -5.75 | 141.25 | 0.266 |
| 44 | 104 | -4.75 | 158.49 | 0.335 |
| 45 | 105 | -3.75 | 177.83 | 0.422 |
| 46 | 106 | -2.75 | 199.53 | 0.531 |
| 47 | 107 | -1.75 | 223.87 | 0.668 |
| 48 | 108 | -0.75 | 251.19 | 0.841 |
| 49 | 109 | 0.25 | 281.84 | 1.059 |
| 50 | 110 | 1.25 | 316.23 | 1.333 |
| 51 | 111 | 2.25 | 354.81 | 1.679 |
| 52 | 112 | 3.25 | 398.11 | 2.113 |
| 53 | 113 | 4.25 | 446.68 | 2.660 |
| 54 | 114 | 5.25 | 501.19 | 3.349 |
| 55 | 115 | 6.25 | 562.34 | 4.216 |
| 56 | 116 | 7.25 | 630.96 | 5.308 |
| 57 | 117 | 8.25 | 707.95 | 6.683 |
| 58 | 118 | 9.25 | 794.33 | 8.413 |
| 59 | 119 | 10.25 | 891.25 | 10.591 |
| 60 | 120 | 11.25 | 1000.00 | 13.333 |
| 61 | 121 | 12.25 | 1122.02 | 16.786 |
| 62 | 122 | 13.25 | 1258.93 | 21.132 |
| 63 | 123 | 14.25 | 1412.54 | 26.604 |
| 64 | 124 | 15.25 | 1584.89 | 33.492 |
| 65 | 125 | 16.25 | 1778.28 | 42.164 |
| 66 | 126 | 17.25 | 1995.26 | 53.081 |
| 67 | 127 | 18.25 | 2,238.72 | 66.825 |
| 68 | 128 | 19.25 | 2511.89 | 84.128 |
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