Keywords: rf, tuner, catv, tv tuners, tuner design Related Parts

 TUTORIAL 808

# CATV dBm, dBmV, and dBµV Conversions

 © Jul 17, 2002, Maxim Integrated Products, Inc.

Abstract: Cable television systems are based on 75Ω interfaces, while most RF test equipment is 50Ω impedance. This paper presents the needed conversions between power and voltage levels in the two environments. Two tables are provided for easy look-up of the appropriate conversion factor.

#### Introduction

CATV circuits operate in a 75Ω environment. Most RF laboratories equipped with standard test instruments employ 50Ω as the standard interface impedance.

In this application note, it will be shown that:
dBmV = 46.9897 + dBm50Ω
dBmV = 48.7506 + dBm75Ω
dBµV = 60 + dBmV
dBµV = 106.98 + dBm50Ω
dBµV = 108.75 + dBm75Ω

#### dBmV and dBµV

Most CATV measurements are referenced to voltage and measured in dBmV or dBµV. In the classic definition, dBmV is referenced to 1mVRMS and output voltage (VOUT) is measured in mVRMS (Equation 1). Since Equation 1 is a ratio of voltage, it can also be measured in mVP-P referenced to 1mVP-P or any voltage unit as long as the same units are used.
Inspection of Equation 1 shows dBmV to be independent of impedance.

In the classic definition, dBµV is referenced to 1µVRMS and output voltage (VOUT) is measured in µVRMS (Equation 2). Since Equation 1 is a ratio of voltage, it can also be measured in µVP-P referenced to 1µVP-P or any voltage unit as long as the same units are used.
Inspection of Equation 2 shows dBµV to be independent of impedance.

#### Conversion of dBm to dBmV

dBm is defined in Equation 3.
POUT is measured in mW. The dBm is referenced to 1mW. Equation 3 does depend on impedance of the load as shown in Equation 4. Most RF equipment has a 50Ω load or input impedance. Equation 3 is still valid for any load impedance including 75Ω.

Power depends on load impedance. Equation 4 equates power to voltage and load impedance.
Rearranging terms,
Solving Equation 3 for POUT,
Solving Equation 1 for VOUT,
Substituting Equation 3.1 and Equation 1.1 into Equation 4.1,
Solving for dBmV in terms of dBm,
Using R = 50Ω,
Equation 5.2 is valid for 50Ω measurement equipment.

Solving Equation 5.1 using R = 75Ω,
Equation 5.3 is valid for 75Ω measurement equipment.

Using the same technique it can be shown that the relationship for dBµV to dBmV is

Table 1 and Table 2 show conversions between dBmV, dBµV and dBm in a 50Ω and 75Ω environment.

Table 1. Conversions of Power 50Ω
 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 21 81 -25.99 11.22 2.5E-03 22 82 -24.99 12.59 3.2E-03 23 83 -23.99 14.13 4.0E-03 24 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 2238.72 100.237 68 128 21.01 2511.89 126.191

Table 2. Conversions of Power 75Ω
 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 21 81 -27.75 11.22 1.7E-03 22 82 -26.75 12.59 2.1E-03 23 83 -25.75 14.13 2.7E-03 24 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 2238.72 66.825 68 128 19.25 2511.89 84.128

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 APP 808: Jul 17, 2002 TUTORIAL 808, AN808, AN 808, APP808, Appnote808, Appnote 808