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

 TUTORIAL 808

# CATV dBm, dBmV, and dBµV Conversions

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

Characterizing the S-Parameters of 75Ω Circuits using 50Ω Lab Equipment

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