FIELD INTENSITY and POWER DENSITY - TSCM
FIELD INTENSITY and POWER DENSITY
Sometimes it is necessary to know the actual field intensity or power density at a given distance from a transmitter instead of the signal strength received by an antenna. Field intensity or power density calculations are necessary when estimating electromagnetic interference (EMI) effects, when determining potential radiation hazards (personnel safety), or in determining or verifying specifications.
Field intensity (field strength) is a general term that usually means the magnitude of the electric field vector,
commonly expressed in volts per meter. At frequencies above 100 MHZ, and particularly above one GHz, power density
(PD) terminology is more often used than field strength. Power density and field intensity are related by equation [1]:
PD
'
E2 Z0
'
E2 120B
'
E2 377
[1]
where PD is in space. When
W/m2, E the units
is the of PD
RMS value of the field in volts/meter and 377 ohms are in mW/cm2, then PD (mW/cm2) = E2/3770.
is
the
characteristic
impedance
of
free
Conversions between field strength and power density when the impedance is 377 ohms, can be obtained from Table 1. It should be noted that to convert dBm/m2 to dBFV/m add 115.76 dB. Sample calculations for both field intensity
and power density in the far field of a transmitting antenna are in Section 4-2 and Section 4-8. Refer to chapter 3 on
antennas for the definitions of near field and far field.
Note that the "/" term before m, m2, and cm2 in Table 1 mean "per", i.e. dBm per m2, not to be confused with the division sign which is valid for the Table 1 equation P=E2/Zo. Remember that in order to obtain dBm from dBm/m2 given a certain area, you must add the logarithm of the area, not multiply. The values in the table are rounded to the nearest dBW, dBm, etc. per m2 so the results are less precise than a typical handheld calculator and may be up to ? dB off.
VOLTAGE MEASUREMENTS
Coaxial cabling typically has input impedances of 50, 75, and 93S, (?2) with 50S being the most common. Other types of cabling include the following: TV cable is 75S (coaxial) or 300S (twin-lead), audio public address (PA) is 600S, audio speakers are 3.2(4), 8, or 16S.
In the 50S case, power and voltage are related by:
P ' E 2 ' E 2 ' 50 I 2
[2]
Z0 50
Conversions between measured power, voltage, and current where the typical impedance is 50 ohms can be obtained from Table 2. The dBFA current values are given because frequently a current probe is used during laboratory tests to
determine the powerline input current to the system .
MATCHING CABLING IMPEDANCE
In performing measurements, we must take into account an impedance mismatch between measurement devices (typically 50 ohms) and free space (377 ohms).
4-1.1
E (Volts/m)
7,000 5,000 3,000 4,000 1,000
700 500 300 200 100
70 50 30 20 10
7 5 3 2 1
0.7 0.5 0.3 0.2 0.1
70x10-3 50x10-3 30x10-3 20x10-3 10x10-3
7x10-3 5x10-3 3x10-3 2x10-3 1x10-3
7x10-4 5x10-4 3x10-4 2x10-4 1x10-4
7x10-5 5x10-5 3x10-5 2x10-5 1x10-5
7x10-6 5x10-6 3x10-6 2x10-6 1x10-6
Table 1. Conversion Table - Field Intensity and Power Density PD = E2/Z0 ( Related by free space impedance = 377 ohms )
20 log 106 (E) (dB?V/m)
197 194 190 186 180
177 174 170 166 160
157 154 150 146 140
137 134 130 126 120
117 114 110 106 100
97 94 90 86 80
77 74 70 66 60
57 54 50 46 40
37 34 30 26 20
17 14 10 6 0
(watPtsD/m2)
130,000 66,300 23,900 10,600 2,650
1,300 663 239 106 27
13 6.6 2.4 1.1 .27
.13 .066 .024 .011 .0027 1.3x10-3 6.6x10-4 2.4x10-4 1.1x10-4 2.7x10-5 1.3x10-5 6.6x10-6 2.4x10-6 1.1x10-6 2.7x10-7 1.3x10-7 6.6x10-8 2.4x10-8 1.1x10-8 2.7x10-9 1.3x10-9 6.6x10-10 2.4x10-10 1.1x10-10 2.7x10-11 1.3x10-11 6.6x10-12 2.4x10-12 1.1x10-12 2.7x10-13 1.3x10-13 6.6x10-14 2.4x10-14 1.1x10-14 2.7x10-15
1(d0BLWog/mP2D)
+51 +48 +44 +40 +34
+31 +28 +24 +20 +14
+11 +8 +4 +0 -6
-9 -12 -16 -20 -26
-29 -32 -36 -40 -46
-49 -52 -56 -60 -66
-69 -72 -76 -80 -86
-89 -92 -96 -100 -106
-109 -112 -116 -120 -126
-129 -132 -136 -140 -146
Watts/cm2
13 6.6 2.4 1.1 .27
.13 .066 .024 .011 .0027 1.3x10-3 6.6x10-4 2.4x10-4 1.1x10-4 2.7x10-5 1.3x10-5 6.6x10-6 2.4x10-6 1.1x10-6 2.7x10-7 1.3x10-7 6.6x10-8 2.4x10-8 1.1x10-8 2.7x10-9 1.3x10-9 6.6x10-10 2.4x10-10 1.1x10-10 2.7x10-11 1.3x10-11 6.6x10-12 2.4x10-12 1.1x10-12 2.7x10-13 1.3x10-13 6.6x10-14 2.4x10-14 1.1x10-14 2.7x10-15 1.3x10-15 6.6x10-16 2.4x10-16 1.1x10-16 2.7x10-17 1.3x10-17 6.6x10-18 2.4x10-18 1.1x10-18 2.7x10-19
dBW/cm2
+11 +8 +4 0 -6
-9 -12 -16 -20 -26
-29 -32 -36 -40 -46
-49 -52 -56 -60 -66
-69 -72 -76 -80 -86
-89 -92 -96 -100 -106
-109 -112 -116 -120 -126
-129 -132 -136 -140 -146
-149 -152 -156 -160 -166
-169 -172 -176 -180 -186
mW/cm2
13,000 6,630 2,390 1,060 265
130 66 24 11 2.7
1.3 .66 .24 .11 .027
.013 66x10-4 24x10-4 11x10-4 2.7x10-4 1.3x10-4 66x10-4 24x10-4 11x10-4 2.7x10-6 1.3x10-6 66x10-8 24x10-8 11x10-8 2.7x10-8 1.3x10-8 66x10-10 24x10-10 11x10-10 2.7x10-10 1.3x10-10 66x10-12 24x10-12 11x10-12 2.7x10-12 1.3x10-12 66x10-14 24x10-14 11x10-14 2.7x10-14 1.3x10-14 66x10-16 24x10-16 11x10-16 2.7x10-16
dBm/cm2
+41 +38 +34 +30 +24
+21 +18 +14 +10 +4
+1 -2 -6 -10 -16
-19 -22 -26 -30 -36
-39 -42 -46 -50 -56
-59 -62 -66 -70 -76
-79 -82 -86 -90 -96
-99 -102 -106 -110 -116
-119 -122 -126 -130 -136
-139 -142 -146 -150 -156
dBm/m2
+81 +78 +74 +70 +64
+61 +58 +54 +50 +44
+41 +38 +34 +30 +24
+21 +18 +14 +10 +4
+1 -2 -6 -10 -16
-19 -22 -26 -30 -36
-39 -42 -46 -50 -56
-59 -62 -66 -70 -76
-79 -82 -86 -90 -96
-99 -102 -106 -110 -116
NOTE: Numbers in table rounded off
4-1.2
FIELD STRENGTH APPROACH
To account for the impedance difference, the antenna factor (AF) is defined as: AF=E/V, where E is field intensity which can be expressed in terms taking 377 ohms into account and V is measured voltage which can be expressed in terms taking 50 ohms into account. Details are provided in Section 4-12.
POWER DENSITY APPROACH
To account for the impedance difference , the antenna's effective capture area term, Ae relates free space power density PD with received power, Pr , i.e. Pr = PD Ae. Ae is a function of frequency and antenna gain and is related to AF as shown in Section 4-12.
SAMPLE CALCULATIONS
Section 4-2 provides sample calculations using power density and power terms from Table 1 and Table 2, whereas Section 4-12 uses these terms plus field intensity and voltage terms from Table 1 and Table 2. Refer the examples in Section 4-12 for usage of the conversions while converting free space values of power density to actual measurements with a spectrum analyzer attached by coaxial cable to a receiving antenna.
Conversion Between Field Intensity (Table 1) and Power Received (Table 2).
Power received (watts or milliwatts) can be expressed in terms of field intensity (volts/meter or ?v/meter) using equation [3]:
Power received (Pr ) '
E2 480B2
c2 f2
G
[3]
or in log form:
10 log Pr = 20 log E + 10 log G - 20 log f + 10 log (c2/480B2)
[4]
Then
10 log Pr = 20 log E1 + 10 log G - 20 log f1 + K4
[5]
Where
K4 ' 10 log
c2 @ 480B2
conversions
(Watts to mW)
as required (volts to ?v)2(Hz to MHz or GHz)2
The derivation of equation [3] follows:
PD= E2/120B Eq [1], Section 4-1, terms (v2/S)
Ae = 82G/4B Eq [8], Section 3-1, terms (m2)
Pr = PDAe
Eq [2], Section 4-3, terms (W/m2)(m2)
^ Pr = ( E2/120B )( 82G/4B) terms (v2/m2S)(m2)
8 = c /f Section 2-3, terms (m/sec)(sec)
Pr Watts (dBW)
mW (dBm)
Values of K4 (dB)
E1
f1 (Hz) f1 (MHz)
volts/meter 132.8
12.8
? v/meter
12.8
-107.2
volts/meter 162.8
42.8
? v/meter
42.8
-77.2
f1 (GHz) -47.2 -167.2 -17.2 -137.7
^Pr = ( E2/480B2 )( c 2 G/f 2) which is equation [3] terms (v2/m2S)( m2/sec2)(sec2) or v2/S = watts
4-1.3
Volts
700 500 300 200 100
70 50 30 20 10
7 5 3 2 1
0.7 0.5 0.3 0.2 0.1
.07 .05 .03 .02 .01 7 x 10-3 5 x 10-3 3 x 10-3 2 x 10-3 1 x 10-3 7 x 10-4 5 x 10-4 3 x 10-4 2 x 10-4 1 x 10-4 7 x 10-5 5 x 10-5 3 x 10-5 2 x 10-5 1 x 10-5 7 x 10-6 5 x 10-6 3 x 10-6 2 x 10-6 1 x 10-6 7 x 10-7 5 x 10-7 3 x 10-7 2 x 10-7 1 x 10-7
dBV
56.0 53.9 49.5 46.0 40.0
36.9 34.0 29.5 26.0 20.0
16.9 14.0 9.5 6.0
0
-3.1 -6.0 -10.5 -14.0 -20.0
-23.1 -26.0 -30.5 -34.0 -40.0
-43.1 -46.0 -50.5 -54.0 -60.0
-64.1 -66.0 -70.5 -74.0 -80.0
-84.1 -86.0 -90.5 -94.0 -100.0
-104.1 -106.0 -110.5 -114.0 -120.0
-124.1 -126.0 -130.5 -134.0 -140.0
Table 2. Conversion Table - Volts to Watts and dBFA (Px = Vx2/Z - Related by line impedance of 50 S)
dBFV
176.0 173.9 169.5 166.0 160.0
156.9 154.0 149.5 146.0 140.0
136.9 134.0 129.5 126.0 120.0
116.9 114.0 109.5 106.0 100.0
96.9 94.0 89.5 86.0 80.0
76.9 74.0 69.5 66.0 60.0
56.9 54.0 49.5 46.0 40.0
36.9 34.0 29.5 26.0 20.0
16.9 14.0 9.5 6.0
0
-3.1 -6.0 -10.5 -14.0 -20.0
Watts
9800 5000 1800 800 200
98 50 18 8 2
0.8 0.5 0.18 0.08 0.02 9.8 x 10-3 5.0 x 10-3 1.8 x 10-3 8.0 x 10-4 2.0 x 10-4 9.8 x 10-5 5.0 x 10-5 1.8 x 10-5 8.0 x 10-6 2.0 x 10-6 9.8 x 10-7 5.0 x 10-7 1.8 x 10-7 8.0 x 10-8 2.0 x 10-8 9.8 x 10-9 5.0 x 10-9 1.8 x 10-9 8.0 x 10-10 2.0 x 10-10 9.8 x 10-11 5.0 x 10-11 1.8 x 10-11 8.0 x 10-12 2.0 x 10-12 9.8 x 10-13 5.0 x 10-13 1.8 x 10-13 8.0 x 10-14 2.0 x 10-14 9.8 x 10-15 5.0 x 10-15 1.8 x 10-15 8.0 x 10-16 2.0 x 10-16
dBW
39.9 37.0 32.5 29.0 23.0
19.9 17.0 12.5 9.0 3.0
0 -3.0 -7.4 -11.0 -17.0
-20.1 -23.0 -27.4 -31.0 -37.0
-40.1 -43.0 -47.4 -51.0 -57.0
-60.1 -63.0 -67.4 -71.0 -77.0
-80.1 -83.0 -87.4 -91.0 -97.0
-100.1 -103.0 -107.4 -111.0 -117.0
-120.1 -123.0 -127.4 -131.0 -137.0
-140.1 -143.0 -147.4 -151.0 -157.0
dBm
69.9 67.0 62.5 59.0 53.0
49.9 47.0 42.5 39.0 33.0
29.9 27.0 22.5 19.0 13.0
9.9 7.0 2.6 -1.0 -7.0
-10.1 -13.0 -17.7 -21.0 -27.0
-30.1 -33.0 -37.4 -41.0 -47.0
-50.1 -53.0 -57.4 -61.0 -67.0
-70.1 -73.0 -77.4 -81.0 -87.0
-90.1 -93.0 -97.4 -101.0 -107.0
-110.1 -113.0 -117.4 -121.0 -127.0
dBFA
142.9 140.0 135.5 132.0 126.0
122.9 120.0 115.5 112.0 106.0
102.9 100.0 95.6 92.0 86.0
82.9 80.0 75.6 72.0 66.0
62.9 60.0 55.6 52.0 46.0
42.9 40.0 35.6 32.0 26.0
22.9 20.0 15.6 12.0 6.0
2.9 0 -4.4 -8.0 -14.0
-17.1 -20.0 -24.4 -28.0 -34.0
-37.1 -40.0 -44.4 -48.0 -54.0
4-1.4
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