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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