antenna factor

AN_HF_1008_Antenna_Factors of 4

Antenna Parameters Antenna Gain Directivity and Conversion Factor The background for combining various antennas with the Selective Radiation Meter SRM-3000

If you use the Selective Radiation Meter SRM-3000 with Narda antennas you donrsquot need to worry about antenna factors The instrument automatically reads them from an EEPROM contained in the

plug of the auxiliary control cable Sometimes though you may want to use antennas from other

manufacturers with the SRM In such cases the antenna factors and correction values can be imported into the instrument

This process is simplified by using the free SRM-Tools PC software or the more sophisticated SRM-TS application which automatically utilize the tables of values that are usually provided in EXCEL or CSV formats

by the antenna manufacturers The software can accept values given as conversion factors antenna factors or antenna gain and then converts them

automatically You donrsquot need to worry about the

conversion either Nevertheless it is useful to know something about the physical and mathematical background to

the conversion This Application Note gives you a brief outline of this

copy 2008 Narda Safety Test Solutions GmbH Sandwiesenstr 7 72793 Pfullingen Deutschland Tel +49 7121 9732-777 Fax +49 7121 9732-790 E-mail supportnarda-stsde wwwnarda-stsde

Applicaton Note

Antenna factors in the PC-Software SRM-TS

AN_HF_1008_Antenna_Factors Page 2 of 4

Principles It is useful in field strength measurements to characterize the receiving

antenna by its conversion factor KE as well as by the antenna gain The relationship between them is described here

The (lossless) receiving antenna used has a gain of G (or directivity) referred to a virtual isotropic receiver It has an absorption area of

πλ4

2

sdot== GS

PA

e

ee (1)

In the homogeneous far-field the power density Se gives the available receive power level

πλ

η 4

2

0

2

sdotsdot=sdot= GE

ASP eee where πη 1200 = [Ω] (2)

With impedance matching this results in a voltage U0 across the load

impedance R0 = 50 Ω of the receiver

00

2

00 4RGERPU e sdot

sdotsdotsdot=sdot=

ηπλ

(3)

Conversion factor to gain conversion The conversion factor KE of the antenna is defined as the ratio of the

electric field strength E to the output voltage U0 at the measuring receiver with 50 Ω input impedance

50480441 2

00

0

00

0 πηπηπλ

sdotsdot

=sdotsdotsdot=

sdotsdotsdot==

Gc

f

RGc

f

RGU

EK

oE (4)

Using the speed of light in a vacuum c0 = 29979106 ms this gives the

following equation between quantities

G

f

G

fKE

7339979299

7339979299

sdot=sdot= MHzMHz (5)

Since it is usually easier in field strength measurements to work with voltage and field strength levels ie logarithmic quantities it is practical

to take the logarithm of the conversion factor

EE Kk log20 sdot= in units of dB (1m) (6)

The logarithm of the conversion factor is usually called the antenna factor (AF) even though strictly speaking it is not a factor but rather the logarithm of a factor

Receiving antenna in an electromagnetic field

R0 Pe Se


From equation (5) we can then derive the following relationship between

the antenna factor and the antenna gain g in dBi (referred to the isotropic receiver)

( ) gfkE -dB - MHz 770729log20 sdot= (7)

where

( )Gg log10 sdot= dB (8)

Examples Example 1 Tuned λλλλ2 dipole at its particular resonance frequency

Gain (directivity) Antenna

factor (AF)

f [MHz] G [1m] g [dBi] kE [dB(1m)] 100 164 215 808 300 164 215 1762 1000 164 215 2808 3000 164 215 3762

Example 2 Biconical dipole antenna SBA 9113


factor (AF)

f [MHz] G [1m] g [dBi] kE [dB(1m)] 500 028 -546 2967 600 109 039 2540 750 112 051 2722 1000 086 -067 3090 2000 120 080 3545 3000 082 -087 4064

Example 3 Log periodic antenna USLP 9143


factor (AF)


Tuned λ2 dipoles

are suitable for precision measurements at a fixed

frequency The antenna gain gi of 215 dBi means

they are very sensitive They are not suitable

however for multi-frequency environments such as

are normally found where measurements for human

safety limit values need to be made

Biconical dipole antennas

provide high sensitivity with antenna gain gi in the

region of 0 dBi but the frequency range covered is not

as broad as that of a broadband dipole antenna

(example 4)

Log periodic antennas

are extremely sensitive having an antenna gain gi of

5 to 7 dBi At the same time they are highly

directional and have a relatively high bandwidth They

are therefore eminently suitable for determining the

direction of radiation sources If they are to be used

for measuring the overall field exposure level in terms

of human safety limit values however a complicated

and very precise procedure is required if all radiation

components are to be detected reliably


Example 4 Single-axis antenna 353101 for SRM-3000


factor (AF)

f [MHz] G [1m] g [dBi] kE [dB(1m)]

27 468E-06 -5330 5216 100 380E-04 -3420 4443 300 562E-03 -2250 4227 900 661E-02 -1180 4111 1000 832E-02 -1080 4103 1800 188E-01 -725 4258 2100 174E-01 -760 4427 2500 166E-01 -780 4599 2800 141E-01 -850 4767 3000 891E-02 -1050 5027

Example 5 Three-axis antenna 350101 for SRM-3000


factor (AF)

f [MHz] G [1m] g [dBi] kE [dB(1m)] 100 100E-05 -5000 6023 300 562E-04 -3250 5227 900 129E-02 -1890 4821 1000 178E-02 -1750 4773 1800 562E-02 -1250 4783 2100 417E-02 -1380 5047 2500 282E-02 -1550 5369 2800 243E-02 -1615 5532 3000 216E-02 -1665 5642

Author Dr Rainer Bitzer Narda Safety Test Solutions

The single-axis E-field antenna 353101

covers an extremely wide frequency range from

27 MHz to 3 GHz It is suitable for measuring overall

field exposure levels using the pendulum method and

is the antenna of choice in applications where the

sensitivity of the three-axis E-field antenna 350101

(example 5) is insufficient

Isotropic measurements can also be made with the

single-axis antenna There is a special antenna holder

available for this which allows you to place the

antenna in a sequence of three defined positions This

method is supported by a wizard function in the SRM

basic unit

The three-axis E-field antenna 353101

measures isotropically ie non-directionally so it is a

real ldquoall-rounderrdquo for practically all measurements

determining limit values at a location or for human

safety purposes Its broad frequency range from

75 MHz to 3 GHz is obtained at the expense of

relatively low sensitivity but this is completely

adequate for demonstrating equipment limit values

and for most public area emission measurements


Principles It is useful in field strength measurements to characterize the receiving

antenna by its conversion factor KE as well as by the antenna gain The relationship between them is described here

The (lossless) receiving antenna used has a gain of G (or directivity) referred to a virtual isotropic receiver It has an absorption area of

πλ4

2

sdot== GS

PA

e

ee (1)

In the homogeneous far-field the power density Se gives the available receive power level

πλ

η 4

2

0

2

sdotsdot=sdot= GE

ASP eee where πη 1200 = [Ω] (2)

With impedance matching this results in a voltage U0 across the load

impedance R0 = 50 Ω of the receiver

00

2

00 4RGERPU e sdot

sdotsdotsdot=sdot=

ηπλ

(3)

Conversion factor to gain conversion The conversion factor KE of the antenna is defined as the ratio of the

electric field strength E to the output voltage U0 at the measuring receiver with 50 Ω input impedance

50480441 2

00

0

00

0 πηπηπλ

sdotsdot

=sdotsdotsdot=

sdotsdotsdot==

Gc

f

RGc

f

RGU

EK

oE (4)

Using the speed of light in a vacuum c0 = 29979106 ms this gives the

following equation between quantities

G

f

G

fKE

7339979299

7339979299

sdot=sdot= MHzMHz (5)

Since it is usually easier in field strength measurements to work with voltage and field strength levels ie logarithmic quantities it is practical

to take the logarithm of the conversion factor

EE Kk log20 sdot= in units of dB (1m) (6)

The logarithm of the conversion factor is usually called the antenna factor (AF) even though strictly speaking it is not a factor but rather the logarithm of a factor

Receiving antenna in an electromagnetic field

R0 Pe Se





where




factor (AF)




factor (AF)




factor (AF)


Tuned λ2 dipoles











(example 4)














factor (AF)


27 468E-06 -5330 5216 100 380E-04 -3420 4443 300 562E-03 -2250 4227 900 661E-02 -1180 4111 1000 832E-02 -1080 4103 1800 188E-01 -725 4258 2100 174E-01 -760 4427 2500 166E-01 -780 4599 2800 141E-01 -850 4767 3000 891E-02 -1050 5027



factor (AF)















basic unit














where




factor (AF)




factor (AF)




factor (AF)


Tuned λ2 dipoles











(example 4)














factor (AF)


27 468E-06 -5330 5216 100 380E-04 -3420 4443 300 562E-03 -2250 4227 900 661E-02 -1180 4111 1000 832E-02 -1080 4103 1800 188E-01 -725 4258 2100 174E-01 -760 4427 2500 166E-01 -780 4599 2800 141E-01 -850 4767 3000 891E-02 -1050 5027



factor (AF)















basic unit













factor (AF)


27 468E-06 -5330 5216 100 380E-04 -3420 4443 300 562E-03 -2250 4227 900 661E-02 -1180 4111 1000 832E-02 -1080 4103 1800 188E-01 -725 4258 2100 174E-01 -760 4427 2500 166E-01 -780 4599 2800 141E-01 -850 4767 3000 891E-02 -1050 5027



factor (AF)















basic unit










antenna factor

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