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NEW METHOD FOR CONFORMANCE ASSESSMENT

OF RADIO TRANSMITTERS

Kristian Karlsson Jan Carlsson

TR 589 Approved 2006-02

NT TECHN REPORT 589 Approved 2006-02

Nordic Innovation Centre project number: 04166

Authors: Kristian Karlsson Jan Carlsson Institution:

SP Sveriges Provnings- och Forskningsinstitut

Title:

New method for conformance assessment of radio transmitters Abstract:

In this project a measurement of the effective radiated power (ERP) is compared to a measurement of the total radiated power (TRP). ERP is measured according to ETSI inside an anechoic chamber and TRP is measured inside a reverberation chamber. The measured TRP value is related to the ERP value via an estimated maximum directivity of the test object. The comparison is performed for three active radio units with terminal antennas at their carrier frequencies and their first five harmonic frequencies. The uncertainty of an ERP measurement according to ETSI is compared to the uncertainty of an estimation of the ERP value via the TRP measurement as proposed in the new method.

Abstrakt:

I projektet jämförs en ERP (Effective Radiated Power) mätning med en TRP (Total Radiated Power) mätning. ERP mäts enligt ETSI standard inuti en hel- eller halvdämpad kammare och TRP mäts i en modväxlande kammare. Ett approximerat värde på provobjektets maximala direktivitet används för att relatera TRP värdet till ERP värdet. I projektet har en jämförelsemätning utförts för tre aktiva terminaler, både vid bärfrekvensen och vid dess fem första harmoniska övertoner. En osäkerhetsbudget har även tagits fram för att jämföra osäkerheten vid en ERP mätning enligt ETSI standard med osäkerheten i den nya metoden då ERP värdet skattas med den maximala direktiviteten tillsammans med TRP värdet.

Technical Group: Safety and Reliability

ISSN: 0283-7234

Language: English, Swedish abstract

Pages: 16 p. + 3 appendices

Key Words: Reverberation chamber, mode stirred chamber, effective radiated power, total radiated power, spherical modes

Distributed by: Nordic Innovation Centre Stensberggata 25 NO-0170 Oslo Norway

Report Internet address: www.nordicinnovation.net

i

Contents Overview ................................................................................................................................ ii Introduction ............................................................................................................................ 1 Abbreviations ......................................................................................................................... 3 Project overview..................................................................................................................... 4 ERP measurement procedure, overview ................................................................................ 5

Uncertainties of ERP-measurement ................................................................................... 6 TRP measurement in RC, overview....................................................................................... 7

TRP uncertainties ............................................................................................................... 9 Theory, TRP and ERP.......................................................................................................... 10

Converting TRP to ERP ................................................................................................... 10 Estimated maximum directivity of an antenna enclosed by a sphere .............................. 11 Uncertainty of ERP measurement via TRP measurement and maximum directivity estimation ......................................................................................................................... 13

Conclusions .......................................................................................................................... 15 References ............................................................................................................................ 16

Appendix 1. Measurement of Effective Radiated Power in Reverberation Chamber Appendix 2. Measurement of Total Radiated Power in Reverberation Chamber Appendix 3. New method for conformance assessment of radio transmitters:

Round Robin test

ii

Overview In this project a measurement of the effective radiated power (ERP) is compared to a measurement of the total radiated power (TRP). ERP is measured according to ETSI inside an anechoic chamber and TRP is measured inside a Reverberation Chamber (RC). The measured TRP value is related to the ERP value via an estimated maximum directivity of the test object. The comparison is performed for three active radio units with terminal antennas at the carrier frequency ( )Cf and the first five harmonic frequencies ( ), 2,3, 4,5,6Cn f n⋅ = that can be detected. The uncertainty of an ERP measurement according to ETSI is compared to the uncertainty of an estimation of the ERP value via the TRP measurement as proposed in the method.

1

Introduction The protection of the radio spectrum is since a long time a legal matter all over the world. Radio transmitters have to conform to detailed requirements regarding spectrum use. These are mainly national but in Europe the technical requirements are harmonized under the Radio and Telecommunications Terminal Equipment (R&TTE) Directive. The spectrum plans are still not fully harmonized. The radio standards cover basic requirements including restrictions on carrier power and spurious emissions. The test methods are developed by ETSI [1]. Two alternative measurements are described: Conducted carrier power and Effective Radiated Power (ERP). Conducted power shall be measured when the transmitter is delivered with a general antenna connector. Radiated power shall be measured when the transmitter has an integral antenna or a dedicated antenna connected with a special connector. Spurious emissions outside the carrier band shall always be measured as radiated power. The methods measure two different things, power fed to the antenna and the effective radiated power. The antenna efficiency and gain will make the results different. In the ETSI standards certain test sites are specified which are listed below. However, they all suffer from different drawbacks. Some of them are e.g. expensive while others have problems with accuracy. Open area test sites/semi anechoic chambers The measurements are done over a ground plane either outdoor or in a semi anechoic chamber. Open area test sites require a large space and are often disturbed by adjacent noise sources. Semi anechoic chambers solve the background noise problem but are expensive. The measurement procedure includes not only a search for the frequencies with high radiation but also the direction where the highest level is measured. Especially for high frequencies it is necessary to investigate a large number of directions. Often the search is limited to one plane around the transmitter which increases the uncertainty and decreases the repeatability in the method, this is especially true for higher frequencies. Even when the method is limited to a plane the method is time consuming. Fully anechoic chambers If the chamber is built also with a non-reflective floor some of the problems are avoided. However, the accuracy and repeatability is still poor and the test site is still expensive and requires large space. Stripline The latest version of the standard allows also the use of a stripline for radiation measurements. This is a cheap measurement device but can only be used as a complementary method due to its limited frequency range. It is also difficult to perform measurements of the complete radiation pattern using a stripline. To sum up, the standardized methods to measure ERP and spurious emissions suffer from the following problems: poor uncertainty and repeatability, especially at higher frequencies, long measurement time and expensive test sites. Several new methods have been proposed that tries to avoid the problems mentioned above. The RC is of certain interest. The chamber is a simple metal box and thus inexpensive. The chamber size determines the lower frequency

2

limit (the bigger chamber the lower limit) but the upper limit is determined by the instrumentation only. The simple construction creates a measurement situation where the chamber resonances are a part of the measured value. This is handled by a statistical approach where the chamber geometry is changed e.g. by a stepwise rotating metallic structure and a large number of measurement samples. The measured result is the Total Radiated Power (TRP) which is similar to the conducted power but also takes the antenna efficiency into account. The RC has been investigated in detail and measurement methods are already introduced in standards like IEC 61000-4-21. The aim of the project is to introduce a new method for conformance assessment of radio transmitters using an RC which: * is not as expensive as current test facilities * will produce more accurate results * will produce results with better repeatability * is based on existing standardised measurement methods

3

Abbreviations NA Network Analyzer RC Reverberation Chamber, also called Mode Stirred Chamber (MSC) TRP Total Radiated Power ERP Effective Radiated Power

4

Project overview Deliverables from the project will be three documents: two measurement methods [2] and [3], a technical report (this document) and a round robin test report [4]. The measurement method will contain how to measure TRP in an RC including uncertainty budget. The technical report will contain a description, validation and total uncertainty budget of the measurement method. The proposed method is verified in a Round Robin test [4]. An overview of the project can be found in Fig. 1.

Fig. 1. Flowchart of project.

5

ERP measurement procedure, overview The ERP test procedure below is extracted from [1] and is adapted to conform to a document on this level of abstraction: 1) On a test site (Anechoic, semi anechoic or open area test site) the EUT shall be placed at

the specified height on a non-conducting support and in the position closest to normal use as declared by the manufacturer.

2) The test antenna shall be orientated for vertical polarization and the length of the test antenna shall be chosen to correspond to the frequency of the transmitter.

3) The test antenna shall be connected to a measurement receiver, see Fig 2. 4) The transmitter shall be switched on without modulation (if possible) and the

measurement receiver shall be tuned to the frequency of the transmitter under test. 5) The test antenna shall be raised and lowered through the specified range of height until a

maximum signal level is detected by the measuring receiver. (If a test site with ground plane is used).

6) The transmitter shall then be rotated through 360° in the horizontal plane until the maximum signal level is detected by the measuring receiver.

7) The maximum signal level detected by the measuring receiver shall be noted. 8) The transmitter shall be replaced by a substitution antenna connected to a signal generator.

Below 1 GHz a dipole is recommended to be used, above a waveguide horn antenna. See Fig 2.

9) The substitution antenna shall be orientated for vertical polarization and the length of the substitution antenna shall be adjusted to correspond to the frequency of the transmitter.

10) The test antenna shall be raised and lowered through the specified range of height to ensure that the maximum signal is received. (If a test site with ground plane is used).

11) The input signal to the substitution antenna shall be adjusted to the level that produces a level detected by the measuring receiver equal to the level noted while the transmitter radiated power was measured (corrected for the loss in the cable between the signal generator and the substitution antenna).

12) The input level to the substitution antenna shall be recorded as power level tP . 13) The measurement shall be repeated with the test antenna and the substitution antenna

orientated for horizontal polarization. 14) The measure of ERP is the larger of the two power levels recorded ( tP ), at the input to the

substitution antenna, corrected for gain ( tG ) compared to a half wavelength dipole (not isotropic gain) of the substitution antenna if necessary:

t tERP P G= ⋅ (1a)

or in dB:

, ,dBm t dBm t dBdERP P G= + (1b)

6

Fig. 2. ERP measurement procedure. Depending on the magnitude of the received signal either an

attenuator or a pre-amplifier might be needed between the substitution antenna and the measurement receiver.

Uncertainties of ERP-measurement The maximum uncertainty allowed for ERP measurement is according to [1] chapter 11 equal to ± 6dB, but uncertainties as low as ± 4dB are achieved at many test sites around the world. Besides the uncertainty above, the method suffers from three factors causing measERP ERP≠ :

1) The measurement procedure suggests a search for the maximum directivity according to: a) height scan b) azimuth scan. This search will not necessarily find the maximum directivity, especially not at higher frequencies.

2) The measurement procedure suggests the EUT to be placed in the position closest to normal use as declared by the manufacturer. A significant underestimation of ERP might appear due to polarisation mismatch between EUT and test antenna.

3) Reflections in the substitution antenna are neglected in (1a) and (1b). Although matched antennas are to be used it can cause an over estimation of ERP of about 10% or 0.8 dB.

7

TRP measurement in RC, overview The measurement is performed in an RC according to [5], see fig. 3a and 3b. First the Chamber Gain ( CG ) is measured, then the power from the EUT ( avP ). These two results are then combined to give TRP. The measurement procedure basically is as follows: Chamber gain measurement 1) Determine number of independent samples necessary to achieve the required accuracy. 2) Calibrate the NA at the calibration planes marked as red circles in Fig. 3b. 3) Connect reference and measurement antennas as shown in Fig. 3b. If a directive antenna is

used, such as a horn antenna, it should be directed into a corner of the chamber. 4) Measure 11S , 21S and 22S for all independent stirring positions. 5) Calculate the averages of the complex values of 11S and 22S over all stirrer positions.

6) Frequency stir 11S , 22S over a certain bandwidth (e.g. 5 MHz). Now 11S and 22S represent the free space reflection coefficients of the measurement and reference antennas, respectively. Frequency stirring means computing a moving average in the frequency domain.

7) Calculate P according to (2a), includes averaging over all stirring positions.

( )2

21

2 2

11 221 1

SP f

S S=⎛ ⎞⎛ ⎞− −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(2a)

where − means averaging over all independent stirring positions and xxS denotes

frequency stirring of 11S and 22S .

8) Frequency stir P over a certain bandwidth (e.g. 25 MHz). This gives P . 9) Calculate the chamber gain according to (2b):

( )( )

2

111C

Dip

P f SG f

L

⎛ ⎞−⎜ ⎟⎝ ⎠= (2b)

where ( )P f denotes averaged over independent samples and frequency stirred ( )P f and

DipL are losses in the reference antenna.

Active unit measurement 10) Mount the active unit onto its holder inside the RC. Set the active unit into proper

operation mode via commands on the optional communication antenna link or directly on the active unit when applicable. Make sure that batteries of the active unit are fully charged.

11) Terminate the reference antenna properly outside the RC. 12) Measure the CW or pulsed power received in the measurement antenna(s) and average

over all independent samples avP⇒ . 13) Finally, compute TRP according to:

( )av

C

PTRPG f

= (3)

8

Fig. 3a. Picture of RC at SP. On the left: broadband measurement antenna, middle: active unit under

test (PMR radio), lower right: absorbing material, background: mechanical stirrer.

Fig. 3b. Setup in RC during chamber gain measurement. The platform stirrer and load are not mandatory for RC measurement, but such installations improve the accuracy for a given RC.

9

TRP uncertainties The standard uncertainty of the TRP measurement is calculated in [2] and has been determined in accordance with EAL Publication EAL-R2. The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k=2, which for a normal distribution corresponds to a coverage probability of approximately 95%. This uncertainty depends on the instrumentation and number of samples used in the measurement. As shown in [2] a measurement uncertainty less than 1 dB can be achieved with reasonable effort, an example can be seen in Fig. 4.

100 200 300 400 500 600 700 800 900 10000,5

1,0

1,5

2,0

Mea

sure

men

t Unc

erta

inty

[dB]

No. of samples

Fig. 4. Measurement uncertainty as a function of frequency. Lower limit is set due to instrumentation

uncertainties.

10

Theory, TRP and ERP The ideal value of ERP is the transmitted signal measured in the direction in which the EUT has its maximum directivity ( )max max,θ ϕ . Such a test requires measurements over the entire sphere surrounding the EUT. However, accurate directivity measurement is difficult and time consuming. For some EUT it can be totally impractical. During a standardized ERP measurement in an (semi) anechoic chamber the EUT is (height scanned plus) rotated until maximum signal is received for both horizontal and vertical polarisation. This is an approximation of the ideal ERP, limited by test angles of the EUT and the performance of the measurement site. The approximation is good if the EUT has a very simple radiation pattern (e.g. dipole like), but at higher frequencies the EUT might become large compared to a wavelength and the radiation pattern becomes complicated, see example of loop antenna at higher frequencies, Fig. 5.

V1

y

z

x

Fig. 5. Loop antenna with voltage excitation (left) and cut of normalized gain (right). The loop has

radius 0.5m. Radiation pattern at 950 MHz (which equals 9.95ka = where k is the wave number and a is the radius of the minimum sphere encircling the antenna under test), { }90, 0,360θ ϕ= ∈ . The

radiation pattern has been computed using a MoM program [6]. The suggestion is to predict ERP with a TRP measurement corrected with an estimate of the maximum directivity. TRP can be measured in a RC with high precision and is connected to ERP as described in (9) derived below.

Converting TRP to ERP The power density at a certain distance r from an antenna fed with power tP can be expressed as:

( )2

,4

t tPGrθ ϕ

ρπ

= (4)

11

We can use this power density to express TRP as the surface integral over a closed surface around the antenna:

22

0 0

sinTRP r d dπ π

ρ θ θ ϕ= ⋅∫ ∫ (5)

(4) into (5):

( )2

0 0

, sin4

tt

PTRP G d dπ π

θ ϕ θ θ ϕπ

= ⋅∫ ∫ (6)

We can verify (6) with an isotropic antenna, i.e. ( ), 1tG θ ϕ = :

2

0 0

1 sin 44 4

t tt

P PTRP d d Pπ π

θ θ ϕ ππ π

= ⋅ ⋅ = =∫ ∫ (7)

ERP is the effective radiated power in the direction where the EUT has maximum directivity: ( )max max max,tD Dθ ϕ = . Compute ERP from TRP:

2

max max0 0

sin4

tt

PERP D d d PDπ π

θ θ ϕπ

= ⋅ ⋅ =∫ ∫ (8)

TRP is independent of the radiation pattern of the antenna and we can therefore express ERP in terms of TRP:

maxERP TRP D= ⋅ (9)

From (9) we see that the difference between ERP and TRP is the maximum directivity of the antenna. In practice, the factor between ERP and TRP will not be as large as maxD because of the uncertainties described in 1) and 2) in “Uncertainties of ERP-measurement” above. For small antennas (low directivity) the measured value of the maximum directivity is very close to the real maximum directivity because of the smooth dipole-like radiation pattern, and for large antennas (spurious emissions at higher frequencies might have high directivity) the measured value of the maximum directivity might be far from the actual maximum directivity.

Estimated maximum directivity of an antenna enclosed by a sphere To compute ERP from TRP we need, according to (9), the maximum directivity of the EUT. To estimate the maximum directivity out of an arbitrary EUT a general treatment of radiation from a sphere is performed. In [7] and [8] the maximum directivity of an EUT enclosed by a sphere is derived:

( )2max

3, 1

2 , 1

kaD

ka ka ka

≤⎧⎪= ⎨+ >⎪⎩

(10)

where 2k π λ= is the wave number and a is the radius of the sphere. These expressions are based on optimal combination of spherical modes.

12

The scope of this report is measurement procedures for active terminal antennas, i.e. antennas which are omni directional. Therefore it is very unlikely that either the carrier frequency or the unintentional emissions of the EUT transmits with as high directivity as in (10). Instead statistical treatments of the directivity, where the coefficients of the modes are considered to be independent variables, are performed [9, 10]. The expected value for maxD based on this assumption can be estimated by:

( )( ) ( )2max

2

1.55, 1

1 10.577 ln 4 8 , 12 8 16

ka

Dka ka ka

ka ka

≤⎧⎪

⎡ ⎤= ⎨ + + + >⎢ ⎥⎪ +⎢ ⎥⎣ ⎦⎩

(11)

which is the function we use to estimate maxD . In fig. 6 equations (10) and (11) are plotted together with the maximum directivity from two simple antennas (dipole and loop antenna) enclosed by a sphere of radius a. We can see that the independent spherical modes (11) fit reasonable well with the maximum directivity of the dipole and loop antenna. In this case no deviation from (11) larger than 2 dB is found.

Fig 6. Maximum directivity according to equations (10) - (11) and two canonical antennas. The

maximum directivity of the loop antenna is computed with a MoM program [6] and the maximum directivity of the dipole antenna is extracted from [11].

13

Uncertainty of ERP measurement via TRP measurement and maximum directivity estimation As mentioned in chapter “TRP uncertainties” uncertainties less than 1 dB can be achieved with a reasonable number of samples during a TRP measurement. This value corresponds to an expansion factor k=2 (i.e. a confidence level of 95.45%) and thus the standard deviation due to such a TRP measurement is 0.103TRPσ = . The maximum uncertainty accepted according to [1] is 6 dB, which for k=2 corresponds to a total standard deviation

0.375TOTσ = . The total standard deviation is a combination of the uncertainty from the TRP measurement and the difference between the maximum directivity and equation (10) called

DMAXσ . If we assume DMAXσ to be rectangular distributed, the total standard deviation can be expressed as:

22 2

3DMAX

TOT TRPσσ σ= +

(12) From (12) we can calculate the maximum allowed DMAXσ to fulfil a certain uncertainty budget. E.g. a total error of 6 dB requires 0.624DMAXσ < or 4.3 dB and a total error of 4 dB requires 0.490DMAXσ < or 3.0 dB. In fig. 7 and 8 below the maximum directivity of two radio units are computed and compared to (11). The radio units consist of a PEC block and an attached patch or wire antenna. The radio units are defined in fig. 7. The maximum directivity of both units has a deviation from (11) within the 3 dB limit for all frequencies, i.e. a total uncertainty of 6 dB can be achieved. Actually, for most of the frequencies the deviation is within the 3 dB limit, i.e. a total uncertainty of 4 dB.

a)

b)

Fig. 7. Simple model of mobile radio unit with a) probe fed patch antenna, b) wire antenna. The computations are performed with WIPL-D [12].

14

Fig. 8. Maximum directivity according to equations (11) and two antennas defined in fig. 7. The

maximum directivities of the two antennas are computed with a MoM program [12].

15

Conclusions A new ERP test method is derived during the project, see [3]. It is possible to perform TRP measurements of a EUT and relate it to ERP within the uncertainty (6 dB) suggested in ETSI EN 300 086-1. Measurement of ERP via TRP is more accurate than the old type of ERP measurement.

16

References

1. ETSI EN 300 086-1, v1.2.1 (2001-3) 2. K. Karlsson and J. Carlsson “Measurement of Total Radiated Power in Reverberation

Chamber”, provided together with this document, 2005. 3. K. Karlsson and J. Carlsson “Measurement of Effective Radiated Power in

Reverberation Chamber”, provided together with this document, 2005. 4. K. Karlsson and J. Carlsson “New method of conformance assessment of radio

transmitters: Round Robin test”, provided together with this document, 2005. 5. TCO Development, TCO’01 Certification of mobile phones, TCO Development,

Stockholm, Sweden 6. J. Carlsson, Wire-MoM for Windows, http://www.sp.se/electronics/RnD/software/ 7. R. F. Harrington, "Effect of antenna size on gain, bandwidth and efficiency", Journal

or Research of the National Bureau of Standards – D. Radio Propagation, vol. 64D, No. 1, January-February 1960, pp. 1-12.

8. Hansen, J.E., “Spherical Near-Field Antenna Measurements.” Peter Peregrinus, London, 1988.

9. G. Koepke, D. Hill, and J. Ladbury, “Directivity of the test device in EMC measurements,” IEEE Intl. Symp. Electromag. Compat., Washington, DC, pp. 535-539, 2000.

10. P. Wilson, G. Koepke, J. Ladbury, and C. L. Holloway, “Emission and immunity standards: replacing field-at-a-distance measurements with total-radiated-power measurements,” IEEE Intl. Symp. Electromag. Compat., Montreal, Canada, 2001.

11. C. A. Balanis, “Antenna theory: analysis and design” Harper & Row, publishers, New York, 1982.

12. B. M. Kolundzija, J. S. Ognjanovic, T. K. Sarkar, “WIPL-D, Electromagnetic modelling of composite metallic and dielectric structures”, 2000 Artech House, INC.

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Measurement of Effective Radiated Power in Reverberation Chamber 1. Scope This method describes how to measure the Effective Radiated Power (ERP) from an active unit. The method is intended for small (height, width and length < 0.5m) active units. In the method the value of ERP is calculated as the product of the estimated maximum directivity and the Total Radiated Power (TRP) of the test object, which is measured in a Reverberation Chamber (RC) according to [1].

2. Field of application This method applies to ERP measurements of small (height, width and length < 0.5m) active units. The frequency range is not explicitly restricted in this method, but the lower frequency limit will be determined by the dimensions of the RC, and the upper frequency limit by the instrumentation. The TRP value is an isotropic parameter of the transmitter, i.e. no angular information about the transmitter can be extracted from the measurements. This method serves as an alternative to ERP test methods developed by ETSI [2].

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3. References References necessary for the application of the method: 1. K. Karlsson and J. Carlsson “Measurement of Total Radiated Power in Reverberation

Chamber”, provided together with this document, 2005. 2. ETSI EN 300 086-1, v1.2.1 (2001-3) Scientific references: 3. G. Koepke, D. Hill, and J. Ladbury, “Directivity of the test device in EMC

measurements,” IEEE Intl. Symp. Electromag. Compat., Washington, DC, pp. 535-539, 2000.

4. G. J. Freyer, and M. G. Bäckström, “Comparison of anechoic & reverberation chamber coupling data as a function of directivity pattern,” IEEE Intl. Symp. Electromag. Compat., Washington, DC, pp. 615-620, 2000.

5. P. Wilson, G. Koepke, J. Ladbury, and C. L. Holloway, “Emission and immunity standards: replacing field-at-a-distance measurements with total-radiated-power measurements,” IEEE Intl. Symp. Electromag. Compat., Montreal, Canada, 2001.

6. Hansen, J.E., “Spherical Near-Field Antenna Measurements.” Peter Peregrinus, London, 1988.

7. J. Carlsson, Wire-MoM for Windows, http://www.sp.se/electronics/RnD/software/ 8. C. A. Balanis, “Antenna theory: analysis and design” Harper & Row, publishers, New

York, 1982. 9. B. M. Kolundzija, J. S. Ognjanovic, T. K. Sarkar, “WIPL-D, Electromagnetic modelling

of composite metallic and dielectric structures”, 2000 Artech House, INC.

4. Definitions

maxD Maximum directivity ERP Effective Radiated Power RC Reverberation Chamber, also called Mode Stirred Chamber (MSC) TRP Total Radiated Power

5. Test method We can express ERP in terms of TRP (which is independent of the radiation pattern of the antenna) according to:


i.e. the difference between ERP and TRP is the maximum directivity, maxD , of the transmitting unit. The first step in the test procedure is to enclose the test object by a sphere, a sphere which has the smallest possible radius to enclose the test object entirely. The maximum directivity of the test object is estimated in (4) and its value depends on the radius (in wavelengths) of the

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enclosing sphere. The result from (4) is a superposition of independently excited spherical modes. Independently excited modes are used because it is very unlikely that the test object for a certain spurious emission will act as a high directive antenna, such as a parabolic antenna. It is more likely that the possible modes excited by the test object will be combined in some statistical way. In (4) the coefficients of the modes are considered to be independent variables, see [3 - 6]. For small antennas (low directivity) the estimated value of maxD is very close to the real maximum directivity because of the smooth dipole-like radiation pattern, and for large antennas (spurious emissions at higher frequencies) the estimated value of maxD is instead a superposition of independently excited spherical modes. Second step is to measure TRP of the test object. Third, and final step, is to calculate ERP according to (1). The measurement uncertainty is determined in Appendix A.

5.1 Equipment This method contains no measurements; these are all performed in the TRP measurement procedure [1]. Only equipment needed for this method is a computer which is used to estimate the maximum directivity according to equations (2-5). For certain frequencies and sizes of the test object, the maximum directivity is already calculated and provided in Appendix B.

5.2 Pre-conditioning of test samples All units within the test object must be identified (including cables). Such identifications could be type, serial number, internal registration number etc. Accessories to the test object, which are used during the test, must be identified as well. If a simulation tool is used, this must be identified with e.g. version number and date. All this information must be entered into the report.

5.4 Test procedure and data processing 1) This test is performed at the carrier frequency and at spurious emissions outside the carrier

band. 2) Measure the largest dimension of the test object; this will be the diameter ( )d of the

enclosing sphere. Calculate the radius ( )a of that sphere:

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2a d= (2)

3) Calculate the wave number ( )k according to:

2 2 fk

cπ πλ

= = (3)

where is f the frequency and c is the speed of light. 4) Calculate the maximum directivity according to:

( )( ) ( )2max

2

1.55, 1

1 10.577 ln 4 8 , 12 8 16

ka

Dka ka ka

ka ka

≤⎧⎪

⎡ ⎤= ⎨ + + + >⎢ ⎥⎪ +⎢ ⎥⎣ ⎦⎩

(4)

5) Measure TRP of the test object [1]. 6) Calculate ERP according to:


5.5 Applicability This method is applicable for ERP measurements of active units. The method is intended for small (height, width and length < 0.5m) test objects. This method serves as an alternative to ERP test methods developed by ETSI [2].

ERP is computed from the TRP value, which is a measure from a reproducible multipath environment. TRP measurements are repeatable with deterministic uncertainties.

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Appendix A - Uncertainty of ERP measurement via TRP measurement and maximum directivity estimation The standard uncertainty of the ERP measurement is calculated below and has been determined in accordance with EAL Publication EAL-R2. The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k=2, which for a normal distribution corresponds to a coverage probability of approximately 95%. As mentioned in [1] uncertainties less than 1 dB can be achieved with a reasonable number of samples during a TRP measurement. This value corresponds to an expansion factor k=2 (i.e. a confidence level of 95.45%) and thus the standard deviation due to such a TRP measurement is 0.103TRPσ = . The maximum uncertainty accepted according to [2] is 6 dB, which for k=2 corresponds to a total standard deviation 0.375TOTσ = . The total standard deviation is a combination of the uncertainty from the TRP measurement and the difference between the maximum directivity and equation (4) called DMAXσ . If we assume DMAXσ to be rectangular distributed, the total standard deviation can be expressed as:

22 2

3DMAX

TOT TRPσσ σ= +

(6) From (6) we can calculate the maximum allowed DMAXσ to fulfil a certain uncertainty budget. E.g. a total error of 6 dB requires 0.624DMAXσ < or 4.3 dB and a total error of 4 dB requires

0.490DMAXσ < or 3.0 dB. In Fig. 1 equation (4) is plotted together with the maximum directivity from two simple antennas (dipole and loop antenna) enclosed within a sphere of radius a. We can see that the independent spherical modes (4) fit reasonable well with the maximum directivity of the dipole and loop antenna. In this case no deviation from (4) larger than 2 dB is found, i.e. for all frequencies the deviation is within the 3 dB limit, and a total uncertainty of 4 dB can be achieved.

1/6

Figure 1. Maximum directivity according to equation (4) and two canonical antennas. The maximum directivity of the loop antenna is computed with a MoM program [7] and the maximum directivity of

the dipole antenna is extracted from [8]. In Fig. 2 and 3 below, the maximum directivity of two radio units are computed and compared to (4). The radio units consist of a PEC block and an attached patch or wire antenna. The radio units are defined in Fig. 2. The maximum directivity of both units has a deviation from (4) within the 4.3 dB limit for all frequencies, i.e. a total uncertainty of 6 dB can be achieved. Actually, for most of the frequencies the deviation is within the 3 dB limit, i.e. a total uncertainty of 4 dB.

1/7

a)

b)

Figure 2. Simple model of mobile radio unit with a) probe fed patch antenna, b) wire antenna. The computations are performed with WIPL-D [9].

Figure 3. Maximum directivity according to equation (4) and two example antennas defined in Fig. 2.

The maximum directivities of the two antennas are computed with WIPL-D [9].

1/8

Appendix B – Estimated maximum directivity

TABLE B2. ESTIMATED MAXIMUM DIRECTIVITY (DB SCALE)

0.10 0.12 0.14 0.17 0.19 0.21 0.23 0.26 0.28 0.30

400 1.90 1.95 2.24 2.49 2.70 2.88 3.04 3.18 3.31 3.43 800 2.79 3.11 3.37 3.59 3.77 3.93 4.07 4.20 4.31 4.42

1200 3.43 3.73 3.97 4.17 4.34 4.49 4.62 4.74 4.85 4.94 1600 3.85 4.14 4.37 4.56 4.72 4.86 4.99 5.10 5.20 5.29 2000 4.17 4.44 4.66 4.85 5.00 5.14 5.26 5.36 5.46 5.55 2400 4.42 4.68 4.89 5.07 5.22 5.35 5.47 5.57 5.66 5.75 2800 4.62 4.88 5.09 5.26 5.40 5.53 5.64 5.74 5.83 5.91 3200 4.79 5.04 5.25 5.41 5.56 5.68 5.79 5.89 5.97 6.05 3600 4.94 5.19 5.38 5.55 5.69 5.81 5.91 6.01 6.10 6.17 4000 5.07 5.31 5.50 5.66 5.80 5.92 6.02 6.12 6.20 6.28 8000 5.86 6.07 6.24 6.38 6.50 6.60 6.70 6.78 6.85 6.92

12000 6.28 6.47 6.63 6.76 6.87 6.96 7.05 7.13 7.19 7.26 16000 6.55 6.74 6.89 7.01 7.11 7.21 7.29 7.36 7.42 7.48 20000 6.76 6.93 7.08 7.19 7.30 7.38 7.46 7.53 7.59 7.65 24000 6.92 7.09 7.23 7.34 7.44 7.52 7.60 7.67 7.73 7.78 28000 7.05 7.22 7.35 7.46 7.56 7.64 7.71 7.78 7.84 7.89 32000 7.16 7.32 7.45 7.56 7.66 7.74 7.81 7.88 7.93 7.99 36000 7.26 7.42 7.54 7.65 7.74 7.82 7.89 7.96 8.01 8.07

1/9

TABLE B2. ESTIMATED MAXIMUM DIRECTIVITY (LINEAR SCALE)

0.10 0.12 0.14 0.17 0.19 0.21 0.23 0.26 0.28 0.30

400 1.55 1.57 1.68 1.77 1.86 1.94 2.01 2.08 2.14 2.20 800 1.90 2.05 2.17 2.28 2.38 2.47 2.55 2.63 2.70 2.77

1200 2.20 2.36 2.49 2.61 2.72 2.81 2.9 2.98 3.05 3.12 1600 2.43 2.59 2.73 2.86 2.97 3.06 3.15 3.23 3.31 3.38 2000 2.61 2.78 2.93 3.05 3.16 3.26 3.36 3.44 3.52 3.59 2400 2.77 2.94 3.09 3.22 3.33 3.43 3.52 3.61 3.69 3.76 2800 2.90 3.08 3.22 3.36 3.47 3.57 3.67 3.75 3.83 3.90 3200 3.02 3.19 3.35 3.48 3.59 3.70 3.79 3.88 3.96 4.03 3600 3.12 3.30 3.45 3.59 3.70 3.81 3.90 3.99 4.07 4.14 4000 3.22 3.40 3.55 3.69 3.80 3.91 4.00 4.09 4.17 4.24 8000 3.86 4.05 4.21 4.35 4.47 4.58 4.67 4.76 4.84 4.92

12000 4.24 4.44 4.60 4.74 4.86 4.97 5.07 5.16 5.24 5.32 16000 4.52 4.72 4.88 5.02 5.15 5.25 5.35 5.44 5.53 5.60 20000 4.74 4.94 5.10 5.24 5.37 5.48 5.57 5.66 5.75 5.82 24000 4.92 5.12 5.28 5.42 5.55 5.66 5.75 5.85 5.93 6.00 28000 5.07 5.27 5.43 5.57 5.70 5.81 5.91 6.00 6.08 6.16 32000 5.20 5.40 5.56 5.71 5.83 5.94 6.04 6.13 6.21 6.29 36000 5.32 5.52 5.68 5.82 5.95 6.06 6.16 6.25 6.33 6.41

2/1

Measurement of Total Radiated Power in Reverberation Chamber

1. Scope This method describes how to measure the Total Radiated Power (TRP) from an active unit in a reverberation chamber (RC). The method is based on [1] but the uncertainty budget is improved. The method is intended for small (height, width and length < 0.5m) active units. In short, a measurement is performed as follows: The RC is excited with the active unit. The transmitted power is measured with the measurement antennas in the RC. The result is then corrected with the chamber gain ( )CG between a (lossless) reference antenna and the measurement antennas. 2. Field of application This method applies to TRP measurements of small (height, width and length < 0.5m) active units. The frequency range is not explicitly restricted in this method, but the lower frequency limit will be determined by the dimensions of the RC, and the upper limit by the instrumentation. The TRP value is an isotropic parameter of the transmitter, i.e. no angular information about the transmitter can be extracted from the measurements.

2/2

3. References References necessary for the application of the method: 1. TCO Development, TCO’01 Certification of mobile phones, TCO Development,

Stockholm, Sweden 2. IEC 61000-4-21 Scientific references: 3. K. Rosengren, P.-S. Kildal, C. Carlsson and J. Carlsson, “Characterization of antennas for

mobile and wireless terminals in reverberation chambers: Improved accuracy by platform stirring”, Microwave Optical Technol. Lett., Vol. 30, No. 6, pp. 391-396, Sep. 20, 2001.

4. P.-S. Kildal, C. Carlsson and J. Yang, ”Measurement of free-space impedances of small antennas in reverberation chambers”, Microwave Optical Technol. Lett., Vol. 32, No. 2, pp. 112-115, Jan. 20, 2002.

5. P.-S. Kildal and K. Rosengren, “Electromagnetic analysis of effective and apparent diversity gain of two parallel dipoles”, IEEE Antennas and wireless propagation letters, Vol. 2, pp. 9-13, 2003.

6. A. Wolfgang, J. Carlsson, C. Orlenius, P.-S. Kildal, “Improved Procedure for Measuring Efficiency of Small Antennas in Reverberation Chambers,” IEEE AP-S International Symposium and URSI Science Meeting, Columbus, Ohio, USA, Jun. 22 – 27, 2003.

7. D. A. Hill, “Electronic mode stirring for reverberation chambers”, IEEE Trans. Electromagn. Compat., vol. 36, pp. 294-299, 1994.

8. P-S Kildal and C. Carlsson, “Detection of a polarisation imbalance in reverberation chambers and how to remove it by polarisation stirring when measuring antenna efficiencies”, Microwave Optical Technol. Lett., vol. 34, no. 2, pp. 145-149, July 2002.

9. M. Bäckström, O. Lunden and P.-S. Kildal, Review of radio Science 1999-2002. New York: Wiley, IEEE Press, 2002, ch. Reverberation chambers for EMC susceptibility and emission analyses, pp. 429-452.

10. D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk, “Aperture Excitation of Electrically Large, Lossy Cavities”, IEEE Trans. Electromagn. Compat. vol. 36, no. 3, pp. 169-178, Aug. 1994.

4. Definitions NA Network Analyzer RC Reverberation Chamber, also called Mode Stirred Chamber (MSC) Rx antenna Measurement antenna TRP Total Radiated Power Tx antenna Reference antenna

2/3

5. Test method Some basic theory of RC provided in ref. [1]-[10]. This method describes how to measure TRP in an RC. It can be used for mobile phones as in [1], but also for other types of radiating units. Basically a TRP measurement is performed as follows: 1. Determine the number of required samples, N, and stirring scheme for the measurement

frequency and wanted accuracy. 2. The chamber gain is measured and averaged for N independent samples between a

lossless reference antenna (or a reference antenna with known loss which is compensated for) and the measurement antenna(s).

3. The active unit is located in the RC and its transmitted power is measured and averaged for N independent samples by one or more Rx antennas. (Several Rx antennas might be used if polarisation stirring is used).

4. The power measured from the active unit is corrected with the chamber gain to achieve TRP of the active unit.

Total measurement uncertainty is determined in Appendix A. 5.1 Equipment Instrumentation during the measurement: • NA, for measurement of chamber gain. • Power monitoring device. CW or pulsed power measurement of active unit. • Thermometer, for temperature measurement to secure instrumentation accuracy. • Tx antennas with known ohmic losses. • Rx antennas. • Control software. Controlling stirrers and instrumentation. See Fig. 1 for description of instrumentation setup. 5.2 Testing environment The test is performed in an RC [1], [2]. TRP of an active device with known TRP is measured before the test object is measured to verify the measurement setup. The temperature shall be checked before, during and after the measurement. The temperatures shall be entered into a temperature log and the temperature during the measurement shall be entered into the report as well. If the temperature differs from what is stated in the method, it shall be noted in the report, though it might affect the uncertainty of the measurement. The requirement of the temperature range depends on the uncertainty specifications of the instrumentation.

2/4

The moisture shall be within the range defined by the instrumentation. Unexpected occurrences with lab or equipment during measurement (e.g. electrical or instrumentation fault) shall be noticed in a log file. Data entered into the log file shall contain name of the operator and sufficient information about the occurrence. 5.3 Pre-conditioning of test samples All units within the test object must be identified (including cables). Such identifications could be type, serial number, internal registration number etc. Accessories to the test object, which are used during the test, must be identified as well. If a simulation tool is used, this must be identified with e.g. version number and date. All this information must be entered into the report. Make sure that batteries of the active unit are fully charged prior to the test. 5.4 Test procedure and data processing A calibration setup is shown in Fig. 1. The measurement of the Chamber gain is performed with a NA and the calibration planes are marked as red circles in Fig. 1. If an additional antenna is needed for control of the active device, it must be present in the RC and properly terminated during measurement of the chamber gain. This is because of the change in chamber gain due to losses in the optional control antenna. The frequency dependent chamber gain ( CG ) is defined as:

( )( ) ( ) ( )

22 2

11,11, 11,11 113

y yx x z z

CDip Dip Dip

P f SP f S P f SG f

L L L

⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞−− −⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎜ ⎟= + +

⎜ ⎟⎜ ⎟⎝ ⎠

(1a)

or if only one Rx antenna is used:

( )( )

2

111i

CDip

P f SG f

L

⎛ ⎞−⎜ ⎟⎝ ⎠= (1b)

where:

( )2

21

2 2

11, 221 1i

i

SP f

S S=⎛ ⎞⎛ ⎞− −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(1c)

and:

2/5

( )iP f denotes frequency stirred ( )iP f . Index i denotes the transfer function between the test antenna and Rx antenna no. i

xxS are the S-parameters from the NA − means averaging over mechanical and platform stirring positions

xxS denotes frequency stirring of xxS DipL losses in the reference antenna

The measurement and computation of the Chamber gain is performed as follows: Chamber gain measurement 1. Determine number of independent samples necessary to achieve the required accuracy,

see table T1 in Appendix A1. 2. Calibrate the NA at the calibration planes marked as red circles in Fig. 1. Measure in 1

MHz steps in an appropriate frequency range. 3. Connect Tx and Rx antennas as shown in Fig. 1. (NA port 1 to Rx antennas and NA port 2

to the Tx antenna). If a directive antenna is used, such as a horn antenna, it should be directed into a corner of the chamber.

4. Measure 11S , 22S and 21S for each mechanical and platform stirring position. 5. Calculate the averages of the complex values of 11S , 22S over all stirrer positions.

6. Frequency stir 11S , 22S over a certain bandwidth (e.g. 5 MHz). Now 11S and 22S represent the free space reflection coefficients of the Rx and Tx antennas, respectively. Frequency stirring means computing a moving average in the frequency domain.

7. Calculate iP according to (1c), includes averaging over all stirring positions. 8. Frequency stir iP over a certain bandwidth (e.g. 25 MHz). 9. Calculate the chamber gain according to (1a) or (1b), where the three terms originate from

optional polarisation stirring (more than one Rx antenna). Active unit measurement 1. Mount the active unit onto its holder inside the RC. Set the active unit into proper

operation mode via commands on the optional communication antenna link or directly on the active unit when applicable. Make sure that batteries of the active unit are fully charged.

2. Terminate the Tx antenna properly outside the RC. 3. Measure the CW or pulsed power received in the Rx antenna(s) and average over all

independent samples avP⇒ or if three Rx antennas are used: , , ,, ,av A av B av CP P P . 4. Compute TRP according to (2):

( )av

C

PTRPG f

= or ( )

, , ,

3av A av B av C

C

P P PTRP

G f+ +

= (2)

Setup • If an additional antenna is needed for control of the active device, it must be present in the

RC and properly terminated during measurement of the chamber gain. • It is important that no object in the RC which affects the electrical field is closer to each

other (or any wall/ceiling/floor of the chamber) than half a wavelength. • To increase the number of available modes in the RC it is advantageous to load the RC

with lossy materials such as RF-absorbers.

2/6

Figure 1. Setup in RC during chamber gain measurement

Example Example of Chamber gain around 900 MHz in an RC with dimensions 2.47x3.07x2.45 meters, Fig 2. Reference antenna is a half wave dipole and measurement antennas are three orthogonally oriented (polarisation stirring) monopoles mounted in the chamber walls.

Figure 2. Example of chamber gain

2/7

Competence and training needs Although an RC is both easy and relatively cheap to build, it does require some experience to use it in a proper way. It is recommended to read reference [2] to derive some basic knowledge about the RC. Further reading in references [1]-[11] will of course gain the understanding in this area. 5.5 Applicability This method is applicable for TRP measurements of active units RC. The method is intended for small (height, width and length < 0.5m) test objects. The frequency range is not explicitly restricted in this method, but the lower frequency limit will be determined by the dimensions of the RC, and the upper limit by the instrumentation. The TRP value is an isotropic parameter of the transmitter, i.e. no angular information about the transmitter can be extracted from the measurements. The RC provides a reproducible multipath environment, and the measurements are repeatable with deterministic uncertainties. TRP measurements in RC have been compared to measurements in traditional measurement sites (e.g. anechoic chambers) several times and is nowadays an well accepted method for omni-directional parameters of the antenna.

2/8

Appendix A - Uncertainty budget The total uncertainty is a combination of uncertainties originating from the instrumentation (Network Analyzer (NA) and power measuring unit) and the RC itself. The RC is handled in A2 and A3, NA and power meter in A5. The total uncertainty is derived in A1. The computed uncertainty is a relative uncertainty. The reported expanded uncertainty of measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k=2, which for a normal distribution corresponds to a coverage probability of approximately 95%. The standard uncertainty of measurement has been determined in accordance with EAL Publication EAL-R2. Contents A1 Total uncertainty of the measurement procedure A2 Chamber gain uncertainty A3 Active device uncertainty A4 Uncertainty due to losses in reference antenna A5 Reflection coefficient correction uncertainty A1 Total uncertainty of the measurement procedure The total radiated power from an active device is calculated according to:

( )2

111rec

C dip

P SP

G L

−=

⋅ (1)

where recP is the power received from the active device averaged over independent samples,

see A3. ( )2

111 S− is a correction for the reference (Tx) antenna during chamber gain

measurement, see A2. CG is the chamber gain, see A2 and dipL is the losses in the Tx antenna, see A4. The total uncertainty of equation (1) can be expressed as:

2 2 2 2 2Pr 11,P ec s corr Gc Ldipσ σ σ σ σ= + + + (2)

where Pσ is the total uncertainty, Precσ is the uncertainty from the measurement of the active device, 11,S corrσ is the uncertainty due to the correction of the Tx antenna, Gcσ is the uncertainty from the chamber gain measurement and Ldipσ is the uncertainty due to the measurement of the losses in the Tx antenna. The total uncertainty in percent according to (2) is calculated in table T1 and an example is shown in table T2. The uncertainty in dB in table T2 is calculated as:

( )max

10log 1dB Pkσ σ= ±⎡ ⎤⎣ ⎦ (3)

2/9

where k is the coverage factor. k=2 corresponds to a coverage probability of approximately 95%.

TABLE T1. TOTAL UNCERTAINTY

Factor Std. uncertainty

Distribution Sens. coeff.

Contribution to std. uncertainty

recP Precσ Normal* 1 2,1

3Power offset

Nσ

+

( )2

111 S− 11,S corrσ Rectangular 1 11, 3S corrσ

CG Gcσ Normal* 1 22 221, ,1

3 3 3S NA OFFSETA B

Nσσ σ

+ + +

dipL Ldipσ Normal 1 Ldipσ

P Pσ 2 22 2 2, 21, ,11, 22

3 3 3 3 3Power offset S NA offsetS corr A B

LdipNσ σσ σ σ σ+ + + + + +

* Due to central limit theorem

TABLE T2. EXAMPLE: TOTAL UNCERTAINTY AT 800 MHZ, 200 INDEPENDENT SAMPLES (In the example the instrumentation has the following characteristics: Power meter offset accuracy 5.9%, NA

11S accuracy 0.5 dB (nominal value -9dB), NA 21S offset accuracy 0.2 dB (measured values 0 to -40 dB)),

where the reflection coefficient correction uncertainty ( ,A Bσ σ ) is calculated in A5. See also Fig. 1 and 2. Factor Std.

uncertainty Distribution Sens.

coeff. Contribution to std. uncertainty

recP Pr ecσ Normal* 1 21 0.059 0.078200 3

+ =

( )2

111 S− 11,S corrσ Rectangular 1 0.018 3 0.010=

CG Gcσ Normal* 1 221 0.0230.015 0.073

200 3+ + =

dipL Ldipσ Normal 1 0.029

P Pσ 2 2 2 2P 0.078 0.010 0.073 0.029 0.111σ = + + + = Or in dB (k=2, 95% confidence interval):1.1dB

* Due to central limit theorem

2/10

0 100 200 300 400 500 600 700 800 900 10000,00

0,05

0,10

0,15

0,20

0,25

Sta

ndar

d de

viat

ion

[-]

No. of samples

Fig. 1. Standard deviation as function of number of samples with instrumentation uncertainties as defined in table T2.

100 200 300 400 500 600 700 800 900 10000,5

1,0

1,5

2,0

Mea

sure

men

t Unc

erta

inty

[dB

]

No. of samples

Fig. 2. Measurement uncertainty as function of number of samples with instrumentation uncertainties as defined in table T2.

A2 Chamber gain uncertainty The chamber gain ( CG ) is defined as:

( )( ) ( ) ( )

22 2

11,11, 11,11 113

y yx x z z

CDip Dip Dip

P f SP f S P f SG f

L L L

⎛ ⎞⎛ ⎞⎛ ⎞ ⎛ ⎞−− −⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎜ ⎟= + +

⎜ ⎟⎜ ⎟⎝ ⎠

(4.a)

where:

2/11

( )2

21

2 2

11, 221 1i

i

SP f

S S=⎛ ⎞⎛ ⎞− −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(4.b)

and: ( )fPi

denotes frequency stirred ( )fPi . Index i denotes the transfer function between the reference antenna and Rx antenna no. i.

xxS are the S-parameters from the NA.

− means averaging over N mechanical and platform stirring positions.

xxS denotes frequency stirred xxS .

DipL losses in the reference antenna, which has to be corrected for.

The two factors (A and B) of the denominator in (4.b) are (if good antennas are used) small

corrections of the reference level iP . For a good antenna 2

11,iS is a small positive value and

thus the factor 2

11,1 iA S⎛ ⎞= −⎜ ⎟⎝ ⎠

is less than but very close to one. We will focus our study on

the 11S parameter but the results are valid for the 22S parameter as well, see A5. Using A5, we can write the expression (4.b) as:

( )22

21,21 2

21, ,

IDEAL

i NA OFFSET

SSP f S

A B A B= = ⋅

⋅ ⋅ (5)

where A and B are the factors in the denominator described above and their rectangular distributed uncertainties are Aσ and Bσ , see A5. 21,IDEALS is the ideal chamber transfer function, without measurement uncertainty and 21, ,NA OFFSETS is the offset error in the NA. Actually, we should as well take into account the random error of the NA, but those variations appear together with the wanted variations from the RC and are much smaller than the wanted RC variations. Those variations can therefore be neglected. Now, the relative uncertainty of the reference level iP can be expressed as:

22 221, ,2 1

3 3 3S NA OFFSETA B

Pi Nσσ σ

σ = + + + (6)

where 2

21Sσ is the total relative uncertainty of the average of the ideal amplitude squared of a transfer measurement in the chamber. 2

21S is exponentially distributed and has therefore a relative uncertainty equal to one. 2

21, ,S NA OFFSETσ is the offset error in the NA and is rectangular distributed. The total uncertainty in (4.a) can be expressed with (6) as well, just interpret the different polarizations as an increase of the number of independent samples.

2/12

A3 Active device uncertainty The averaged power from the active device is calculated as:

,1

1 N

rec rec ii

P PN =

= ∑ (7)

where ,rec iP is the received power for each independent stirrer position. The uncertainty of

,rec iP , i.e. ,Prec iσ , consists of the wanted statistical variations in the RC and the uncertainty in the power measuring device. The uncertainty in the power measuring device can be divided into a random error and an offset error. Based on the same assumptions as in A2 the random variations of the power measuring device can be neglected. Remaining parts are the rectangular distributed offset error and the RC standard deviation:

2 2, ,2 2

21,1 1

3 3Power offset Power offset

Prec S RCN Nσ σ

σ σ= + = + (8)

A4 Uncertainty due to losses in reference antenna When measuring the chamber gain the NA is calibrated at planes defined in the main document, Fig. 1. Port 1 is calibrated at the connector of the reference (Tx) antenna and port 2 is calibrated at the connector(s) of the measurement (Rx) antenna(s). The losses in the Rx antenna(s) are present both during chamber gain and active device measurement. They can be interpreted as a part of the chamber gain and needs not to be corrected for. The losses in the Tx antenna is only present during the chamber gain measurement and must therefore be corrected for. We have to estimate the loss in the Tx antenna in some way. If the Tx antenna is a dipole antenna the loss can be estimated as follows: short-circuit the Tx antenna and measure 11S . The wave goes two ways, half the measured value is the loss in the Tx antenna. The uncertainty can be estimated as the square root (we are only interested in the half 11S value (in dB)) of the uncertainty for a reflection measurement with a NA at a certain frequency at a certain level. A5 Reflection coefficient correction uncertainty The relative error originating from the correction of the reflection coefficient at the antenna port can be estimated as:

( )

( )2

11,

11 2

11,max

1

1

true

S

error

S

Sσ

−=

− (9)

In (9) 11Sσ is estimated from the maximum error, i.e. we have a rectangular distribution. The reflection coefficient ( 11S ) is measured with a NA which provides different accuracy depending on the level of 11S and frequency. Consider the example below: A NA which can measure a reflection coefficient of -10 dB at 800 MHz with an accuracy of 0.2 dB, will, if maximum error occurs, measure -9.8 dB instead of the true value -10 dB. -10 dB will produce a factor ( )2

111 0.900S− = and -9.8 dB will produce a factor ( )2111 0.895S− = , i.e. an error

less than 0.6%.

3/1

Nordic Innovation Centre Project: 04166 Ver. 1.0

New method for conformance assessment of radio transmitters: Round Robin test Test objects The test includes three test objects: a PMR radio, wireless microphone and a triple band mobile phone, see table 1. For each test item each round robin test participant should measure at the carrier frequency ( )Cf and at the first five harmonic frequencies

( ), 2,3, 4,5,6Cn f n⋅ = that they can detect. We will limit this test to emissions at a maximum of five harmonics per test object. Each test was started with fully loaded batteries. Priority In table 1 an order of priority is listed, in case the time is not enough for all test items.

TABLE 1. TEST OBJECTS - FREQUENCIES AND PRIORITIES Test object Model Carrier

Frequency [MHz]

Channel Priority

PMR radio ONDICO Familje Radio V1.10 446 1, code -- 1 Microphone IMG Stage line TXS-820HT 863 NA 1

914.8 124 2 1710.2 512 1

Mobile phone SONY Ericsson K500i (test phone)

1909.8 810 2

3/2

Calibration procedure Calibration is performed according to four different methods: Laboratory Test-site Description SP Reverberation

Chamber Total radiated power combined with analytical estimate of maximum directivity

NEMKO Oy Semi-anechoic chamber

According to ETSI standard

NEMKO Oy Anechoic chamber


NEMKO COMLAB

Semi-anechoic chamber


Ericsson Microwave Systems

Compact range (anechoic chamber)

In-house procedures for directivity and total radiated power

Result To make a realistic validation of the proposed method it is validated with real commercial products. These products are already compliant to the standards, and therefore their harmonics are very low. This result in difficulties in measuring the actual level of their harmonics, and all test-sites has not reported values for all the cases. Moreover, according to the Round Robin test schedule, SP was supposed to perform the measurements as the last test participant and due to time issues no harmonics were measured at SP at all. They will be measured and reported later on. The measured values are reported in figures 1 - 4 and tables 2 - 5. Photographs of the test setup at the different test-sites are shown in figures 5 - 7. In figure 1 ERP values at the carrier frequencies of the test objects are shown. In figure 2 these values are normalized to the total radiated power of the test objects respectively. I.e. in figure 2 the directivities of the test objects are shown as indirectly reported from the different test-sites. After the normalization some values appear below 0 dB (grey zone) which corresponds to a maximal directivity of the test object less than 1 (linear scale), which is unphysical (an isotropic source has directivity equal to 1, all other sources has maximum directivity larger than 1). This indicates that the values in those points are to low, i.e. the ERP measurement procedure did not find the angle of maximal radiation. In figure 3 data from figure 2 is reused and presented with error bars. The error bars stated in SP:s ERP plot are not error bars but instead 4 dB limits. 4 dB is an acceptable error for an ERP test method. The new method very well fit into those limits. In figure 4 the total radiated power measured in the reverberation chamber at SP and at the compact range at Ericsson Microwave Systems is compared. The average values are computed for frequencies where Ericsson Microwave Systems did measure the total radiated power. Otherwise the values from SP’s measurement are used for normalization. The difference between Ericsson Microwave Systems and SP is less than 0.8 dB for all frequencies.

3/3

Figure 1. ERP values at the carrier frequency of the test objects.

Figure 2. Test results at the carrier frequency of the test objects. The results are normalized to an

average value of the total radiated power measured at Ericsson Microwave Systems and the reverberation chamber at SP (or the SP values at frequencies where Ericsson Microwave Systems did not carry out the measurements). Values below 0 dB (grey zone) corresponds to a maximal directivity

of the test object less than 1. This indicates that the values in those points are to low, i.e. the ERP measurement procedure did not find the angle of maximal radiation.

3/4

Figure 3. Test results at the carrier frequency of the test objects with error bars. In each figure the

normalized ERP (normalized to the total radiated power) is compared to a reference directivity measured at Ericsson Microwave Systems. The error bars stated in SP:s ERP plot are not error bars but

4 dB limits for an acceptable ERP test method. The new method very well fit into those limits.

Figure 4. Total radiated power measured in compact range at Ericsson Microwave Systems and in

reverberation Chamber at SP. The average value is computed for frequencies where Ericsson Microwave Systems did measure the total radiated power. Otherwise the values from SP’s

measurement are used for normalization. The difference between Ericsson Microwave Systems and SP is maximum 0.8 dB.

3/5

TABLE 2. RESULT, SP, to be continued Carrier frequency

Test object Size, object [mm]

Max. Directivity

[dB]

TRP

[dBm]

ERP

[dBm] PMR Radio

130 1.9 21.18 23.1

Microphone

246 3.24 0.40 3.6

Mobile phone, Ch. 124

108 1.97 33.06 35.0


108 3.02 24.29 27.3


108 3.19 30.80 34.0

TABLE 2. RESULT, SP, continued Harmonic 1


Max. Directivity

[dB]

TRP

[dBm]

ERP

[dBm] PMR Radio

130 2,25 - -

Microphone

246 4,25 - -


108 3,13 - -


108 4,06 - -


108 4,21 - -

TABLE 2. RESULT, SP, continued Harmonic 2


Max. Directivity

[dB]

TRP

[dBm]

ERP

[dBm] PMR Radio

130 2,92 - -

Microphone

246 4,79 - -


108 3,74 - -


108 4,61 - -


108 4,75 - -

3/6

TABLE 3. RESULT, NEMKO COMLAB, SEMI-ANECHOIC CHAMBER

ERP [dBm] Test object Carrier

frequency Harmonic

1 Harmonic

2 Harmonic

3 Harmonic

4 Harmonic

5 PMR Radio

21.3 -46.5 -41.4 - - -

Microphone

0.4 -36.6 -37.4 -37.0 -43.5 -


34.2 -53.3 - -49.2 - -


24.1 -33.1 -39.1 - - -


30.1 -33.9 -48.2 - - -

TABLE 4. RESULT, NEMKO OY, SEMI-ANECHOIC CHAMBER ERP [dBm] Test object

Carrier frequency

Harmonic 1

Harmonic 2

Harmonic 3

Harmonic 4

Harmonic 5

PMR Radio

22.9 -44.0 -44.5 -61.1 -51.9 -59.7

Microphone

3.1 -31.1 -35.7 -36.9 -42.8 -39.4


33.6 -53.9 -48.9 -35.5 -51.2 -47.2


25.8 -38.6 -43.4 -44.1 -38.9 -37.6


31.1 -36.0 -42.0 -41.8 -30.5 -41.0

3/7

TABLE 4. RESULT, NEMKO OY, ANECHOIC CHAMBER

ERP [dBm] Test object Carrier

frequency Harmonic

1 Harmonic

2 Harmonic

3 Harmonic

4 Harmonic

5 PMR Radio

20.7 -45.7 -42.8 -57.7 -51.7 -56.6

Microphone

0.9 -28.9 -34.6 -38.2 -44.1 -40.3


31.3 -51.1 -46.7 -37.0 -46.8 -44.6


23.5 -36.6 -41.0 -41.7 -40.7 -38.6


30.1 -35.6 -41.7 -42.0 -31.1 -38.8

TABLE 5. RESULT, ERICSSON MICROWAVE SYSTEMS, to be continued Carrier frequency Harmonic 1 Test object

TRP

[dBm]

Max. Directivity

[dB]

ERP

[dBm]

TRP

[dBm]

Max. Directivity

[dB]

ERP

[dBm] PMR Radio

NA NA NA NA NA NA

Microphone

0.2 4.2 4.4 -33 5.6 -27.4


- 0.8 - - - -


24 4.4 28.4 - - -


30 3.7 33.7 - - -

TABLE 5. RESULT, ERICSSON MICROWAVE SYSTEMS, continued Harmonic 2 Test object

TRP

[dBm]

Max. Directivity

[dB]

ERP

[dBm] PMR Radio

NA NA NA

Microphone

-40 5.8 -34.2


- - -


- - -


- - -

3/8

Figure 5. PMR radio mounted in reverberation chamber at SP Swedish National Testing and research

institute.

Figure 6. GSM phone mounted in semi-anechoic chamber at NEMKO COMLAB.

3/9

Figure 7. PMR radio mounted in anechoic chamber at NEMKO Oy.

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