Impedance Uncertainty Contribution of Artificial Networks (AN, AMN and ISN) Application Note

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Gerald Reynolds
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Impedce Uncertainty Contribution of Artificial Networks (AN, AMN d ISN) Application Note Products: R&S EN4200 R&S EN216 R&S ESH2-5 R&S ESH3-5 R&S ESH3-6 R&S ENY21 R&S ENY41 R&S ENY81 R&S ENY81-CA6

1 Impedce Uncertainty Contribution of Artificial Networks (AN, AMN d ISN) Application Note Products: R&S EN4200 R&S EN216 R&S ESH2-5 R&S ESH3-5 R&S ESH3-6 R&S ENY21 R&S ENY41 R&S ENY81 R&S ENY81-CA6 This application note describes how to determine the uncertainty bounds for a given artificial network impedce for estimate of the combined stdard measurement uncertainty using the Rohde & Schwarz Software AN Impedce Uncertainty Contribution. Application Note Mfred Stecher d Jens Medler EE23_0e

2 Table of Contents Table of Contents 1 Impedce Uncertainty Contribution of Artificial Networks3 1.1 Overview Uncertainty calculation Uncertainty bounds Maximum Deviation Calculator Literature EE23_0e Rohde & Schwarz AN Uncertainty Contribution 2

3 Impedce Uncertainty Contribution of Artificial Networks 1 Impedce Uncertainty Contribution of Artificial Networks Overview 1.1 Overview For Artificial Mains Networks (AMNs) in CISPR [1], the amount of U cispr was calculated based on the assumption of uncertainty circle (see Fig. 1), which in fact is impedce tolerce circle. In Figure 1, the center of the circle is the inal load impedce of the AMN for a given frequency. j25 Ω phase boundaries magnitude boundaries Tolerce Circle (CISPR ) ϕ ϕ AMN AMN Impedce 0 Ω 50 Ω Figure 1: Definition of impedce magnitude d phase tolerces Existing network alysers however do not allow to specify a tolerce circle for the impedce. Therefore the CISPR decided for CISPR [2] to use the original specification of the magnitude tolerce d to add a specification of the phase tolerce. Using trigoetric functions, a value of φ 11,5 degrees follows from / 0,2. For other artificial networks (ANs), e.g. the Asymmetrical Artificial Network (AAN), which in some stdards, e.g. CISPR 22, is called Impedce Stabilization Network (ISN), CISPR specifies both magnitude d phase tolerces of the network load impedce. 1.2 Uncertainty calculation Where the phase requirement cnot be met, the measured phase gles may be taken into account in the uncertainty budged in accordce with CISPR [1]. Guidelines for the calculation of the uncertainty is given in Annex I of CISPR [2]. Figure 2 shows the principle circuit for the calculation. 1EE23_0e Rohde & Schwarz AN Uncertainty Contribution 3

4 Impedce Uncertainty Contribution of Artificial Networks Uncertainty calculation 0 Figure 2: An EUT connected to ideal AN d its flow-graph representation For the example of the ideal 50 Ω/50 µh AMN, 1/Y, with Y 1/R j/ωl, (1) where R 50 Ω d L 50 µh For other ANs, similar values apply. For the real ANs, is replaced by. For the calculation, we use the reflection coefficients corresponding to d the unknown EUT impedce in a 0 impedce system, which are + 0, 0 + for the ideal artificial network. 0 ( 1+ )( 1 2( 1 ) + 0 (2) 0 ) (3) 0 + for the real artificial network. 0 ( 1+ )( 1 2( 1 ) In general, will not equal, d so the measured voltage will differ from. The maximum value of this contribution to measurement uncertainty is given by the extremes of the magnitude of the ratio of to, ) 0 1EE23_0e Rohde & Schwarz AN Uncertainty Contribution 4

5 Impedce Uncertainty Contribution of Artificial Networks Uncertainty bounds (4) 1.3 Uncertainty bounds CISPR uses the concept of impedce tolerce circle of the actual impedce centred on the inal impedce (see Figure 1), with + α exp( jθ ), where 0 α 0, 2 d 0 θ < 2π (5) The value of is unknown d unbounded. However, by choosing the arbitrary value of the normalizing impedce 0 to be real (e.g. 50 Ω), the magnitude of cnot be greater th unity, allowing to be written as ρ exp( jφ ), where 0 ρ 1 d 0 φ 2π (6) Physical considerations suggest that the extremes of (4) are likely to be found when α d ρ take their maximum values of 0,2 d 1,0 respectively. The results in the following table are calculated for the 50 Ω/50 µh AMN with α 0,2 d ρ 1, using all possible combinations of θ d φ, when each were taken in 1 degree steps [3]. Freq MHz Max db Min db Table 1: Extremes from (4) for the 50 Ω/50 µh AMN [3] The largest values in Table 1 occur at 150 khz d were used for calculating U cispr in CISPR To solve the task of calculating the maximum ratio of to for a given measured impedce, R&S have developed the program AN Impedce Uncertainty Contribution which is combined with this Application Note. 1EE23_0e Rohde & Schwarz AN Uncertainty Contribution 5

Maximum Deviation Calculator Uncertainty bounds 2 Maximum Deviation Calculator The calculator allows the calculation of the uncertainty bounds for a given impedce of a real artificial network, e.g. from the calibration report.

6 Maximum Deviation Calculator Uncertainty bounds 2 Maximum Deviation Calculator The calculator allows the calculation of the uncertainty bounds for a given impedce of a real artificial network, e.g. from the calibration report. It also allows the calculation of the uncertainty bounds where the phase tolerce of the AN cnot be met d thus allows a better estimate of the combined stdard uncertainty of conducted emission measurements d whether it is below or above U cispr in CISPR [1]. Figure 3: User interface of the AN Impedce Uncertainty calculator After entering the absolute impedce data (frequency, magnitude d phase) of the AN d pressing the button Calculate, the calculator will return the maximum deviation in db of the measured voltage level from the reference voltage level, see Figure 3. When using AN together with a measuring receiver, the reference voltage level will be measured for y EUT source impedce if the AN impedce agrees with the inal impedce. The magnitude of the EUT reflection coefficient will approach 1. As it is not easy to predict the phase for the maximum deviation, the phase is shown as the second result. 1EE23_0e Rohde & Schwarz AN Uncertainty Contribution 6

7 Literature Uncertainty bounds 3 Literature [1] CISPR :2003, Specification for radio disturbce d immunity measuring apparatus d methods Part 4-2: Uncertainties, statistics d limit modelling Measurement instrumentation uncertainties [2] Amendment 2:2006 to CISPR :2003, Specification for radio disturbce d immunity measuring apparatus d methods - Part 1-2: Radio disturbce d immunity measuring apparatus - Ancillary equipment Conducted disturbces [3] CISPR/A/WG2(Ad-hoc Measurement Uncertainty/Hunter) EE23_0e Rohde & Schwarz AN Uncertainty Contribution 7

8 About Rohde & Schwarz Rohde & Schwarz is independent group of compies specializing in electronics. It is a leading supplier of solutions in the fields of test d measurement, broadcasting, radiomonitoring d radiolocation, as well as secure communications. Established more th 75 years ago, Rohde & Schwarz has a global presence d a dedicated service network in over 70 countries. Compy headquarters are in Munich, Germy. Environmental commitment Energy-efficient products Continuous improvement in environmental sustainability ISO certified environmental magement system Regional contact Europe, Africa, Middle East customersupport@rohde-schwarz.com North America TEST-RSA ( ) customer.support@rsa.rohde-schwarz.com Latin America customersupport.la@rohde-schwarz.com Asia/Pacific customersupport.asia@rohde-schwarz.com This application note d the supplied programs may only be used subject to the conditions of use set forth in the download area of the Rohde & Schwarz website. R&S is a registered trademark of Rohde & Schwarz GmbH & Co. KG; Trade names are trademarks of the owners. Rohde & Schwarz GmbH & Co. KG Mühldorfstraße 15 D München Phone Fax

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