Jan Sroka

Warsaw University of Technology

*Original article translated from Polish.*

**Introduction**

The quantity of interest (measurand) by the measurement of radiated disturbances is either electric or magnetic field strength. It is detected with an antenna and converted to the signal in the 50Ω coaxial system. This signal is transmitted to the measurement receiver via coaxial cables and a feedthrough^{2}. Components of the transmission paths are usually characterized with scattering parameters (S-Parameters). The factor *F* transducing the measurand to the signal recorded by the measurement receiver in sense of this paper neglects reflections (mismatching). Such factors are commonly used in EMC test houses. This simplification imposes error which can be used as a correction. To this error the adjective “mismatch” is attributed and complying with the document [1] the symbol *δM* is assigned. As a matter of course the relation between the measurand and the voltage recorded with the receiver is a product (*F x δM*) or a sum (*F + δM*) of the transducer factor and the mismatch error, depending on the scale used (linear or dB).

**Antenna Factors**

By radiated disturbances magnitude of either electric or magnetic field intensity (|E| or |H|) is sensed with an antenna located in the far field zone [2]. The measurands Q can be generalized as below:

Two features of the antenna namely the antenna factor F_{A} (magnitude) and reflections at the antenna feeding-point Γ_{S} (complex) being on par with the impedance Z_{S} are evaluated in the calibration process. Only magnitude of the antenna factor is measurable, therefore F_{A} is a frequency dependent real variable.

The antenna factor F_{A} is the ratio between the magnitude of field intensity at the place of antenna location and the magnitude of voltage at the antenna feeding-point |U|, provide the measurement instrument at the antenna feedingpoint is reflection free (Γ_{L} = 0).

The magnitude of electromotoric force (EMF) |ε| in the equivalent circuit of the antenna (Figure 1) is proportional to the filed intensity. It is valid for electric field as well as for magnetic field antenna.

By assigning the equivalent circuit with the 50Ω load as shown in Fig.1 and setting calibration features and relation Equation 2 in it, the antenna factor FA can be derived

Neglecting load reflections in Equation 3 (Γ_{L} = 0) is justified if the measurement instrumentation is traceably calibrated and mismatch is compensated but never the less reflections on the receive input do exist and they contribute by the mismatch error of the measurement path by disturbance measurement.

**Mismatch Error by Junction Antenna-Receiver**

If the antenna is connected directly to the measurement receiver (dotted branch in Figure 1), voltage drop across the receiver input *U* is as follows:

The combination of Equation 4 and Equation 3 yields:

Taking into account the mismatch on the receiver input (Equation 14) yields:

It is visible that

is the mismatch error of radiated disturbances by the direct connection antenna-receiver.

**Mismatch Error By Antenna-Receiver Connected Via Inserted Path**

Usually the antenna is connected to the receiver via the path composed of two coaxial cables and the feedthrough in between Figure 2, mounted in the chamber wall. This situation coincides with the scheme shown in Figure 7b, where the source is an antenna, the load is a receiver and an inserted path between Port-1 and Port-2 is characterized with the complex matrix of S-parameters.

By setting together the constitutional formula of the insertion loss (Equation 15) and the voltage drop across the receiver input by direct connection of the antenna (Equation 5), and then applying the receiver mismatch Equation 14 to the voltage drop U2, the relation between |Q| and the registered voltage |UR| can be found:

The recalculation factor of the composition: antenna-inserted path is a product of the antenna factor and the path attenuation

and

is the mismatch error of radiated disturbances by connecting

the antenna with the receiver via the path.

**Remarks On Antenna and Receiver Reflections**

The reflection Γ_{S} at the antenna feeding-point is present in the mismatch error by not inserted and inserted path (Equation 7 and Equation 10, respectively.)

Electric antennas are calibrated in the fully anechoic i.e. reflection free chambers. The same electromagnetic environment exist by the measurements of radiated disturbances in the fully anechoic rooms. Therefore Γ_{S} in this environment is a deterministic, complex variable independent on the antenna height above the floor and on the antenna polarization.

However, by the measurements of electric disturbances in a semi-anechoic chamber, by which the height of the antenna above the floor is scanned, moreover the polarization and sometimes the tilting is changed, Γ_{S} is a variable dependent on the all mentioned parameters^{3}. Strictly speaking extremes of Γ_{S} depending on the antenna height, polarization and tilting should be found. They constitute the range of variations for Γ_{S} as a random variable. Fortunately this variation is very weak. Therefore in this paper Γ_{S} is regarded as a deterministic variable by the typical antenna height, separately for the horizontal and the vertical polarization.

Another simplification stems from the fact that Γ_{S} is almost independent on the EUT, thanks to the far field conditions by disturbance measurement. Therefore, influence of the EUT on Γ_{S} can be neglected by testing.

Variation of the reflection Γ_{S} in the antenna feedingpoint does not take place by testing with the magnetic antennas, because the calibration and the measurement are performed in the same environment, i.e. in the semi anechoic chambers at the fixed height over the floor only by one polarization.

Measurement of the complex reflection Γ_{L} at the receiver input is possible but expensive. The alternative source of information about it can be the technical specification of the receiver. Usually two extremes can be found there i.e. the extremes of |Γ_{L}| with attenuation switched off and on at the receiver input. By radiated measurements the input attenuator of the receiver is always switched off in order not to worsen the signal to noise ratio and to keep possibly big distance of the noise floor to the limits defined in the standard according to which the measurement is performed. If the preamplifier at the receiver input is available, it is switched on in order to improve these two features.

The approach presented in the document [1] consists on such setting the extremes of the mismatch error *δM _{A-I-R}* in the dB scale (Equation 10) that the argument of the log function is an arithmetic sum of magnitudes of all components.

Furthermore, it is assumed that Equation 11 constitutes the range of variation of the ten-dimensional random variable (five complex random variables) with approximately U-shaped probability distribution [2]. Consequently, the semi-range of variation a and the expected value E are as follows:

The ratio √2 of *a* (Equation 12) to the standard uncertainty *u* applies due to the U-shaped distribution. Strictly speaking this distribution is not valid^{4}.

Actually, the mismatch error Equation 10 is a two-dimensional random variable, while only complex |Γ_{L}| is random. The proper and efficient way to estimate it is application of the Monte Carlo method [3], [6], [7]. The author, similarly as in his previous paper [4], used facilities of the Mathcad 13 with its pseudo-random generator with the uniform probability distribution. The expected value *E(X)* was calculated as the arithmetic mean and the standard uncertainty u as u = √E(X2) – E2(X).

**Calculus of the Propagated Distribution Parameters**

Scattering parameters of the path were measured with the vector network analyzer ZVRE from R&S in the frequency range from 30MHz to 1GHz in 801 logarithmically distributed frequency points. The kit 85032B TYPE-N from HP was used for the calibration.

The measurement setup with the receiver type ESIB40 from R&S was considered. According to the manual, the voltage standing wave ratio at the receiver input is not greater than 2.0 by 0dB attenuation at it (V SWR ≤ 2.0). Furthermore, it is not greater than 1.2 if the input attenuation is at least 10dB (V SWR ≤ 1.2), in the whole frequency range from 20Hz to 40GHz. Transposed into the reflection, it means |Γ_{L}| < 0.34 for the 0dB input attenuation. This reflection was taken because as it was explained earlier by radiated emission the attenuator at the receiver input is switched off. There were generated 180 uniformly distributed random magnitudes |Γ_{L}| in the range [0; 0.34]. Each time they were accompanied by 180 random arguments of Γ_{L} in the range [-π;π].

The measurement path is composed of the 9m coaxial cable in the semi-anechoic chamber, feedthrough and 3m coaxial cable in the commando room. Magnitude of of the scattering parameters of the path are shown in Figure 3.

The wide band, BiLog antenna type EMCO3141 was considered. The reflection Γ_{S} at the feeding-point of the antenna was measured in the empty semi-anechoic chamber by 1.5m and by 1.7m antenna height above the floor by the horizontal and the vertical polarization respectively. Their frequency dependent magnitudes are shown in Figure 4. Only slide divergence can be observed.

Comparison of the results of the CISPR and the Monte Carlo approach for the horizontal and the vertical antenna polarizations are shown in Figure 5 and Figure 6. The extremal standard uncertainties in the bands C (30MHz – 300MHz) and D (300MHz – 1GHz) are gathered in Table 1 and Table 2.

**Conclusion**

According to the document, [1] the mismatch error *δM _{A-I-R}* (Equation 10) by the measurement of the radiated emission is a ten-dimensional random variable with approximately U-shaped probability distribution. Its range of variation is estimated generously (Equation 11). Calculation of the parameters of this distribution (the expected value and the standard uncertainty) is straightforward.

By the measurement of electrical disturbances in the semi-anechoic chamber, the reflection Γ_{S} at the antenna feeding-point is deterministic if it is regarded individually for the horizontal and vertical antenna polarization. In such a situation, the mismatch error (Equation 10) is a two-dimensional random variable due to the random complex reflection Γ_{L} at the receiver input. The Monte Carlo method can be easily applied for solving such problem.

In the paper an example of two above mentioned approaches was calculated. The expected values are negligible small in both approaches. It concerns particularly the band D. The standard uncertainty calculated with the CISPR approach is unduly and unnecessarily enlarged.

In the band C, there is a coincidence of big reflection Γ_{S} at the antenna feeding-point and big extreme of the receiver reflection Γ_{L}. This concludes with much bigger uncertainty than in the band D.

**Appendices**

**9.1 Receiver Mismatch**

If reflection Γ_{L} on the input of the measurement receiver is considered, then signal registered and displayed by the receiver U_{R} is not the same as signal U on receiver input. They are related as follows:

**9.2 Insertion loss Γ _{I}**

It is ratio between voltage U across the junction of the source and the load if the source is connected directly to the load (Figure 7a) and voltage U2 across the load if a two port is inserted between the source and the load (Figure 7b).

In the case of the reflection-less source (Γ_{S} = 0) and load (Γ_{L} = 0) insertion loss is reciprocal to the transmission factor S_{21}. Magnitude of it is called attenuation *A.*

**References**

[1] CISPR 16-4-2: 2003, Specification for radio disturbance and immunity measuring apparatus and methods – Part 4-2: Uncertainties, statistics and limit modeling – Measurement instrumentation uncertainty. IEC, 2003.

[2] J. Sroka, Measurement Uncertainty in EMC Testing, Radio-Frequency Emission. OWPW, Monography, 2009.

[3] R. Ba¸bka, Uncertainty of conducted emission measurements in EMC . Warsaw University of Technology, Dissertation, 2009.

[4] J. Sroka, Mismatch Correction by Measurement of Conducted Radio Disturbances With AMN . IEEE Trans. on EMC Vol. 53 No. 2 pp. 534 – 536, May, 2011.

[5] J. Sroka, Mismatch Error by Measurement of Radiated Disturbances in EMC Testing. PRZEGLA˛D ELEKTROTECHNICZNY (Electrical Review), PL ISSN 0033- 2097, ROK LXXXVIII NR 2 pp. 92-95, 2012.

[6] Joint Committee for Guides in Metrology (JCGM), Evaluation of measurement data – Supplement 1 to the “Guide to the expression of uncertainty in measurement” – Propagation of distributions using a Monte Carlo method. JCMG 101:2008. Freely available at OIML web side, www.oiml.org.

[7] C.,F.,M. Carobbi, The GUM Supplement 1 and the Uncertainty Evaluations of EMC Measurements . IEEE EMC Society Newsletter, Issue No. 225, 2010.

[8] C.,F.,M. Carobbi, M. Cati and C. Panconi, Note on the Expected Value and Standard Deviation of the Mismatch Correction . IEEE Trans. Electromagn. Compat. vol. 53, no. 4, pp.1098-1099, Nov. 2011.

**Prof. Jan Sroka** is with the Warsaw University of Technology, IETiSIP, Koszykowa 75, 00-662 Warszawa, Poland ([email protected]) and with the EMC-Testcenter

Zürich AG, Schaffhauserstr. 580, 8052-Zürich, Switzerland ([email protected])

He is also the scientific EMC consultant by the ASTAT Sp. z o. o. Pozna´n (www.astat.com.pl).