Common EMC Measurement Terms - All-Electronics.de...The only specific requirements are found in IEC 801 - 3 and IEC 1000 - 4 - 3, which, if the analysis of the requirement is performed,

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According to Krause1, “A radio antenna may be defined as thestructure associated with the region of transition between aguided wave and free space, or vice versa”. The EMC testcommunity uses specialized versions of radio antennas formeasuring electric and magnetic field amplitudes over a verybroad frequency spectrum.

EMC test engineers must perform very precise measurements.Sometimes the terms used in describing these measurementscan be confusing. This section describes the meaning of some ofthese terms.

Antenna Factor

This is the parameter of anEMC antenna that is used inthe calculations of fieldstrength during radiatedemissions measurement. Itrelates the voltage output ofa measurement antenna tothe value of the incident field producing that voltage. The unitsare volts output per volt/meter incident field or reciprocalmeters. As can be seen in the derivations, the analyticalexpression for Antenna Factor (AF) has the equivalent offrequency in the numerator, thus AF will typically increase withincreasing frequency. EMCO antennas used for radiatedemissions testing are individually calibrated (the AF is directlymeasured) at all appropriate measurement distances. Thecalibrations produce values that are defined as the “equivalentfree space antenna factor”. This antenna factor is measuredby EMCO using the three antenna measurement method overa ground plane. The calibration procedure corrects for thepresence of the reflection of the antenna in the ground plane,giving the value that would be measured if the antenna were in“free space”. The typical antennas used for measurements arebroadband antennas such as BiConiLogTM and log periodicantennas. In case of any disagreement, a “reference antenna”—a tuned resonant dipole—is considered to be the arbiter formeasurement purposes.

Transmit Antenna Factor

The Transmit Antenna Factor(TAF) is similar to the AF inthat it describes the perfor-mance of an EMC antenna overits frequency range ofoperation. This parameterrelates the E-field produced byan antenna, at a given distance, to the input voltage at the inputterminals of the antenna. The units are volts/meter producedper volt of input, so the final units are reciprocal meters just asthe AF. The AF and TAF are not the same nor are they recipro-

cal, though the AF and TAF can be computed from eachother. The expressions for these computations may be foundin the section “Antenna Terms and Calculations”. The TAF isnot a direct function of frequency, but it is a function ofdistance.

Antenna Pattern

The antenna pattern is typicallya polar plot of the relativeresponse of an antenna as afunction of viewing angle. The“on-axis” viewing angle wherethe response of the antenna is amaximum is called “theboresight axis”. The patternshows the response of the antenna as the viewing angle isvaried. Typically, simple antennas exhibit a “dipole response”where the pattern of the antenna is donut shaped with thedipole on the common axis of the donut. More complexantenna patterns are approximately pear shape with thebottom of the pear facing away from the antenna.

Gain

The gain of the antenna is aparameter that describes thedirectional response of the antennacompared to an isotropic source, atheoretical antenna that radiatesthe same amount in all directions.The higher the gain, the better theantenna concentrates its beam in a specific direction. Thesimple example is a light bulb compared to a flashlight. Theflashlight, with its reflector, concentrates the light in onedirection, where the light bulb produces light in all directions.

Bandwidth

The bandwidth of an antennais the operating frequencyrange of the antenna and isexpressed in MHz.

Typical EMC antennas willhave a ratio of upper usefulfrequency to lowest useful frequency on the order of 5 to 1.Some unique designs provide ratios of as much as 25 to 1. Thisratio is a dimensionless ratio, i.e., it has no units.

Common EMC Measurement Terms

sb

Emitec

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Beamwidth

This parameter is thedescriptor of the viewingangle of the antenna, inthe plane of measure-ment, typically where theresponse has fallen to onehalf the power receivedwhen the antenna is perfectly aligned. EMC antennas arenormally designed to provide a viewing angle in the primaryplane, approaching 60° between the half power points wherethe response of the incident is 3 dB down, if at all possible.The only specific requirements are found in IEC 801 - 3 andIEC 1000 - 4 - 3, which, if the analysis of the requirement isperformed, translates into a minimum viewing angle of 28 °(± 14 °) at the 1 dB down points. The 1 dB down response isusually compatible with the 3 dB down value of 60 °.

Reflection Coefficient

The voltage reflection coefficient, typically ρ, is the ratio of thevoltage reflected from the load of a transmission line to thevoltage imposed on the load of the same transmission line. Itsvalues vary from zero to one. When the load impedance is“matched” to the source impedance (has the same value),and the characteristic impedance of the transmission line,then the reflection coefficient is quite small (no reflection),approaching zero. When there is “mismatch” (the loadimpedance differs from the characteristic impedance) thereflection coefficient can approach one (almost all incidentpower is reflected).

The reflection coefficient is usually determined by a measure-ment of the Voltage Standing Wave Ratio.It is then computed from:

| ρ | =(VSWR–1 )

(VSWR+1 )

VSWR

The Voltage Standing Wave Ratio (VSWR) is a measure of themismatch between the source and load impedances. Numeri-cally, it is the ratio of the maximum value of the voltagemeasured on a transmission line divided by the minimumvalue.

When the value is high, most of the power delivered from agenerator is reflected from the antenna (load) and returnedto the generator. The amount of power not reflected isradiated from the antenna. This means that the generatorrating for an antenna with a high VSWR can be quite high.Users should choose an antenna with a low VSWR whenpossible. As a practical matter, this may not always bepossible, particularly at lower frequencies.

RF Power Terms As Applied To Antennas

There areseveral waysof discussingRF power asused to exciteantennas forthe generationof electromagnetic fields. This set of related definitions isprovided to understand the definitions as used in thiscatalog.

Forward Power — The output from an amplifierthat is applied to an antenna input to generate anelectromagnetic field.

Reflected Power — When mismatch exists at theantenna port, a fraction of the power applied (theforward power), is reflected from the antenna backtoward the amplifier. This is termed the reflectedpower.

Net Power — The power applied to the antenna thatis actually radiated is called the net power or radiatedpower. It is the difference between the forward powerand the reflected power. Usually, this value cannot bedirectly measured, but is computed from the directmeasurement of forward and reflected power bytaking the difference:

Pnet

(W ) = Pforward

(W ) – P reflected

(W )

In this catalog the Net Power is the power value that is requiredas an input to an antenna to generate a specific E-field level.

Polarization

The orientation of the measurement axis of a linearlypolarized antenna with respect to the local ground plane.Vertical polarization occurs when the measurement axis ofthe antenna is perpendicular to the local ground plane.Horizontal polarization occurs when the measurement axis isparallel to the local ground plane. Most EMC test specifica-tions require measurements in both vertical and horizontalpolarizations of the measurement antenna.

1 John D. Krause, Ph.D., Antennas, McGraw-Hill, New York, 1950, p. 1.

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Definition of Antenna FactorDefinition of Antenna FactorDefinition of Antenna FactorDefinition of Antenna FactorDefinition of Antenna FactorThis term is traditionally tied to the recieve antenna factor,the ratio of field strength at the location of the antenna to theoutput voltage across the load connected to the antenna.

.➊ AF = E

Vwhere:

AF = Antenna Factor, meters –1

E = Field Strength, V/m or µV/mV = Load Voltage, V or µV

Converting to dB (decibel) notation gives:

.➋ AFdB(m –1) = 20 log E

or: V

.➌ AFdB(m–1) = EdB(V/m) – VdB(V)

The antenna factor is directly computed from:

.➍ AF = 9.73 (m –1 )λ √ g

where:

λ = Wavelength (meters)g = Numeric Gain

In the same sense, for magnetic fields, as seen byloop antennas:

.➎ AFH dB(S/m) = H dB(A/m) – VdB(V)

In terms of flux density (B-Field):

.➏ AFB = AF H + 20 log (µ)

.➐ AFB = AF H – 118, T / V

Loop antennas are sometimes calibrated in terms of equivalentelectric field, where:

.➑ AFE dB(m–1)= AFH dB(S/m) + 20 log η

.➒ AFE dB(m–1)= AFH dB(S/m) + 20 log (120 π), or

= AFH dB(S/m) + 51.5 dBwhere:

η = the Impedance of Free Space

= 120 π Ω

11111 Conversion of Signal Levels from mW to Conversion of Signal Levels from mW to Conversion of Signal Levels from mW to Conversion of Signal Levels from mW to Conversion of Signal Levels from mW to µVVVVVin a 5in a 5in a 5in a 5in a 500000Ω SystemSystemSystemSystemSystemVoltage and power are equivalent methods of stating a signallevel in a system where there is a constant impedance. Thus:

.➊ P = V 2

Rwhere:

P = Power in WattsV = Voltage Level in VoltsR = Resistance Ω

For power in milliwatts (10–3

W), and voltage inmicrovolts (10

–6V),

.➋ VdB(µV) = PdBm + 107

Power Density to Field StrengthPower Density to Field StrengthPower Density to Field StrengthPower Density to Field StrengthPower Density to Field StrengthAn alternative measure of field strength to electric field ispower density:

.➊ Pd = E 2

0

120 π

where:

E = Field Strength (V/m)P = Power Density (W/m2 )

Common Values:

E PD

200 V/m 10.60 mW/cm2

100 V/m 2.65 mW/cm2

10 V/m 26.50 µW/cm2

1 V/m 0.265 µW/cm2

Power Density at a PointPower Density at a PointPower Density at a PointPower Density at a PointPower Density at a Point

.➊ Pd = Pt Gt0

4 π r2

In the far field, where the electric and magnetic fields arerelated by the impedance of free space:

Pd = Power Density (W / m2 )

Pt = Power Transmitted (W)

Gt = Gain of Transmitting Antenna

r = Distance from Antenna (meters)

22222

33333

44444

Antenna Calculations

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Friis Transmission FormulaFriis Transmission FormulaFriis Transmission FormulaFriis Transmission FormulaFriis Transmission FormulaThe Friis Transmission formula describes Power received by anantenna in terms of power transmitted by another antenna:

.➊ Pr = PtGtGr λ2

(4 π r) 2

where:Pr = Power Received (W)

Pt = Power Transmitted (W)

Gr = Numeric Gain of ReceivingAntenna

Gt = Numeric Gain of TransmittingAntenna

r = Separation Between Antennas(meters)

λ = Wavelength (meters).

Electric Field vs Power Transmitted (Far Field)Electric Field vs Power Transmitted (Far Field)Electric Field vs Power Transmitted (Far Field)Electric Field vs Power Transmitted (Far Field)Electric Field vs Power Transmitted (Far Field)The electric field strength at a distance from a transmittingantenna such that the electric and magnetic field values arerelated by the impedance of free space is:

.➊ E V / m = √30PtG t

r

where the terms are as defined above.

For simple radiating devices having low gain, far fieldconditions exist when:

.➋ r ≥ λ 0

2 π

where:λ = Wavelength (meters)

For more complex antennas having higher gain values,far field conditions exist when:

.➌ r ≥ 2D 20

λ

where:D = Maximum Dimension of

the Antenna (m)

Relationship of Antenna Factor and Gain in aRelationship of Antenna Factor and Gain in aRelationship of Antenna Factor and Gain in aRelationship of Antenna Factor and Gain in aRelationship of Antenna Factor and Gain in a5555500000 Ω SystemSystemSystemSystemSystem

55555 77777

.➊ GdB = 20 log (f MHz)– AFdB(m –1) – 29.79

Power Required to Generate a Desired Field StrengthPower Required to Generate a Desired Field StrengthPower Required to Generate a Desired Field StrengthPower Required to Generate a Desired Field StrengthPower Required to Generate a Desired Field Strengthat a Given Distance when Antenna Factors are Knownat a Given Distance when Antenna Factors are Knownat a Given Distance when Antenna Factors are Knownat a Given Distance when Antenna Factors are Knownat a Given Distance when Antenna Factors are Known

.➊ PdB(W ) = 20 log10 ( E desired (V / m))+ 20 log10 (d m)– 20 log10 ( f MHz)+ AFdB(m –1) + 15

Relationship Between Frequency and WavelengthRelationship Between Frequency and WavelengthRelationship Between Frequency and WavelengthRelationship Between Frequency and WavelengthRelationship Between Frequency and Wavelengthin Free Spacein Free Spacein Free Spacein Free Spacein Free Space

.➊ f λ = c

where:

f = Frequency (Hz)

λ = Wavelength (meters)

c = Velocity of Light

= 3 x 108 m/s

a simpler relationship is:

.➋ λ = 300

f MHz

Decibel FormulasDecibel FormulasDecibel FormulasDecibel FormulasDecibel FormulasA decibel is one tenth of a Bel, and is a ratio measure ofrelative amplitude. In terms of power, the number ofdecibels is ten times the logarithm to the base 10 of theratio.

In terms of power:

.➊ d B = 10 log10 (P1 / P2)where P1 and P2 are in watts.

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In a constant impedance system, power references can be madebetween different measurement points. They can also be related tovoltage or current measurements:

.➋Power Ratio = 10log

10(P1/P2)

= 10 log10

V12/R 10

V22

/R2

= 20 log10

V10

V2

– 10 log10

R 10

R2

for a constant impedance system.

.➌ R1= R

2

and:

.➍Pwr Ratio (dB)= 20 log

10

V10

V2

Also:

.➎ GdB

= 10log(g)

.➏ VdB(reference)

= 20log(V/Vreference)

.➐ PdB(reference)

= 10log(P/Preference)

where a typical reference for voltage is microvolts and atypical reference for power is milliwatts.

The reverse relationships are:

.➑ g = 10GdB/10

.➒ V = 10VdB(reference)/20

.➓ P = 10PdB(reference)/10

Transmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorThe transmit antenna factor of an antenna is computed fromthe gain or receive antenna factor, and is a measure of thetransmitting capabilities of that antenna. It is valid under theconditions of measurement of the receive antenna factor, ina 50 Ω system.

.➊ TAFdB(m –1)=GdB – 2.22 –20log

10(dm)Where:

TAFdB(m –1) = Transmit Antenna Factor

GdB

= Antenna Gain ofTransmitting Antenna

dm= distance(m)

Alternatively:

.➋ TAFdB

= 20log(fMHz)–AFdBm –1

– 32.0–20log(rm)

Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-sity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volt /t /t /t /t /metermetermetermetermeterAntenna transmitting capabilities are often given in terms ofthe input power to an antenna to generate 1V/m at one ormore distances. The input power required to develop adifferent electric field level value is found by:

.➊ PdB(W) =P

dB(W)(1V/m) + 20log10(EdesiredV/m)

1111111111

1212121212

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In a constant impedance system, power references can be madebetween different measurement points. They can also be related tovoltage or current measurements:

.➋Power Ratio = 10log

10(P1/P2)

= 10 log10

V12/R 10

V22

/R2

= 20 log10

V10

V2

– 10 log10

R 10

R2

for a constant impedance system.

.➌ R1= R

2

and:

.➍Pwr Ratio (dB)= 20 log

10

V10

V2

Also:

.➎ GdB

= 10log(g)

.➏ VdB(reference)

= 20log(V/Vreference)

.➐ PdB(reference)

= 10log(P/Preference)

where a typical reference for voltage is microvolts and atypical reference for power is milliwatts.

The reverse relationships are:

.➑ g = 10GdB/10

.➒ V = 10VdB(reference)/20

.➓ P = 10PdB(reference)/10

Transmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorTransmit Antenna FactorThe transmit antenna factor of an antenna is computed fromthe gain or receive antenna factor, and is a measure of thetransmitting capabilities of that antenna. It is valid under theconditions of measurement of the receive antenna factor, ina 50 Ω system.

.➊ TAFdB(m –1)=GdB – 2.22 –20log

10(dm)Where:

TAFdB(m –1) = Transmit Antenna Factor

GdB

= Antenna Gain ofTransmitting Antenna

dm= Distance(m)

Alternatively:

.➋ TAFdB

= 20log(fMHz)–AFdBm –1

– 32.0–20log(rm)

Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-Computing Power Required for a Specific Field Inten-sity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volsity Given Power Required to Generate 1 Volt /t /t /t /t /metermetermetermetermeterAntenna transmitting capabilities are often given in terms ofthe input power to an antenna to generate 1V/m at one ormore distances. The input power required to develop adifferent electric field level value is found by:

.➊ PdB(W) =P

dB(W)(1V/m) + 20log10(EdesiredV/m)

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TO CONVERT FROM: Unit System: SI (MKS) CGS

Magnetic Qty.: B H B H B Units: teslateslateslateslatesla amp-turn/mamp-turn/mamp-turn/mamp-turn/mamp-turn/m gaussgaussgaussgaussgauss oerstedoerstedoerstedoerstedoersted gammagammagammagammagammateslateslateslateslatesla 1 4π x 10-7† 10-4 10-4† 10-9

amp-turn/mamp-turn/mamp-turn/mamp-turn/mamp-turn/m 7.96 x 105‡ 1 79.57747‡ 79.57747 7.96 x 10-4‡

gaussgaussgaussgaussgauss 104 4π x 10-3† 1 1† 10-5

oerstedoerstedoerstedoerstedoersted 104‡ 4π x 10-3 1‡ 1 10-5‡

gammagammagammagammagamma 109 4π x 102† 105 105† 1

SI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & Abbreviations

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TO:

MULTIPLY BY ABOVE VALUE

pico 10-12 p

nano 10-9 n

micro 10-6 µmilli 10-3 m

kilo 103 k

Mega 106 M

Giga 109 G

QUANTITY NAME SYMBOL

SI Base UnitsSI Base UnitsSI Base UnitsSI Base UnitsSI Base Units

Conversion Table for Magnetic UnitsConversion Table for Magnetic UnitsConversion Table for Magnetic UnitsConversion Table for Magnetic UnitsConversion Table for Magnetic Units

length meter m

mass kilogram kg

time second s

electric current ampere A

PREFIX MULTIPLIER SYMBOL

area square meter m2

volume cubic meter m3

frequency hertz Hz s-1

mass density kilogram per cubic meter kg/m3

speed, velocity meter per second m/s

angular velocity radian per second rad/s

acceleration meter per second squared m/s2

angular acceleration radian per second squared rad/s2

force newton N kg•m/s2

pressure pascal Pa N/m2

work, quantity of heat joule J N•m

power watt W J/s

quantity of electricity coulomb C A•s

potential difference volt V W/A

electric field strength volt per meter V/m

electric resistance ohm Ω V/A

capaticitance farad F A•s/V

magnetic flux weber Wb V•s

inductance henry H V•s/A

magnetic flux density tesla T Wb/m2

magnetic field strength ampere per meter A/m

admittance siemens S 1/Ωelectricantenna factor per meter 1/m

magnetic antenna factor siemens per meter s/m

QUANTITY NAME SYMBOL

† Assumes µ = 1; if µ ≠1, multiply by value of µ to convert from H to B.‡ Assumes µ = 1; if µ ≠1, divide by value of µ to convert from B to H.1 tesla ≡ 1 weber/m2.

For example, 1 tesla = 104 gauss.1 gauss = 79.6 ampere-turns/m in an unloaded coil (µ = 1).If µ = 2.50, 1 tesla = 7.96 x 105 / 2.50 = 3.18 x 105 amp-turns/m.

CONSTANT COMPUTATIONAL VALUE

Speed of light c = 2.99792458 x 108 m/s

in a vacuum: ≈3.00 x 108 m/s

Permitt ivity 0 = 1/(µc2) F/m

constant : ≈ 8.85 x10-12 F/m

Permeabi l i ty µ0 =4π x 10-7 H/mconstant : ≈ 1.26 x 10-6 H/m

SI Derived UnitsSI Derived UnitsSI Derived UnitsSI Derived UnitsSI Derived Units

SI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & AbbreviationsSI Prefixes, Multipliers, & Abbreviations

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Understanding Radiated Emissions Testing

In a radiated emissions test, electromagnetic emissionsemanating from the equipment under test (EUT) are measured.The purpose of the test is to verify the EUT’s ability to remainbelow specified electromagnetic emissions levels duringoperation. A receive antenna is located either 3 or 10 metersfrom the EUT. In accordance with ANSI C63.4, the receiveantenna must scan from 1 to 4 meters in height. The scanninghelps to locate the EUT’s worst-case emissions level.

Figure 1 shows a block diagram of an emissions test system suchas might be used for ANSI C63.4 testing. The test set-up iscomposed of a receive antenna, a first interconnecting cable, apreamplifier, a second interconnecting cable, and a radio noisemeter (receiver or spectrum analyzer).

The purpose of each of the components of theradiated emissions test setup are:

The Receive AntennaThe performance measure of this antenna in relating the valueof the incident E-field to the voltage output of the antenna is theAntenna Factor. This is usually provided by the manufacturer indB with units of inverse meters. A variety of antennas can beused for these measurements. Typically, a combination of twoantennas is used to cover the frequency range from 30 MHz to1000 MHz—a biconical covering the frequency range of 30 to200 MHz and a log periodic covering the frequency range of 200to 1000 MHz. New antenna technology, such as EMCO’sBiConiLogTM antenna, can cover the complete frequency range.This Antenna Factor is shown at A.

The First Interconnecting CableThis cable connects the antenna output to the preamplifierinput. There is a reduction in measured signal amplitude due tolosses in the cable. To increase accuracy, these losses need to beadded to the measured value of the voltage out of the antennato compensate for the losses. Cable loss is shown at B.

The PreamplifierThe preamplifier is typically used with spectrum analyzers tocompensate for the high input noise figure typical of suchdevices. Receivers may not need this device. The amplifiermakes the measured signal larger, thus the final answer must becorrected by subtracting the gain of the preamplifier. Preampli-fier gain is shown at C.

The Second Interconnecting CableThis cable connects the output of the preamplifier to the radionoise meter. There is a reduction in measured signal amplitudedue to losses in the cable. To increase accuracy, these lossesneed to be added to the measured value of the voltage out of theantenna to compensate for the losses. Cable loss is shown at D.

The Radio Noise Meter

Typically, the radio noise meter is either a receiver or aspectrum analyzer. Either is essentially a 120 kHz bandwidth,tunable, RF microVolt meter calibrated in dB µV. A signalresponse is shown in Figure E.

The calculation of the measured E-field signal levelis then given by:

E(dB µ V/m) = V(dB µ V) + CL1(dB) – PAG(dB) + CL

2(dB) +

AF(dBm-1)

where:E(dB µ V/m) = Measured E-field

V(dB µ V) = Radio Noise Meter Value

CL1(dB) = Loss in Cable 1

PAG(dB) = Preamplifier gain

CL2(dB) = Loss in Cable 2

AF(dBm-1) = Antenna Factor

This computed value can be compared to the publishedspecification limit for determination of whether the measuredvalue is less than the specification limit, thus showing compli-ance with the requirement.

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stin

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Figure 1. Radiated Emissions Test

Notes on Figure 1 A is the Antenna Factor (AF) versus frequency. The units

are meters–1. The AF relates the RF voltage output of anantenna to the E-Field causing the voltage to appear.

B, D are the reduction in signal that is caused by losses in theinterconnecting coaxial cables.

C is the low noise figure preamplifier gain, which can varywith frequency.

E is the value measured at some frequency by the 120 kHzbandwidth radio noise meter.

Figure 1. Radiated Emissions Test

E(dB µ µ µ µ µ V/m) = V(dB µ µ µ µ µ V) + CL1(dB) – PAG(dB) + CL

2(dB) + AF(dBm–1)

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In a radiated immunity test, a test signal of RF energy,typically three or ten volts per meter, is directed at theequipment under test (EUT), and the EUT’s reaction to thistest signal is analyzed. The purpose of the test is to demon-strate the ability of the EUT to withstand the excitation of thesignal, without showing degraded performance or failure. Themore immune a product is to this test signal, the better itshould operate when other electronic or electrical equipmentis present in its environment.

Figure 1 shows a block diagram of an immunity test systemsuch as might be used for IEC 61000-4-3 testing. The testsetup is composed of a signal generator, an amplifier, aforward/reverse power coupler with its associated powermeter, a radiating antenna, and an omni-directional E-fieldprobe system.

The purpose of each of the components of theradiated immunity test setup is:

The Signal GeneratorThe signal generator is used to provide the test signal. It shouldhave adequate output resolution to allow precise setting of thereference level of the E-field to within 1 % of the desired level.The signal generator must be capable of providing the desired80 % AM with a 1 kHz sine wave for testing. A typical signalgenerator output is shown at A.

The AmplifierThe amplifier increases the test signal strength to levels, thatwhen applied to the antenna, will produce the desired E-fieldlevels. Note that EMC test amplifiers are specified with aminimum gain. Due to the extremely wide bandwidth, they canshow ripple of several dB in the pass band. The amplifier mustbe operated in a linear mode to assure repeatability. A typicalamplifier response is shown at B.

The Forward / Reverse Power CouplerThe forward / reverse power coupler is placed in-line with theamplifier output to the antenna input, as near to the antenna aspractical. The difference in the forward and reverse power (thenet power) is recorded to determine the input level necessaryfor developing the desired test signal, and to show that thisdesired input to the antenna is developed during testing. This isshown at C.

The AntennaThe antenna generates the desired E-field. Its performance ingenerating the E-field is given by the Transmit AntennaFactor (TAF), as shown at D.

The Omni-directional Probe SystemThe probe system is used to directly measure the value of thefield strength, at E.

Figure 2 shows a graphical display of the signals of the immunitytest system. This figure also includes computations of the signallevels at a specific frequency of 100 MHz.

The output level is given by:

E(dB µ V/m) = SGout

(dB µ V) + AG(dB) + TAF(dB) m–1)

where:E(dB µ V/m) = The E-field test level

SGout

(dB µ V) = The signal generator output

AG(dB) = Amplifier gain

TAF(dB) m–1) = The transmit antenna factor

The variables and terms in the expression above are used forcalibration test setups. They demonstrate how instrumentationand facility factors contribute to meet the typically requiredE-field uniformity value of – 0.0 dB, + 6.0 dB. Remember thatactual testing to demonstrate that the EUT will not malfunctionwhen exposed to the desired level requires the addition of 80 %amplitude modulation with a 1 kHz sine wave to the test signal.This, in turn, requires an additional 5.1 dB 10 x log

10 [(1.8)2]of

linear gain from the amplifier than is found during calibration.

Understanding Radiated Immunity Testing

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Figure 1. Radiated Immunity Test

Notes on Figure 1

❶

A is signal generator output.

B is amplfier gain versus frequency.

C is signal generator output + amplifier gain (= input toantenna.

D is transmit antenna factor (TAF).

E is E-field level generated (= input to antenna + (TAF).

Figure 1. Block Diagram of Typical Immunity Test Setupwith Signal Levels & Characteristics Added

❷ For immunity testing, test distance is from tip of antenna.

❸ Immunity amplifiers are typically specified at minimumgain. Pass band ripple is result of extra wide bandwidths.

Probe

F/O Link

Probe

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Figure 2. Radiated Immunity Test

Notes on Figure 2

❶ Required test field is10 V/m (= 20 dB V/m = 140 dB µ V/m).

❷ At 100 MHz TAF is – 8.66 dB => Vin to Antenna is140 – (–8.66) = 148.66 dB µV.

❸ At 100 MHz Signal Generator Output isAntenna Input – Amplifier gain(= 148.86 – 47 = 101.86 dB µV = 123 µV).

Figure 2. Graphical Representation of Immunity Test System Signal

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8282828282

Introduction

This Application Note explains three separate methods for thecalculation of input power to an antenna to achieve a specificvalue of E-field for immunity or susceptibility testing, at aspecific distance from the antenna. The estimates of requiredpower agree well between the three methods (See Table 2.), soany of the three methods can be used as a function of informa-tion available regarding the antenna.

Calculations

This section describes three completely different, independentmethods for calculating the input power required for a givenE-field value as a function of frequency, at a given distance fromthe antenna. Inherent assumptions are that bore-sightalignment exists from the antenna to the point where the E-fieldis evaluated, and that ideal propagation conditions exist.

The three methods are:

The Friis Transmission Formula

The Transmit Antenna Factor

Using information from published catalog or data sheetvalues of E-field for a given reference level of E-field.

Input power to an antenna to develop specified E-field value isreadily accomplished, given some combination of the followinginformation:

numerical gain, Gi

gain in dB, Gi , (dB), and

antenna factor, AF (dB m-1).

The required information is:

distance from the transmitting antenna reference point,

frequency, and

required E-field level.

Expressions for computing any of these input variables, given avalue for one, are shown in Table 1.

Table 1.

Expressions for Computing Gi

, Gi (dB), and

AF(dB m-1), Given A Value for One Parameter

Sample values, at 100 MHz, used in the calculations are:

numerical gain over an isotropic antenna, Gi , = 2.05,

gain in dB of the antenna, Gi , (dB) = 3.1 dB,

Antenna Factor , AF (dB m-1) = 7.1 dB m-1

Figure 1 shows the geometry assumed for the calculations, andsome of the important variables.

Figure 1.

Geometry for the Calculation of Input Powerfor a Given E-Field

Note that the reference point for calibration is different forthe two standards applied for calibration of E-field generatingantennas. The Society of Automotive Engineers AerospaceRecommended Practice 958 is applied for calibration of antennasused in MIL-STD testing, for a spacing of 1 meter, tip-to-tip. TheAmerican National Standards Institute C63.5 is applied from

Computing Required Input Powerfor a Given E-Field Level

at a Given Distance

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feed point for biconical dipole antennas, and, as shown, fromthe mid-point of all elements of a log periodic antenna’selement array. These measurement reference points on theantennas are important because they define the starting point ofthe distance to the point in free space, where the value of the E-field is defined.

These calculations are valid for estimates of input power whentesting will be conducted in an anechoic chamber. The ARP andANSI calibration methods produce a value for AF that isreferred to as the “equivalent free space antenna factor”. Thismeans that the effects of the calibration environment areremoved from the antenna factor, and that the numerical valuesare very close to that which would be measure if the antennahad, in fact, been calibrated under true free space conditions.

Method I Using the Relationship for E-field at aDistance Derived from Ohm’s Law for FreeSpace and the Friss Transmission Formula:

A variant of the Friss transmission formula is:

It relates the E-field [E (V/m)] produced at a distance [r (m)]due to net input RF power [Pt (W)] being applied to an antennawith known gain[G

t ], (see Figure 1).

Solving for input power gives:

As an example calculation, suppose that a 10 V/m field wasrequired at 3 meters for immunity testing. If the antenna chosenis a log periodic antenna with a gain of 2.05 at 100 MHz, theinput power required is:

Method II Using Transmit Antenna FactorThe transmit antenna factor is a measure of the effectiveness ofthe given antenna in transmitting electromagnetic power. Itrelates the RF voltage [Vin

(Volts)] to the E field [E| d

(V/m)] at adistance [d(m)] from the antenna, as determined at the distanceof calibration of the antenna. (See Figure 1.) It is given by:

For the example given, Gt = 3.1 dB and d = 3m

Thus:

Remembering that:

Then:

or:

and:

To compute input power requirements, a linear value forvoltage is required:

Then the required power input is:

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8484848484

Method III Calculation of Required Input Power UsingPublished Graphical Data:

Using the graphical data, it is estimated that the input powerrequired for 10 V/m at 3 meters is 0.15 W. A typical plot ofinput power for a given E-field level is shown in Figure 2.

Figure 2.

Typical Plot of the Input powerfor a Specific E-Field Value

As seen in Figure 2, the 100 MHz value for input power for1 V/m is approximately 0.15 W.

Computing the input power in dB:

The desired E-field strength is 10 V/m:

Then power for 10 V/m is

Or, substituting the actual values:

The linear value of the input power is:

Comments

Three different computations of the desired input power, asshown above, give three similar answers. The results aresummarized in Table 2. Examination of these answers revealsthat the variance of the three answers is just under 2.5%, usingthe largest of the answers as a reference.

Table 2.

Summary of Results

Method of Computation Answer

Friss Transmission Formula 14.63 W

Transmit Antenna Factor 14.69 W

Using Published Chart Values 15.00 W

The larger value obtained from using the Chart Values is likelyto be due to inaccuracy in reading the chart. This value is 4.67 %(about 0.2 dB) larger than the other values, with more preciseinput. Comparing the two values with numerical input datagives a 0.03 dB difference.

Note that the Friss Transmission Formula, used in Method l,does not consider the effects of the ground plane. The answerderived from this formula agrees with the answer derived usingMethod ll’s “equivalent free space antenna factor” valuemethodology. The results from these first two Methods alsoagree with Method lll’s answer. This is derived using a graphicalportrayal of the transmit antenna factor as computed from themeasured antenna factor.

Cautions

These computed values are based on the nominal conditions of“free space” testing, i.e., testing in a Anechoic Chamber, tocontain the fields generated. They are useful estimates for otherconditions, but engineering judgment must be applied to theselection of amplifier in all cases.

Other adjustments for sizing the input amplifier include theantenna input VSWR. At the upper and lower ends of theirbandwidth, some antennas will have a VSWR that far exceedsthe nominal value. In this case a correction, as shown inFigure 3, should be applied.

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Figure 3.

Correction for Input Power Required,when the Antenna Input VSWR Exceeds 2:1.

If a numerical result is desired, the VSWR correction can becomputed from:

Remember also that the amplifier must be operated in its linearoperating range, at least 1 dB below the 1 dB compressionpoint.

In addition, no amplifier is as reliable running close to or atmaximum rated power, thus an allowance for rating to assurethat the amplifier is running at about 90 % of rated power willproduce almost indefinite operation. This adds anotherapproximately 1 dB to the required output power.

Note that the ANSI calibration distance for measurement of theantenna factor (AF) of log periodic antennas (at the center ofthe element array), is different than the distance where theimmunity test calibration is performed (measured from the tipof the antenna). The ratio of these distances, in dB, should beadded to the power amplifier rating to more closely estimatethe required power input level. For a typical EMCO large logperiodic antenna, this difference in distance is just under1 meter. If the calibration distance is 3 meters from the tip ofthe antenna, the correction would be 20 x log

[ 4m ÷ 3m] =

2.5 dB. Smaller antennas will need a lesser allowance.

With respect to sizing the amplifier for use with a givenantenna, remember that most calibration measurements areconducted with continuous wave (CW) excitation of theantenna. When actual testing is accomplished, it is usuallyaccomplished with amplitude (AM) modulation. The mostrecently published specification requires 80 % AM with a1 kHz sine wave. This requires an amplifier with 1.8 times thelinear voltage output range of the CW signal. This, in turn,requires the amplifier output to be (1.8)2 larger than for theCW case, since power input increases as the square of theinput voltage. This means that the power amplifier gain willneed to be 10 x log [(1.8)2] = 5.1 dB greater than needed forthe CW case.

A summary of these factors is shown in Table 3.

Table 3.

Summary of Input Power Allowancesfor Sizing an Amplifier

Factor Allowance (dB)

True Linear Operation 1.0

Calibration Distance 2.5

Modulation Allowance 5.1

TOTAL 8.6

Thus, any amplifier input computed for use may actuallyneed a 8.6 dB higher rating for proper continuous operation.

In addition, if the antenna input VSWR is more than 2:1,additional compensation for the reflected power from theantenna port is required.

NOTE: Cable loss is not considered in this allowance table since itis a factor of cable length.

DERIVATION AND USE OF FORWARD POWER GRAPHSDERIVATION AND USE OF FORWARD POWER GRAPHSDERIVATION AND USE OF FORWARD POWER GRAPHSDERIVATION AND USE OF FORWARD POWER GRAPHSDERIVATION AND USE OF FORWARD POWER GRAPHS

Forward Power graphs in this catalog are derived from severalmethods and each chart indicates which method was used. SinceSAE and ANSI antenna factors are typically within a few dB of free-space antenna factors, graphs indicating “Forward Power DerivedFrom AF” are valid for free-space environments, such as a fullyanechoic chamber or an absorber-treated ground plane. Graphsindicating “Forward Power Measured Over Conducting Ground” arevalid only for the specific geometry listed (antenna/field probe heightand separation) on an OATS or in a large high quality semi-anechoicchamber. Graphs indicating “Forward Power Measured Over FerriteGround” generally fall between the ground plane and free-spacevalues. As with the ground plane numbers, these results are strictlyvalid for the same geometry on an OATS or a semi-anechoicchamber with comparable ferrite panels on the floor. Small chamberpower requirements depend on the chamber’s dimensions andantenna location. Typically, small chamber power requirements willfall in the vicinity of the conducting and ferrite-ground results.

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8686868686

R E F E R E N C ER E F E R E N C ER E F E R E N C ER E F E R E N C ER E F E R E N C EAntenna Selection by Test Type

2 0 MHz - 2 0 0 MHz 3104C Biconical

3 0 MHz - 3 0 0 MHz 3 1 2 4 Calculable Biconical

3 0 MHz - 3 0 0 MHz 3110B Biconical

2 0 0 MHz - 2 GHz 3106 Dbl Rdg Waveguide

1 GHz - 1 8 GHz 3115 Dbl Rdg Waveguide

3 0 MHz - 1 GHz 3121C Dipole

2 6 MHz - 2 GHz 3142B BiConiLogTM

8 0 MHz - 2 GHz 3 1 4 4 Log Periodic

2 0 0 MHz - 5 GHz 3 1 4 7 Log Periodic


3 0 Hz - 5 0 MHz 3301B Rod - Active

1 0 kHz - 3 0 MHz 6 5 0 2 Loop - Active

1 kHz - 3 0 MHz 6 5 0 7 Loop - Active

1 0 kHz - 3 0 MHz 6 5 1 2 Loop - Passive

2 0 MHz - 3 0 0 MHz 3 1 0 9 Biconical



2 6 MHz - 2 GHz 3 1 4 0 BiConiLogTM


9 6 0 MHz - 4 0 GHz 3 1 6 0 Std Gain Horns









2 0 0 MHz - 1 GHz 3 1 0 1 Conical Log Spiral










1 GHz - 1 0 GHz 3 1 0 2 Conical Log Spiral





2 0 0 MHz - 2 GHz 3 1 0 6 Dbl Rdg Waveguide

1 GHz - 1 8 GHz 3 1 1 5 Dbl Rdg Waveguide








SAE J1113 RADIATED EMISSIONS

2 0 MHz -200 MHz 3104C Biconical














2 0 Hz - 5 MHz 6 5 1 1 Loop - Passive


IEC/CISPR/EN RADIATED EMISSIONS

2 0 MHz - 3 0 0 MHz 3109 Dbl Rdg Waveguide








9 6 0 MHz - 4 0 GHz 3 1 6 0 Log Periodic


1 kHz - 3 0 MHz 6 5 0 9 Loop - Passive




2 0 0 MHz - 2 GHz 3106 Dbl RdgWaveguide


1 8 GHz - 4 0 GHz 3116 Dbl Rdg Waveguide








FCC 15 RADIATED EMISSIONS

















FCC 18 RADIATED EMISSIONS

IEC/CISPR/EN RADIATED IMMUNITY

SAE J551 RADIATED IMMUNITY

VCCI RADIATED IMMUNITY






2 0 MHz - 3 0 0 MHz 3109 Dbl Rdg Waveguide



2 6 MHz - 2 GHz 3 1 4 0 BiConiLog








VDE RADIATED EMISSIONS

CISPR/EC RADIATED EMISSIONS





VCCI RADIATED EMISSIONS9 6 0 MHz - 4 0 GHz 3 1 6 0 Std Gain Horns











1 kHz - 3 0 MHz 3 3 0 3 Rod - Active


NSA 65-6 TRANSMIT



NSA 65-6 RECEIVE

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1 8 GHz - 4 0 GHz 3 1 1 6 Dbl Rdg Waveguide

4 0 0 MHz - 6 GHz 3164 Diag Dual Polar Horn






3 0 Hz - 5 0 MHz 3301B Monopole (Rod)




NACSIM RADIATED EMISSIONS










4 0 0 MHz - 6 GHz 3164 Diag. Dual Polar Horn







2 0 Hz - 5 0 0 kHz 7 6 0 4 Coil - Transducer














2 0 Hz - > 5 0 kHz 7603 Magnetic Field Coil











1 8 GHz - 4 0 GHz 3 1 1 6 Dbl Rdg Waveguide









MIL-STD-1541 RADIATED EMISSIONS





26 MHz - 2 GHz 3140 BiConiLogTM
















1 kHz - 3 0 MHz 3 3 0 3 Rod - Passive


MIL-STD-285 TRANSMIT












MIL-STD-285 RECEIVE

MIL-STD-461E RADIATED SUSCEPTIBILITY

MIL-STD-1541 RADIATED SUSCEPTIBILITY

4 4 0 MHz - 4 6 0 MHz 3125 Dipole (450)

5 9 0 MHz - 6 1 0 MHz 3125 Dipole (600)

8 2 4 MHz - 9 1 5 MHz 3125 Dipole (870)

9 3 5 MHz - 960 MHz 3125 Dipole (950)

1 6 0 0 MHz -1620 MHz 3125 Dipole (1610)

1 7 1 0 MHz -1785 MHz 3125 Dipole (1750)

1 8 0 5 MHz -1880 MHz 3125 Dipole (1840)

1 8 5 0 MHz -1910 MHz 3125 Dipole (1880)

2 4 4 0 MHz -2460 MHz 3125 Dipole (2450)

2 9 9 0 MHz -3010 MHz 3125 Dipole (3000)

400 MHz - 6 GHz 3164 Diag Dual Polar Horn

TELECOM

MIL-STD-461E RADIATED EMISSIONS

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8888888888

Antenna Selection by Frequency

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8989898989

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9090909090

Conical Log Spiral 31013101310131013101 200MHz- 200-300 MHz(L&R) 1GHz +/- 2.8 dB

300-850 MHz+/- 0.8 dB

850-1000 MHz+/- 1.4 dB

Conical Log Spiral 31023102310231023102 1GHz- 1-10 GHz(L&R) 10GHz +/- 0.8 dB

Conical Log Spiral 31033103310331033103 100MHz- +/- 2.0 dB Type B(L&R) 1GHz

Biconical 3104C3104C3104C3104C3104C 20MHz- 20-200 MHz 200MHz 20-30 MHz200MHz +/- 1.2 dB +/- 0.9 dB +/- 1.0 dB

30-200 MHz+/- 0.9 dB

Biconical 31093109310931093109 20MHz- 20-30 MHz 20-30 MHz 20-30 MHz300MHz +/- 1.0 dB +/- 0.9 dB +/- 1.0 dB

30-200 MHz 30-300 MHz 30-300 MHz+/- 1.4 dB +/- 0.9 dB +/- 0.9 dB

200-300 MHz+/- 2.0 dB

Biconical 3110B3110B3110B3110B3110B 30MHz- 30-200 MHz 20-200 MHz 20-30 MHz300MHz +/- 1.2 dB +/- 0.8 dB +/- 1.0 dB

200-300 MHz 30-300 MHz+/- 2.2 dB +/- 0.9 dB

BiCal 31243124312431243124 30MHz- 300MHz - 300 MHz300MHz +/-0.50 dB

Double-Ridged 31063106310631063106 200MHz- 0.2-1.9 GHzWaveguide 2GHz +/- 1.0 dB

Horn 1.9-2.0 GHz+/- 1.3 dB

Double-Ridged 31153115311531153115 1GHz- 1-18 GHzWaveguide 18GHz +/- 0.3 dB

Horn

Double-Ridged 31163116311631163116 18GHz- 18-30 GHzWaveguide 40GHz +/- 0.8 dB

Horn 30-40 GHz+/- 1.3 dB

Diagonal Dual 31643164316431643164 400 MHz - .4-6 GHzPolarized Horn 6 GHz +/- 1.0 dB

Octave Horns 3161-013161-013161-013161-013161-01 1GHz- 1-2 GHz2GHz +/- 0.9 dB

Octave Horns 3161-023161-023161-023161-023161-02 2GHz- 2-4 GHz4GHz +/- 0.5 dB

Octave Horns 3161-033161-033161-033161-033161-03 4GHz- 4-4.5 GHz8GHz +/- 1.0 dB

4.5-7.5 GHz+/- 0.4 dB7.5-8 GHz+/- 1.3 dB

Dipole 3121C3121C3121C3121C3121C 30MHz-4 Balun Kit4 Balun Kit4 Balun Kit4 Balun Kit4 Balun Kit 1GHz

Dipole 3121C3121C3121C3121C3121C 30MHz- 30-60 MHz 30-60 MHzBalun 1Balun 1Balun 1Balun 1Balun 1 60MHz +/- 0.9 dB +/- 1.0 dB


TYPETYPETYPETYPETYPE MODELMODELMODELMODELMODEL FREQUENCYFREQUENCYFREQUENCYFREQUENCYFREQUENCY SAE, ARP 958SAE, ARP 958SAE, ARP 958SAE, ARP 958SAE, ARP 958 ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5 ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5 IEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEENUMBERNUMBERNUMBERNUMBERNUMBER RANGERANGERANGERANGERANGE 1M1M1M1M1M 3M3M3M3M3M 10M10M10M10M10M 1309, ANSI C63.41309, ANSI C63.41309, ANSI C63.41309, ANSI C63.41309, ANSI C63.4

Expanded Uncertainty Values for Antenna Calibrations (95% Confidence)

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9191919191


375-400 MHz 375-400 MHz+/- 1.4 dB +/- 1.4 dB

Dipole 3121C3121C3121C3121C3121C 400MHz- 400-700 MHz 400-700 MHzBalun 4Balun 4Balun 4Balun 4Balun 4 1GHz +/- 1.0 dB +/- 1.6 dB

700-1000 MHz 700-1000 MHz+/- 1.4 dB +/- 2.1 dB

DB3&4 Tuned 140-400 MHz 140-400 MHz+/- 0.8 dB +/- 0.8 dB

400-1000 MHz 400-1000 MHz+/- 1.0 dB +/- 1.0 dB

BiConiLog 3142B3142B3142B3142B3142B 26MHz- 26-30 MHz 26-30 MHz 26-30 MHz2GHz/ +/- 1.4 dB +/- 1.5 dB +/- 2.1 dB

26MHz- 30-1000 MHz 30-1000 MHz 30-1000 MHz1.1GHz +/- 0.8 dB +/- 1.0 dB +/- 1.0 dB

1-2 GHz 1-2 GHz 1-2 GHz+/- 1.2 dB +/- 1.3 dB +/- 1.4 dB

LPA 31443144314431443144 80MHz- +/- 2.0 dB, Type B 80-2000 MHz 80-2000 MHz2GHz +/- 0.9 dB +/- 0.8 dB

LPA 31473147314731473147 200MHz- 200-2000 MHz 200-1000 MHz 200-1000 MHz5GHz +/- 0.5 dB +/- 0.8 dB +/- 0.8 dB


2-5 GHz 2-5 GHz+/- 1.5 dB +/- 1.5 dB

LPA 31483148314831483148 200MHz- 200-1000 MHz 200-1000 MHz 200-1000 MHz2GHz +/- 0.6 dB +/- 0.9 dB +/- 0.8 dB


Rod 3301B3301B3301B3301B3301B 30Hz- 30Hz-50MHz41 inch Rod41 inch Rod41 inch Rod41 inch Rod41 inch Rod 50MHz +/- 0.3 dB

Rod 33033303330333033303 1kHz- 1kHz-10kHz30MHz +/- 1.0 dB

10kHz-30MHz+/- 0.1 dB

Loop 65026502650265026502 10kHz- (TBD)30MHz

Loop 65076507650765076507 1kHz- (TBD)30MHz

Loop 65096509650965096509 1kHz- (TBD)30MHz

Loop 65116511651165116511 20Hz- (TBD)5MHz

Loop 65126512651265126512 10kHz- (TBD)30MHz

Coil 76037603760376037603 20Hz- No Cal/VSWR Only50kHz

Coil 76047604760476047604 20Hz- No Cal/VSWR Only500kHz

Coil 76057605760576057605 30Hz- No Cal Req50kHz

Coil 76067606760676067606 30Hz- No Cal Req50kHz

TYPETYPETYPETYPETYPE MODELMODELMODELMODELMODEL FREQUENCYFREQUENCYFREQUENCYFREQUENCYFREQUENCY SAE, ARP 958SAE, ARP 958SAE, ARP 958SAE, ARP 958SAE, ARP 958 ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5 ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5ANSI C63.5 IEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEEIEEE 291, IEEENUMBERNUMBERNUMBERNUMBERNUMBER RANGERANGERANGERANGERANGE 1M1M1M1M1M 3M3M3M3M3M 10M10M10M10M10M 1309, ANSI C63.41309, ANSI C63.41309, ANSI C63.41309, ANSI C63.41309, ANSI C63.4

Expanded Uncertainty Values for Antenna Calibrations (95% Confidence)

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Data effective 8 June 1998. EMCO Laboratory capabilities include all products produced by EMCO and models of the same technology produced by other

manufacturers. Uncertainty values reflect the uncertainty analysis conducted using 1997 data. Values released are valid with a 2 sigma (95%) confidence level

and are representative of the measurement quality conducted by the EMCO Laboratory using the industry recognized standards listed above.

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Laboratory Standards Compliance List

SAE, ARP 958 - 1997, Society of Automotive Engineers, Aerospace Recommended Practice 958, Electromagnetic InterferenceMeasurement Antennas; Standard Calibration Method.

ANSI C63.4 - 1992, American National Standard, Methods of Measurement of Radio-Noise Emissions from Low-Voltage Electricaland Electronic Equipment in the Range of 9 kHz to 40 GHz.

ANSI C63.5 - 1988, American National Standard, Calibration of Antennas Used for Radiated Emission Measurements inElectromagnetic Interference (EMI) Control.

ANSI C63.6 - 1988, American National Standard, Guide for the Computation of Errors in Open Area Test Site Measurements.

ANSI C63.7 - 1992, American National Standard, Guide for Construction of Open-Area Test Sites for Performing Radiated EmissionMeasurements.

ANSI Z540-1 - 1994, American National Standard, Calibration Laboratories and Measuring and Test Equipment - GeneralRequirements.

ANSI Q91 - 1994, Quality Systems - Model for Quality Assurance in Design, Development, Production, Installation and Servicing.

ISO Guide 25 - 1990, International Standards Organization, General Requirements for the Competence of Calibration and TestingLaboratories.

IEEE 291 - 1991, Institute of Electrical and Electronics Engineers, Standard Methods for Measuring Electromagnetic Field Strengthsof Sinusoidal Continuous Waves, 30 Hz to 30 GHz.

IEEE Std 1309 - 1996, Institute of Electrical and Electronics Engineers, Standard for Calibration of Electromagnetic Field Sensorsand Probes, Excluding Antennas, from 9 kHz to 40 GHz.

NIST Technical Note 1297, 1994 edition, National Institute of Standards and Technology, Guidelines for Evaluating and Expressingthe Uncertainty of NIST Measurement Results.

NIS 81, Edition 1, May 1994, NAMAS, The Treatment of Uncertainty in EMC Measurements.

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IntroductionOver the past couple of years, thetopic of measurement uncertainty hascome to the forefront in the interna-tional EMC community. In brief, theintention of measurement uncer-tainty is to take the more traditionalterms of precision, accuracy, randomerror, and systematic error used inscientific circles and replace themwith a single term. This termrepresents the total contribution tothe expected deviation of a measure-ment from the actual value beingmeasured1-2.

In general, precision is a measure ofrandom error, or how closely re-peated attempts hit the same point ona target, while accuracy is a measureof systematic error, or how closethose attempts are to the center of thetarget. It is obvious that bothcontributions must be accounted forin order to determine the quality of ameasurement, although the combina-tion of the two can sometimes bemore subtle than might be expected.There has been some discussion overwhether the term reproducibility isalso replaced by uncertainty since theconcept of reproducibility mustcontain variations in the equipmentunder test (EUT) and therefore doesnot represent the same quantity asmeasurement uncertainty3.

A Statistical Approach toMeasurement Uncertainty

MICHAEL D. FOEGELLEEMC Test Systems, Austin, TX

Despite the fact that most authors have skirted the subject of Type Aanalyses, the method is not so difficult that it should be avoided altogether.

The methods for determining ameasurement uncertainty have beendivided into two generic classes:· Type A represents a statistical

uncertainty based on a normaldistribution.

· Type B represents uncertaintiesdetermined by any other means.In last year’s ITEM, Manfred

Stecher wrote an article describingthe introduction of uncertaintyevaluations into various EMCstandards and explained the tech-nique typically used to determinemeasurement uncertainties for EMCmeasurements4. (A similar paper wasalso presented at the 1996 IEEEInternational EMC Symposium inSanta Clara, CA.5) The article gives anadequate introduction to the Type Bevaluation method, which usesindividual measurements, manufac-turers specifications, and eveneducated guesses to determine acombined uncertainty. However, theauthor is a little too quick to discardthe statistical Type A uncertaintymeasurement as impractical. To besure, the Type A analysis does sufferfrom the very pitfalls which Mr.Stecher points out. However, with abit of care it is possible to obtain asignificant amount of useful informa-tion from the technique.

The advantage of a Type Auncertainty measurement is thatwhen done correctly, the resulting

value is irrefutable since it has beendetermined from real world measure-ments. The biggest complaint I hearfrom engineers being exposed to theType B uncertainty budget methodfor the first time is the fact that toomany of the terms are either poorlydefined by equipment manufacturersor must simply be estimated. Inmany cases, the chosen values may betoo stringent in order to provide asafety margin. On the other hand, thedesire for smaller total uncertaintiescan lead to using smaller estimationsthan is realistic for some terms thatare hard to determine.

Antenna manufacturers have easyaccess to a vast database of antennacalibrations with which to determinestatistical trends. However, as thedata shown here will demonstrate, itis not necessary to have an extremelylarge sample to get acceptable results.The real issue in using a statisticalapproach is in determining where itfails and using a Type B analysis to fillin the gaps. The document NIS 81,“The Treatment of Uncertainty inEMC Measurements”, released byNAMAS1, recommends this exactapproach.

Certainly a Type A analysis of a setof measurements can be expected toinclude all random errors of theentire measurand and none of itssystematic errors. But does thatmean that the Type A uncertainty

Reprinted from ITEM 1998, Courtesy of R&B Enterpises.

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contains only the random portion ofthe individual terms which might beused in a Type B analysis? Certainlynot. It is not possible to completelyseparate random and systematiceffects into individual categories2.Random effects such as positioningerror[6] or cable length and fre-quency dependence of standingwaves can serve to randomize suchsystematic errors as site imperfec-tions or mismatch errors. Intention-ally varying the setup betweenrepeated measurements can do thesame.

The discussion presented here willfocus primarily on antenna calibra-tion measurements, which havemany similarities to radiatedemissions measurements. However,many of the techniques demon-strated will be applicable to radiatedsusceptibility and conducted tests.Despite the fact that most authorshave skirted the subject of Type Aanalyses, the method is not sodifficult that it should be avoidedaltogether. In fact, many of the moredifficult terms to determine for atypical Type B analysis are alreadyincluded in the random error of thetotal measurement, thus reducing theoverall task.

Type A Evaluation ofUncertaintyRandom effects cause repeatedmeasurements to vary in an unpre-dictable manner. The associateduncertainty can be calculated byapplying statistical techniques to therepeated measurements. An estimateof the standard deviation, s qk( ) , of aseries of n readings, qk , is obtainedfrom

s qn

q qk kk

n

( )( )

( )=−

−=

∑11

2

1

where q is the mean value of

measurements. The random compo-

nent of the uncertainty may bereduced through repeated measure-ments of the EUT. In this case, thestandard deviation of the mean, s q( ) ,given by:

s qs q

nk( )

( )=

represents the uncertainty of theresulting mean. This last point hasbeen misinterpreted by some due to aconfusing statement in section 3.2.6of NIS 81, “The standard uncertainty,u xi( ) , of an estimate xi of an inputquantity q is thereforeu x s qi( ) ( )= .” This statement iscertainly true, but some readers haveconstrued it to mean that the stan-dard uncertainty of a single measure-ment qk is given by s q( ) .7-8 This istrue if n = 1so that s q s qk( ) ( )= .This is explained more clearly insection 3.2.3 of NIS 81 where theconcept of predetermination isdiscussed.

Time constraints and otherpractical considerations will oftenmake it unfeasible to perform morethan a single measurement on anEUT. However, repeat measurementscan be performed on a similar EUT topredetermine s qk( ) as the expectedstandard uncertainty of an individualmeasurement. If a smaller uncer-tainty due to random errors isdesired, multiple measurements canbe made and the value of s q( ) re-duced accordingly. The value of usedin this case is the number of mea-surements made on the EUT, not thenumber of measurements used in thepredetermination.

It should be noted that variationsin the EUT as a function of time, aswell as that of multiple like EUTs as inthe method demonstrated here, willbe included in the uncertaintydetermined through this method. Forthis reason, and to provide a means todetermine some of the systematiccontributions to the uncertainty, it isrecommended that a stable reference

radiating source such as a combgenerator or amplified noise sourcebe used as the EUT for uncertaintydeterminations. This provides arepeatable EUT which, when used inconjunction with “round robin” typetesting, can allow determination ofeven the systematic elements of yourmeasurement uncertainty to withinthe uncertainty of the round robintest. This type of EUT also provides abroad continuous frequency range foruncertainty determination as op-posed to the random spectrum pointsof a typical EUT. If a referencesource is not available, a number ofthe same benefits may be obtainedusing a stable signal generator andappropriate radiating antenna.However, transmit cable placementand other effects will add someadditional random error and thismethod does not lend itself to inter-site comparisons.

Uncertainty Example:Antenna CalibrationAntenna calibrations have uncer-tainty aspects similar to that of bothradiated emissions and susceptibilitytests. However, the one systematicelement missing from the test is theabsolute value of the fields (or signallevels) involved. Thus, the test onlydepends on the linearity of theinstrumentation and not its absolutecalibration. However, this does noteffect the validity of this method fordetermining Type A uncertainties forEMC tests since the systematic errorin field level cannot be determined bythis method without inter-sitecomparisons or other tests usingmultiple methods to determine theabsolute field level.

To obtain the data shown here, asample of 26 different antennascalibrated over a three-and-a-halfmonth period was used. The anten-nas were identical log-periodicantennas with a frequency span of 200

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MHz to 1 GHz. The time period spanned from mid-Augustthrough the end of October, providing a significantvariation in temperature and weather conditions. Thedata were measured at 1601 frequency points using avector network analyzer, low loss cables, and a positioningtower with 0.1 cm positioning resolution. The test wasperformed at a 10-meter separation, 2-meter transmitheight, and 1- to 4-meter scan height per ANSI C63.5 on anopen area test site (OATS). The vector network analyzerused has over 100 dB of available dynamic range andsuperior external noise rejection, making it ideal for useon an OATS where ambients would be a problem fortraditional spectrum analyzer/tracking generator combi-nations. Since the network analyzer does not offer amax-hold or other such functionality traditionally seenon a spectrum analyzer, it is necessary to perform themax-hold by transferring individual traces to a control-ling PC and allowing the test software to perform the max-hold.

To facilitate this method, it is also necessary to step thetower and take frequency sweeps at discrete heights sincethe network analyzer cannot sweep the entire frequencyband fast enough to get acceptable height resolution whenthe tower moves continuously. Tests with tuned dipoleshave shown that the variation in the antenna factor at 1GHz for a 1-cm step, a 5-cm step, and a single frequencypoint continuous motion max-hold is less than ±0.02 dB.If the tower step size was too large, or the sweep time tooslow in the case of a continuous motion, the measurementcould be expected to introduce a systematic error sincemissing a peak signal would always result in a measure-ment lower than the real value. This error exists forscanned height radiated emissions tests as well as antennacalibrations. For an antenna calibration, this error wouldresult in a larger antenna factor than is actually the case.

The standard deviation of the 26 antenna factors andtheir maximum deviations from the average are shown asa function of frequency in Figure 1. The negative of thestandard deviation is also shown for comparison to thenegative deviation. The symmetry of the positive andnegative deviations is a first indication of how closely thesample approximates a normal distribution. An asym-metrical envelope would be a cause for concern andindicate the need for separate positive and negativeuncertainty values at the minimum.

Neglecting, for the moment, any additional contribu-tions to the uncertainty due to systematic errors, thesedata indicate that the expanded uncertainty ( k = 2 ) of anindividual calibration is less than ±0.5 dB at all frequen-cies. That means that an uncertainty of ±0.5 dB withgreater than 95% confidence can be claimed for this

UNCERTAINTY TERMS FROM NIS-81

Estimated standard deviation from a sample of readings:

s qn

q qk kk

n

( )( )

( )=−

−=

∑11

2

1

Standard deviation of the mean of readings:

s qs q

nk( )

( )=

Standard uncertainty (of the mean of readings) resulting froma type A evaluation:

u x s qi( ) ( )=

Standard uncertainty for contributions with a normalprobability distribution:

u xU

ki( ) =

where U represents the expanded uncertainty of thenormal distribution (last item below).

Standard uncertainty for contributions with rectangularprobability distribution:

u xa a

ii i( ) =

−+ −

2 3

for an asymmetrical distribution, where ai+ and ai− arethe bounds of the rectangular region, or

u xa

ii( ) =3

for a symmetrical region with bounds ± ai .

Standard uncertainty for contributions with U shapedprobability distribution:

u xa a

ii i( ) =

−+ −

2 2

for an asymmetrical distribution, where ai+ and ai−are the bounds of the U shaped region, or

u xa

ii( ) =2

for a symmetrical region with bounds ± ai or whereai is the larger of ai+ or ai− .

Standard uncertainty in terms of the measured quantity:u y c u xi i i( ) ( )= ⋅

Combined standard uncertainty:

u y u yc ii

N

( ) ( )==∑ 2

1

Expanded uncertainty:

U k u yc= ⋅ ( ) or U k u yp c= ⋅ ( )

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Antenna Factor Deviation From Average

-1

-0.5

0

0.5

1

1.5

2

2.5

3

200 300 400 500 600 700 800 900 1000

Frequency (MHz)

Deviation (dB)

+SD'

-SD'

Max'-Avg'

Min'-Avg'Max-AvgMin-Avg

calibration. A second verification ofthis claim is the fact that, with theexception of the negative deviationabove 950 MHz, none of the antennasin the sample had antenna factors

which deviated from the averagemore than ±0.5 dB. This provides anadded level of confidence in thequality of this uncertainty value.

It should be noted that this data

Figure 1. The Standard Deviation, Maximum Minus Average, and Minimum Minus Averageof the Antenna Factors from a Set of Twenty-six Identical Antennas. Neglecting any additionalsystematic errors, the expanded uncertainty (k=2) for an individual antenna factor would thenbe twice the standard deviation for a value of approximately ±0.5 dB with greater than 95%confidence at all frequencies.

Antenna Factor Deviation From Average

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

200 300 400 500 600 700 800 900 1000

Frequency (MHz)

Deviation (dB)

+SD

-SD

Max-Avg

Min-Avg

represents calibrations of 26 differentantennas performed at differenttimes. About fifty percent of theantennas were directly off theproduction line, but the other halfwere re-calibrations of antennas asmany as ten years old. Although onemight expect a batch of antennas tobe as close to identical as possible,this sample surely must contain someamount of manufacturing uncer-tainty. If this manufacturing uncer-tainty is non-zero, then it must alsobe contained within the aboveuncertainty. Since the “perfect”antenna, in terms of manufacturingquality, is defined by the average of allantennas, this uncertainty must betotally random.

Although this manufacturinguncertainty may add to the totalcalibration uncertainty measured bythis technique, as long as the resultinguncertainty is within an acceptablerange, it does not matter whether ornot the contribution is large or small.In this case, there is also the addedbenefit that the intentional introduc-tion of totally random effects due to

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Figure 2. The Effect of EUT Variation on the Standard Deviation. Note the Difference in the Maximum Deviation for the Primed Sample Vs. Un-primed. The effect on the standard deviation is sufficient to equal or surpass the maximum deviation in the un-primed sample.

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the antennas may help to randomizethe systematic contributions to thetotal measurement uncertainty. Foremissions measurements, this isequivalent to using multiple identicalEUTs to determine the Type Auncertainty. As long as variations inthe EUTs do not add excessivecontributions to the random error, itis possible to obtain a suitableuncertainty value from tests ofmultiple EUTs.

This is not to say that multipleEUTs always provide an acceptablemethod for performing this type ofuncertainty calculation. One or twoEUTs with significant deviationsfrom the norm can introduce asignificant change to the resultinguncertainty, as demonstrated inFigure 2. One additional antenna, adifferent model which varies signifi-cantly from the average at differentfrequencies, was introduced to thesample to demonstrate the possibleeffects.

Note that for most of the fre-quency range, the deviation is below1 dB, yet the contribution of oneadditional antenna is sufficient tochange the standard deviation suchthat it is larger than the originalmaximum deviations at mostfrequencies. As this example shows,when working with relatively smallsamples, it is important not tointroduce factors which may exag-gerate the error in the measurement.Likewise, it is important to avoidarbitrarily discarding data because itmakes the result look bad!

Figure 2 also demonstrates thedifference between systematic errorsand random errors. One sample witha large systematic error (not presentin the other samples) can have asignificant effect on the uncertainty,since it changes not only the standarddeviation, but also the mean of thesamples. This causes the negativemaximum deviation (minimum -

average) to be larger than before,even though the absolute value of theminimum curve is the same.

Note that the standard deviationshown in Figure 2 would still allow theclaim of ±0.5 dB for the expandeduncertainty from 200 to 600 MHz. Itis perfectly acceptable (and oftennecessary due to band breaks inequipment) to generate frequencydependent uncertainties. Theexpanded uncertainty from 600 to 800MHz could then be set at ±0.8 dB andfrom 800 MHz to 1 GHz at ±1.2 dB.

Cleanup:Type B EvaluationIn order to develop a final value forthe expanded uncertainty, it isnecessary to make an evaluation of all

Table 1. Various Possible Contributions to Measurement Uncertainty, along with TypicalAccepted Distribution Types and Possible Contributions to Both Random and SystematicErrors. (For items which might have both random and systematic contributions, alowercase X represents the typically smaller or less likely contribution.)

of the typical contributions touncertainty to determine which termsare included in the Type A result. Inthis case, nearly every effect exerts arandom contribution due to theconsiderable variation in test setupand conditions over the allotted timeperiod. Factors such as temperatureand humidity effects, ground planequality due to ground moisture,ground plane warping with tempera-ture , test cable lengths, cable connec-tion quality, cable calibration, etc. allvaried significantly over the sample.Table 1 lists some of the typicalentries in a Type B uncertaintybudget and suggests which ones arelikely to be totally random, system-atic, or a combination of the two.The listed distribution type repre-

ContributionContributionContributionContributionContribution DistributionDistributionDistributionDistributionDistribution RandomRandomRandomRandomRandom SystematicSystematicSystematicSystematicSystematic AF CalAF CalAF CalAF CalAF Cal RERERERERE RIRIRIRIRITypeTypeTypeTypeType

Antenna factor Normal X X

Cable calibration Normal X X X

Coupler calibration Normal X X

Receiver/probe linearity Rectangular X x X X X

Receiver level detection Rectangular x X X X

Antenna directivity Rectangular X X

AF variation with height Rectangular X X

Antenna phase center Rectangular X X

Field uniformity Rectangular X X

Frequency interpolation Rectangular X x X X

Distance measurement Rectangular X x X X X

Height measurement Rectangular X x X X

Site imperfections Rectangular X x X X

Mismatch U-shaped X x X X X

Temperature effects Rectangular X X X X

Setup repeatability Type A X X X X

Ambient signals Rectangular X x X X

EUT repeatability Type A X X X

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sents the typical accepted distributiontype for that entry. Note that mostcalculated values are assumed to berectangular, which may often be amore stringent criteria than isnecessary.

For the antenna calibration examplegiven, only a few possible systematicerrors may need to be accounted for.In general, a purely systematic erroris likely to have a U-shaped distribu-tion since it always represents adeviation to one side of the real value.A common example of this type ofcontribution is that of cable mis-match. Since a perfect match isrepresented by zero reflection and amismatch in any direction results innon-zero reflection, the statisticalprobability that there is somemismatch causes the peaks of thedistribution to occur away from thezero (matched) value. The effect ofmismatch is to change the detectedlevel by reflecting the power backtowards the source. It can alsogenerate standing waves in cableswhich then serve to increase ordecrease the detected signal based onthe frequency and cable length. Astanding wave is a systematic error ina fixed system for a given frequency.However, over frequency, the effect iseither constructive or destructive,giving a net random contribution. Inthe case of antenna calibrations, themismatch at the antenna is a part ofthe calibration, so standing waves arethe only contribution of concern. Allother cable contributions are in-cluded in the cable calibration, whichis part of the random error contribu-tion.

Another systematic error contri-bution which generates a U-shapeddistribution is the max-hold heightstep. For continuous height scanning,this is a function of sweep time versustower speed. Since the “correct”value is a maximum, any deviation

from the correct value can only beless than the correct value. Asmentioned previously, this error wasverified to be less than ±0.02 dB. Thiserror is a good example of thedifference between performing aType B analysis of an entire test setupor using a mixed Type A and Type Banalysis. The height step has bothrandom and systematic components,but the random components wouldbe measured in a Type A analysis.Thus the contribution to the mixedType B analysis is not the same as thatfor the Type B-only analysis.

The final and most troublingcontribution is that of site imperfec-tions. Fortunately several factorsmitigate this contribution somewhat.Temperature changes over the testperiod caused dimensional changesin the surface of the metal groundplane which would have randomizedthe effects somewhat. Also, similar tothe effects of standing waves, theimperfections in the ground planewill have different effects at differentfrequencies. Variations in antennapositioning with respect to sitedefects will randomize these effects aswell[6, 9]. Thus there is a highprobability that there will be “worstcase” points throughout the fre-quency band which will capture thesite imperfection effects in a Type Aanalysis. However, there is always thelikelihood of a significant systematiceffect which is not easily determined.It should also be noted that NIS-81classifies site imperfections as arectangular distribution. This islargely due to the fact that existingsite verification techniques do notprovide for individual determinationof the random and systematiccontributions from the site.

For EMC measurements, a goodpair of antennas may be used todetermine the normalized siteattenuation (NSA) of a test site anduse the deviation of that value from

theoretical for the site contribution.However, in the case of antennacalibration, this option is circular.Since the uncertainty of an NSAmeasurement can be no better thanthat of the antenna calibration, theuncertainty of the resulting antennacalibration could never be better thanthe NSA measurement plus itsuncertainty!

Two options remain for antennacalibrations. The first is to attempt“round-robin” testing to compareone site to others and use the averagevalue as the perfect site. The secondmethod, to be published as anamendment to CISPR 16-1 in 1998,involves using calculable dipoles toverify that a site matches a perfecttheoretical ground plane through anexhaustive sequence of tests10.

Comparisons between antennameasurements made using the sametest system on the NIST (Boulder,CO) OATS and the OATS used for theantenna calibrations given in theexamples show the variation betweenthe sites to be on the order of 0.5 dB.This variation is of the same order ofmagnitude as the random uncertaintycontribution and thus an individualtest is insufficient to draw a conclu-sion on the systematic error contri-bution of the site. It should bereiterated here that the assumption ofa “golden site” for comparisonpurposes is not recommended.Instead the use of round-robin testingfor determination of a statisticallyperfect site, or the new CISPR methodfor site verification is recommendedfor validation of an antenna calibra-tion site.

Total UncertaintyThe combined standard uncertainty,u yc ( ) , of a quantity y is computedfrom the square root of the sum ofsquares (RSS) of the individualcontributions u xi( ) . If an individual

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uncertainty component does notdirectly correspond to themeasurand, it must first be convertedinto the proper form by applying theappropriate conversion factor orfunction, u y c u xi i i( ) ( )= ⋅ . Forexample, a positioning uncertainty incentimeters must be converted intoits effect on the field in dB before itcan be applied to the antenna factoruncertainty. Then, for N uncorrelatedindividual components, the com-bined standard uncertainty is:

u y u yc ii

N

( ) ( )==∑ 2

1.

The expanded measurement uncer-tainty, U, is then determined bymultiplying the combined standarduncertainty by the desired coveragefactor, k, which determines the levelof confidence in the uncertaintyvalue. Thus,U k u yc= ⋅ ( ) . For therecommended 95% level of confidence,

k = 2 .Using 0.5 dB for the expanded

uncertainty of the random contribu-tion and 0.75 dB as a rectangulardistribution for the remainingcontribution due to site imperfec-tions and any other systematic effects,

u yc ( ). .

.=

+ =

052

0 753

052 2

Using k =2 this results in a totalcombined expanded measurementuncertainty of 1.0 dB. Since therandom error contribution is asignificant portion of the total( u y u qc k( ) / ( ) < 3 ) it is necessaryto use an adjusted value for thecoverage factor, k p . In this case, thevalue is around 2.01, but in the case ofonly a few samples, this value couldbe as large as 3 to 14.

ConclusionWhile there are inherent difficultiesin performing a Type A analysis of atest setup, it is important not todismiss the concept altogether. It is arelatively simple matter to obtainsufficient measurement data toproduce an acceptable measure of thetotal random contribution to theuncertainty. This has the advantageof providing a measured value andthus limits the number of assump-tions necessary to arrive at a totalexpanded uncertainty value. Theability to prove uncertainty claimswith measured data is likely tobecome more important as new EMCregulations are put into effect.

References1. NIS 81, Edition 1, The Treatment

of Uncertainty in EMC Measure-ments, NAMAS, May 1994.

2. Barry N. Taylor and Chris E.Kuyatt, NIST Technical Note 1297,1994 Edition, Guidelines forEvaluating and Expressing theUncertainty of NIST MeasurementResults, NIST.

3. C63 EMC Measurement Uncer-tainty Workshop, April 29-30,1996.

4. Manfred Stecher, “MeasurementUncertainty in EMC,” ITEM 1997,pp. 58-64, 246, 1997.

5. Edwin L. Bronaugh and John D.M. Osburn, “A Process for theAnalysis of Measurement andDetermination of MeasurementUncertainty in EMC Test Proce-dures,” 1996 InternationalSymposium on EMC, Santa Clara,CA, August 19-23, 1996, pp. 245-249.

6. Heinrich Garn, “Uncertainties inthe Calibration of Broadband EMITest Antennas by Using a Refer-ence Antenna,” 1997 Mode-Stirred Chamber, AnechoicChamber, and OATS OperatorsMeeting, April 28-May 1st, 1997.

7. Brent Dewitt, Daniel D. Hoolihan,“An Analysis of MeasurementUncertainty with Respect to IEC1000-4-3,” 1997 InternationalSymposium on EMC, Austin, TX,August 18-22, 1997, pp. 365-369.

8. Edwin L. Bronaugh, “Uncertaintyof the Frequency Spectra Pro-duced by a Reference Radiator,”Compliance Engineering, 1997Reference Guide, pp. A101-A108.

9. Peter McNair, “UnderstandingOpen Area Test Site Perfor-mance,” 1997 Antenna Measure-ment Techniques AssociationSymposium, November 17-21,1997, Boston Massachusetts, pp.25-30.

10. Jasper J. Goedbloed, “Progress inStandardization of CISPR AntennaCalibration Procedures,” 1995International Zurich Symposiumon EMC, March 7-9, 1995, pp. 111-116.

Dr. Michael D. Foegelle received his Ph. D. inPhysics from the University of Texas atAustin, where he performed theoretical andexperimental research in both CondensedMatter Physics and EMC. He performedcontract EMC research with Dr. J. D. Gavendaof UT for IBM and Ray Proof where hehelped to develop a semi-anechoic chambermodeling system. In 1994 he began workingfor EMCO in Austin Texas, where he is aPhysicist and Senior Principle DesignEngineer. There he has developed theadvanced calibration software used by theEMC Test Systems Calibration Laboratory,and a number of new products, including ahigh speed isotropic field probe and a virtualdevice controller. He has authored orcoauthored a dozen papers in the areas ofEMC and Condensed Matter Physics. (512)835-4684, ext. 650.

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ITEM 1999 1

ZHONG CHEN

EMC Test Systems

Austin, TX

Since their first introduction in 1994at the Roma International Sympo-sium on EMC,1 bicon/log hybridantennas have become very popu-

lar in EMC labs worldwide. Because thereare no band breaks in frequency sweep,test time and effort are reduced. EMC en-gineers have assumed that performance ofthese antennas is simply that of a biconicalantenna at a lower frequency range untilit transitions to a regular log periodic di-pole array (LPDA) antenna at higher fre-quencies. Questions have been raisedabout this assumption, and some havesuggested that a higher measurement un-certainty (U) should be used due to thecharacterization of the phase center posi-tion and antenna pattern variation fromthat of a dipole on which emission andsite validation standards are based. Verylimited research has been conducted onthe uncertainty evaluation of these hybridantennas, despite the fact that more andmore EMC engineers have come to realizethat predicting and reducing measurementuncertainty has become an important as-pect of EMC testing.

Most antenna manufacturers and cali-bration labs provide individually calibratedantenna factors (AF) with associated U val-

ues. A thorough understanding of thesevalues is essential. EMI and normalized siteattenuation (NSA) tests are performed overa conducting ground plane. Calibrationlabs may be able to provide very accuratecalibrations of the free-space AFs, whichare intrinsic properties of the antennas.Studies have shown that antenna perfor-mance can change by a few decibels overa ground plane, and this effect is antennatype specific. In many cases, the perfor-mance of a bicon/log hybrid antenna overa ground plane is different from that of abicon or a log antenna. A good free-spaceAF with a low U does not always translateinto a low U in the EMI or NSA measure-ment due to the influence from the con-ducting ground.

This article will address several aspectsof measurement uncertainty related to thebicon/log hybrid antenna application. Theyare: the height dependency of the hybridantenna AF above a conducting groundplane; the geometry and polarization-de-pendent AF and NSA measurement; activephase center variation with frequency;antenna beam pattern; and the compari-sons of a bicon/log hybrid with separatebicon and log antennas. Some manufac-turers also apply capacitive loading on thebow tie elements to improve the low fre-quency performance of these antennas.This article also explains how this loadingimpacts the measurement U.

Understanding the measurementuncertainties of the bicon/log

hybrid antennaMeasurement uncertainty associated with the bicon/log hybrid antenna for

radiated emissions and site validation tests relate to many factors, including

height dependency, polarization and loading.

Reprinted with permission from ITEM 1999.

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2 ITEM 1999

HEIGHT/POLARIZATIONDEPENDENCY ABOVE ACONDUCTING GROUNDPLANEAF is defined as the ratio of the inci-dent electric field over the receivevoltage at a 50-ohm load connectedto the feed point of the antenna. Thefree-space AF is obtained when theantenna is in free-space and the in-cident electromagnetic field is a planewave. The free-space AF is an intrin-sic property of the antenna, just likethe physical length of a ruler, andshould not vary no matter how thecalibration is performed. However,just like heat or cold can change thelength of a ruler, the environment inwhich the antenna is used can alsoimpact the AF. EMI and NSA mea-surements are performed over a con-ducting ground plane, and unliketemperature, which does not changea ruler all that much, the groundplane can change the AF by as muchas 2 or 3 dB depending on the po-larization and height. Different typesof antennas also interact with theground plane differently, causing theeffect on the AF to be antenna spe-cific.

Figure 1 shows a traditional bicon/log hybrid antenna, while Figure 2shows an enhanced model for im-proved low frequency performance.Let us use the traditional model

shown in Figure 1 to illustrate thedependency of the AF on heightabove a conducting ground plane.Figures 3 and 4 show numerically-calculated AFs at heights of 1 m, 2m, 3 m and 4 m for a horizontally orvertically-polarized antenna. Noteagain that the EMI or NSA measure-ments are typically performed for aheight scanning from 1 m to 4 m. Ifwe were to use a free-space AF oran AF calibrated at a fixed height todo a measurement at a different

height, no matter how accurate thecalibration is, there exists an error.

We may be tempted to say we justneed to use a matrix of AFs, so thatat each different height we could usea different AF. However, for differ-ent frequencies, AFs are different; fordifferent polarizations, AFs are dif-ferent; for different separation dis-tances, AFs are also different. It be-comes a practical issue for calibra-tion in all these different cases andrequires applying a complicatedmulti-dimensional matrix of AFs dur-ing an EMI test.

Instead of this complicated webof AFs, is there an acceptable com-promise if we are willing to sacrificea little bit of accuracy? It turns out

that the free-space AF provides anacceptable average. As shown in Fig-ure 3, the free-space AF falls right inthe middle for most of the frequen-cies. This is also why the ANSI, CISPRand other international standardshave moved toward the use of free-space AF for product EMI test in re-cent years. However, it is also clearthat we may be able to get a nearperfect free-space AF, but it wouldnot be perfect for our typical EMI orNSA measurements, simply because

a typical measurement condition isnot free-space. For total measure-ment U, in addition to the antennacalibration U obtained from antennacalibration labs, we must assess ad-ditional uncertainty values for theantenna and geometry-dependenttest setups.

STANDARD SITE METHODCALIBRATION ANDIMPLICATIONS ON NSAMEASUREMENTSANSI C63.5 calibration calls for athree-antenna-method calibrationover a ground plane, commonlyknown as the standard site method.In this measurement, the receive an-tenna is scanned in heights from

1 m to 4 m. NSA measurement asdefined in ANSI C63.4 is simply thereverse of the ANSI C63.5 antennacalibration procedure. The only sig-nificant difference is that for NSAmeasurement, the site is the un-known, where for antenna calibra-tion, the AFs are the unknowns.

A common question when follow-ing the NSA measurement proce-dures is “I calibrated my antennasvery recently. When I use the AF todo my test, with separate bicons and

Figure 2. Enhanced model of the

bicon/log hybrid antenna.

Figure 1. Traditional bicon/log hybrid

antenna.

… for different frequencies, AFs are different; for different polarizations, AFs

are different; for different separation distances, AFs are also different.

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ITEM 1999 3

log antennas, I can pass the NSA re-quirement, but when I use the hy-brid antennas, I failed the test. Is thatdue to my antennas or my site?”Other questions are “I need to cali-brate my antennas for site validation;which AFs do I need?”, and “Do Ineed free-space AF, 3-m or 10-m cali-bration, and how about height andpolarization?”

It was explained above how AFschange under different geometries

and how free-space AF can be usedfor product EMI test as an acceptableaverage. To better answer the abovequestions, we need to quantify ex-actly how much different geometriesaffect the performance of a specificantenna. For NSA measurement,since we are dealing with a tightertolerance, we want to decrease ourmeasurement uncertainties. We willshow that the free-space AF approxi-mation becomes inadequate. Let us

first look at some antennas calibratedper the ANSI C63.5 standard sitemethod. Figure 5 shows the result-ing AFs for a separation distance of 3m, with the receive antenna scannedfrom 1 to 4 m in height.

In the standard site method, thediscrepancy results not only from theheight variation, but also from otherfactors, such as the non-plane waveillumination of the receive antenna,mutual coupling between the transmitand receive antennas, and the dipoleantenna pattern assumption made inthe theoretical model.2 As shown inFigure 5, using a single AF to do anNSA test for all these geometries is acrude approximation. One thing tonote is that Figure 5 only shows thedifference in the AF for a single an-tenna under different geometries.

For an NSA measurement, thereare two antennas involved, transmitand receive. The resulting differenceis the sum of two antennas. For ex-ample, at 180 MHz, the free-spaceAF is different from the AF for thevertical polarization (h1 = 1.5 m) by2 dB. If a free-space AF were to beused for an NSA site validation mea-surement, the NSA error just due tothe AF difference would be 4 dB (2dB from the transmit antenna, and 2dB from the receive antenna). Thus,it is unlikely a site would pass theNSA 4-dB requirement under thiscondition.

This answers the first question ofwhether the NSA failure is due to theantenna or site: it is probably nei-ther the site or the antenna calibra-tion that is at fault. Perhaps the an-swer lies in the method being used,and whether the correct AF is ap-plied. Because the NSA procedure issimply the reverse of the procedurefor an ANSI antenna calibration, ifthe NSA geometry stays the same asthe calibration geometry, the errorsshown in Figure 5 exactly cancel.

This also answers the secondquestion of which antenna calibra-tion is needed for a site validationtest; the geometries for site valida-tion and antenna calibration need tobe identical to get the lowest mea-

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Figure 4. Numerically-calculated bicon/log hybrid AF at different heights for

vertical polarization above a conducting ground plane. Manufacturer-published

data are also shown as triangles.

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Figure 3. Numerically-calculated bicon/log hybrid AF at different heights for

horizontal polarization above a conducting ground plane. Manufacturer-

published data are also shown as triangles.

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4 ITEM 1999

surement uncertainty. However,there is one catch. The antenna cali-bration site needs to be very good,because any errors generated in theantenna calibration will be trans-ferred to the site validation test.

Let us look at the results in Figure5 from another perspective. If weassume that the transmit antenna isthe equipment under test for an emis-sion measurement, and we use thefree-space AF to qualify the EMI fromthis piece of equipment, the differ-ence between the different geom-etries and the free-space AF is theerror in our measurement. For theexample given in Figure 5, this erroris 2 dB in some cases. The biconicalantenna was also studied for thesame circumstances,2 and the errorswere shown to be about 1 dBsmaller. For lowest U, a biconicalantenna is recommended.

ACTIVE PHASE CENTERVARIATION WITHFREQUENCYThe radiating elements for a bicon/log hybrid antenna move from thebigger elements in the back to thesmaller elements in the front as thefrequency goes up. The radiatingposition for a specific frequency iscommonly referred to as the active

phase center. It appears that the elec-tromagnetic fields are radiated fromthat center.

Because the phase center moveswith frequency, other common ques-tions people ask are: “Where do Imeasure the distance from the bicon/log hybrid antenna for my test?Should I measure from the tip of theantenna or from the center of theantenna?” A typical answer is to mea-sure from the tip for an immunitytest, and from the center for an emis-sion measurement, as specified bythe ANSI, CISPR and IEC standards.It is rather clear that this position isjust an approximation during the fre-quency sweep. Thus, uncertaintiesare introduced in the measurementsby assuming a fixed position.

The question arises for bicon/loghybrid antennas from different manu-facturers; these antennas may not havethe same design or the same length.Are their uncertainties different in anEMI test? The answer is absolutely yes.The next question is whether this er-ror can be estimated. This questionmay be answered by simply lookingat the E d

max formulation.*If we can assume that a bicon/log

hybrid antenna acts like a series ofdipoles radiating in different posi-tions at different frequencies, E d

max

should not be calculated for a fixeddistance. For example, when we per-form a 3-m calibration below 100MHz, the bow tie elements are ac-tive. If the antenna is 1 m long andthe reference position is the centerof the antenna, we are in fact per-forming a 4-m test (0.5 m additionfor each antenna). Figure 6 showsthe E d

max values for a horizontally-po-larized antenna with the transmit an-tenna at 1 m height. It shows thatmore than 2 dB of error can be ex-pected just due to the active elementsbeing different from the referencepoint.

For antenna calibration, if the ac-tive center can be accurately char-acterized, applying E d

max for the cor-rect distances will rectify the error.For a radiated emission test, if thefree-space antenna factor is used,this error cannot be amended, andbecomes part of the measurementuncertainty. On the other hand, if abiconical or dipole antenna is used,this phase center is well-defined,and a lower measurement uncer-tainty is achieved. A log antenna cansuffer from the same phase centererror, but conceivably, a single logantenna is shorter than the hybrid.The phase center error would besmaller. For a critical test where lowmeasurement uncertainty is desired,a simple dipole, bicon and/or logantenna are preferred over the hy-brid antenna.

ANTENNA DIRECTIVITY ANDBEAM PATTERNThe intent of the ANSI C63.4 NSAand emission measurement is to usea field sensor with a dipole pattern(because the Roberts’ Dipole is theundisputed reference). If the antennapattern is different from a dipole, itwould not be an issue if the mea-surement were performed in a free-space environment as long as we cankeep the antenna pointing to theequipment under test at all heights(boresighting).

For a measurement over a con-ducting ground plane, however,there is a signal reflection from the

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Figure 5. Numerically-calculated bicon/log hybrid AF obtained using the 3-m

ANSI C63.5 standard site method. The receive antenna is scanned from 1 to 4 m

with a step size of 0.05 m. “h1” is transmit height.

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ITEM 1999 5

ground plane. The reflected field enters the antennapattern at an angle. The addition of the direct and re-flected signal will not add the same way if the antennapattern is different. There are certain pattern variationsfrom that of a dipole for the hybrid antenna.1 Any de-viation due to the antenna pattern needs to be treatedas a source of measurement uncertainty. Bicon antennapatterns have been illustrated to be close to those ofdipoles,4 so, again, this error is smaller for the biconicalantennas.

CAPACITIVE-LOADING(LOW-FREQUENCY IMPROVEMENTS) FORCERTAIN BICON/LOG HYBRIDThe VSWR for a hybrid such as the sample shown inFigure 1 is on the order of 20:1 at the 30-MHz range,which means that about 80% of the forward power isreflected back to the source. To generate a certain fieldlevel for a radiated immunity test, a huge amplifier issometimes needed. Several manufacturers introduced ca-pacitive-loading to their antennas, such as shown in Fig-ure 2, to improve the mismatch condition. This improve-ment is most useful for radiated immunity tests.

For emission tests, the loading elements can couplestrongly with the ground when polarized vertically. Fig-ure 7 is an example of the antenna factors at differentheights for a vertically-polarized antenna with an L-shaped enhancement. This L-shaped enhancement is avariation of the T-shaped bow tie shown in Figure 2.Even though we could treat such coupling as part of the

measurement uncertainty, this value would be unaccept-ably large, as is the case in Figure 7 (on the order of 5 dB).

The solution for making such an antenna suitable forboth radiated emission and radiated immunity testing isto make the end-loadings removable. For immunity test-ing, the end-loadings are left on to gain the better match(thus requiring a smaller amplifier for a fixed field level).Since the purpose of the immunity test is to generate agiven field level, as long as we can measure the gener-ated field, this coupling is not an issue. In addition, mostimmunity tests are performed in a fully-lined anechoicroom, or over a partially absorber-lined ground plane,and this coupling is not as significant.

For an emission measurement, the end-loading shouldbe removed. The antenna in that case would simplyperform like a traditional bicon/log hybrid antenna. Onething to note is that the antenna does not need to becalibrated for use in immunity mode, thus saving thecost of calibration for both emission and immunity con-figurations.

CONCLUSIONSThis article has presented several issues of measurementuncertainties related to the bicon/log hybrid applica-tion. Many general measurement uncertainty related is-sues are not discussed here since they are not particularto this type of antenna. These include cable mismatchuncertainty, site irregularity, site edge diffractions, etc.In an actual measurement, these factors all play impor-tant roles in the total measurement uncertainty evalua-tion. On the other hand, an important issue which tendsto be ignored by many EMC engineers is the antenna-specific uncertainties. In most cases, care must be takenwhen using different antennas and their associated an-tenna factors. A compromise must be made betweenthe ease of measurement and the accuracy of the mea-surement.

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horizontally-polarized antenna. The transmit antenna height

is 1 m, and the receive antenna height is scanned from 1 to

4 m.

* E d

max is a concept introduced by Smith, German, and Pate3 and later

adopted by the ANSI C63 standard site method and NSA formulation.

It represents the maximum electric field in a height scan for a tuned

dipole with a radiated power of 1 pW.

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Figure 7. Numerically-modeled AF for a vertically-polarized

bicon/log hybrid with an L-shaped end-loading.

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REFERENCES1. S. J. Porter, A. C. Marvin, “A New Broadband EMC Antenna for

Emissions and Immunity,” Roma International Symposium on EMC;

Rome, Italy, September 1994.

2. Z. Chen, M. Foegelle, “A Numerical Investigation of Ground Plane

Effects on Biconical Antenna Factor,” IEEE International Sympo-

sium on EMC; Denver, Colorado, 1998.

3. A. A. Smith Sr., R. F. German, and J. B. Pate, “Calculation of Site

Attenuation from Antenna Factors,” IEEE Transactions on Electro-

magnetic Compatibility, Vol. 24, No. 3, August 1982, pp. 301-311.

4. M. J. Alexander, M. H. Lopez, M. Salter, “Getting the Best out of

Biconical Antennas for Emission Measurements and Test Site Evalu-

ation,” IEEE International Symposium on EMC; Austin, Texas, 1997.

ZHONG CHEN received his M.S.E.E. degree in electromagnetics from the

Ohio State University at Columbus. He has been with EMC Test Systems

(ETS) since 1996, where he is now a senior electromagnetics and an-

tenna engineer. He is a member of the IEEE AP, MTTS, and EMC Societies.

(512) 835-4684 ext. 627. E-mail: [email protected].

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Common EMC Measurement Terms - All-Electronics.de...The only specific requirements are found in IEC 801 - 3 and IEC 1000 - 4 - 3, which, if the analysis of the requirement is performed,