December 18, 2020

## Guidance on magnetic field strength radiated emission measurements (9 kHz – 30 MHz)

This notice provides guidance to ensure that radiated emission measurements in the frequency range 9 kHz to 30 MHz are properly assessed and reported, according to Innovation, Science and Economic Development Canada (ISED)’s technical standards.

**1. Introduction**

A number of ISED technical standards include radiated emission limits in the frequency range of 9 kHz to 30 MHz. Traditionally, all radiated emission limits in this frequency range were expressed in terms of electric field strength, such as in units of μV/m or dB(μV/m). However, at the present, most (but not all: see ICES-004) ISED technical standards specify limits for radiated emissions in this frequency range in terms of magnetic field strength (see RSS-Gen, RSS-216 and ICES-001). Additionally, while all these ISED technical standards include the measurement method using the shielded loop antenna (the so-called “60 cm” loop), some standards (see RSS-216 and ICES-001) also allow the alternative measurement method using the large loop antenna system (LLAS).

**2. Small loop antenna**

This section is specific to the measurement method using the small shielded loop antenna placed at a given distance (the “measurement distance”) from the equipment under test.

**2.1 Antenna factor**

Radiated emission measurements in the frequency range of 9 kHz to 30 MHz are performed using a shielded loop antenna. The antenna factor is a scalar quantity that allows the determination of the magnitude of the incident magnetic field strength from the voltage level measured at the coaxial output port of the loop antenna:

*H[dB(μA/m)] = V[dB(μV)] + AF*

^{H}[dB(S/m)]

where *AF ^{H}* is the magnetic antenna factor, having a unit of S/m, or Ω

^{-1}m

^{-1}, which is

*dB*(

*S/m*) or

*dB*(Ω

^{-1}m

^{-1}) in logarithmic units.

Due to historical reasons (radiated emission limits in this frequency range were previously specified in units of electric field strength), many antenna calibration labs still provide by default the so-called “electrical” antenna factor, while the magnetic antenna factor is sometimes only available as an option (on demand). However, it is easy to convert from one to the other using the free space impedance:

*AF*

^{E}[dB(m^{-1})] = AF^{H}[dB(Ω^{-1}m^{-1})] +Z_{0}[dBΩ]

where *AF ^{E}* is the “electric” antenna factor, having a unit of m

^{-1}, or dB(m

^{-1}) in logarithmic unit, and

*Z*is the free-space impedance, equal to (120π) Ω≈ 377Ω, or 20 log 120π ≈ 51.5 dBΩ in logarithmic unit.

_{0}

It is important to recognize that *AF ^{E}* is only a mathematical construct and not the true electrical antenna factor of the shielded loop antenna. This type of antenna is required to have a poor response to electrical field and optimized response to magnetic field (in accordance with 4.3.3 of CISPR 16-1-4 Ed.4.1). The true electric antenna factor is equal to the ratio between the magnitude of the electric field at the antenna location and the voltage appearing on the coaxial output port of the antenna (all quantities expressed in linear units). Nonetheless,

*AF*can be used to correctly evaluate the magnitude of the electric field the antenna is immersed in provided the antenna is in the far field of the radiating source. This is strictly due to the fact that the E and H components of the field are related to each other by the free-space impedance,

^{E}*Z*, in the far field of the radiating source (and not due to the fact that the

_{0}*AF*reflects in any way the actual electric field detected by the loop antenna the latter does not measure the electric field; it measures the magnetic field and the electric field can then be deduced from that).

^{E}

When the measurements are performed in the near field of the radiating source (as is the case in practice with most radiated emission measurements at these frequencies), the E and H components of the field are no longer related to each other by the free-space impedance, Z_{0}. Thus, using *AF ^{E}* in this case will not correctly evaluate the true magnitude of the electric field the loop antenna is immersed in. That would necessitate another type of antenna, having an optimized response for electric field, instead of magnetic field (e.g. a rod antenna). However, where the limit is expressed in units of electric field (such as in ICES-004) and the loop antenna is used for measurements, the

*AF*value calculated as per the above (using the free-space impedance and the magnetic antenna factor) shall be used for calculating the value of the electric field before comparing with the limit.

^{E}

**2.2 Reporting**

The test report needs to show how the field strength value was determined for comparing with the limit.

When the limit is in terms of magnetic field, the following equation applies:

*H[dB(μA/m)] = V[dB(μV)] + L*

_{C}[dB] - G_{PA}[dB]+ AF^{H}[dB(S/m)]

where

*H* is the magnetic field strength (to be compared with the limit),

*V* is the voltage level measured by the receiver or spectrum analyzer,

*L _{C}* is the cable loss,

*G*is the gain of the preamplifier (if used), and

_{PA}*AF*is the magnetic antenna factor.

^{H}

The *G _{PA}* term is only included in the equation when an external preamplifier is used in the measurement chain, in front of the receiver or spectrum analyzer. An external preamplifier is not usually necessary (or even advisable, due to risk of saturating the input mixer of the receiver) when an active loop antenna is used. In that case, the antenna factor of the loop already includes the gain of its built-in preamplifier.

If the “electrical” antenna factor is used instead, the above equation becomes:

*H[dB(μA/m)] =V[dB(μV)] + L*

_{C}[dB] - G_{PA}[dB] + AF^{E}[dB(m^{-1}) ] - 51.5 [dBΩ]

where *AF ^{E}* is the “electric” antenna factor, as provided by the antenna calibration laboratory.

When the limit is in terms of electric field, the following equation applies:

*E[dB(μV/m)] = V[dB(μV)] + L*

_{C}[dB] - G_{PA}[dB] + AF^{E}[dB(m^{-1}) ]

or, if the magnetic antenna factor is used:

*E[dB(μV/m)] = V[dB(μV)] + L*

_{C}[dB] - G_{PA}[dB] + AF^{H}[dB(S/m)] + 51.5[dBΩ]

The display of the receiver (or spectrum analyzer) __ shall not__ be configured in units of current, e.g. μA or dB(μA). That conversion is calculated inside the receiver (or spectrum analyzer) using its input impedance, which is 50 Ω, while the magnetic field calculation is based on the free-space impedance of 377Ω.

**3. Large loop antenna system (LLAS)**

When using the LLAS, the measurement result is the magnitude of the induced current, in the large loop antenna (LLA) used for measurements, due to radiated magnetic field emissions from the equipment under test, which is placed at the centre of the LLAS. As such, the following equation applies in this case:

*I[dB(μA)] = V[dB(μV)] + L*

_{C}[dB] - G_{PA}[dB] + T_{CP}[dBS]

where

*I* is the induced current (to be compared with the limit),

*V* is the voltage level measured by the receiver or spectrum analyzer,

*L _{C}* is the cable loss,

*G*is the gain of the preamplifier (if used), and

_{PA}*T*is the transfer admittance of the current probe placed on the LLA used for the measurement.

_{CP}

The ideal value of the transfer admittance is 1 A/V; that is 0 dBS (per Annex C of CISPR 16-1-4). Any deviation from this value has to be accounted for in the formula above.

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