EMC
Last Updated: Apr 9th, 2008 - 15:00:00
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Transmitted Power and Electric Field Limits for EMC Compliance for Unlicensed Short Range for Unlicensed Short Range Radio Devices: A Comparative Study
Apr 1, 2008
by Inam Rahim, Intelligent Mechatronic Systems, Inc.
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In the recent years, scores of low power wireless devices (LPDs, also known as short range devices, or SRDs) in the unlicensed RF bands have emerged in the market, and their numbers are growing. New applications are being developed, as wires are continuously being replaced by radio waves. Unlicensed low power radio bands are getting crowded and design engineers are busy creating new devices.
The regulatory bodies, including the Federal Communications Commission (FCC) in the United States, Industry Canada in Canada (whose requirements closely follow those of the FCC), and ETSI in the European Union (EU), classify LPDs and SRDs radio devices which radiate very small power (i.e., a fraction of a watt or close to a watt). However, the demand on radio operating range is continuously increasing, and RF engineer have to make vital decisions about maximum output power delivered to antennas for desired operating ranges without violating the regulatory limits in the given region.
Further, the allowable output power limits for similar devices in the U.S. and the EU are often expressed in different units or terminologies, which can create confusion when it comes to finding equivalence. For example, power expressed in milliwatts may be conducted power or radiated power expressed as ERP, EIRP, or electric field in some cases. Also, the conducted power limit may be specified as peak, average or quasi-peak, which are all different.
Often for similar devices, not only the magnitudes of emissions limits but methods of measurement may also vary between the regions. Understanding the relationship between limits of various regions and being able to compare them can make the task of the design engineer easier.
In this article, we define the relationships in the output power limits expressed by FCC and ETSI for some very common short range, low power RF transmitting devices in popular unlicensed bands.
Radiated RF Energy – A Typical RF Transmission Link The power radiated from a transmitting antenna is the function of total power input to the antenna, and the antenna properties. The design engineer has more control over the power developed at the output amplifier (antenna input), but less control over the radiated power, due to several uncertainties with the antenna, like its VSWR, radiation efficiency, and so on.
The RF power transport path illustrated in Figure 1 shows an RF link from the LPD/SRD to the antenna, and the radiated field from it. P1 is the conducted power at the device output, and P2 is power available after cable loss. Both can be measured by direct connection with instruments. Once the antenna is connected, P3 radiates out, while P4 is reflected back to the source.
Figure 1: A typical RF power link from transmitter to a reference point with its loss components. Antenna is ideal isotropic emitter with spherical field.
So here are the complexities. Antennas for the devices under discussion are small, compared to normal dipole or monopole dimensions and are not very efficient, making it difficult to precisely estimate the radiated power P3. The last quantity in the Figure 1 is E1, the electric field at distance r, and the corresponding quantity Pd, the power density.
The goal of the design engineer is to get the desired range within the regulatory power limits. Therefore, a valid question would be what power should be delivered at the antenna port by the power amplifier, if the maximum power limit is specified as ERP, EIRP, or e.i.r.p, plain mW or as electric field? Essentially, we wish to find some relationships between quantities in Figure 1 and the limits specified by the applicable regulatory bodies.
All field measurements are assumed to be done in the far field (r >= λ/2π or r >= 2 d2/λ, for electrically small antennas). Thus, for measurement at 3 m and short device antennas (d << λ), the frequencies above approximately 17 MHz fall within far field definition.
EIRP, ERP and Conducted Power
Radiated power may be expressed in many different ways, such as power density, watts per sq. meter, or as field strength at some distance. Regulatory bodies use terms such as ERP (effective radiated power), EIRP (effective isotropically radiated power), or field strength. To confuse matters further, regulatory bodies sometimes use term e.i.r.p (equivalent isotropically radiated power) with small letters, or may use both terms interchangeably.
In most cases, the output from low power transmitting devices is measured as field strength due to embedded antennas, even though the limit might be expressed as conducted power. In fact, field strength is the only physical quantity that can be measured outside the physical device (the rest are just calculations).
Because SRD/LPD antennas are short compared to the wavelength λ, they are inefficient [9] and, their directivity or gain is also small [8]. For these reasons, ETSI combines their radiated power and the gain together as part of EIRP (equivalent isotropically radiated power, or e.i.r.p). It also includes the duty cycle of transmission in it. Thus, the ETSI expression for EIRP (e.i.r.p) is given as in [6] sec. 5.7.2.2, all in dB:
P = A + G + log (1/x) (1)
where A is the average conducted power fed to the antenna, measured by an instrument, G the antenna gain, and x is the transmitter duty cycle (Ton/(Ton + Toff)).
In Figure 1, electric field E and Pd at r-m from the antenna are related by another ETSI definition for the EIRP (effective isotropic radiated power) according to [5] Annex D as:
EIRP = Pd x Area of Sphere (2)
(sphere of radius r, the distance from antenna)
That makes perfect sense due the word ‘isotropic’ in its definition. Further, in this section, it is related to ERP as:
EIRP = ERP / G
Thus,
EIRP = ERP / 1.62
(Effective Isotropically Radiated Power for a dipole)
So, according to ETSI:
EIRP = ERP – G (3)
(powers in dBm and gain G in dBi (2.14 dB))
On the other hand, the FCC uses EIRP terminology only for ultra-wideband systems at UHF and microwave frequencies, and defines it as Equivalent Isotropic Radiated Power, e.g., in Reference [1] sec. 15.501 para. (k), as follows:
EIRP = Ps + G (4)
(G is any value of gain, all in dB)
Where Ps is the power sent to the antenna (conducted power), and G is antenna gain (any value). The FCC again defines EIRP according to [10], where EIRP and ERP are related in dB, as:
EIRP = ERP + G (5)
(G = 1.64 or 2.14 dB, the dipole antenna gain)
Compare Equation 5 with the ETSI definition. Apparently, Ps and ERP are equivalent for a dipole antenna, but ERP is not considered the same quantity by the FCC and ETSI. And one may think of Ps = P2 in Figure 1, but antenna efficiency and VSWR are not parts of the equations. Therefore, the field created E may not be an exact indication of the power P2 or Ps sent to the antenna. This fact will be apparent in some examples later in this article. The FCC also gives the following relation in [10]:
EIRP (dBm) = E (dB μV/m) – 95.2 (6)
(For 3-m from antenna)
Which is equivalent to Equation 2, but ETSI calls it effective instead of equivalent. Also note that Equations 1 and 2 give different results for EIRP.
Let us now understand the conducted power (which is measured in peak, average, or quasi-peak) all can be related to each other mathematically or by some accepted definitions from the regulatory bodies. The instantaneous power of communication signals depends upon modulation type, and average power depends upon its time domain behavior (e.g., duty cycle) required by an application. Most low power devices are assumed to operate intermittently, and often higher power levels are allowed if the duty cycle is low. Basic relations between various power terms are given as:
Pav = 1/T ∫T P(t) dt: The average power integrated over time T which can vary depending upon the signal type. For example, for time division duplex (TDD) devices such as Bluetooth time T must be sufficiently larger than several transmit cycles to happen ([5] sec. 5.7.2.2).
Pqp: Quasi peak transmitted power measured at the output of device through an R-C charge / discharge circuit doing physical integration (in a specified bandwidth) as recommended in sec. 4 of [6].
Ppk = max. P(t): Maximum instantaneous power generally measured by a spectrum analyzer or similar receiver.
In case of Figure 1, a typical link showing powers at various points in a transmitter path, basic relations between various quantities are as following:
P2 = P1 – PcL
(PcL is the cable loss)
P3 = P2 - P4 - PaL
(P4 is the reflected power and PaL is antenna loss)
The reflected power P4 can be estimated easily from antenna VSWR information, which can readily be measured by a directional wattmeter or network analyzer. The VSWR is related to incident and reflected voltage ratios as follows:
P4 / P1 = Vr2 / Vi2 = |ρ|2
where Vr is reflected and Vi is the input or incident voltage, and ρ is reflection coefficient.
And the ρ is related to VSWR as:
|ρ| = (VSWR -1)/(VSWR +1)
or
P3 = P1- P4 – PcL- PaL = P1 (1- |ρ|2) - PcL- PaL (7)
writing P4 in terms of P1.
For small antennas, for example, with typical VSWR of 2, P4 is not large (only 11% reflection), but PaL can be large due to poor radiation efficiency which is not easy to measure [9].
Radiated Power and Electric Field
We assume that the power from an antenna radiates in a perfect sphere, such that the field is uniform, or isotropic, at its surface. The energy conversion relations between power and the field given in numerous texts are as follows:
Pd = P / 4 π r2
where Pd is the power density at r meters and P is the radiated power. Power density Pd and electric field are also related, as:
Pd = E2 / Z0
where E is the electric filed in V/m and the Z0 is free space impedance (Z0 =μ / ε =120 π , Ω).
Combining these two equations, and relating E with P3, we get:
E2 = 120 π P / 4 π r2
or
E2 = 30 P / r2 (8)
E= sqrt (30 P) / 3
(E-field at r = 3 meters)
The radiated power appears as electric field E given by Equation 8 at r-m from antenna. The standard measurement distance for most EMC purposes is 3 m. Thus, rewriting Equation 8 in terms of power, we get:
P = E2 r2 / 30
P = 0.3 E2
(P in W, and E in V/m at 3 m from antenna)
In dB it can be written as:
P (dBm) = 20 log E (dB μV/m) - 95.3 (9)
Equation 9 is standard equation between power and electric field, but which power from Figure 1: P2 or P3? Some standards suggest it is P2, but we will investigate that later in this article.
If we place another antenna in the space at some distance r from the radiating source, the power received by the antenna depends upon antenna effective area and the power density in the field. The antenna effective area, Aeff, is given by:
Aeff = G. λ2 / 4π
where G is the antenna gain.
Combining equations for power density with effective antenna area, we get Friss’ transmission equation between two antennas; the power received Pr by receiving antenna is:
Pr = Pd . Aeff
= (P3 / 4 π r2 .)( Gr. λ2 / 4π)
Pr = P3 Gr λ2 / (4 π r)2
(transmit antenna gain is implicit in P3)
In a more general form, the power received can be written with both transmit and receive antenna gains as:
Pr = Pt Gt Gr λ2 / (4 π r)2 (10)
Pt is radiated power from antenna with no gain information, and Gt and Gr are the gains of the transmit and the receive antennas. If we assume an ideal isotropic system, then both Gt = Gr =1 Generally, for a simple dipole antenna, the value of gain is 1.62. Pr in watts is resulting power at r meters from the source, which is transmitting P3 watts.
In logarithmic terms, this equation can be written as:
Log (Pr) = - 22 + 10 log (Pt) + 10 log G1 +
10 log G2 + 20 log λ – 20 log r (11)
Measurement Methods and Regulations – Some Examples
In the following paragraphs, we shall consider a few examples of some SRDs/LPDs operating in different frequency bands, and try to correlate the specified limits expressed in various terms (e.g., conducted power, EIRP, ERP, E-field). We will compare the limits allowed between different standards/requirements in the EU (ETSI) and in North America (the FCC and Industry Canada).
Example 1: Short Range Devices
Suppose the SRD is a common RKE device operating in North America in the 315 MHz band and in the EU in the 433 MHz band. For such devices, Table 1 shows the allowed limits for both regions:
Industry Canada RSS-210 Annex 1, together with Table 4 and Table 5 in this regulation, specify same limits as the FCC in units and magnitude.
If we assume the ETSI limit of 10 mW ERP as radiated power equivalent to P3 in Figure 1, and use Equation (4) to calculate equivalent E-field at 3-m from antenna, we get:
E = sqrt (30 x10x10-3) / 3 = 0.182 V/m
or
E = 182,574 μV/m, isotropic
which is orders of magnitude larger than the FCC limit (10,960 μV/m at 433 MHz), but is generally expected to be comparable or less. (See Table 1 for range of values of E-field.)
| Reg. Body | Test Conditions | Standard & section(s) | FCC
| 260 – 470 MHz, 3750 to 12500 uV/m, at 3-m (or 6040 μV/m at 315 MHz, RKE freq.) | FCC 15.231 | ETSI
| 25 MHz to 1 GHz, Power class 8, 10 mW (The ERC/REC 70-03 allows 10 mW ERP).
| ETSI EN 300-220-1 |
Table 1: Short range devices transmitter power limits
Now we do a reverse calculation on the FCC limits of electric field at 3 meters to obtain equivalent power P3 from Equation 4 for 433 MHz band, as follows:
P3 = (10960) 2x 10-12 x 9 / 30 = 35.5 μW = -14.5 dBm
The ETSI limit is 10 mW ERP or 10 dBm which, when compared to the above results, can be misleading (a difference of 24 dB), unless methods of measurements used for ERP and the effects of the antenna are accounted for.
Comments
The measurement method of ERP, as specified in ETSI EN 300 220-1 sec. 8.3 using a substitution antenna, suggests that the ERP is actually the power fed to a resonant dipole. Therefore, it is equivalent to P2 in Figure 1, and not P3.
In practice, a typical antenna used for SRDs might be only 2 or 3 cm long, which is very small compared to a dipole antenna for above frequencies (λ = 0.95 m for 315 MHz, or λ =0.7 m for 433 MHz), and therefore will be inefficient due to its small radiation resistance [8]. For a practical device, if the antenna is, say, 3-cm long, at 433 MHz its radiation resistance would be:
Rr = 160 π2 (L / λ )2 = 160 π2 ( 0.03 / 0.7 )2 = 1.42 Ω
which is very small compared to any resistance value in the RF power circuit.
However, unless antenna loss resistance is known, the radiation efficiency cannot be determined and it is not easy to estimate relationship between P1 and P3. But, as can be seen Rr << 50 Ω, typical source resistance the actual transmitted power and electric field could be an order of magnitude less than the calculation above.
On the other hand, power radiated from a resonant dipole antenna with 10 mW input will be significantly greater than 35.5 μW, required for the FCC field strength limit. Therefore, it may be argued that ETSI allows much higher transmitted power levels if one can use an efficient antenna, but it would mean a larger device size.
The FCC specification of limits in this case makes more sense because it looks at the final quantity of concern, that is, the electric filed strength at 3 m. This can be measured with relative ease and only the receiver antenna-factor is the variable in such measurements. This is not difficult to measure, and most antenna manufacturers specify it.
Example 2: Low Power Devices, or LPD II
Table 2 shows output power limits for both the United States and the EU.
| Reg. Body | Test Conditions | Standard & section(s) | FCC
| 88 – 108 MHz, 250 μV/m at 3-m | FCC 15.239 | ETSI
| 25 – 2000 MHz, Cordless audio, LPD II, -43 dBm ERP | ETSI EN 301 357-1 |
Table 2: Low power device power limits
Industry Canada RSS-210 Annex 2, A2.8 is applicable with same limits as FCC. (Refer to Table 2 for power and E-field limits values for LPD II devices.)
Again, let us assume that ETSI limit of -43 dBm ERP is the power transmitted from the antenna and it is P3 as in Figure 1:
-43 dBm = 50 nW
E = sqrt (30 x 50x10-9) / 3 = 409 μV/m = 52 dB μV/m
Comments
The FCC limit of 250 μV/m (or 48 dB μV/m) is only 4 dB lower than ETSI limit, and both are reasonably comparable.
According to ETSI specified measurement method in sec. 8.2.1.3 of the above standard, power is measured indirectly by measuring electric field at 3 m from antenna, and converted to power by using common formulas between E-field and ERP or EIRP given in Annex D of that standard. The recommended antenna size is less than λ/10; therefore, the power at the input of the antenna must be much higher than -43 dBm (50 nW), due to poor antenna efficiency.
Example 3a: 2.4 GHz digitally modulated FH systems
Looking at Table 3a, we notice that both standards specify power limits, which appear very close in value. The FCC is generally more generous with limits, 1W power output at full hopping rate in this case. However, looking at exact definition of the power in both cases, we find some differences. The FCC specifies peak conductive power, which seems clear and straight forward, but no specific method is prescribed to measure it. The antenna gain is assumed to be less than 6 dBi; therefore, FCC-15.247 sec.(a) & (b) are applicable. But ETSI specifies EIRP which, in this case, is essentially a conducted measurement as below, rewriting Equation 1:
P (dBm) = A + G + 10 log (1/x) =< 20
Where P is the EIPR limit, A is the average output power (sec. 5.7.2.2), G is antenna gain, and x is the transmitter duty cycle.
| Reg. Body | Test Conditions | Standard & section (s) | FCC
| 2400 -2483.5 MHz Min 15 hop Ch, 125 mW pk. conducted. And for 75 hop Ch, 1W pk. conducted
| FCC 15.247 (b) -1 | ETSI
| 2400 -2483.5 MHz Min 15 hop Ch. 100 mW EIRP | ETSI EN 300 328 sec. |
Table 3a: Power limits, 2.4 GHz band devices, operating with FH spread spectrum modulation
Comments
Since the typical antenna size used (1 to 1.5 cm) in such devices is comparable with the wavelength λ =12.5-cm, at such frequencies though still close to λ/10, better antenna efficiency compared to other two devices is expected. Therefore, it may be assumed that the actual radiated power will not be too low. However, ETSI includes antenna gain G into the limits; thus, sufficient margin should be provided at the conducted power output point (P1) to account for the antenna gain.
For instance, say the duty cycle is 35%, the antenna gain is 2.5 dB, and other losses are 1.5 dB. This gives maximum allowed average output A as:
A =< 20 -2.5 – 3.97
or
A =< 13.5 dBm
Average power of up to 13.5 dBm can be higher than 20 dBm peak with such low duty cycles.
Example 3b: 2.4 GHz Digitally Modulated Spread Spectrum Systems (other than FH system)
The limit is specified as the maximum power spectral density (PSD) in both standards as seen in Table 3b. It is fully or partly a conducted measurement in both cases. The FCC specifies both conducted and radiated power, but ETSI specifies a method of measurement ([6], sec. 5.7.3, step 4), which takes into account the antenna gain and the transmission duty cycle in addition to the conducted power output D measured in zero span (which is essentially the peak power). This is different from FH case above, where conducted power A is average power. Moreover, in case of a directive or high gain antenna, the allowed PSD magnitude “D” must be reduce to satisfy limits. The duty cycle in case of non-FH systems is another parameter that requires further consideration.
The FCC however allows 1W maximum conducted power into the antenna, which is easier to measure and control.
| Reg. Body | Test Conditions | Standard & section (s) | FCC
| 2400 -2483.5 MHz ant gain < 6dBi, 1W average conducted. Ant Gain > 6 dBi, PSD, 8 dBm in 3-kHz BW | FCC 15.247 sec. b-3
FCC 15.247 sec. e | ETSI
| 2400 -2483.5 MHz. PSD 10 mW in 1 MHz BW EIRP | ETSI EN 300 328 sec. (4.3) |
Table 3b: Power limits 2.4 GHz devices working with non-FH digital spread spectrum
Comments
The PSD can be calculated as Ppsd = Pa / Δf, where Pa is the average power in the Δf frequency band. The FCC stresses narrow band power control while ETSI stresses wideband control, thus allowing higher narrow band excursions. The antenna size would be same as in above case around λ/10 at such frequencies, and similar system performance would be expected with respect to transmitted power.
Conclusions
The transmitted power limits and measurement methods for LPDs/SRDs with respect to North American and EU requirements has been studied, and some variation in the definitions of power measurement terminology, such as ERP, EIRP or e.i.r.p., used by the regulatory bodies has been noted. Equipment designers should take note of regulatory requirements of the target market regions, and strive for compliance by taking into account the power measurement methods being used in the respective regions. n
Inam Rahim is with Intelligent Mechatronic Systems, Inc., and can be reached at irahim@intellimec.com.
References
- Federal Communication Commission CFR 47 rules FCC part-15 sub part C.
- Industry Canada “Low power License Exempt Radio-communication Devices Cat. 1 Equipment”, RSS-210, Sept. 2005.
- ERM, “EMC Standard for Radio Equipment and Services Part 1: Common Technical Requirement”, ETSI EN 301 489-1
- ERM, “Short Range Devices (SRD); Radio Equipment to be used in 25 -1000 MHz range with power levels up to 500 mW”, ETSI EN 300 220-1
- ERM, “Cordless Audio Devices in the range 25 MHz to 2000 MHz”, ETSI EN 301 357-1
- ERM; Wideband Transmission Systems; Equipment Operating in 2.4 GHz band and using Wideband Modulation”, ETSI EN 300 328
- “Radio Disturbance and Immunity Measuring Apparatus – Conducted Disturbances”, CISPR 16-1-2
- “Radiated Power and Field Strength from UHF ISM Transmitters”, Larry Burgess”, High Frequency Electronics, Nov. 2006. Summit Technical Media LLC.
- “Cellular Handset Antenna Efficiency Measurements Using the Wheeler Cap”, White paper, Skyworks Solutions Inc. April 2007.
- “A Local Government Official Guide to RF Safety: Rules, Procedures,& Practical Guidance”, Appendix A, line #17, June 2000
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