
Keywords: Shortrange radio, ISM Band Radio, 260470MHz ISM Band, UHF Transmitter, FCC Part 15.231, RKE, TPM, Wireless Home Security, Wireless Remote Control, Wireless Radio Transmission, RF Field Strength, 315 MHz ISM Band, 433 MHz ISM Band, 900 MHz ISM Band
Related Parts


Radiated Power and Field Strength from UHF ISM Transmitters

Abstract: Shortrange radios that operate at the Industrial, Scientific, and Medical (ISM) frequencies from 260MHz to 470MHz are widely used for remote keyless entry (RKE), home security, and remote control. A critical performance measurement for the radio transmitter is the power that it radiates from the antenna. This power must be high enough to make the link between the transmitter and receiver reliable, yet it must not be so high that it exceeds the radiation limits established in Part 15.231 of the FCC Regulations. This application note discusses the relationship between FCC fieldstrength requirements in the 260MHz to 470MHz frequency range and the radiated power and typical quantities measured on a test receiver. Tables will illustrate the values that a designer can expect to obtain in field tests.
Introduction
Very often the antennas in the transmitters for applications in the 260MHz to 470MHz Industrial, Scientific, and Medical (ISM) frequency band are so small that they radiate only a small fraction of the power available from the transmitter's power amplifier. This makes measuring the radiated power a very important task. This measurement is complicated because the radiation limits in Part 15.231 of the FCC Regulations are expressed as field strength (volts/meter) at a distance of 3 meters from the transmitter. In addition, the receive antenna, its placement, and the units used on the measuring receiver all affect the measurement of radiated power.
This application note will explain both the relationship between radiated power to field strength and the units used in the measurement receiver. Tables will illustrate the relationship between FCC fieldstrength requirements in the 260MHz to 470MHz frequency range and the radiated power. The typical quantities measured on a test receiver will be shown. By understanding this relationship and knowing some conversion factors, the user can determine whether measurements made at a test receiver indicate that the transmitter is close to its radiated power goal.
The Relationship Between Field Strength and Radiated Power
Power transmitted from an antenna spreads out in a sphere. If the antenna is directional, the variation of its power with direction is given by its gain, G(Θ, Φ). At any point on the surface of a sphere with radius, R, the power
density (PD) in watts/square meter is given by Equation 1.
This expression is simply the power radiated by the transmitter, divided by the surface area of a sphere with radius, R. The gain symbol, G
_{T}, has no angular variation. This is because most of the antennas used in the 260MHz to 470MHz ISM frequency band are very small compared to the operating wavelength and, therefore, have patterns that do not vary sharply with direction. The gain is often quite small because the antennas are very inefficient radiators. For this reason, P
_{T} and G
_{T} are kept together and taken to mean the Effective Isotropic Radiated Power (EIRP) of the transmitter and antenna combination. Consequently, EIRP is the power that would be radiated from an ideal omnidirectional, i.e., isotropic, antenna.
The power density at a distance, R, from the transmitter can also be expressed as the square of the field strength, E, of the radiated signal at R, divided by the impedance of free space, designated in Equation 2 as
η_{0}. The value of η
_{0} is 120πΩ, or about 377Ω.
Combining these two equations results in a simple conversion of the EIRP, which is P
_{T}G
_{T} to field strength, E, in volts/meter.
Alternately, Equation 3 can be rearranged to express EIRP in terms of the field strength.
At the 3meter distance of the FCC requirements, the relationship is even simpler.
As an example, the FCC limit on average field strength at 315MHz is about 6mV/meter. Using Equation 5, the limit on average radiated power is 10.8µW, or 19.7dBm.
The conversion from field strength to EIRP is further complicated because some documents express field strength in a logarithmic, or dB, format. In the example above, the field strength of 6mV/meter could also be expressed as 15.6dBmV/meter or 75.6dBµV/meter.
Finally, the FCC radiation limits change with frequency over the 260MHz to 470MHz band. This change means that, at every frequency, one needs to calculate the field strength per the FCC requirement formula, then convert from one measurement unit to the other. In Part 15.231 the FCC sets the fieldstrength limit at
3750µV/meter at 260MHz, and allows a linear increase to 12500µV/meter at 470MHz.
Table 1 combines Equation 1 through Equation 5 with the FCC formula for average fieldstrength limits. The data in Table 1 thus provide a quick conversion at 5MHz frequency intervals for the multiple ways of characterizing the radiation strength. The gain of the transmitting antenna is assumed to be 0dB.
Table 1. EIRP vs. FCC Part 15.231 Average FieldStrength Limits 
Frequency MHz 
Field Strength µV/meter 
Field Strength dBµV/meter 
EIRP mW 
EIRP dBm 
260 
3750 
71.5 
0.004 
23.7 
265 
3958 
72.0 
0.005 
23.3 
270 
4167 
72.4 
0.005 
22.8 
275 
4375 
72.8 
0.006 
22.4 
280 
4583 
73.2 
0.006 
22.0 
285 
4792 
73.6 
0.007 
21.6 
290 
5000 
74.0 
0.007 
21.1 
295 
5208 
74.3 
0.008 
20.9 
300 
5417 
74.7 
0.009 
20.6 
305 
5625 
75.0 
0.009 
20.2 
310 
5833 
75.3 
0.010 
19.9 
315 
6042 
75.6 
0.011 
19.6 
320 
6250 
75.9 
0.012 
19.3 
325 
6458 
76.2 
0.013 
19.0 
330 
6667 
76.5 
0.013 
18.8 
335 
6875 
76.7 
0.014 
18.5 
340 
7083 
77.0 
0.015 
18.2 
345 
7292 
77.3 
0.016 
18.0 
350 
7500 
77.5 
0.017 
17.7 
355 
7708 
77.7 
0.018 
17.5 
360 
7917 
78.0 
0.019 
17.3 
365 
8125 
78.2 
0.020 
17.0 
370 
8333 
78.4 
0.021 
16.8 
375 
8542 
78.6 
0.022 
16.6 
380 
8750 
78.8 
0.023 
16.4 
385 
8958 
79.0 
0.024 
16.2 
390 
9167 
79.2 
0.025 
16.0 
395 
9375 
79.4 
0.026 
15.8 
400 
9583 
79.6 
0.028 
15.6 
405 
9792 
79.8 
0.029 
15.4 
410 
10000 
80.0 
0.030 
15.2 
415 
10208 
80.2 
0.031 
15.0 
420 
10417 
80.4 
0.033 
14.9 
425 
10625 
80.5 
0.034 
14.7 
430 
10833 
80.7 
0.035 
14.5 
435 
11042 
80.9 
0.037 
14.4 
440 
11250 
81.0 
0.038 
14.2 
445 
11458 
81.2 
0.039 
14.0 
450 
11667 
81.3 
0.041 
13.9 
455 
11875 
81.5 
0.042 
13.7 
460 
12083 
81.6 
0.044 
13.6 
465 
12292 
81.8 
0.045 
13.4 
470 
12500 
81.9 
0.047 
13.3 
The Relationship Between Measured Receiver Power and Radiated Power
If one restricts the units of measurement to received power and radiated power, then the relationship between received to transmitted power is well known. It is the basis for spaceloss calculations in communication systems.
Starting with the power density at a distance, R (Equation 1), the power received by an antenna at this distance is simply the power density multiplied by the
effective area of the receive antenna. The effective area of an antenna is defined by Equation 6.
The quantity, λ, is the wavelength of the transmission. Multiplying the density in Equation 1 by the effective area of the receive antenna leads to the familiar freespaceloss equation.
Equation 7 says that if the receive antenna gain is near unity (which is the case for a small antenna like a quarterwave stub), the power loss at 3 meters for a transmission at about 300MHz (corresponding to a 1meter wavelength) is approximately (1/12
π)², or 31.5dB for a receiving antenna with unity gain. Although this value will probably vary from 25dB to 35dB, depending on the gain of the receiving antenna, this is a good first check of the transmitter, antennas, and test setup. If, for example, one expects an RKE transmitter circuit board to radiate 20dBm of power, then one should see somewhat less than 50dBm of power on a spectrum analyzer connected to a receive antenna with approximately unity gain, placed 3 meters away.
The Relationship Between Measured Receiver Voltage and Radiated Power
In many measurements intended to demonstrate compliance with FCC regulations, the receiver measures the RF voltage at the measurement antenna rather than the power. This happens because the FCC wants fieldstrength measurements, not EIRP. Because the units of field strength are volts/meter (or mV/meter or µV/meter), converting a voltage measurement to volts/meter through a calibration constant is intuitively easier.
Receive antennas manufactured primarily for measuring electromagnetic compliance have a calibration constant in units of 1/(meters). (We will discuss the meaning and derivation of this calibration constant below.) It is, thus, important that we show how the voltage measurement relates to the EIRP. When the receiver picks up the power from the antenna, the power becomes a voltage across a load resistor, Z
_{0}, which is usually 50Ω. Relating the receive voltage to the receive power by Equation 8,
and substituting this into Equation 7, yields an expression (Equation 9) for the received voltage in terms of the EIRP.
The Relationship Between Measured Receiver Voltage and Field Strength
Relating the received power, and ultimately the received voltage, to field strength can be done by using the approach shown in Equations 6 and 7. The power density is multiplied by the effective area of the receive antenna. The only difference in Equation 10 is that the power density is now expressed in terms of the field strength, E, as in Equation 2.
Remembering that P
_{R} is related to the received voltage by Equation 8 leads to Equation 11, which links V
_{R} to E.
Taking the square root of both sides shows that the received voltage is just a coefficient times the field strength. Given that most receivers have Z
_{0} = 50Ω and that η0 = 120πΩ, the equation reduces to the simple result in Equation 12.
The coefficient linking the field strength, E, to the receive voltage, V
_{R}, is usually given as the ratio of E to V
_{R}. This is because V
_{R} is the measured quantity and E is the quantity that is compared to the FCC requirements. Manufacturers of antennas used for fieldstrength measurements list this coefficient, called the Antenna Factor (AF), in their data sheets as a function of frequency.
In terms of the variables in Equation 12, the antenna factor is given below.
The units in Equation 13 are either in (meters)
^{1} or in a dB ratio given by 20 log
_{10} [volts/meter)/volts]. The antenna gain is expressed in terms of the power gain, so a 6dB antenna gain is a factor of 4, and a 10dB antenna gain is a factor of 10, etc. If the wavelength is 1 meter (300MHz frequency) and the antenna gain is 6dB, then the AF in Equation 13 is 4.87 (meters)
^{1}, which would be 13.6dB (meters)
^{1}.
One of the most commonly used receiving antennas for fieldstrength measurements is a LogPeriodic Antenna (LPA) with a gain that is independent of frequency over its intended measurement range. This means that its AF increases linearly with frequency. A typical LPA, the TDK RF Solutions Model PLP3003, has an AF of 14.2dB at 300MHz, or 5.1 meters
^{1}. Its AF vs. frequency is shown in
Figure 1. Following Equation 13, the gain of this antenna is 5.6dB at 300MHz.
Figure 1. Antenna Factor (AF) vs. frequency of a typical measurement antenna.
If we apply the information from Equation 13 and Figure 1 to the FCC average fieldstrength limit of
_{5417µV/meter} at 300MHz, we would expect to see 1056µV measured at a 50Ω input receiver. Expressing this in dB, the 74.7dBµV/m field strength in the FCC limits would appear as 60.5dBµV in the receiver, which corresponds to
46.5dBm of power across a 50Ω load. This result is consistent with the earlier powerloss estimate. (See above where we determine that a 20dBm EIRP signal at the source would be received at about 50dBm in a receiver.)
Voltage and Power at the Measurement Receiver
Table 2 shows the voltage that would be measured with an antenna and a 50Ω receiver in compliance with the FCC fieldstrength limits. The AF used in Table 2 comes from the specifications for the Log Periodic antenna in Figure 1.
Table 3 shows the power that would be measured with the same equipment. Table 3 uses the effective radiated power from a transmitter and antenna that corresponds to the fieldstrength limits, then applies the space loss and receive antenna gain to determine the power across a 50Ω load. The results in both tables are mutually consistent. Consequently, these tables give designers and users of shortrange UHF transmitters a set of reference numbers to help determine whether they are meeting the FCC requirements and are radiating the needed power.
Practical Measurement Considerations
The tables in this application note give approximate values for measured power and voltage as a function of specifications such as field strength and EIRP. These values will vary when different measurement antennas are used. There are also several correction factors that one needs to make in the course of a measurement. Cable losses and mismatch losses must be taken into account, and they are frequency dependent. The measurement environment, especially the reflection from the ground or floor, can make a significant difference (as much as 6dB) in the measured receiver voltage. The ground reflection needs to be calibrated by using another reference antenna, usually a dipole. The polarization of the radiating antenna needs to matched as best as possible with the polarization of the measurement antenna. The directional pattern of the radiating device needs to be considered, even if the radiating antenna is electrically small (under 1/6 of a wavelength), because the package, test mount, and coaxial cable ground shields can introduce directional variation.
The fieldstrength numbers in these tables refer to the limits on the
average power permitted by the FCC. Radiating a peak power level up to 20dB more than the average power limits is permitted, provided that the duration of the transmissions and the duty cycle obey some restrictions. Consequently, one needs to consider power levels that are significantly higher than those found in these tables. Because the measured values follow the fieldstrength limits dB for dB, adjusting the expected measurement level to ensure proper device function is not difficult. If, for instance, a product has a dutycycle profile that permits a peak field strength at 315MHz that is 10dB higher than the FCC average field strength, then the peak field strength can now be 19.1µV/meter, or 85.6dBµV/meter. A glance at Table 2 and Table 3 indicates that the expected measured voltage and power should be in the 71dBµV and 36dBm range.
Once all these effects are measured and accommodated, then one can use the tables presented here to determine whether the transmitter is performing as designed.
Table 2. Measured Receiver Voltage as a Function of FCC FieldStrength Limits 
Frequency MHz 
Field Strength µV/meter 
Field Strength dBµV/meter 
Meas. Antenna Gain 
Meas. Antenna Gain, dB 
Meas. Antenna Factor, 1/meter 
Meas. Antenna Factor, dB(1/m) 
Meas. Recv. Voltage, µV 
Meas. Recv. Voltage, dBµV 
260 
3750 
71.5 
3.6 
5.6 
4.4 
13.0 
844 
58.5 
265 
3958 
72.0 
3.6 
5.6 
4.5 
13.1 
874 
58.8 
270 
4167 
72.4 
3.6 
5.6 
4.6 
13.3 
903 
59.1 
275 
4375 
72.8 
3.6 
5.6 
4.7 
13.4 
931 
59.4 
280 
4583 
73.2 
3.6 
5.6 
4.8 
13.6 
958 
59.6 
285 
4792 
73.6 
3.6 
5.6 
4.9 
13.8 
984 
5939 
290 
5000 
74.0 
3.6 
5.6 
5.0 
13.9 
1009 
60.1 
295 
5208 
74.3 
3.6 
5.6 
5.0 
14.1 
1033 
60.3 
300 
5417 
74.7 
3.6 
5.6 
5.1 
14.2 
1056 
60.5 
305 
5625 
75.0 
3.6 
5.6 
5.2 
14.3 
1079 
60.7 
310 
5833 
75.3 
3.6 
5.6 
5.3 
14.5 
1101 
60.8 
315 
6042 
75.6 
3.6 
5.6 
5.4 
14.6 
1122 
61.0 
320 
6250 
75.9 
3.6 
5.6 
5.5 
14.8 
1143 
61.2 
325 
6458 
76.2 
3.6 
5.6 
5.6 
14.9 
1163 
61.3 
330 
6667 
76.5 
3.6 
5.6 
5.6 
15.0 
1182 
61.5 
335 
6875 
7637 
3.6 
5.6 
5.7 
15.2 
1201 
61.6 
340 
7083 
77.0 
3.6 
5.6 
5.8 
15.3 
1219 
61.7 
345 
7292 
77.3 
3.6 
5.6 
5.9 
15.4 
1236 
61.8 
350 
7500 
77.5 
3.6 
5.6 
6.0 
15.5 
1254 
62.0 
355 
7708 
77.7 
3.6 
5.6 
6.1 
15.7 
1270 
62.1 
360 
7917 
78.0 
3.6 
5.6 
6.2 
15.8 
1286 
62.2 
365 
8125 
78.2 
3.6 
5.6 
6.2 
15.9 
1302 
62.3 
370 
8333 
78.4 
3.6 
5.6 
6.3 
16.0 
1318 
62.4 
375 
8542 
78.6 
3.6 
5.6 
6.4 
16.1 
1333 
62.5 
380 
8750 
78.8 
3.6 
5.6 
6.5 
16.3 
1347 
62.6 
385 
8958 
79.0 
3.6 
5.6 
6.6 
16.4 
1361 
62.7 
390 
9167 
79.2 
3.6 
5.6 
6.7 
16.5 
1378 
62.8 
395 
9375 
79.4 
3.6 
5.6 
6.8 
16.6 
1388 
62.9 
400 
9583 
79.6 
3.6 
5.6 
6.8 
16.7 
1402 
62.9 
405 
9792 
79.8 
3.6 
5.6 
6.9 
16.8 
1414 
63.0 
410 
10000 
80.0 
3.6 
5.6 
7.0 
16.9 
1427 
63.1 
415 
10208 
80.2 
3.6 
5.6 
7.1 
17.0 
1439 
63.2 
420 
10417 
80.4 
3.6 
5.6 
7.2 
17.1 
1451 
63.2 
425 
10625 
80.5 
3.6 
5.6 
7.3 
17.2 
1463 
63.3 
430 
10833 
80.7 
3.6 
5.6 
7.4 
17.3 
1474 
63.4 
435 
11042 
80.9 
3.6 
5.6 
7.4 
17.4 
1485 
63.4 
440 
11250 
81.0 
3.6 
5.6 
7.5 
17.5 
1496 
63.5 
445 
11458 
81.2 
3.6 
5.6 
7.6 
17.6 
1506 
63.6 
450 
11667 
81.3 
3.6 
5.6 
7.7 
17.7 
1517 
63.6 
455 
11875 
81.5 
3.6 
5.6 
7.8 
17.8 
1527 
63.7 
460 
12083 
81.6 
3.6 
5.6 
7.9 
17.9 
1537 
63.7 
465 
12292 
81.8 
3.6 
5.6 
7.9 
18.0 
1546 
63.8 
470 
12500 
81.9 
3.6 
5.6 
8.0 
18.1 
1556 
63.8 
Table 3. Measured Receiver Power as a Function of EIRP 
Frequency MHz 
Field Strength µV/meter 
EIRP mW 
EIRP dBm 
Meas. Antenna Gain 
Meas. Antenna Gain, dB 
Meas. Recv. Power, µW 
Meas. Recv. Power, dBm 
260 
3750 
0.004 
23.7 
3.6 
5.6 
0.014 
48.5 
265 
3958 
0.005 
23.3 
3.6 
5.6 
0.015 
48.2 
270 
4167 
0.005 
22.8 
3.6 
5.6 
0.016 
47.9 
275 
4375 
0.006 
22.4 
3.6 
5.6 
0.017 
47.6 
280 
4583 
0.006 
22.0 
3.6 
5.6 
0.018 
47.4 
285 
4792 
0.007 
21.6 
3.6 
5.6 
0.019 
47.1 
290 
5000 
0.007 
21.2 
3.6 
5.6 
0.020 
46.9 
295 
5208 
0.008 
20.9 
3.6 
5.6 
0.021 
46.7 
300 
5417 
0.009 
20.6 
3.6 
5.6 
0.022 
46.5 
305 
5625 
0.009 
20.2 
3.6 
5.6 
0.023 
46.3 
310 
5833 
0.010 
19.9 
3.6 
5.6 
0.025 
46.2 
315 
6042 
0.011 
19.6 
3.6 
5.6 
0.025 
46.0 
320 
6250 
0.012 
19.3 
3.6 
5.6 
0.026 
45.8 
325 
6458 
0.013 
19.0 
3.6 
5.6 
0.027 
45.7 
330 
6667 
0.013 
18.8 
3.6 
5.6 
0.028 
45.5 
335 
6875 
0.014 
18.5 
3.6 
5.6 
0.029 
45.4 
340 
7083 
0.015 
18.2 
3.6 
5.6 
0.030 
45.3 
345 
7292 
0.016 
18.0 
3.6 
5.6 
0.031 
45.1 
350 
7500 
0.017 
17.7 
3.6 
5.6 
0.031 
45.0 
355 
7708 
0.018 
17.5 
3.6 
5.6 
0.032 
44.9 
360 
7917 
0.019 
17.3 
3.6 
5.6 
0.033 
44.8 
365 
8125 
0.020 
17.0 
3.6 
5.6 
0.034 
44.7 
370 
8333 
0.021 
16.8 
3.6 
5.6 
0.035 
44.6 
375 
8542 
0.022 
16.6 
3.6 
5.6 
0.035 
44.5 
380 
8750 
0.023 
16.4 
3.6 
5.6 
0.036 
44.4 
385 
8958 
0.024 
16.2 
3.6 
5.6 
0.037 
44.3 
390 
9167 
0.025 
16.0 
3.6 
5.6 
0.038 
44.2 
395 
9375 
0.026 
15.8 
3.6 
5.6 
0.039 
44.1 
400 
9583 
0.028 
15.6 
3.6 
5.6 
0.039 
44.1 
405 
9792 
0.029 
15.4 
3.6 
5.6 
0.040 
44.0 
410 
10000 
0.030 
15.2 
3.6 
5.6 
0.041 
43.9 
415 
10208 
0.031 
15.0 
3.6 
5.6 
0.041 
43.8 
420 
10417 
0.033 
14.9 
3.6 
5.6 
0.042 
43.8 
425 
10625 
0.034 
14.7 
3.6 
5.6 
0.043 
43.7 
430 
10833 
0.035 
14.5 
3.6 
5.6 
0.043 
43.6 
435 
11042 
0.037 
14.4 
3.6 
5.6 
0.044 
43.6 
440 
11250 
0.038 
14.2 
3.6 
5.6 
0.045 
43.5 
445 
11458 
0.039 
14.0 
3.6 
5.6 
0.045 
43.4 
450 
11667 
0.041 
13.9 
3.6 
5.6 
0.046 
43.4 
455 
11875 
0.042 
13.7 
3.6 
5.6 
0.047 
43.3 
460 
12083 
0.044 
13.6 
3.6 
5.6 
0.047 
43.3 
465 
12292 
0.045 
13.4 
3.6 
5.6 
0.048 
43.2 
470 
12500 
0.047 
13.3 
3.6 
5.6 
0.048 
43.2 
The article was published in the November 2006 issue of
High Frequency Magazine.
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APP 3815: Mar 01, 2007
APPLICATION NOTE 3815,
AN3815,
AN 3815,
APP3815,
Appnote3815,
Appnote 3815
