# Conversions for RF exposure measurements

The new regulations concerning the Maximum Permissible Exposure (MPE) to radio frequency electromagnetic radiation (FCC OET Bul. 65, updated August 1997) have brought to the surface many terms, relating to RF measurements, that were seldom heard by technicians in the past.

It may help to understand how these measurement units, such as W/m2 or mW/cm2, relate to each other and to other RF measurement units such as mV/m, V/m, mW at receiver input and others. This discussion is limited to far-field, free-space, plane-wave propagation.

Power density The unit of measurement for power density is used to quantify the intensity of RF power per unit of surface area. Generally, it is stated in watts per square meter (W/m2) or milliwatts per square centimeter (mW/cm2). Conversions between W/m2 and mW/cm2 are made by using Formulas 1 and 2 in the sidebar below. (See original issue).

A formula that is useful in determining RF power density at a given distance from a transmitter is given as Formula 3. This formula is for free-space propagation. In Formula 3, Pd is power density in W/m2, G is the numeric ratio of the antenna gain (not dB), Pt is the transmitter power in watts,and d is the distance between the transmitter and receiver antennas in meters.

In the example shown in Figure 1 at the right, the transmitter has a power output of 1,000W, and the antenna is a halfwave (lambda/2) dipole. The distance from the transmitter antenna to the receiver antenna is 1 mile (1,610m). Both antennas are lambda/2 dipoles. What is the power density at the receiving antenna? A lambda/2 dipole has a gain of 2.15dB over the isotropic, and so the numeric gain factor is 10(dB/10), or 1.64. Using the formula for power density, we find that the power density is 5.0348*10to the -5 W/m2.

Converting to field intensity The intrinsic impedance of free space is 120pie, or 377ohm. We can find the field intensity in V/m by substituting our calculated power density (V/m2) and free-space impedance into Formula 8 as shown in the sidebar:

V/m=square root of Pd*377 =square root of 5.0348*10to the -5*377 =square root of 0.0189811196 =0.137772

Thus, the power density in W/m2 is converted to field intensity in V/m. This value can be converted to mV/m by multiplying by 106 to yield 137,772mV/m, or 137.772mV/m.

Converting to mV at the receiver unit To this point, we have not incorporated frequency into the calculations. However, if we wish to determine the signal level at the input to the receiver, we will have to take frequency into account. The formula shown below can be used to calculate the antenna factor (K) for use in a following formula.

K=20logF-GR-32 (for 50V systems)

where K 5 antenna factor in dB/m F 5 frequency in MHz GR 5 antenna gain (dBd)

Formula 4 in the sidebar (see original issue) can be used to calculate the signal level at the receiver input (in mV) from the field intensity at the antenna (in V/m)

where K 5 antenna factor in dB/m L 5 line loss in dB

Let’s assume that the operating frequency is 460MHz and that the line loss is 0dB. Using the formula for antenna factor (K), we find that K 5 121.3dB/m. The field intensity, as found previously, was 137,772mV/m. The antenna gain (dBd) 5 0 because the antenna is a l/2 dipole. Plugging these values into the formula yields a signal level of 11,862mV at the receiver input. This can be converted to dBm at the receiver input by using Formula 5 in the sidebar on page 8 (see original issue).

Plugging in 11,862 yields a dBm level of 225.5dBm.

Free space path loss The path loss between a transmitter output and a receiver input with lambda/2 dipole antennas on each end, and propagation in free space, can be determined from the following formula:

L=32.6+20logF+20logD

where L 5 path loss in dB F 5 frequency in MHz D 5 distance between antennas in miles

The frequency is 460MHz, and the distance is 1 mile. Plugging these values into the formula yields a path loss of 85.8dB. Remember, the transmitter output was 1,000W, or 60dBm. If we subtract the path loss from 60dBm, we get

60-85.8=-25.8dBm

at the receiver input. This agrees closely with the figure obtained previously in our calculations.

Converting power density to mV Recapping the preceding steps, we have: * determined the power density that exists at the receiving antenna. * converted the power density to V/m. * converted V/m to mV/m. * converted mV/m to mV at the receiver input. * converted mV at the receiver input to dBm.

We then confirmed the dBm figure by using the formula for path loss and subtracting this path loss from the transmitter output in dBm.

This time we will convert the power density at the antenna in V/m2 directly to mV at the receiver input. Use Formula 6 as shown in the sidebar, where Pd is power density in V/m2, K is antenna factor in dB/m and L is line loss in dB.

Previously, we have determined that the power density (V/m2) is 5.0348 3 10-5 and the antenna factor (K) is 21.3dB/m. We have assumed a line loss of 0dB. Substituting antenna factor and power density into the formula, we get a level of 11,857mV at the receiver input. This is equal to 225.5dBm.

Convert transmitter output powerto receiver input power Formula 7 in the sidebar will yield the receiver input power in a more direct manner. We must know the transmitter power, the distance between antennas, the numeric gain factor of the antenna and the wavelength (lambda/2). In Formula 7, Pr is receiver power input in watts, Pt is transmitter power output in watts, G is the gain ratio of the antenna (not dB), lambda is the wavelength in meters, and R is the distance between the transmit and receive antennas. This is for free space propagation.

Using the previous example for comparison, where the transmitter power is 1,000W, the frequency is 460MHz (lamda=0.652 meters), and the distance between the receiver and transmitter antennas is 1 mile (1,610 meters). Substituting these values into the formula will produce a result of 2.79326*10to the -6, or 2.793mW. This is equal to 0.002793mW. Since dBm=10 log(P), where P is in milliwatts, we get

10log(0.002793)=-25.5dBm

You will note that this correlates with our previous calculations.

OET Bulletin 65 The FCC’s Office of Engineering & Technology (OET) has issued an updated Bulletin 65. This bulletin provides useful information concerning Maximum Permissible Exposure (MPE) limits. There are a few interesting points in the bulletin.

* 30MHz to 300MHz _ The human body is most sensitive to radio frequency (RF) radiation in this frequency range, and this is reflected by the lowest MPE listed in the bulletin. The MPE for this frequency range is a power density (Pd) of 1mW/cm2 or 10W/m2. Expressed as electric field strength (E), this is equivalent to 61.4V/m. Expressed as magnetic field strength (H), this is equivalent to 0.163A/m. You may notice that the E field strength divided by the H field strength is equal to 377ohm.

The power density is equal to 61.42/377=10W/m2, or 1mW/cm2. This MPE level represents a very high field intensity or power density level. A field intensity of 61.4V/m, or 61,400,000mV/m, would produce a level of 36.7dBm across a 50ohm load or receiver input at 160MHz using a standard lambda/2 dipole antenna with no line loss.

To further illustrate just how much power this represents, refer to Figure 2 above. Here, a 50ohm resistor is connected to a standard lambda/2 dipole through a lossless transmission line. Under far-field, plane-wave conditions, if the field intensity at the antenna is 61.4V/m (equal to the MPE at 160MHz), then the voltage across the 50ohm resistor will be 15.3V. This would produce a power of 15.3^2/50, or 4.7W. If the resistor connected to the test antenna were rated at 1/4W, then the resistor would soon burn up!

* Worst-case prediction _ On page 19 of OET Bulletin 65, the formula for a “worst-case or conservative prediction” is given. It is the same formula as Formula 3 in the sidebar. For example, if a transmitter is operated at 100W, at 160MHz, using a lambda/2 dipole, the power density at 10 meters from the antenna would be 0.13W/m2. This is almost 19dB below the MPE level. Using the same example, even 3m from the antenna would produce a worse-case power density prediction of 1.5W/m2. This is 8dB below the MPE.

Summary The new FCC MPE limits for RF electromagnetic fields should be taken seriously. I would not wish to be exposed to a radiation level that could quickly melt a 1/4W resistor! Enforcement of this new standard should make for a safer environment for the general public and especially for those of us who make our living in or near an RF environment.

This column hasn’t even scratched the surface. Bulletin 65 is a lengthy document with some good information that can help you better understand what the MPE is all about. Bulletin 65 is available over the Internet at www.fcc.gov/oet. Click on “RF Safety!” Three supplements, A, B, and C, are also available. dealing with the broadcast industry, amateur radio, and mobile and portable equipment.

It is important to raise the level of awareness of the potential risks for long-term exposure to RF electromagnetic radiation. It is not something that should cause us to panic. However, we must ensure that the RF radiation from our transmitters is under the MPE limits.

Although far-field measurements can be made with a spectrum analyzer and a calibrated antenna (one for which the antenna factor, K, is known); measurements in the near-field area can be extremely tricky and require special instrumentation and probes. If you question whether a site is within MPE limits, get a competent consulting firm to do on-site measurements to ensure compliance. Many firms will be offering this service because it is sure to become a hot topic with regulatory agencies such as the Occupational Safety and Health Administration (OSHA). Be sure to select a consultant with proper experience and expertise in this area. If in doubt_check it out!

Until next time_stay tuned!

Kinley, a certified electronics technician, is regional communications manager, South Carolina Forestry Commission, Spartanburg, SC. He is a member of the Radio Club of America. He is the author of Standard Radio Communications Manual: With Instrumentation and Testing Techniques, which is available for direct purchase. Write to 204 Tanglewylde Drive, Spartanburg, SC 29301. Kinley’s email address is [email protected].