MPX96
AND MPX2000 ANTENNA CONSIDERATIONS 

The MPX96 and MPX2000 must be used with the proper antenna in order not to violate FCC regulations concerning radiated field strength limits. The field strength must be limited to 250 microvolts per meter at a distance of 3 meters from the antenna. The field strength is regulated so as to limit range to a reasonable value. This rule would then imply a field of 25 microvolts per meter at 30 meters or approximately 100 feet from the transmitter, and 2.5 microvolts per meter at 1000 feet according to theory. In practice, using a typical pocket stereo with a sensitivity of 5 to 10 microvolts at the antenna terminals, this means about 50 to 100 feet useful range. Assuming for simplicity that the RF output is constant in all directions, if we consider an imaginary 10 foot radius sphere with the MPX96 at the center, the power density per square meter for a field strength of 250 uv/m will be equal to e^2/R, where R is 120*pi ohms or 377 ohms, the impedance of free space, which is the square root of u/e, (corresponding to the formula used in transmission line theory Z = sqr(L/C)) where u = 4 x pi x 10 (exp 7) henrys per meter and e = 8.85 x 10( exp 12) farads per meter. Therefore the power per square meter will be e^2/R or 625 x 10(exp10)/377 watts, or 1.655 X 10(exp10) watts per square meter. Since a sphere of 3 meters has a surface area of 4 x pi x R^2, this sphere has a surface area of 113 sq meters, the total allowable radiated power is 165.5 X 10(exp10) or 16.55 nanowatts maximum. But, any reasonable RF oscillator circuit operating at typical bias conditions used in RF transistors (5 to 12 volts Vcc, and 2 to 10 ma Icc) will generate RF power levels from typically 1 to 20 mw. This is 0.25 to 1 volt into 50 ohms. Therefore in a practical sense, most of this power is not radiated in a typical LP part 15 application. Of course, less power could be generated but practical considerations are another factor. 16.55 nanowatts is slightly less than 917 microvolts into 50 ohms. The RF output of the transmitter could be padded down or attenuated, but then the antenna would have to radiate all this power with no loss. A better and more practical approach is to use a short antenna that is not matched to the transmitter as a radiator and simply dissipate excess power into a resistor load that is non radiating. Power levels of 10 mw or so are easier to work with from a measurement standpoint with simple equipment such as hobby class frequency counters and homemade RF voltmeter circuits such as detector probes, and are representative of the power levels found in receiver circuits, oscillators, and low level transmitter stages. This allows for proper setup of the transmitter circuits without specialized equipment. Also, since antenna environment may be unpredictable and subject to tremendous variation, matching the antenna using low level signals and critical tuning adjustments is not practical for the hobbyist. Lower levels are best derived via attenuators and other lossy devices. A "plug and play" approach is best for the antenna system. The approach taken in the MPX96 and MPX2000 uses a short whip with a low radiation resistance of typically 1 to 2 ohms and a capacitive reactance of several hundred to a thousand ohms or more. A 56 ohm resistor terminates the transmitter and about 0.7 volts is impressed across the antenna. This antenna will have an RF current of around 1 milliampere flowing in it due to the high capacitive reactance. If the radiation resistance is 1 ohm, one microwatt of RF energy (I x R) will be radiated. While this is 53 times the amount required for 16.55 nanowatts and would provide a field strength over eight times the legal limit, this is an ideal case assuming free space and a perfect ground plane. In practice, we have no real ground plane except the 4 X 4 inch PC board. Environmental conditions in the house such as walls wiring, plumbing, and metallic structures cause attenuation. Losses are therefore much higher than theory would indicate. It is impossible to predict the actual conditions in practice so measurements were made using a pocket stereo receiver and a signal generator feeding the antenna system. Range was just about 100 feet with a 0.7 volt level into the antenna, so the results appear in the ballpark so to fit the 250 uv/meter requirement. As a practical matter, in real life it would be impossible to guarantee the 250 uv/m limit at any given point other than in free space, but the intent of the law is to limit range and interference and if the signal is too low past 100 feet to be useable, this would be reasonable evidence that no one is being interfered with and this should keep the FCC happy. It is up to the user to see that range is limited to no more than that necessary and 100 feet should cover almost any home adequately. The 12 inch antenna is the largest that should be used and in applications where few signal obstructions are encountered, a 4 to 6 inch whip will be found adequate in many cases. Note that any excessive radiation is a violation and may get you in trouble with the FCC. These transmitters put out no more RF power than equipment such as RF signal generators used for service work, wireless mikes, and LO circuits in TV and radio receivers. It is not how much power is generated but how much of this is actually radiated that counts. 

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