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EMBED Equation.3 (1)
where Pr is the received power in milli-watts, Pt is the transmitted power in milli-watts, GR is the gain of the receive antenna and circuitry, Gt is the gain of the transmit antenna and circuitry, c is the speed of light, R is the radius in meters, and f is the frequency in hertz.
Converting to power ratio units, or dBms, and solving for the transmit power,
EMBED Equation.3 (2)
with Gt and GR being estimated as unity. Plugging in values, the power transmitted can be estimated as
EMBED Equation.3 (3)
A typical value extracted from the utilized system on the chip (SOC) for a receive power, or sensitivity, is -97 dBm. With this number, a transmit power of -10.8 dBm would be required.
Using the 2.4GHz frequency band, however, results in the noise floor becoming significant. Many routers, cellular devices, and general electronic devices utilize the 2.4GHz band for their applications. As a result, estimates extracted from online data show that the noise floor could rest anywhere between -90dBm and -60dBm.
For the application of this project, the Gordan Field House and RITs campus in general has wireless internet throughout, with many other unknown applications, making the noise floor a possible significant opponent. To achieve a good signal to noise ratio (SNR), and thus an acceptable bit error rate (BER), the received signal power should be at minimum above the noise floor.
Using the possible maximum power output from the SOC of 4.5 dBm, the noise floor allowed for a SNR of 1 would be,
EMBED Equation.3 (4)
Any SNR above 1 would have to be achieved with a larger transmit power. Not knowing a good estimate for the noise floor of the areas of application, a power amplifier with a maximum output power of 20 dBm allows for a noise floor of,
EMBED Equation.3 (5)
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