Calculating link budget
From NASA, getting data back from that spacecraft zooming past Pluto, the link budget tells NASA the datarate (even with error correction) would be about 100 bits (12 bytes, or about 12 pixels) per second.
The transmitted power was about 10 watts.
The TX antenna gain at 9GHz? with 2 meter dish, thus 60 wavelengths across, has gain of approximately 60 * 60.
The energy, tho &quot;focused on Earth&quot; has some Billions and Billiions of miles to spread out, in a Range * Range behavior.
The surface area of a hemisphere, with Billion Mile radius, is 0.5 * (4 * PI * Radius^2) = 6 * Bil * Bil ~~ 1e+19 square miles.
Scaled by 25,000,000 square feet per square mile, the surface area of that hemisphere is ~~~ 1e+26 square feet.
The Deep Space Network antennas (3 are 70 meters across, or 40,000 square feet area, or about 1e+5 square feet) intercept some of the energy.
The cooled MASER amplifiers at the focus of these parabolic dishes have systemic noise temperature of 20 degree Kelvin, tho some of the components operate colder than that.
Boltsmann says Vnoise = sqrt( 4 * K * Temperature * Bandwidth * Resistance), and noise power is proportional to K * Temperature * Bandwidth * Resistance.
Notice the noise power is proportional to Tempereature, thus the noise power is 10:1 lower than at room temperature.
You can combine these observations in numerous ways, to compute &quot;link margin&quot; or &quot;link budget&quot;, or to conclude a RADAR SYSTEM must have 10MegaWatt transmitter power and have 10 microsecond pulses, for a probability_of_detection of a plane at 50 miles of 0.99, in air defense. Determined by the size of the rotating segment_of_parabola antenna.
You can also design chirped (FM_swept) L_band systems where the possibility of post-processing of the received &quot;pulse&quot; permits reduction of TX power and reduces the ability of targets to detect the incoming energy.
Or you can compute the maximum datarate to be used in moving data back from Pluto, given you only want 1 bit error per 10 images.
Or you can compute the antenna size needed, for aliens on a nearby star system to detect humanity's most powerful and continuous transmissions ---- the 15,000 cycle per second horizontal sync pulses of our NTSC television broadcasts.
How important are these concepts? Decades about, NASA decided to add a 3 meter region around each of their 3 biggest dishes.
That extra area provides about 0.5 dB more gain. With Shannon_Limit maxed out, we get pixels back from Pluto.