Attenuation:
dB = 10 log10(Pr/Ps)
loss of power during transmission
we transmit 10W and recieve 9W, what's the attenuation in decibels?
10 * log_10 (9W/10W) <- log base 10.
or
10 * log (9/10) / log(10) <- any log base (often e).
= -0.45757
brush up on logs: https://www.youtube.com/watch?v=sULa9Lc4pck
Nyquist Bandwidth
C = 2B log2 M
Bandwidth is 8kHz, number of votage levels is 4, what's the max capacity?
C = 2 * 8000 * log(4)/log(2) <- any log
C = 32000.00000
or
C = 32kbps
if capacitry is 32kbps, and we're using 4 votage levels, what's the bandwidth?
.... 8kHz
Shannon Capacity
--signal to noise ratio in decibels
SNRdB = 10 log10 signal power / noise power
C = B log2 (1 + SNR)
we're transmitting at 31W, noise on the wire estimated to be 1W,
bandwidth is 8kHz, what's the max error free capacity?
SNR = 31/1 = 31
C = 8000 * log(1 + 31) / log(2)
C = 40000 = 40kbps
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we're transmitting at 40kbps, 2% of the bits arrive flipped.
what's the error free capacity of this channel?
assume we have a wire that indicates when an error occurs [e.g. 40kbps, a 1 for an error and 0 for no-error]. what's the entropy of this signal?
H = -(0.02*log(0.02)/log(2) + (1 - 0.02)*log(1 - 0.02)/log(2) )
H = 0.14144
every symbol (1 or 0) of this "error channel" is actually 0.14144 bits of information.
we're transmitting 40kbps of these errors: 40000 * 0.14144.
5657.6bps of errors...
total capacity is 40kbps, errors are 5.657kbps, leaving:
40000 - 5657 = 34343 bits/second for error-free-capacity.
~ 34.3kbps
max length of LAN: http://theparticle.com/cs/bc/net/ether.pdf
MaxLength = (2 × 108) × (51.2 × 10−6/2) = 5120m