Telecom formula sheet

Sine wave: y = A sin(2𝜋f t), t = time in seconds, f = frequency in Hertz (cycles/sec), A = amplitude

Square wave: y = sin(2𝜋f t) + 1/3 sin(2𝜋(3f)t) + 1/5 sin(2𝜋(5f)t) + 1/7 sin(2𝜋(7f)t) + ...

Decibels: 10 log10 Pout/Pin

decibels
 ratio      
10 dB
 10×
20 dB
 100×
3 dB
 2×
5 dB
 ~ 3×
6 dB
 4×
7 dB
 5×

Nyquist: C = 2B log2 M  (or C = 2B for binary)

Shannon: C = B log2 (1+SNR)

B = band-width, C = maximum data rate, M = # of signal levels, SNR = signal-to-noise ratio

A = log2(B) ⟷ 2A = B, eg 7 = log2(128) because 27 = 128

Thermal noise: N0 = kT, T in Kelvins, N0 in Watts/Hz, k = 1.38 x 10-23 J/K

NRZ: 0=high, 1=low
NRZI: 0 = no transition, 1 = transition
Manchester: NRZI alternating with transitions due to the clock signal
Bipolar-AMI: 0 = no signal, 1 = alternating positive and negative for successive 1-bits
B8ZS: same as bipolar, but 0000 0000 is replaced by 000+−0−+ or 000−+0+−, depending on whether previous 1-bit was + or −.

T-Carrier, other TDM

DS0: 64kbps voice line
DS1: 24 DS0’s plus 1 bit
DS2: 4 DS1’s plus bit-stuffing (pulse-stuffing) room
DS3: 7 DS2’s / 28 DS1’s, plus bit/pulse stuffing room
STS-1: 51.84 Mbps
STS-N: N × STS-1, exactly