- excludes excess noise - modulates on a higher frequency without interference - multiple transmitters can operate at the same time without frequency

Communication Theory Flashcards by Katie McManus

noise

unwanted signal pertubation that is always present

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internal noise

thermal, shot, flicker

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external noise

atmospheric, extra-terrestrial, man-made

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noise power from thermal noise

Pn = kT 𐤃f

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k variable value

1.38e-23

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𐤃f =

bandwidth

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RMS voltage

en = sqrt(4kT𐤃fR)

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noise power with a resistor

Pn = (en/2)^2/R

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converting to dB

10log(P1/P2)
20log(V1/V2)

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noiseless system NR = ? NF = ?

NR = 1 NF = 0

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NR =

(S/N)in / (S/N)out

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NF =

10log(NR)

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Noise ratio for cascaded system

NR = NR1 + NR2-1/P1 + … NRn-1/(P1P2…Pn)

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what stage dominates in a cascading system

first

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SNR max =

input signal / power of thermal noise

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effective noise =

noise performance

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effective noise =

Te = Pn/(PgkB)

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relationship between noise ratio and noise temperature

F = 1+ Te/To Te = To(F-1)

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all amplifiers introduce

some noise

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bandwidth =

range of frequencies

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bandpass filters

remove noise and channel interference

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modulation

impressing the signal onto a carrier wave so it can be transmitted at the carrier frequency

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when the carrier frequency is ____________ transmition signal is ____________

higher, lower

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passband filters

excludes excess noise
modulates on a higher frequency without interference
multiple transmitters can operate at the same time without frequency

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modulation equation

v(t) = Vp*sin(wt+phi)

amplitude

sin(wt)

frequency

phi

phase

modulation can be

analogue or digital

change in amplitude

change in carrier frequency

change in phase

FM and PM are also called

angle modulation

amplitude is related to the

modulating signal

carrier constant of AM signal

Ac*cos(2*pi*ft)

amplitude modulated carrier wave =

m(t)cos(2*pi*ft)

amplitude modulation pros/cons

pros: used for envelope detection -> simple and cheap cons: transmitter needs a lot of power -> expensive

amplitude modulation equation

AM = [Ac+m(t)]cos(2*pi*ft)

in AM, message signals can be recovered using

envelope detection

modulation does what to the spectrum

shifts it either right or left

upper sideband limit

USB = fc+fm

lower sideband limit

LSB = fc-fm

fc>= W

avoids overlap

fc=W

main carrier frequency

fc/W >1

avoid distortion

AM envelope condition

(Ac+m(t))>0

envelope detection condition as mp is peak amplitude

Ac>= mp

AM modulation index

u = mp/Ac

inequality for envelope detection based off modulation index

0<=u<=1

coherent detection condition

Ac1

prerec for undistorted envelope

u<=1

tone modulation index

u = Am/Ac

modulation index for multi-tones

u = u1+u2+...+un

efficiency power

n = useful/total n = Ps/(Dc+Ps) n = Pm/(Ac^2+Bn)

tone modulation power efficiency

n = u^2/(2+u^2) * 100%

am coherent

translates frequency of sidebands back to baseband

DSB-AM coherent detection oscillation

oscillating source needs to be oscillating at the same frequency as the carrier source

RC conditions

RC>1/fc RC<1/W

RC for an AM envelope =

RC = sqrt(1/Wfc) W = message signal bandwidth

clearly defined envelope conditions

wc>2piW wc= 2pif

DC components can be

blocked by high pass filters

ripples can be reduced by

low pass filters

Voice AM examples

emergency services, taxi, military, airport

generalised carrier signal

x(t) = Ac cos(wt+θ)

angular frequency

wi = dθ(t)/dt

phase angle

θ(t) = integral from -infinity to t (wi(a))da

varying the angle

encodes info of phase on carrier signal

phase deviation

𐤃θ = km(t)

peak phase

𐤃θ = |km(t)|

FM angular frequency

wi = wc +km(t)

frequency deviation

𐤃f = k/2pi * m(t)

power of AM modulated wave

power = Ac^2 /2

power of an am modulated wave is dependent on

amplitude

max frequency deviation in FM

𐤃w max = kf*mp 𐤃f = k/2pi * mp

bandwidth of an angle modulated signal is

finite

bessel functions

Jn(D) = (-1)^n*Jn(D)

as bandwidth increases in the FM spectrum

spread increases power of carrier frequency decreases

AM signals

low bandwidth low efficiency no info in the carrier transmission

FM signals

complex high efficiency wide bandwidth better noise performance

multiplexing

combines signals from different sources

sideband filters help

avoid overlap

FDM example

broadcast radio

FDM

signals seperated in frequency occuplied limited portion of channel occupy allocated frequency always band-limited to avoid overlap

TDM

seperated in time access to the entire channel fraction of total time is allocated used to multiplex digital signals

Xfm =

Ac*cos(2*pi(fct)) + Am/2*cos(2*pi(fc+fm)t)+Am/2*cos(2*pi(fc-fm)t)

Communication Theory Flashcards

(85 cards)