Elements of imperfect transmission
1) imperfect Logon :
C$r-with regard to the logon directed between a generator and a utilizzatore the following cases can be introduced:
Ideal source with connected constant R resistance to a utilizzatore with resistance Zu(f) ¹ R e ru(f) ¹ 0
It is had that it marks directed them is faithful and not risente of the idealità of the utilizzatore that instead is all represented from does not mark reflected them.
Connected not ideal source to an ideal utilizzatore
The transfer is imperfect sin from the origin
and characterized from the reflection coefficient on the 
generator
Source and utilizzatore both not ideal
It marks directed them he is not faithful and it is function of rg(f) and of ru(f) moreover rebelling is had also of marks reflected them.
2) unexpected Effect additive in escape :
where r(t) it is marks them that base is obtained in
escape from a real channel in band adapted to the 0 ends
when comes applied to it it marks them x(t) whilex(t) are the answer of a idealizzato channel
represented with quadripolo having a function of 
transfer. The unexpected effect is little meaningful
in how much can also contain a faithful addend.
3) Disturbance :
where 
is marks them faithful, in it tu it is chosen so that 
is maximum while gu it is determined so that 
, in practical
per² both the correlations are not notes while it is famous 
, the value of tu obtain then imposing are maximum 
, the
value comes then used in order to calculate 
Sotto such conditions obtains that the received
power is equal to the sum of the useful power and the disturbing
power. In a generalized manner the disturbance is sum of one
member dd employee from marks
them entering and of one member d from
independent it, has 
that is.
4) Representation equivalent of an imperfect channel :
The outline is constituted from quadripolo an ideal Qu to which it is applied it marks them x(t) and it supplies in escape marks them useful xu(t), such it marks them comes sended to a sommatore is directly that through quadripolo distorting a QD that supplies the member dD(t). To the sommatore the (t) of the independent disturbance comesalsoapplied the member d from marks them of income and in escape it is had marks received them r(t).
5) Transmission in a linear channel varying time :
Time varying when the impulsive answer of the same one
varies in the time in aleatory way and independent from it marks them
entering, for semplicità is had a linear channel supposes of having a
linear channel in which the single attenuation he is variable and with
an evolution much slow one, the correspondent transfer function can be
decomposed in two 
terms where Hc(f) can be thought equal to the
waited for function of transfer 0H(f) for f < fM
being fM the maximum contained
frequency in the stationary process entering x(t), antitransforming
H(f, t) the impulsive answer is obtained that convoluita with it
marks them x(t) supplies marks them of escape from the channel 
.
From considerations on the correlation one finds that it
marks them useful xu received
coincides with r(t) therefore marks them of escape is not affection
from disturbs but the channel is not stationary in particular is
obtained the relation between 
the powers
therefore pu² to be represented with an only having block
trasmettenza H0(f)gs(t) and characterized from an
attenuation 
dove 
is the attenuation attended in absence of variability of the
attenuation while 
is the additional attenuation
due exactly to the fact that the channel introduces variable
attenuation. If it marks them of income has opportune
characteristics can be gained from marks them of escape r(t) the
instantaneous value of the additional attenuation Tos(t), this operation is carried out
from a circuit AGC that goes to act on the amplification of a variable
amplifier so that it supplies in escape marks them ideal x0(t).
6) Transmission in an ideal channel invariant time :
A channel that is rappresentabile with quadripolo a having
LTI function of 
transfer but that it does not
satisfy the conditions for the ideal transfer in all the band of
frequencies interested from marks them of income, gives to place to
linear distortion invariant time which substantially is divided in the
two species:
Distortion for cut of band: Supponiamo that the channel is behaved as a rectangular
filter low-pass filter, its function of transfer will be of the 
type which a impulsive answer corresponds 
that introduces a time of climb of the not null
impulse of escape and moreover the answer is not null for t<0
therefore the filter is unattainable antimotive and therefore
physically, low-pass filter real instead introduces a impulsive answer
with the same time of climb but duration limited in (0, 2t0) therefore motive, its answer to a
generic one marks them x(t) from place to smussamento of the shape
of temporal wave in escape and elongazione in the time.
Linear distortion in band:
This kind of distortion from place to a
variation of the function of transfer of the H(f) channel regarding
the function of ideal transfer H0(f), such relative scostamento is 
, estrinsecando H(f) and antitrasformandola obtains the
impulsive answer h(t) that convoluita with x(t) it gives back marks
received them r(t) that evidences the presence, beyond to marks
attended them x0(t), of an
unexpected effect 
due exactly to not the
linearity of the channel, therefore a linear channel invariant time
can be represented with quadripolo ideal having a characteristic H0(f) whose it marks them
of escape x0(t) endures
the distortion of the quadripolo distorting with H characteristicand(f) which it produces in
escape marks them unexpected and(t) that 0 sum tox(t) giving itself place to r(t). It is
observed that in the case of small distortion of amplitude and phase
in band base that is if has 
and 
the relative scostamento of 
the
function of transfer can carry out in the an approximation of
the exponential by means of Mac Laurin 
obtaining
from which taking advantage of the linearity of the antitransformed
one of Fourier the two effects inattesi 
e are had directly 
The distortions introduced from the channel can
be eliminated by means of it use of a having equalizzatore function of
transfer 
for fm < |f| < fM, which
it can be inserted in whichever point of the system and must be
characterized from enough 
large a delay to
render antimotive the equalizzatore.
7) Transmission in presence not static linearity :
It marks them that she obtains in escape from a quadripolo
not linear is 
where 
is the answer to the small marks them that it is supplied from a
quadripolo ideal when the unexpected effect è 
that assumes more and more great proportions how much the more marks
them of income is such to go to interest the part not linear of the
characteristic of the device, that for it marks them in traslata band
makes that the information associated to the envelope comes
considerable distorted while the information associated to the
instantaneous phase substantially remains immutata.
Carrying out a decomposition in series of Mac Laurin of
the unexpected effect additive has 
deduces
that the number of terms to take in consideration is function of the
entering power in particular the how much the more entering power is
high, many more terms is necessary to consider, in kind if they
consider 5. The greater problem of the distortion not linear
statics is that they come produced of the frequencies that go to
interest the channels adjacent.
The methods in order to reduce the effects of the static linearity are not following:
to) back-off the power in income comes reduced so as to to interest the region linear of the characteristic, however it is had that also the escape power consequently is reduced that goes to discapito of the segnale/rumore relationship.
b) filtering becomes part to goes them of the quadripolo not to delineate a filter with optimal selettività which it eliminates the products generates the not linear device to you.
c) the binoculars come use you of the identical quadripoli everyone of which have in income a power that is inferior of 3dB regarding that it would have if it were alone, the gain total is equal to the gain of everyone of the two component quadripoli, but having carried out a back-off of 3dB it obtains that the unexpected effects of 2° the order are reduced of 3dB while those of 3° the order are reduced of 6dB and therefore via, if then a logon of Push-Pull type is carried out obtains the cancellation of the unexpected effects of equal order.
d) predistortion is put to goes
them of the quadripolo not to delineate a quadripolo with
complementary characteristic 
.
8) Effect of the thermal noise on a resistore to absolute temperature T closed on an adapted bipole:
The thermal noise from place to a having process spectral
density of constant power 
with K=1,38*10-23J/K.
9) Disturbi independent agents on a linear channel:
Draft of orthogonal processes regarding that profit, having itself physical causes of nature is intrinsic that extrinsic to care of others the quadripoli that concatenando constitute the considered channel. They are observable to the escape of the quadripolo therefore in a general schematizzazione only have a having sommatore as incomes the trasmissivo means and a generator of disturbs independent dT(t) while the escape is sended to the quadripolo receiving.
The disturbance total is dT(t) = dTo(t) nQ(t) where:
dTo(t) = nTo(t) nAe(t) d(t) dp(t) is disturbs inherent trasmissivo means, in particular:
nTothe (t) it is the intrinsic Gaussian noise of which had trasmissivo means to thermal, quantico noise and of scintillation
nAe(t) is extrinsic the Gaussian noise of which had trasmissivo means to disturbs atmospheric and crafts them
dI(t) is the which had disturbance to interferences with marks them pertaining to other trasmissivi channels
dp(t) is a impulsive disturbance which had to isolated causes
nQ(t) is instead the Gaussian noise receiving equivalent of the quadripolo.
10) Gaussian Noise system additive:
It disturbs impulsive demand a detailed study in function
of the tipologia of the trasmissivo channel while for the noise to
Gaussian nature a study to general character is possible, in
particular the Gaussian noise ns of the system turns out to be the sum of the Gaussian noise
of trasmissivo means nTo(t)
= nTo(t) nAe(t) having spectral density NTo(f) (…than in
the case trasmissivo means it is found in thermal equilibrium to the
temperature of 290K and is finished in income on an adapted resistore
distributes to the door of receiving escape a
spectral density of constant 
power ) and the noise equivalent which had to
quadripolo nthe Q(t) which
if connected in conditions of adaptation to both the doors and in
absence of mark them useful or of it disturbs to its income produces
in escape a spectral density of power Nint(f), however the not noisy Q can be thought
quadripolo receiving adding to its income one additiva source of
Gaussian noise with spectral density of power 
.
11) synthetic Largenesses that express the Gaussian noise in invariant linear quadripoli time:
Admitted that the adaptation conditions are satisfied the
generated Gaussian noise from trasmissivo means to its escape it can
be simulated finishing the door of income of quadripolo receiving the
Q on a resistore characterized from a 
temperature dictates to temperature equivalent of noise of
trasmissivo means. Analogous the noise produced from Q brought
back in income can be simulated connecting in income a having
resistore temperature 
. The spectral density
of N noiseu in receiving
escape from quadripolo the Q can be obtained multiplying the G(f) gain
for the spectral density of noise in income to the same 
where TS is the
temperature of noise of the system.
A largeness that has preceded the temperature of noise in
the description of subject systems to disturbs independent is the
figure of noise
given exactly from the relationship
between the effective spectral density of the noise in escape 
and the spectral density of power 
that
the all in the case system would be had in escape in absence of inner
noisinesses to quadripolo the LTI is to the temperature
TTo = T0 = 290K. Replacing 
is obtained
that become simpler it gives back to the
relation between the temperature of noise and the figure of 
noise, moreover is possible to obtain the
figure of present total noise simply integrating the density in the
definition of the figure of 
noise.
An ulterior characterization of quadripolo by means of
the band the equivalent of noise is moreover possible 
where Gor is the maximum gain of the quadripolo that
usually band is had to center whose importance resides in the fact
that the quadripolo considered can be replaced with a quadripolo
passes band with function of rectangular transfer 
.
12) Noise of quadripoli in cascade:
A chain of quadripoli you mail in cascade introduces to
the door of income of first a spectral density of noise that is the
sum of the spectral density that they are obtained bringing back in
income the spectral density that everyone of the constituent
quadripoli has to its income that is to the income of quadripolo the
equivalent, has 
being 
, it is characterized therefore from a temperature of 
noise and a figure of noise 
.
13) Techniques of reduction of the effects of disturb independent:
For it marks them in band base puts a filter passes band for disturbs independent to Gaussian character and a limiter for disturbs impulsive which from place to distortion and therefore it needs of a filter to its escape. In the case of it marks them in traslata band instead the realization of the filter with good selettività is much complex and therefore it is rerun to the technical superheterodyne in order to carry marks them to an intermediate frequency more lowland for which the filtering is simpler.
In the case that marks them useful is to constant
envelope, to the aim to maintain this characteristic, comes practiced
the limitation also in traslata band, it is had that the value Tos of the limitation threshold
must respect the inequality 
where todp is the value of peak of the
disturbance of relative amplitude.
