Foundations of the transmission

It marks them in the transmission

1) It marks them real expressed in terms of the complex envelope:

It marks them real in traslata band s_m(t) can be expressed in terms of its complex envelope being w_c the relative pulsation to one contained frequencyf _c to the inside of the monolatero phantom, is had:

where the module i(t) is such to combine the maximums of the harmonic oscillation carrying while the phase j(t) of the complex envelope comes said instantaneous phase of marks them in traslata band. It is observed that to_c(t), to_s(t), i(t), f(t) can be independent vehicles of information.

 

2) instantaneous Pulsation and instantaneous shunting line:

From the relation one deduces that it marks them is to continuous phase if the instantaneous amplitudes are continuous and the envelope is not never null, for such marks them beyond to the phase f(t) can be made reference to the pulsation istantanea and the instantaneous shunting line of pulsation.

 

3) It marks them faithful in band base and traslata band:

For the fidelity definition marks them in band base is y(t) = g x(t-t₀), this formulation concurs in fact to maintain the full correlation between x(t) and y(t). For it marks them in traslata band makes reference instead the complex envelope and the relation is where is an arbitrary real constant.

 

4) Conditions so that the transfer between a generating bipole and a utilizzatore bipole happens in correct way:

The simpler logon previews the direct connection of a generator and of a utilizzatore, it is v(t) that i(t) they are vehicles of the information and the correct transfer happens alone if v(t) and i(t) they are proporziona them, the conditions under which that happens is:

to)       the generating bipole G it is rappresentabile as an ideal generator of tension or supplied current of constant, real and positive resistance inner of R value, that guarantees that the empty tension to and_g(t) is proporziona them to the current short circuit_gthe (t)

b)       the bipole utilizzatore U is rappresentabile with a real stiffness and positive R_u that it guarantees that v(t) and i(t) they are of marks them faithful between they (…in fact v(t) = R i(t)) and to and_g(t) and_gthe (t)

The useful instantaneous power is the its maximum value characterizes the ideal transfer and it is had for Z_g(f) = Z_u(f) = R that is a particular case of the condition of adaptation of power .

 

 

5) direct and reflected Tensions and currents:

In the case that the utilizzatore is not adapted Z_u(f) ¹ R is had that v(t) and i(t) they are not proporziona them of it between of they of to and_g(t) therefore is not faithful to it to the contrary of how much is had for the following largenesses:

v_d(t) represents the useful tension while v_r(t) represents the undesired tension. The instantaneous power is simply sum of the direct power and the reflected power, without mixed terms which elidono mutual.

 

6) It marks directed them and it marks reflected them:

In the case in which in trasmissivo means it does not have sense to speak about tensions and currents, it is rerun to marks expressed them like root of the instantaneous power, they are had that is marks directed them and it marks reflected them . For homogeneity with the definitions of tensions and currents direct and these reflected laddove have physical sense, have the relations: , .

 

7) Coefficient of reflection:

Transforming the definitions of it marks directed them v_d(t) and of it marks reflected them v_r(t) obtains where is the reflection coefficient, in the dominion of the time instead is had where h_ru it is the reflected impulsive answer that is marks reflected them that it is had when marks directed them is the d of Dirac.

 

8) sufficient Conditions for the ideal connection:

A generator is considered that it sendes marks directed them x_de(t) to a system of transmission from which it can receive marks reflected them x_king(t), marks them in escape from the system of transmission x_du(t) comes sended to a utilizzatore which reflected member can supply one x_ru(t). The connection is ideal if it respects the following conditions

to)                    x_de(t) = x₀(t)

b)                    x_king(t) = 0

c)                    x_ru(t) = 0

d)                    x_du(t) = gx_de(t-t₀)

being x₀(t) one faithfully marks them that veicola the information.

 

9) Relation between the power of marks directed them and the power of marks reflected them:

Application of the conditions of ideal transmission

 

10) impulsive Answers reflected and transmitted for a quadripolo:

Draft of the functions h_ij that they are present in the two transformations

Where x_d1 and x_r1 indicate respective i mark them direct and glares to the door 1 (…income) of quadripolo and analogous the x_d2 and x_r2 to door 2 (…exited) of the same one. It is spoken about impulsive answers reflected if the = j while it is spoken about impulsive answers transmitted if the ¹ j.

 

11) and quadripolo physically ideally realizable realizable Quadripolo:

All its real reflected impulsive answers are mark them of energy that is:

to)       they belong to L₁ that is are absolutely integrabili

b)       they are real

c)       is null motives that is for t < 0

the quadripolo he is instead only ideally realizable in the case that comes less the causalità.

 

12) linear Quadripolo varying time:

It is a quadripolo for which the impulsive answers depend on the time of application of the d of Dirac.

13) Parameters of spread:

Draft of the transformed ones of Fourier of the impulsive answers reflected, being the quadripolo mutual is had that the trasmettenze are between equal they H₁₂(f) = H₂₁(f) like pure reflectances H₁₁(f) = H₂₂(f), these last ones are both null ones in the case of quadripolo adapted to both the doors therefore have the relation where the trasmettenza H₂₁(f) = H(f) is said transfer function and is worth the relation between the powers .

 

14) Function of equivalent transfer in band base:

In the case of it marks them in band traslata in absence of reflections the function of transfer of the quadripolo is H(f), the part H (f) of the phantom that lies on the skillful semiplan can be brought back in the origin through one translation obtaining:

that the function of transfer in band is not other that base for the complex envelopes.

 

15) ideal Quadripolo:

E' characterized from the following parameters of spread:

H₁₁(f) = 0 H₂₂(f) = 0 H₂₁(f) =

such relations must be valid however the band is wide of marks them to transmit.

 

16) perfect Utilizzatore:

Draft of a utilizzatore for which the reflection coefficient is r_u(f) = 0 per f_m £ |f| £ f_M.

 

17) perfect Quadripolo in band base:

Draft of a quadripolo that it satisfies the following conditions:

to)       it is to delineate and invariant time

b)       in useful band reflectances H ₁₁ (f) and₂₂H (f) arenull

c)       in useful band is constant |H(f)| = |H₂₁(f)|

d)       in useful band it is proporziona them to frequenza the arg|H(f)| = arg|H₂₁(f)|.

in short the gain of insertion and the delay of insertion must be constant in band.

 

18) perfect Quadripolo in traslata band:

Draft of a quadripolo that it satisfies the following conditions:

to)       it is to delineate and invariant time

b)       in useful band reflectances H ₁₁ (f) and₂₂H (f) arenull

c)       in useful band is constant |H₂₁(f)|

d)       in useful band arg|H₂₁(f)| is linear function of the frequency

in short the gain of insertion and the delay of group of insertion must be constant in band.

 

19) Converter of frequency:

Draft of a quadripolo not linear (…in how much generates not present frequencies in marks them of income) characterized from the function of transfer in band base.

The quadripolo the ideal transmission in traslata band concurs if a function of transfer in band exists base and in the useful bands it is had:

to)       reflectances H ₁₁ (f) and₂₂H (f) arenull

b)       |H_C(f)| he is constant

c)       arg|H_C(f)| is linear function of the frequency

Quadripoli, channels and perfect systems of transmission

 

20) perfect trasmissivo Means :

He is rappresentabile with quadripolo a passive, mutual LTI and adapted, in which the two doors they are separated from a distance r, such to render the necessary delay not negligible so that it marks them propaghi completely, is had that is .

 

21) Attenuation of insertion in trasmissivi means  :

in the case of carrying physicists

in the case of carrying radio

where to it is the constant of attenuation of the line and r₁ is a value of reference for the distance.

It is observed that the attenuation introduced from a carrying physicist is much greater one of that one introduced from a carrying radio.

 

22) Selettività of a pass-high or pass-low filter:

where f_t it is the cut frequency that separates the passing band from the dark band and Df_t is the width of the transition interval.

 

23) Selettività of a filter pass-band or eliminate-band:

where f_to it is the center frequency band and ₃B the bandwidth to â?"3dB.

 

24) perfect Amplifier :

It is constituted from the cascade of a filter and of an ideal amplifier, it operates like an ideal amplifier in the passing band and like a filter to the external frequencies to it.

 

25) Converter of frequency :

A filter is had in income pass-band centered on the frequency f_ce of marks them of income, this marks strikes them in an ideal multiplier with marks them coming from from a local oscillator, marks them in escape from the multiplier then passes for a filter pass-band centered on the frequency of wished escape in fact to the escape of the multiplier is had marks them where the representation of the cosine in terms of complex esponenziali has been used.

 

26) Typology of frequency converters:

Perfect converter in salita is had in the case in which are hadf _cu =f _ce f₀ > f_ce

Perfect converter in discesa is had in the case in which is hadf _cu =f_ce - f₀ < f_ce

Nearly-perfect converter in discesa is had in the case in which -f ₀ is hadf_cu = f_ce e f_ce< f₀< 2f_ce

Nearly-perfect converter in salita is had in the case in which -f ₀ e is had f _cu = f _ce f₀ > 2f_ce

The nearly perfect converters beyond to the translation in frequency of mark execute them its ribaltamento and coniugio, however they can equally concur the ideal transmission for marks them in tightened traslata band in how much characterizes to you from real complex envelope or with constant argument.

 

27) Channel of perfect transmission:

All the perfect (in the which case function…of transfer is constituted from the cascade of quadripoli is the product of the transfer functions, the insertion gain is the product of the insertion gain and the time of delay is equal to the sum of the times of delay) can also be present complementary converters or a single converter in the which case is spoken about perfect traspositore.

 

28) typical Structure of a system of transmission of marks them:

Compound from trasmissivo means and…a brace of such active quadripoli is constituted from a transmission channel (that in the assigned band the channel has a unitary gain) to the whose two ends are a modulator and a demodulatore, having task to adapt marks them to the characteristics of trasmissivo means, the blocks that concur the treatment of above all mark them in band base in the numerical case, and of the external processors having the task to optimize the performances of the channel in the case of not perfect transmission.