DE504876C - Replica for pupinized telephone lines - Google Patents

Description

The invention relates to replicas of pupinized telephone lines. The task of making satisfactory replicas for lines is to indicate some relatively simple and cheap combinations of impedance elements, which at all telephone frequencies have an impedance which is almost the same is like the impedance at the input end of the line.

Since the input impedance of a loaded line depends on the relative position of the first load coil to the point from which it is measured deviates the design of the pupinization is influenced by the location of the point where the first Coil should be, d. H. by the so-called run-up length. Four ways for the species of the beginning of the line can be distinguished:

α start of the line in the middle of a loading coil;

b a fraction χ from the center of the load coil; χ is positive if the part of this load coil connected in the cable to be simulated is less than half (0.5);

c in the middle of the cable length lying between two loading coils;

d at a point at a distance χ from the center of this part; χ is positive if the fraction of this cable length is less than half (0.5).

The invention consists in an arrangement of elements having inductance, capacitance and resistance, the values of which can be determined in terms of the constants of the line to be modeled, as will be given later in more detail. This determination can be made for the cases α and c and a wide range of values χ in the cases b and d .

In this description, two line simulations are described, of which the first refers by name to case a , but can be adapted to case b , while the second mainly relates to case c, but can be adapted to case d.

It is mathematically easier to first consider the cases α and b and then to develop the solutions for the cases c and d from the solution of these cases of relatively little practical importance.

In the drawings, Fig. 1 shows a scheme of an incomplete replica for a loaded loading cable ending at half the loading coil, Fig. 2 corresponding complete simulation with a series capacitor, Fig. 3 a scheme an incomplete replica for a

Loaded cable ending halfway through the cable route and Fig. 4 the corresponding complete one Replica including a series capacitor.

Let Z be the impedance of a loaded cable arranged according to case α , ti the frequency, H the inductance of each of the loading coils, / the distance between the loading coils, C the capacitance, L the inductance, R. the resistance and 5 the derivative per unit length of the line and ρ = 2 χ ti, while / =] / _. 1 is as usual.

Now G. A. Campbell (Phil. Mag. March 1903) showed that:

y

where Z ₀ and P are given by

-Vl

P =] / (R + JPL) (S + jpC). Since Pl is small compared to I in practice, you can write

tangh - = - 22 (2)

cotgh- = ^;

from Eq. (ι) to (5) one obtains Z-

χ jHp

S can be neglected in comparison with / ρ C and LI in comparison with H. In

in practice the expression · - HpIR

be ignored.

With these approximations, Eq. (6) reduced to

'pe

Y ei 4

Where /; - 2 - 11 and / =] / - r.

In practice, the terms are

and - ^ always less than - ^ ₁ . ρ C Ll

(7)

¹ JlL

Hence will

¹¹ L

egg

~ '* ^c ' Y§i

(8th)

The imaginary expression on the right

j PK +

¹ r + JpLi {(ß + i

2 J '

(5)

(6)

Side of Eq. (8) represents a capacitor

of the capacitance A = - ^ - I / -pn . Hence ng

an element of the line simulation becomes a series capacitor of this capacitance be.

The task is therefore reduced to determining a circuit, its resistance decreases with frequency according to the above relationship and, since in Eq. (8) an inductive component in the imaginary Part is missing, which has zero reactance.

It has been found that the circuit shown in Fig. 1 by choosing more suitable Is able to deliver values for the elements of this result. The values of the elements are related to the electrical constants of the line. no

The value of these elements of the line simulation is shown in the following way certainly:

The impedance of the circuit according to Fig. 1 is given by "5

(9)

(1 - ^ ₂ I ₂ A ') ² -j- £ ^l Rr- (1 -pL ^ Kf + pK ~ f ~'

(XO)

The real part of Z ¹ , which is the resistance component of the impedance of this circuit, is

r
ι + p- (K- r- - 2 KL ₂ ) + p * K * Lr ' ^[1I)

which is of the shape

(12)

i + ap ~ + bp ¹ '

Now the resistance component of the cable impedance matching (Eq. 8)

p-HCl
γ οί γ 4

what can be written for the sake of simplicity

By Ί - Ap-,

(13)

where S =

~ - and A = - Ll 4

if one makes r - B and chooses K and I ₂ accordingly, then the expressions (12) and (13) can have almost the same values over a large range of values ρ.

We have already set r = B so that the terms are equal at frequency zero. Furthermore, the two expressions can be made to have the same values at two other frequencies. These frequencies should be close to the mean value and the upper limit of the speaking frequencies, ie around ωχ = 7000 and ω ₂ = ΐ2οοο.

First, one determines the values of l'JZ ^ Ap * in the vicinity of the two frequencies mentioned above; z. For example, for a medium load cable, the values of \ T-Ap ' ^{1 are} approximately 0.9 and 0.6.

The task now is to achieve

that the expressions

have the values 0.9 and 0.6 at the same frequencies. For the frequency at which J ι - Ap "has the value 0.9, becomes

I - Ap ² = 0.81
Ap- = 0.19

ο __ CVtQ

P- ^ _A '

So you get

,. , 0.19 (3!.

1 = 0.9+ ^Lj f-- + - '"Ji ~ - (14)

and for the other value in a similar way

0.384 «0.246 a

ι = 0.6 +

If you solve the GI. (14) and (15) for α and b, then becomes

b - A- x 1.01 and a = A x 0.396
K- r ¹ - 2 KL ₂ -

ι = A (approximately)
K- r- = 2.396 A
£ 2 = 0.645 B} / A

1.55 VA

In this way, L ₂ , K and r are expressed by the constants of the cable.

The imaginary part of the circuit according to Fig. Ι is according to Eq. (10)

Z ₁ + j »[(L ₈ (I- P-KL ₂ ) -K r«)]

(z-p * KLj2 + p * K * r * ■

If you put the values from the above calculation in the second term of this Expression, this will be

0.905 r Va + 0.645 rA ^3l2 p '\

- p

in practice this will be approximately the same

and therefore represents a negative inductance.

If ^ we make L ₁ - C · 905 r \ '' ~ Ä , then the reactance of the circuit according to Fig. 1 becomes zero, and one has a network which has a resistance without inductive component over the usual telephone frequency range, which is decreases with frequency in the desired manner. To complete the compensation, a series connected capacitor k is removed from the _n C * / JLf

Values ^ I / _Γ τ ₇ required. In this way

K t L. L

the complete replica consists in the arrangement of the elements according to Fig. 2. The The value of each element is determined by the following constants of the cable:

₁ = 0.45 H.

k =

L ₂ = 0.32 HK = 0.77 Cl

H Cl

In practice it can turn out that the simulation can be achieved by changing the calculated Values can be improved by a few percent.

This solution relates to the case a. It is clear that a solution for case b, in which χ is any value between

Claims (4)

0.45 to 0.5 can be obtained by giving L ₁ the value (0.45 to λ;) Η . In order to obtain a simulation for case c, one must start from an expression that corresponds to Eq. (1) corresponds for this case. Such a term is given by HW Malcolm in his book The Theory of the Submarine Telegraph and Telephone Cable. • (16) ι —- tangh— 2 2 If one makes approximations that are similar to those used in the derivation of Eq. (7) from Eq. (1) made are, we get in place of Eq. (8) from Eq. (16): ^Δ - \ Cl \ ~ ,, HCf 4 This can be put in the form: Y ~ CJ jRl γ ■ -Ρ * j Rl JHCl 2 pH Cl : -f HCl • (ι?) The second term approximates the behavior of a series capacitor from Values 2 - while the first expression a resistance that increases with the frequency stood of the form r-. represents where Ki - Ap- B and A have the same meaning as above. As has already been shown, a circuit of the form shown in Fig. 1 can be set up so that the impedance B j / i - Ap * is simulated. Be it notes that the product of B y Ί - Ap- and is equal to B- , which is the value (constant resistance) 2 has. If a circuit is now set up according to Fig. 3, in which a capacitance k _{t is} parallel to a circuit which consists of an inductance L _s in series with a resistor r and has a capacitance L · connected in parallel, the impedance is this circuit I. j ρ A. + I. - I. iP < ~ t " iP k% I.
r (18) if the elements of this circuit have the following values: * i = 4 (19) ⁶ p -r-K r- IPL ₁ + ι (20) (21) (22) If, however, Z ^{1 is} the impedance of the circuit according to Fig. 1, then from Eq. (9) and (22) Z ¹ - Z \ - r- = B ² . Since the circuit according to Fig. 1 almost represents the resistance B \ '\ - Ap " , the circuit according to Fig. 3 must have almost the resistance -. —-—- .?' And therefore equation (17) in Ki - Ap ' ¹ - represent the first part. If the values of L ₂ , L ₁ , K and r are introduced, which have previously been inherited, the result is Iu = 0.32 c / Ll = 0.7s H. In case c , the simulation consists of the circuit according to Fig. 3 with the specified values in series with a capacitance k _s from the values -. The perfect aftermath formation is shown in Fig. 4. Since the short cable length between successive loading coils can approximately be represented by a shunt capacitance Cl , a simulation for the case d, in which χ has any value between 0.45 and 0.5, can be achieved by giving A ₁ the value ( 0.45 to x) Cl is obtained. In practice, the simulation can be improved if the values drop by a few Percentages are changed. Ρλ τ Ε N τ λ ν s P R ü c 11E: i. Simulation for pupinized telephone lines, the input impedance of which is practically the same as the input impedance of a pupin cable beginning in the middle of the load coil, characterized in that the elements of the simulation consist of a capacitance (k) and a self-inductance (L ₁ ) connected in series, which in turn in series with one consisting of two branches, Impedance, one branch of which contains a capacitance (AT) and the other a resistor (r) and a self-inductance (L ₂ ) connected in series with this (Fig. 2). 2. simulation according to claim 1, characterized in that when the series inductance (L ₁ ) changes, the line simulation corresponds to a cable which begins at any point half the length of the load coil. 3. Embodiment of the simulation according to claim 1, the input impedance of which is practically equal to the input impedance of a cable beginning in the middle of a coil field and in which the simulation consists of a capacitor (A ₁ ) shunted to an inductance (L ₃ ) and an inductance in series with this ao parallel circuit consists of a resistor (r) and a capacitor (k ₂ ) , characterized by a capacitor (k ₃ , Fig. 4) located in front of this circuit. 4. simulation according to claim 3, characterized in that by changing the shunt _{capacitance (A 1} ), the line simulation can be used for cables which begin with a run-up length lying between half and full coil field length. 1 sheet of drawings