DE650814C - Wave filter, which is made up of half filter elements - Google Patents

Description

'The invention relates to a wave filter whose attenuation characteristics in the Transmission range is uniform. For that purpose, the wave filter is made of half Filter members built up and a resistance of such magnitude between the half filter sections switched on, that the attenuation characteristic of the filter is made almost the same over the entire frequency range used is.

It is known that the attenuation of every physically realizable filter is not remains uniform over the entire passband but generally increases when one approaches the cut-off frequencies. This attenuation distortion is partly that Attributable to energy consumption occurring in the reactance elements of the filter.- So far special attenuation equalizers were used to remove this distortion. According to the invention, this attenuation distortion is canceled in the filter itself by a resistance in parallel between the half-members of the second type (π-members) of the filter or is connected in series between the sections of the first type (τ elements).

In Fig. 1, a wave filter is shown schematically in which the impedances Z _{1 are connected} in series with the line and the impedances Z ₂ are connected in parallel with the line. The 3 "input terminals of the network are labeled 11 and 12 and the output terminals 13 and 14. For the sake of simplicity, the network is shown in the non-balanced form, while the invention can be applied in the same way to balanced networks. The line between terminals 12 and 14 can be grounded or brought to some other fixed potential.Fig. 1 shows a single full section which begins at both ends with a half-member, so that the impedance of each shunt branch is equal to 2 Z ₂ . The series branch contains two impedances connected in series, each equal to ¹ Z ₂ Z _1. According to the invention, a resistor Z _- J is connected to points 15 and 16. How the size of Z _x must be determined will be explained later.

Fig. 2 shows a different arrangement of the individual elements and gives the same result as the arrangement in Fig. 1. Here a resistor Z _{3 is connected} in series between the two half-sections, each starting with half a cross member. In general, Z _{x is the} reciprocal of Z _y .

Fig. 3 shows a network in which the resistance Z _{x is} an ohmic resistance

"G represents the conductance of this resistance, which compensates for the Caused damping characteristics. We now want the effect that the insert tion of the conductance G on the attenuation deit Network, consider ^. ' If we assume that the stress impedances between which the network is switched on to its final impedances

ίο match, then the impedance, seen in every direction from G , is equal to the impedance Z _{1 of} the filter, which begins with half a series link, if the branch G is interrupted. Therefore, the total admission value of the circle, measured between the

Points 15 and 16, same

if the

Branch G is switched off. When G is turned on, the conductance is at this

Points G + -J-. The loss Θ in Neper,

which is caused by the involvement of branch G can be seen from the following Calculate formula:

where ε is the base of Napier's logarithmic system. If " Θ is small, then ε ^θ = ι -j- Θ. Therefore, small losses with sufficient accuracy are given by the following equation:

¹ - 7

- Ti "

(2)

Since G is a constant, switching on the equalization branch causes a loss that changes with the frequency and is directly proportional to the impedance Z _{1 of} the network, which begins with half a series element.

If a coil chain with constant k is used as the network, the structure shown in Fig. 4 is obtained after switching on the conductance G. The impedance Z ₁ of such a filter, beginning with half a series element, acts like a

I ₂ = ^ ₀ -M ₁ ==

2nfc L

The expression for A ₀ of equation (3) has the same algebraic form as the expression for the impedance starting with half a cross link of a coil chain with resistance through the entire transmission range, which at frequency O with a

starts with a finite value and then drops to 0 at the $ G / enz frequency, and like a

^ Band outside the transmission resistance ^. ^ Mides which is at the cutoff frequency and O * ASF increases an infinite value at the frequency infinite. The loss caused by the conductance G, since it is proportional to Z _1, is illustrated schematically by curve VJ in FIG. 5, where f _c denotes the cutoff frequency. This curve is very suitable to compensate for the usual curve of the uncorrected filter, denoted by 18 in FIG. The curve 18 has a low value at the frequency O and increases as the limit frequency is approached. The attenuation of the filter, which occurs when the compensation branch is switched on, and which forms the sum of curves 17 and 18, is shown by curve 19 in FIG. It can thus be seen that the attenuation through the transmission region is essentially uniform and the screening effect is improved.

It can be shown by theoretical investigations that, with the exception of frequencies in the immediate vicinity of the cut-off frequency, 'the attenuation A _tt in Neper, go, which is caused by η sections of an unchanged coil chain with constant k in the transmission range, is approximated by the following equation :

2wfc L T / i_;

(3)

/ c is the cutoff frequency, jr = '-4-,

Jc ~

is the ratio of resistance to self-induction of a coil. From equation (2) it follows that the loss A _{1 of} the equalizing resistance is given by the following equation:

_ GZ ₀ , _¥

A ₁ -T ^ -VX-X- ■ (4).

Z ₀ is the value of the impedance at frequency O. The total attenuation A _{2 of} the changed network in the transmission range is therefore

GZ _n

η r

0 t j? r

- 3ITc ^ *

(5)

T / i - x *

constant k. provided that the constant - ~ -ζ- represents the value of the impedance at the ^lao frequency O. The one through the rail

On the other hand, the expression given in chung (5) is similar to that for the half-member starting impedance of an m-type filter, provided that the constant

"" - equal to the values of the Impedgjiiz

infc L '1

at the frequency is O and the constant '

- is equal to ι - m ² . The improvement

GZ ₀ + - ^ I ₁ - . njc'L

tion of the constancy of the filter attenuation in the present case is mathematically analogous to the improvement in the constancy of the filter impedance, which is obtained when using filters of the w-type. It is known that "the value m = 0.6 leads to an almost constant characteristic. Because of the relationship

GZ _n

= i - mr

η r

(6)

the conductance G must have the following value in the present case, if a similar constancy of the attenuation is to be ensured through the transmission range:

G = 1.78 -

(7)

nfcZg L '

If the unchanged filter is a coil chain of the wi-type, a selection of different correction curves can be obtained, as indicated in FIG Conductance G is caused in the network. For comparison purposes, curve 20 of Figure 6 shows the correction that can be obtained using a term with constant k . All of these curves are more or less suitable to compensate for the normal damping characteristics of the filter. By appropriately combining them in a multi-link chain, one can achieve a high degree of uniformity of attenuation of the filter in the supra; Achieve carrying range. In some cases, an even better compensation of the attenuation curve can be achieved by using double filter elements of the m-type. The application of the invention is not limited to any particular type of ladder.

If the resistance Z _y of Fig. 2 is a simple ohmic resistance of the value R , the network shown in Fig. 7 results. If one applies the same considerations as in the circuit of Fig. 3, the impedance before branch R is switched on, viewed from this point, is equal to twice the value of the impedance Z _{1 of} the network beginning with the half cross member. When R is on, the impedance is R + 2 Z ₁ '. The loss Θ, which is caused by switching on the resistor R , is given by the following equation:

(8th)

or if minor losses are considered, by

«- ^R

If R is constant, the loss occurring as a result of the equalization branch is inversely proportional to the impedance Z ₁ 'of the network, which begins with half a cross member. If the unchanged network is a coil chain with constant k - as shown in Fig. 8, the correction curve 17 of Fig. 5 is obtained by adding R. This curve is the same as that obtained by introducing branch G. in the network of Fig. 4. It can thus be seen that the network of Fig. 8 is the electrical equivalent of the network of Fig. 4. The equalized characteristic of the network in Fig. 8 is also given by curve 19 in Fig. S.

A similar investigation can be made for symmetrical bandpass filters of the type with constant k. Such networks are drawn in Figs. 9 and 10, which form equivalent circles. A typical attenuation characteristic between the cutoff frequencies Z ₁ and / _{2 of} the non-equalized filter is shown by curve 24 in FIG. 11. The loss caused by the introduction of G or R is given by curve 25 and the resulting equalized characteristic by curve 26.

With an unbalanced bandpass filter, a correction curve can be obtained that either increases or decreases with frequency. For example, the impedance of the band filter no of FIG. 12, which begins with half a series element, decreases with frequency. Therefore, the loss caused by switching on the derivative G is given by curve 27 in FIG. This correction curve is particularly suitable for compensating for the attenuation of a filter that shows too few losses on the lower side of the frequency band. If one uses the network shown in Fig. 14, one obtains curve 28 of Fig. 13. The general Figs. 15 and 16 show modifications of the networks 12 and 14. The costs of the above

The filter arrangement described, in which the filters are equalized in the manner described by introducing a resistor, are greater than the cost of non-equalized filters because of the increase in the number of individual elements of the chain conductor. This is because serial links or transverse links of the original arrangement have to be broken down into two parts. Under normal circumstances, this cost is not great. But you can make it even smaller by introducing a mutual inductance between the two-part inductances. Some examples of this further development of the concept of the invention are shown in FIGS. 17, 18 and 19 and the equivalent circuits shown in Figs. 20, 21 and 22. Fig. 17 shows z. B. an equalized coil chain with constant k, in which the series inductance split into two parts is ordered instead of "two separate coils from a single transformer provided with two windings, which has two identical inductances L, which are coupled by the mutual inductance M. The The equivalent circuit for this network is shown in Fig. 20, which differs from Fig. 4 only in the addition of a negative inductance in the equalization branch. This negative inductance has the size jkf. and is in series with the equalizing derivative G.

Fig. 18 shows how this type of circuit can be applied to a link of a ladder of the first type (τϊ link) without any of the impedance branches of the original arrangement having to be divided into two parts. In parallel with the series impedance Z ₁ is a transformer with two identical windings L of high self-induction. The two windings are in the same direction and are "" coupled to one another by the mutual inductance M, which is essentially equal to L. The lead G lies between the connection point of the transformer winding and the earthed side of the network. The electrical equivalent of the circle in Fig. 18 can be seen in Fig. 21. The equalizing branch in this electrical equivalent consists of a negative impedance - ¹ Z ₄ Z ₁ , which is connected in series with the lead G.

Fig. 19 explains how you can insert an equalizing branch into the T-link without having to split one of the branches into two parts. A transformer with two windings is in fact placed in parallel to the equalizing resistor R , similar to that in Fig. 18, while this entire combination lies between the two series impedances ¹ J ₂ Z ₁ . The Ouerzweig Z ₂ is connected to the common point of the two transformer windings and the earthed side of the network. The equivalent electrical circuit, as shown in Fig. 22, is derived from the resistor R, to which a negative impedance of 4Z ₂ is parallel. The whole combination lies between the two halves of the Ouer link, which has been split into two parts.

If the series impedance of the network to be equalized consists of two or more current paths connected in parallel, it may be necessary to split only one of these current paths into two parts, so that no mutual inductance is required. An example is shown in Fig. 23 where the original arrangement was a double m-type coil chain. The series branch consists of an inductance L ₁ , to which a series circuit of an inductance L ₂ and a capacitance C is connected in parallel. According to the invention, in such a circuit, the inductance L _{x is divided} into two parts which are identical and the derivative G is placed at the point common to these two parts and the earthed side of the network. The equivalent electrical circuit is shown in Fig. 24. From this figure it can be seen that the equalizing branch is in fact connected between the midpoint of the series branch and the grounded line of the network, while a complex reactance lies in series with the lead G. Whether one should use the aids indicated in Figs. 17, 18, 19 and 20 depends on the fact that , if the loss caused by the equalization is low, the equalizing derivative G, if the equalization is carried out according to Fig. 3, or the equalizing resistance R, if the equalization is carried out according to FIG. 7, are also small. It follows that a small impedance, which is connected in series with G in Fig. 3, or a large impedance, which is connected in parallel with R (Fig. 7) does not significantly affect the equalization that can be achieved. Each of the equivalent circuits of Figs. 20, 21 and no is similar to that of Fig. 3 except for one. Impedance is in series with the lead G. Since the magnitude of these added impedances is only a fraction of the normal series impedance of the n ₅ filter in each case, their effect on the transmission range and beyond the attenuation range is neglected. The equivalent circle in Fig. "22 has the same shape as the network in Fig. 7 with" a shunt branch cut in two parts * only that a special impedance parallel to the resistance R

is switched. This parallel impedance is four times as large as the normal one Ouerimpedance of the filter, so that their effect on the equalization is not disruptive. The above considerations are only valid because of the impedance that is in series with the equalizing Resistance, or the admittance that lies parallel to it, is relatively small. This fact leads to another

ίο Modification of the invention in which a large impedance or a large admittance value is switched on in order to improve the equalization. For example, the desired correction curve can be the curve labeled 29 in FIG. 25, while the one that can be achieved is given by curve 30 of the same figure. If we look at the network of Fig. 4, we see that the equalizing branch G essentially diverts the current from the other parts of the network. It dissipates less current near the cutoff frequency because the impedance of the filter decreases as you approach the cutoff frequency. Branch G would dissipate even less current in this area if, instead of remaining constant, its impedance increased with frequency. This can be achieved by connecting an inductor or trap circuit in series with G so that the amplitude of the leakage current is reduced near the cutoff frequency without any significant effect at low frequencies. An example is shown in Fig. 26, where the equalizing branch, which consists of the derivative G and an oscillating circuit L and C in series with it, lies at the terminals of the coil chain beginning with half a series link with constant k . Curve 31 in Fig. 27 shows the attenuation characteristic of the filter in Fig. 26 without equalization, while curve 32 shows the characteristic that can be achieved when the equalizing branch consists of a simple derivative G , and curve 33 shows the characteristic achieved when the trap circuit is connected in series with G. As a unit of damping, the coefficient is ——> - r-

of equation (3), which represents the attenuation of the non-equalized filter at frequency O. It can be seen that the introduction of the trap circuit causes an improvement of about 4: 1 in the quality of the distortion achieved.

The inverse arrangement of the network in Fig. 26 can be seen in Fig. 28, in which the equalizing branch consists of a resistor R with a series connection of L and C in parallel. The equalizing branch is inserted between the external impedance of the filter, which is split into two parts. The characteristics of the filter 28 are the same as those of the curve 33 in FIG. 27.

In some cases the capacitance in Fig. 26 can be omitted, as can the inductance L in Fig. 28, but the degree of equalization is somewhat worsened by this measure. The corresponding networks are shown in Figs. 29 and 30.

Claims (10)

Patent claims: 1. Wave filter, which is made up of half filter elements, characterized in that that a resistance of such a size is connected between the half filter sections that the attenuation characteristic of the filter over the whole used frequency range is almost the same. - 2. Wave filter according to claim 1, characterized characterized in that the resistance is parallel to the line between two half filter elements with a half Begin row link, lies. 3. Wave filter according to claim 1, characterized characterized in that the resistor is in series with the line between two half filter elements with a half Beginning of the link lies. 4. wave filter according to claim 2, wherein one of the series impedances from a Pair of same inductors connected in the same direction in series and with each other are coupled, characterized in that the derivation path to the midpoint of the two inductors and to the other side of the line connected. 5 ·. Wave filter according to claim 2, characterized in that parallel to a series impedance, a pair of equal mutually coupled inductors and the discharge path is connected to the midpoint of the two inductances and to the other side of the line is. 6. wave filter according to claim 3, characterized in that the resistor between two series impedances of the wave filter and that a pair of equal and in parallel with the resistor mutually coupled inductances is connected and the discharge path to the Midpoint of the two inductors and connected to the other side of the line is. 7. The wave filter of claim 2, wherein each series impedance of the filter is from consists of two parallel branches, characterized in that the derivation path to the midpoint of one of the two Branches and connected to the other side of the pipe. 8. wave filter according to claim 2 or 3, characterized in that with the Resistance or the derivation path further reactance elements interconnected to influence the attenuation characteristics of the filter. 9. wave filter according to claim 2 and 8, characterized in that the discharge path consists of a resistor to which a blocking circuit is connected in series, the resonance frequency of which is equal to Cutoff frequency of the filter is. 10. Wave filter according to claim 3 and 8, characterized in that a resonant circuit, the frequency of which is equal to the cutoff frequency of the filter, is parallel to the between two . Series impedances of the filter is switched on resistor. 1 sheet of drawings