RU2728728C1 - Absorbing filter-transformer - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: invention relates to selective transforming circuits of absorbing type and can be used in various receiving-transmitting radio equipment operating up to UHF range. In particular, it can be input part of high-power amplifiers, by means of which due to absorption at low frequencies of parasitic excitations, their stability during matching impedances of transistors with standard resistances, differing from each other by high transformation ratios, increases. Absorbing filter-transformer comprises four capacitors 46–49, three inductive elements 50–52 and two resistors R and r elements 53 and 54, which differ from each other in n-fold: R/r=n>1, where n is transformation ratio equal to ratio of wave resistances of paths at input Z₀ and output Z. At that L₁ and L₂=L₁/n – inductances of elements 50, 51 have magnetic coupling with close to unit by its coefficient:

where M is mutual inductance of elements 50 and 51, and capacitances of elements 46, 47 form electrical connections between similar clamps of inductive elements 50 and 51. With such electrical and magnetic links are given ratios of capacity C₁, C₂ elements 48, 49 and C₃ elements 46, 47 and inductance L₃ of element 52, as well as calculating values of total capacitances C and nC, which provides expansion in

times operating frequencies range, and matching of active resistances, differing from each other by high transformation ratio.

EFFECT: absorbing filter-transformer is proposed.

1 cl, 8 dwg

Description

The proposed device relates to selective transforming circuits of the absorbing type and can be used in various transmitting and receiving radio equipment operating up to the microwave range. In particular, it can be the input part of amplifiers of increased power, with the help of which, due to absorption at low frequencies of parasitic excitations, their stability increases in the process of matching the impedances of transistors with standard resistances differing from each other by high transformation ratios.

соответственно. Причем эти отрезки включены по отношению к входу и выходу последовательно, а по отношению друг к другу - параллельно. Входной импеданс Z_вх такой цепи, нагруженной на импеданс Z_н, описывается выражением [1]:Known filter-transformer of the ring type (See page 49 of the monograph Transistor amplifiers-limiters of the power of harmonic microwave oscillations / A.V. Baranov, S.L. Morugin. - M .: Hotline - Telecom, 2019. - 332 p.) ... This selective transformation network (see Fig. 1) is both an impedance transformer and an even harmonic bandstop filter. It consists of two segments 1 and 2 of microstrip transmission lines (MPL) with wave impedances ρ ₁ , ρ ₂ and lengths

respectively. Moreover, these segments are included in relation to the input and output in series, and in relation to each other - in parallel. The input impedance Z _Rin a chain loaded by an impedance of Z _n is described by expression [1]:

where υ is a value inversely proportional to the transformation ratio

where m _ρ = ρ ₂ / ρ ₁ . Expressions (1), (2) are obtained for the case when the elements Y ₁₁ and Y _{22 of} the conductivity matrix [Y] are equal to zero or under the condition:

Необходимо отметить, что за счет уменьшения v в таком устройстве можно достичь значительно более высоких коэффициентов трансформации. Знак минус в выражении (3) показывает, что один из отрезков МПЛ короче, а другой - длиннее λ/4. Из выражения (2) видно, что уменьшение о может быть обеспечено как за счет уменьшения m_ρ, так и за счет уменьшения длины одного из отрезков

например, при увеличении

(и наоборот). Очевидно, что максимальный коэффициент трансформации достигается, если длина одного из отрезков МПЛ стремится к λ/2. Можно показать также, что на четных гармониках основной частоты рассматриваемая фильтровая структура обладает предельно возможными полосно-заграждающими свойствами. Причем, чем меньше один из отрезков МПЛ отличается от величины λ/2 на кратных 2 частотах, тем уже полоса заграждения на этих частотах и шире полоса пропускания на основной частоте.Devices described by equations similar to (1) are called K-resistance inverters. An ideal impedance inverter behaves at all frequencies in the same way as a quarter-wave section of a transmission line with characteristic impedance.

It should be noted that by reducing v in such a device, it is possible to achieve significantly higher transformation ratios. The minus sign in expression (3) shows that one of the MSL segments is shorter, and the other is longer than λ / 4. From expression (2) it can be seen that a decrease in o can be provided both by a decrease in m _ρ , and by a decrease in the length of one of the segments

for example, when increasing

(and vice versa). Obviously, the maximum transformation ratio is achieved if the length of one of the MPL segments tends to λ / 2. It can also be shown that at even harmonics of the fundamental frequency, the considered filter structure has the maximum possible band-blocking properties. Moreover, the less one of the MSL segments differs from the λ / 2 value at multiples of 2 frequencies, the narrower the stop band at these frequencies and the wider the passband at the fundamental frequency.

The disadvantage of this analogue is a relatively narrow band of operating frequencies, in which it is possible to match resistances that differ from each other by a high transformation ratio. In addition, this filter transformer has significant frequency bands to the left and right of the operating bandwidth, which correspond to the total reflection modes. So, typical frequency bands of absorption of signals in the considered analog are (20-25)% and (10-15)% when coordinated with VSWR = 2 resistances, which have transformation ratios n equal to 1 and 10, respectively.

A selective circuit is known (See Fisher, RE Broad-band twisted-wire quadrature hybrids / RE Fisher // IEEE Transactions on Microwave Theory and Techniques. - 1973. - Vol. 21. - No. 5 (May). - P. 355. -357). Its layout is shown in Fig. 2. The circuit contains load 3 with resistance Z ₀ , two identical 3 dB quadrature directional couplers 4 and 5, which are cascaded to each other using coaxial cables 6, 7 with characteristic impedances Z ₀ and phase lengths ≈23 °. Directional couplers 4 and 5 consist of capacitors 8 - 11 with capacitance C / 2 and electromagnetically coupled inductances L in the form of twisting two wires 12 and 13, as well as 14 and 15. As a result of the optimization of the lengths of coaxial cables in the proposed selective cascade circuit, the bandwidth expansion is demonstrated operating frequencies with an overlap coefficient slightly exceeding an octave when matching resistances in standard paths with Z ₀ . Unfortunately, having acceptable frequency bands in the case of equal resistances of the paths, this selective circuit is generally unable to work in paths with resistances that differ from each other by a high transformation ratio.

The disadvantage of this device and similar selective cascade circuits [2] is the impossibility of providing wide bands of operating frequencies when matching resistances that differ from each other by a high transformation ratio.

Known selective circuit (See RF patent for invention No. 2174737 C2, IPC - 2006.01 HO3 N 7/12, HO1 P 1/20; Bandpass microwave filter / Khrustalev, V.A., Vostryakov Yu.V., Razinkin VP, Rubanovich MA; applicant and patentee Novosibirsk State Technical University - Publ. 10.10.2001, Bulletin No. 28. Its block diagram is shown in Fig. 3. The circuit contains a 3 dB quadrature directional coupler 16, notch filters 17, 18 and loads 19, 20 with resistance Z _0. The first output of the directional coupler 16 is loaded on the series-connected notch filter 17 with load 19, the second output - on the series-connected notch filter 18 with load 20. The ballast arm of the coupler is the output of the device The spectral components of the input signal, falling into the passbands of filters 17 and 18, are fed to the outputs of the working arms of the directional coupler 16 and are reflected from the inputs of these notch filters, the rejection bands of which exactly correspond The bandwidth of the proposed device. The spectral components reflected from the notch filters 17 and 18 enter the output of the device. The spectral components of the input signal, which are out of the passband, are not reflected from the notch filters and enter the absorbing loads 19 and 20. The high matching quality in a wide frequency range is determined only by the frequency properties of the absorbing loads and does not depend on the frequency properties of the three-decibel directional coupler 16, since The notch filters (with the exception of the notch band) are well matched in a wide frequency band that significantly exceeds the operating frequency band of the directional coupler 16. In this case, the operating frequency band of absorbing loads 19 and 20 is usually several times higher than the operating frequency band of the directional coupler 16. Out of the operating frequency band directional coupler to each of the loads will receive signals of unequal amplitude, but, nevertheless, they will not be reflected. This device turns out to be matched in a frequency band significantly exceeding the operating frequency band of the directional coupler. In practice, the quality of matching and the bandwidth of the proposed filter are determined by the quality of the matching and the bandwidth of the absorbing and, as a rule, ultra-wideband loads 19 and 20. Unfortunately, improvement of matching in a wide band is possible here only with the same resistances of all supplying microwave paths and absorbing loads.

The disadvantage of this device is the impossibility of providing wide bands of operating frequencies when matching resistances that differ from each other by a high transformation ratio.

The closest to the proposed technical solution is a selective non-reflective circuit (See Morgan, MA Reflectionless filters // USA Patent No. US 8392495 B2, IPC - 2006.01 G06G 7/02, data of patent March 5, 2013). The circuit diagram of this circuit (See Fig 9 (b)) is shown in Fig. 4. The device is a non-reflective high-pass filter (HPF). The HPF consists of four capacitors 21-24 with capacitances C, four inductive elements 25-28 with inductances L and two resistors 29 and 30 with resistances R equal to the wave impedances of the input Z ₁ and output Z _{2 of the} microwave paths, where Z ₁ = Z ₂ = Z ₀ . The circuit in FIG. 4 is a symmetrical quadripole, in which, depending on the method of its excitation at the input and output, there is a cut line 31, through which either no current flows, or the potentials of the nodes located on it relative to the ground bus are equal to zero. The mode of excitation of ports with signals with the same amplitudes and phases corresponding to zero current through the symmetry line is called a pair or even mode. When both ports are excited with signals with the same amplitudes and phases shifted by 180 °, the mode with zero potentials of the nodes on the symmetry line is called the unpaired or odd (odd) mode. The circuit in FIG. 4, operating in the two noted modes, can be described by [S] -parameters using the reflection coefficients of the corresponding circuits

a Z_even и Z_odd - входные сопротивления эквивалентных цепей, которые соответствуют расщепленным частям исходного фильтра, работающего в четном и нечетном режимах.Where

a Z _even and Z _odd are the input impedances of the equivalent circuits, which correspond to the split parts of the original filter operating in even and odd modes.

From expressions (4) it follows that a symmetrical circuit is matched on both sides when S ₁₁ = S ₂₂ = 0, provided:

Taking into account expression (5), the transmission coefficients of this chain are determined by the formula:

Using the method of calculating the elements of non-reflecting filters [3], we write down the input resistances Z _even , Z _odd for the equivalent circuits in Fig. 5 in the following forms:

where ω is the cyclic operating frequency (in radians / second). The equivalent circuit diagram in FIG. 5 a) is a T-shaped connection of inductors 32, 33 and capacitance 34 with a resistor 36 at its output. At the same time, capacitors 37, 39 and inductance 40 with output resistor 42 are combined into a U-shaped equivalent circuit diagram in FIG. 5 B).

For the equivalent circuits in FIG. 5 described by equations (7), relations (4) - (6) are valid, and their transmission coefficients are found from the expression:

при R=Z₀ и L₁=L₂=Z₀/ω_p, C₁=С₂=1/Z₀ω_p где ω_р - измеряемая в радианах/секунду циклическая частота полюса передаточной функции Н комплексной частоты s. После выполнения аналогичной [3] замены в уравнении (8)

передаточная функция записывается в следующем виде:which is obtained for the normalized frequency

at R = Z ₀ and L ₁ = L ₂ = Z ₀ / ω _p , C ₁ = C ₂ = 1 / Z ₀ ω _p where ω _p is the cyclic frequency of the pole of the transfer function H of the complex frequency s measured in radians / second. After performing a replacement similar to [3] in equation (8)

the transfer function is written as follows:

и нули

The function H in expression (9) has poles

and zeros

The analysis carried out for the symmetrical prototype circuit is valid provided: Z ₁ = Z ₂ = R = 50 Ohm. At the same time, this approach can be generalized to the case of matching the prototype of the resistances Z ₁ and Z ₂ , which differ from each other n-times, for example: Z ₂ = Z ₁ / n, when n> 1. Then in the equivalent circuit, which corresponds to the odd (odd) mode of operation of the prototype, the elements are calculated as follows: L ₂ = L ₁ / n, C ₂ = C ₁ n. Regardless of the value of n, the matching of the resistances R and R / n in the frequency range ω <ω _p remains acceptable here. At the same time, in the passband of the high-pass filter, matching with VSWR = 2 is possible only at low transformation ratios n <2, while the deviations from the symmetry of the circuits are small. These conclusions are confirmed in FIG. 6 graphs of frequency dependences of modules | S ₂₁ | (a) and | S ₁₁ | (b) for n = 1 (curves 1), 3 (curves 2), and 10 (curves 3). These dependences were obtained for a prototype with the parameters of the elements L ₁ = 6.8 nH and C ₁ = 2.7 pF at a frequency of ωp / 2π≈1.2 GHz.

Thus, in spite of the fact that the prototype provides satisfactory matching of resistances differing from each other by a high transformation ratio in the obstacle band, there is almost no matching in the passband at n> 2. Therefore, the disadvantage of the prototype is a narrow band of operating frequencies when matching resistances that differ from each other by a high transformation ratio.

The technical effect to be achieved by the proposed solution consists in expanding the operating frequency band when matching resistances that differ from each other by a high transformation ratio.

где L₁ - индуктивность элемента 50, L₂=L₁/n - индуктивность элемента 51, а М - их взаимная индуктивность, при этом параметры элементов устройства удовлетворяют соотношениям:This effect is achieved by the fact that the absorbing filter-transformer, consisting of the first, second and third capacitors 46, 48 and 49, from the first, second and third inductors 50, 51 and 52, as well as from the first and second resistors 53 and 54 with resistance element 53, equal to the input characteristic impedance Z ₀ , and the common points of the series-connected pairs of elements, the first pair - inductance 50 and resistor 53 and also the second pair - inductance 51 and resistor 54 are connected through a capacitor 48 and, respectively, through a capacitor 49 to a common bus , and the second terminals of the resistors 53 and 54 are connected to each other and to the third inductance 52, the second terminal of which is connected to the common bus, in addition, the free terminal of the element 50 is connected to the first terminal of the capacitor 46 and simultaneously to the input of the device, and the second terminal of the element 51 - to the output of the device, according to the invention, the second terminal of the capacitor 46 is connected to the output path of the device with a characteristic impedance Z = Z ₀ / n> 1, where n is the transformation ratio of the resistances Z ₀ and Z, between the same terminals of inductors 50 and 51, which have common points with resistors 53 and 54 with resistances R and r = R / n, respectively, a coupling capacitor 47 is introduced, and between elements 50, 51 magnetic coupling is introduced with a coefficient close to unity

where L ₁ is the inductance of element 50, L ₂ = L ₁ / n is the inductance of element 51, and M is their mutual inductance, while the parameters of the elements of the device satisfy the relations:

where L ₃ is the inductance of element 52, C ₁ and C ₂ are double the capacitances of elements 48 and 49, and C ₃ is the capacitance of coupling elements 46 and 47, the total value of which is approximately equal to the value of the half total capacitance C that occurs between the case and the connection point of elements 50 and 53, and this total capacity and a similar capacity nC at the connection point of elements 51 and 54 are found from the expressions:

A schematic diagram of the proposed absorbing filter-transformer is shown in Fig. 7. The device contains four capacitors 46-49, three inductive elements 50-52 and two resistors 53 and 54. Moreover, elements 50 and 51 are inductively coupled, and capacitances of capacitors 46 and 47 form an electrical connection between the same terminals of these inductive elements. Elements 53 and 54 - resistors R and r differ from each other n-times: R / r = n> 1, where n is the transformation ratio equal to the ratio of the wave impedances of the paths at the input and output Z ₁ / Z ₂ .

The proposed device works as follows. We use the well-known approach [3] to calculate its elements in order to establish relations similar to equations (8) and (9). Imagine two circuits split along the symmetry line in FIG. 7 as models in FIG. 5 a) and 5 b) with the only difference that by elements 32 and 40 we mean connected elements 50 and 51 in Fig. 7 with inductances L ₁ and L ₂ = L ₁ / n. In addition, capacitors 34, 35 and 37, 39 will be considered elements that have, relative to the case, total capacities C and nC, respectively, at the common connection points in FIG. 7 elements 48, 50, 53, as well as 49, 51, 54. Taking these remarks into account, we rewrite equations (7) in a new one corresponding to two circuits of the circuit in Fig. 7 form:

в которых величина

означает взаимную индуктивность.where Z _in and Z _out are the input and output resistances of inductively coupled elements loaded on resistances R and r. In accordance with the recommendations [4] Z _in and Z _out are found from the expressions:

in which the value

means mutual inductance.

рассчитаем все элементы с учетом этого замечания: L₁=Z₀/ω_p, L₂=Z₀/nω_p, С=1/Z₀ω_p, R=Z₀, r=Z₀/n. Запишем уравнения (10) следующим образом:Using the same methodology [3] in calculating the proposed device, we will normalize the current frequency ω to the frequency of the pole ω _p set for the prototype, which will help with subsequent comparative assessments. For normalized frequency

we calculate all the elements taking into account this remark: L ₁ = Z ₀ / ω _p , L ₂ = Z ₀ / nω _p , С = 1 / Z ₀ ω _p , R = Z ₀ , r = Z ₀ / n. Let us write equations (10) as follows:

If in expressions (11) and (12) we assume at 0 <k <1 the fulfillment of the conditions:

then for the circuits considered above, which are described by resistances Z _even , Z _odd , equations (4) - (6) are fully satisfied. Formally, without taking into account remark (13), the transmission coefficients of the proposed circuit are calculated from the expression:

передаточная функция при отмеченных ниже приближениях может быть записана следующем виде:Assuming in equation (14) the fulfillment of conditions (13), expression (14) completely coincides with equation (8). After passing in equation (14) to complex frequencies by replacing

The transfer function for the approximations noted below can be written as follows:

а числитель - лишь при условии k→1. Принимая во внимание данные предположения, функция H(s) в выражении (15) имеет полюсы:For example, the denominator of the function H (s) can be factorized only up to a small value

and the numerator only under the condition k → 1. Taking into account these assumptions, the function H (s) in expression (15) has poles:

практически приближаются к значениям нулей прототипа только при k→1, когда второй нуль

пропадает, так как в выражении (15) второй сомножитель в числителе и первый сомножитель в знаменателе сокращаются. Основной вывод, который можно сделать из анализа выражения (15), заключается в том, что по отношению к циклической частоте ω_р полюса прототипа циклическая частота

нового полюса s₂ или полюса предлагаемого устройства определяется выражением:Despite the accepted approximations, s ₂ , s ₃ , s ₄ coincide with the poles of the prototype when k = 0 in expression (15) or when there is no magnetic coupling. At the same time, under the conditions of the indicated assumptions, the values of the zeros

practically approach the values of the prototype zeros only for k → 1, when the second zero

disappears, since in expression (15) the second factor in the numerator and the first factor in the denominator are canceled. The main conclusion that can be drawn from the analysis of expression (15) is that in relation to the cyclic frequency ω _{p of the} prototype pole, the cyclic frequency

the new pole s ₂ or the pole of the proposed device is determined by the expression:

From expression (16) it follows that the introduction of a magnetic coupling makes it possible to move the frequency of the pole up the range, and the more efficiently, the closer to unity its coefficient is chosen. Thus, at a 3-dB magnetic coupling coefficient k = 0.707, the pole frequency ω _p increases by a factor of 1.41, and at k = 0.95, by a factor of 3.2. Considering that when ω / ω _p <1 in the prototype, regardless of the value of n, the matching of the resistances R and R / n remains acceptable, it can be assumed that the behavior of the proposed device will be the same. This statement is also confirmed by relations (13).

для текущей циклической частоты со справедливо неравенство:Then, in the proposed device, provided

for the current cyclic frequency with the inequality is true:

больше ω_р в

раз, то значение со также будет больше величины со в

раз.Inequality (17) means that, as in the prototype in the proposed device, the frequency range of matching of different resistances is limited from above by the frequency of the pole. And since in accordance with the formula (16)

more ω _p in

times, then the value of ω will also be greater than the value of ω in

time.

Using the parameters of the elements of the described equivalent circuits, we synthesize the original circuit in Fig. 7. In the process of synthesis, we will take into account the recommendations of [5]. Let us perform operations that do not affect the operating modes of the circuits in Fig. 5, when in the circuit a) no current flows through the line of symmetry 31, and in the circuit b) the potentials of the nodes located on it with respect to the ground bus are zero. In the first circuit, we add a container 35 and interchange elements 33 and 36, and connect their midpoint to the line of symmetry 31. In Fig. 5 b) we move the absolute ground contacts 43 and the output of the capacitor 37 to the virtual ground in the symmetry line 31. In the second circuit, we also add inductance 41 between the virtual and absolute ground. In addition, we introduce new additions to the standard synthesis procedure, which are associated with elements 46- 49. Let us designate elements 46-49 as follows: elements 48 and 49 are capacitors with a capacity of C _1/2 and C _2/2 , respectively, and elements 46 and 47 are coupling capacitors with the same capacitances Cz, with a total coupling capacity 2C ₃ , which is approximately equal to the value of half the total capacity C. In this case, the division of the capacities C ₁ and C ₂ in half and the connection of their second halves to the line of symmetry 31 in FIG. 5 a) and b) also does not lead to a violation of the operating modes of the considered equivalent circuits. In this case, the half capacities of the elements 34 and 39, as well as the half capacities of the elements 35 and 38 form the capacities of the elements 46 and 47, and the elements 33 and 41 are combined into an element 52 with a total inductance L ₃ (See Figs. 5 and 7). As a result of the performed procedures, the proposed absorbing filter-transformer was synthesized, the parameters of the elements of which are calculated from the expressions:

and the values of the total capacities C and nC are found as follows:

Thus, when calculating the parameters of the elements according to the formulas (18) - (21) in the absorbing filter-transformer, in accordance with the formulas (16) and (17), the expansion of the operating frequency range is guaranteed, where the matching of active resistances differing from each other by a high coefficient transformation.

Examples of specific implementation of the device. As such examples, we present the layouts of absorbing filter-transformers, which are developed based on the results of modeling using the recommendations of the book [6]. At low frequencies, the main elements 50 and 51 - inductors with magnetic coupling can be made in the form of a transformer with a magnetic core, at high frequencies - in the form of twisting two wires [7]. When developing two prototypes of the proposed device, we use the model of coupled inductances MUC2, standard for the selected software package [6]. Setting the magnetic coupling coefficients in the MUC2 model equal to 0.9 and 0.95, we calculate the parameters of the elements of each of the layouts using formulas (18) - (21), operating at n = 3 and 10. For the convenience of comparing the characteristics of the prototype and layouts, we calculate at R = 50 Ohm their elements at the same pole frequency ω _p /2π≈1.2 GHz. In the first model for k = 0.9, n = 3, we find the following parameters of the elements: L ₁ = 6.8 nH, L ₂ = 2.2 nH, L ₃ = 1.7 nH, C ₁ /2=1.6 pF, C ₂ /2=7.5 pF, 2C ₃ = 1.32 pF, C / 2 = 1.35 pF. Calculate parameters as elements of the second layout when n = 10 and k = 0.95: L ₁ = 6.9 nH, L ₂ = 0.7 nH, L ₃ = 0.64 nH, C ₁ /2=1.42 pF, C _2/2 = 31 pF, 2C ₃ = 1.35 pF, C / 2 = 1.35 pF. The results of modeling these models in the form of graphs of the frequency dependences of the modules S ₂₁ ⎢ (curve 1), ⎢S ₁₁ ⎢ (curve 2) and ⎢S ₂₂ (curve 3) are shown in Fig. 8 a) (for the first layout) and in Fig. 8 b) (for the second layout). The simulation results obtained above are in good agreement with the theoretical conclusions. So, when the value of k changes from 0.9 to 0.95 in the proposed device, the pole frequency (and, therefore, the range of possible matching) theoretically increases by 1.4 times. An increase of 1.44 times is confirmed experimentally. When the resistances are matched with VSWR = 2 and n = 3, the frequency range of the proposed device is 2.7 times higher than the prototype, and when the resistances are matched, when n = 10, it is 3.9 times higher (See Figs. 6 and 8).

Thus, the considered examples of the specific implementation of absorbing filter-transformers confirm the possibility of expanding the operating frequency band when matching resistances that differ from each other by a high transformation ratio. Moreover, the experimental results fully confirm the obtained theoretical conclusions.

Sources of information

1. Baranov, A.V. Miniaturization of ring-type impedance transformers / A.V. Baranov, M.V. Krentsin // Izv. universities Ser. Radio electronics. - 1990. - No. 9. - S. 90-91.

2. Patent US 3514722, H03H 7/04 (2006.01) Networks using cascaded quadrature couplers, each coupler having a different center operating frequency / J.D. Cappucci; 26 May 1970.

3. Morgan, M.A. Thinking outside the band: Absorptive filtering / M.A. Morgan // 1203.2174.pdf available from March 9, 2012. - [Electronic resource]. - Access mode: http://www.arxiv.org.

4. Matkhanov, P.N. Fundamentals of electrical circuit analysis. Linear circuits: textbook for universities / P.N. Matkhanov. - M .: Higher school, 1981 .-- 333 p.

5. Morgan, M.A. Synthesis of a new class of reflectionless filter prototypes / M.A. Morgan and T.A. Boyd // 1008.3502.pdf available from August 20, 2010. - [Electronic resource]. - Access mode: http://www.arxiv.org.

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Claims (3)

An absorption filter transformer, consisting of the first, second and third capacitors 46, 48 and 49, from the first, second and third inductors 50, 51 and 52, as well as from the first and second resistors 53 and 54 with the resistance of the element 53 equal to the input wavelength resistance Z ₀ , and the common points of series-connected pairs of elements, the first pair - inductance 50 and resistor 53 and also the second pair - inductance 51 and resistor 54, are connected through the capacitor 48 and, respectively, through the capacitor 49 to the common bus, and the second terminals of the resistors 53 and 54 are connected to each other and to the third inductance 52, the second terminal of which is connected to the common bus, in addition, the free terminal of the element 50 is connected to the first terminal of the capacitor 46 and at the same time to the input of the device, and the second terminal of the element 51 is connected to the output of the device, characterized in that that the second terminal of the capacitor 46 is connected to the output path of the device with a characteristic impedance Z = Z ₀ / n> 1, where n is the transformation ratio resistances Z ₀ and Z, between the terminals of the same name of inductors 50 and 51, having common points with resistors 53 and 54 with resistances R and r = R / n, respectively, a coupling capacitor 47 is introduced, and between elements 50, 51 a magnetic coupling with close to unit coefficient

where L ₁ is the inductance of element 50, L ₂ = L ₁ / n is the inductance of element 51, and M is their mutual inductance, while the parameters of the elements of the device satisfy the relations:

where L ₃ is the inductance of the element 52, C ₁ and C ₂ are the doubled values of the capacities of the elements 48 and 49, and C ₃ is the capacitance of the coupling elements 46 and 47, the total value of which is approximately equal to the value of the half total capacitance C between the case and the point connections of elements 50 and 53, and this total capacity and a similar capacity nC at the connection point of elements 51 and 54 are found from the expressions:

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