EP4395068A1 - Rat-race balun and method of reducing rat-race balun footprint therefor - Google Patents

Abstract

A Rat-Race balun includes a transmission line loop and 4 input-output ports P ₁ , P ₂ , P ₃ , P ₄ connected to said transmission line loop, the transmission line section respective between the adjacent ports P ₁ and P ₄ is of electrical length 2 θ ₂ , of impedance Z ₃ and is a line section charged by a capacitor of capacitance C2; where θ ₂ < 135 and the following equalities are verified: $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left(2{\mathrm{\theta }}_2\right)}$$ And $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$ w being equal to 2πf, with f the operating frequency, and Z _P1P4 being the impedance of the unloaded transmission line section of physical length 3λ/4 equivalent to said loaded line section.

Description

Technical area :

The invention lies in the field of Rat-Race type baluns.

Prior technique :

The term balun comes from the English words BALanced (balanced) and UNbalanced (unbalanced).

A balun is an electrical circuit used to make the connection between a symmetrical transmission line (two-wire line or parallel printed lines) and an asymmetrical transmission line (coaxial cable or printed line above a ground plane). A balun is for example made using coiled coaxial cable or a small section of two-wire line wound on a ferrite toroid or on a coreless mandrel (air balun). Such a balun can operate over a wide frequency band (2 to 4 octaves). A balun can also be made using a loop of coaxial cable with an electrical length equal to the half wavelength. The balun is then single-frequency, in fact it works correctly on a narrow frequency band, of a few percent. Baluns are made on printed circuits, with microstrips, striplines for example.

A Rat-Race type balun is a loop-shaped component, classically ring or square, comprising four ports No. 1, 2, 3, 4 such that a signal entering port 1 is divided between ports 2 and 4 out of phase and an incoming signal on port 3 is split between ports 2 and 4 in phase, with port 3 isolated. Its function is therefore to divide a radio frequency (RF) signal of power P into two RF signals of power P/2 or to combine two RF signals of power P/2 into one RF signal of power P.

A Rat-Race type balun can also be used to combine signals: at port 3 the difference between two signals injected at the input of the balun, after re-phasing, one to port 2, the other to port 4 and to port 1 is delivered, after re-phasing, their sum.

US 2022/0263212 describes an example of a Rat-Race type balun.

There is a need to reduce the bulk of Rat-Race type baluns on the electronic supports on which they are integrated.

Summary of the invention :

To this end, according to a first aspect, the present invention describes a Rat-Race balun, comprising a transmission line loop and 4 input-output ports P ₁ , P ₂ , P ₃ , P ₄ connected to said loop of transmission line, said balun being adapted to receive a first signal on port P ₁ , and to divide said first signal into a second signal delivered to port P ₂ and a third signal delivered to port P ₄ , said second signal and said third signal being in phase opposition to each other, wherein the ports adjacent to each other among the ports P ₁ , P ₂ , P ₃ , P ₄ are connected by respective sections of the transmission line loop , and at least some of said sections are capacitor-charged transmission line sections; said balun being characterized in that:
the respective transmission line section between the adjacent ports P ₁ and P ₄ is of electrical length 2 θ ₂ , of impedance Z ₃ and is a line section charged by a capacitor of capacity C2; where θ ₂ < 135 and the following equalities are verified: $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left({\mathrm{2\theta }}_2\right)}$$ And $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$ w being equal to 2 πf , with f the operating frequency, and Z _P1P4 being the impedance of the unloaded transmission line section of physical length 3λ/4 equivalent to said loaded line section.

Such a balun makes it possible to reduce the bulk of Rat-Race type baluns on the electronic supports on which they are integrated.

In embodiments, such a balun will also include at least one of the following characteristics:

• w étant égal à 2πf, avec f la fréquence de fonctionnement, et
• Z_c étant l'impédance de la section de ligne de transmission non chargée de longueur physique λ/4 équivalente à ladite section de ligne chargée ;

• le balun présente une forme de haricot et les ports P₂, P₄ comportent chacun au moins une première section connectée à la ligne de transmission, la première section du port P₂, étant parallèle à la première section du port P₄ ;
• la première section du port P₂ et la première section du port P₄ parallèles entre elles se font face ;
• le balun comporte un transformateur d'impédance chargé par un condensateur entre le port P₁ et la boucle de ligne de transmission.

- each of the respective transmission line sections between P ₁ and P ₂ , between P ₂ and P ₃ , between P ₃ and P ₄ is a line section of electrical length 2 θ ₁ , of impedance Z ₁ and loaded by a capacitor of capacity C and; where θ ₁ < 45° and the following equalities are verified: $$\mathrm{VS}=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_{\mathrm{vs}}\tan \left(2{\theta }_1\right)}$$ And $$Z_1=\frac{Z_{\mathrm{vs}}}{\tan \left({\theta }_1\right)}$$

• w being equal to 2 πf, with f the operating frequency, and
• Z _c being the impedance of the unloaded transmission line section of physical length λ/4 equivalent to said loaded line section;

• the balun has a bean shape and the ports P ₂ , P ₄ each comprise at least a first section connected to the transmission line, the first section of the port P ₂ being parallel to the first section of the port P ₄ ;
• the first section of port P ₂ and the first section of port P ₄ parallel to each other face each other;
• the balun has an impedance transformer loaded by a capacitor between port P ₁ and the transmission line loop.

• w étant égal à 2πf, avec f la fréquence de fonctionnement, et
• Z_P1P4 étant l'impédance de la section de ligne de transmission non chargée de longueur physique 3λ/4 équivalente à ladite section de ligne chargée.

According to another aspect, the invention describes a method of reducing the bulk of a Rat-Race balun comprising a line loop of transmission and 4 input-output ports P ₁ , P ₂ , P ₃ , P ₄ connected to said transmission line loop, said balun being adapted to receive a first signal on port P ₁ , and to divide said first signal in a second signal delivered on port P ₂ and a third signal delivered on port P ₄ , said second signal and said third signal being in phase opposition with each other, in which the ports adjacent to each other among the Ports P ₁ , P ₂ , P ₃ , P ₄ are connected by respective sections of the transmission line loop, and at least some of said sections are capacitor charged transmission line sections, said method comprising the following step implemented by an electronic device for determining Rat-Race balun characteristics:
the respective transmission line section between the adjacent ports P ₁ and P ₄ being of electrical length 2 θ ₂ , of impedance Z ₃ and being a line section charged by a capacitor of capacitance C2, determination of the impedance Z ₃ and the capacity C2, verifying θ ₂ < 135 and the following equalities: $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left({\mathrm{2\theta }}_2\right)}$$ And $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$

• w being equal to 2πf, with f the operating frequency, and
• Z _P1P4 being the impedance of the unloaded transmission line section of physical length 3λ/4 equivalent to said loaded line section.

• chacune des sections de lignes de transmission respectives entre P₁ et P₂, entre P₂ et P₃, entre P₃ et P₄ étant une section de ligne de longueur électrique 2θ ₁, d'impédance Z₁ et chargée par un condensateur de capacité C, détermination de l'impédance Z₁ et de la capacité C, vérifiant θ ₁ < 45° et les égalités suivantes : $$C=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_c\tan \left(2{\theta }_1\right)}$$ et $$Z_1=\frac{Z_c}{\tan \left({\theta }_1\right)}$$ w étant égal à 2πf, avec f la fréquence de fonctionnement, et Z_c étant l'impédance de la section de ligne de transmission non chargée de longueur physique λ/4 équivalente à ladite section de ligne chargée ;
• le balun présente une forme de haricot et les ports P₂, P₄ comportent chacun au moins une première section connectée à la ligne de transmission, la première section du port P₂, étant parallèle à la première section du port P₄ ;
• la première section du port P₂ et la première section du port P₄ parallèles entre elles se font face ;
• le balun comporte un transformateur d'impédance chargé par un condensateur entre le port P₁ et la boucle de ligne de transmission.

In embodiments, such a method will also include at least one of the following characteristics:

• each of the respective transmission line sections between P ₁ and P ₂ , between P ₂ and P ₃ , between P ₃ and P ₄ being a line section of electrical length 2 θ ₁ , of impedance Z ₁ and charged by a capacitor of capacitance C, determination of the impedance Z ₁ and the capacitance C, verifying θ ₁ < 45° and the following equalities: $$\mathrm{VS}=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_{\mathrm{vs}}\tan \left(2{\theta }_1\right)}$$ And $$Z_1=\frac{Z_{\mathrm{vs}}}{\tan \left({\theta }_1\right)}$$ w being equal to 2 πf , with f the operating frequency, and Z _c being the impedance of the unloaded transmission line section of physical length λ/4 equivalent to said loaded line section;
• the balun has a bean shape and the ports P ₂ , P ₄ each comprise at least a first section connected to the transmission line, the first section of the port P ₂ being parallel to the first section of the port P ₄ ;
• the first section of port P ₂ and the first section of port P ₄ parallel to each other face each other;
• the balun has an impedance transformer loaded by a capacitor between port P ₁ and the transmission line loop.

Brief description of the figures:

• [Fig. 1] La figure 1 représente schématiquement un montage de type push-pull dans un mode de réalisation de l'invention ;
• [Fig. 2] La figure 2 illustre le remplacement, dans un schéma fonctionnel de balun, des lignes classiques par des lignes chargées ;
• [Fig. 3] La figure 3 est un schéma fonctionnel de balun dans un mode de réalisation de l'invention ;
• [Fig. 4] La figure 4 illustre une topologie de balun considérée dans un mode de réalisation de l'invention ;
• [Fig. 5] La figure 5 représente une ligne de transmission 3λ/4 classique et une ligne 3λ/4 chargée équivalente ;
• [Fig. 6] La figure 6 représente une ligne 3λ/4 chargée et trois lignes λ/4 chargé équivalentes ;
• [Fig. 7] La figure 7 représente un procédé de réduction d'encombrement de balun dans un mode de réalisation de l'invention ;
• [Fig.8] La figure 8 représente une vue de dessus d'un circuit imprimé de dispositif push-pull du type représenté en figure 1 avec un balun en forme de haricot.

The invention will be better understood and other characteristics, details and advantages will appear better on reading the description which follows, given on a non-limiting basis, and thanks to the appended figures, given by way of example.

• [ Fig. 1 ] There figure 1 schematically represents a push-pull type assembly in one embodiment of the invention;
• [ Fig. 2 ] There figure 2 illustrates the replacement, in a functional balun diagram, of classic lines by loaded lines;
• [ Fig. 3 ] There Figure 3 is a functional diagram of a balun in one embodiment of the invention;
• [ Fig. 4 ] There Figure 4 illustrates a balun topology considered in one embodiment of the invention;
• [ Fig. 5 ] There Figure 5 represents a conventional 3λ/4 transmission line and an equivalent loaded 3λ/4 line;
• [ Fig. 6 ] There Figure 6 represents a charged 3λ/4 line and three equivalent charged λ/4 lines;
• [ Fig. 7 ] There Figure 7 represents a method of reducing balun bulk in one embodiment of the invention;
• [ Fig.8 ] There figure 8 represents a top view of a printed circuit of a push-pull device of the type shown in figure 1 with a bean-shaped balun.

Identical references may be used in different figures when they designate identical or comparable elements.

Detailed description :

There figure 1 schematically represents an electronic processing module 1 of the push-pull type in one embodiment of the invention, for example operating at high frequency and integrated, on a printed circuit, in the last stage of a transmission chain an electronic radiocommunication device.

The processing module 1 includes a power transistor (“High Power Amplifier”), named HPA 11. It operates on the L band (or any other frequency band, in narrow band, for example of width less than 20 MHz, or even at 15 MHz and at powers up to 1.5 kW peak.

As is known, power transistors have a low input impedance compared to the standard impedance 50 Ω and are regularly composed of two chips (similar to two transistors), in push-pull assembly here, which requires have to divide (split) the input signal and phase shift them by 180° before providing them as input to the transistor. The fact that the signals supplied at the input of the HPA 11 are in phase opposition makes it possible to reduce their interference due to amplification on two very close chips.

For this purpose, the processing module 1 comprises, upstream of the HPA 11, a balun 10 in one embodiment of the invention.

The input signal of processing module 1, typically a train of RF pulses in the L band (in the example considered with power In 47 dBm, and load rate 2%), is supplied at the input of port P1 of balun 10. The power of this input signal is P.

The two signals output from ports P2 and P4, of the same power P/2 (at +/-0.2 dB% for example) and in phase opposition to each other, are supplied one as input to one of the two chips of the HPA 11, the other as input to the other of the two chips of the HPA 11.

At the output of the HPA 11, the two amplified signals, in phase opposition, are supplied at the input of a balun 12, one on its port P2, the other on the port P4. The balun 12 puts these signals back in phase with respect to each other and outputs on its port P1, the sum of these two signals put back in phase.

The input impedance of the balun 10 is Z ₀ , which is much greater than each of the input impedances Z _E and output Z _S of the HPA 11. For example, Z ₀ = 50 Ω and Z _E , Z _S less than 20 or even 10 Ω (especially if LDMOS transistor), for example here 2.5 Ω.

The balun 10, here built on a printed circuit board (PCB) with microstrips for example, includes transmission line sections between each port P ₁ , P ₂ , P ₃ , P ₄ .

In a first embodiment, each section of transmission line between two adjacent ports, conventionally, is of physical length (in meters) λ/4 apart from the section between the adjacent ports P ₁ and P ₄ (ie the section which does not include the ports P ₂ , P ₃ ) and which is of physical length 3λ/4, λ being the wavelength corresponding to the central frequency of the input signal of the processing module 1. The electrical length corresponding to the physical length λ/4 is equal to 90°. As is known, the “electrical length” is a theoretical way of expressing the wavelength without having to mention the environment of the circuit: PCB (printed circuit board)... Concretely this consists of considering only a length wave λ corresponds to 360°. Theoretically, for a specific application, it is necessary to keep the same wavelength ratio. The spread of EM waves depend on the medium, therefore depending on the substrate λ (in m) changes, but not its associated length (always 360°).

The impedance of the unloaded transmission line of physical length λ/4 is Z _c .

In a second embodiment, each quarter-wave line section considered in the first embodiment is replaced by its transmission line equivalent charged by a capacitor.

In terms of physical dimensions, these equivalent sections differ, but in terms of behavior (if we study S parameters for example) they are identical, as shown by a narrow band observation.

This modification is detailed in “Compact Tunable 3 dB Hybrid and Rat-Race Couplers with Harmonics Suppression”, Khair Al Shamaileh, Mohammad Almalkawi, Vijay Devabhaktuni, and Nihad Dib, INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY, VOL.7, NO.6, NOVEMBER 2012 , and is illustrated in figure 2 for the case of a ring-shaped balun: each section of transmission line of length λ /4 (as shown on the left of the figure 2 ) is thus replaced (as shown on the right of the figure 2 ) by a section of transmission line of electrical length 2 θ ₁ , of impedance Z ₁ and loaded with capacitor, ie by two sections of transmission line each of electrical length θ ₁ and impedance Z ₁ interspersed with a capacitor placed in parallel, of capacity C, and therefore connected to ground.

We then have the following equalities:
$$Z_1=\frac{Z_{\mathrm{vs}}}{\tan \left({\theta }_1\right)}$$

And $$\mathrm{VS}=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_{\mathrm{vs}}\tan \left(2{\theta }_1\right)}$$

where w is the frequency pulsation, ie ω = 2 πf, with f the operating frequency of the balun, ie the central frequency of the signal.

A reduction in balun size of 52% corresponding in particular to the choice of a value of θ ₁ less than 45° was obtained in an exemplary embodiment.

The reduction ratio depends on the θ ₁ chosen, and also on the PCB (in particular its dielectric permittivity parameter ε _r ) considered. There is a reduction when θ ₁ < 45°: there is a reduction in the line length, which depends a lot on the PCB used. Moreover, as Z1 is inversely proportional to tan( θ ₁ ), that tan( 45°) = 1 and the tan function is increasing on [0;45°] then the impedance of the equivalent lines is greater than that of the original line. In this case there is a reduction in the width of the line, which depends a lot on the PCB used, largely on its thickness.

The capacitance value of the capacitor as well as the impedance of the charged line sections are deduced from the above equations linking them to the electrical length θ ₁ chosen less than 45°. The impedance being a function of the physical width of the microstrip, the latter are determined as a function of the impedance Z ₁ (Z1 here designating the impedance of the characteristic impedance type of the loaded lines, ie the impedance that an input line would have if the latter was of infinite length: it does not depend on the length).

It further follows that the resonant frequency value of the loaded transmission line is adjustable as required by changing the value of C (for example by using varactor type capacitors).

In Shamaileh et al., the impedance change was an effect that is experienced by the authors.

It is proposed here to exploit this change in impedance: the lower the length θ ₁ of the loaded sections, the higher their impedance. When using a balun 10 operating at low impedance, we therefore have more room to maneuver to reduce the length of the lines before reaching the limits of manufacturability associated with line widths. We can therefore obtain a component with very fine lines, of reduced length, operating at low impedances.

However, to meet one of the specificities of the HPA mentioned above, it is precisely necessary to have a balun 10 operating at low output impedances P ₂ , P4.

In a third embodiment of the balun 10, the second embodiment is modified in that the line section 3 λ /4 between the adjacent ports P ₁ , P ₄ is replaced by its equivalent in line loaded with a single capacitor this times, of capacity C2, as shown in the functional diagram of the Figure 3 , this line section is then constituted by two transmission line sections each of impedance Z ₃ and electrical length θ ₂ , interspersed with a parallel capacitor of capacity C2 also connected to ground.

This topology is more restrictive than the previous one exposed in the second embodiment, because the impedance of the two sections replacing the line 3 λ /4 is then, unlike previously, proportional to their electrical length.

This comes from the fact that ${\theta }_2\in \left[\frac{\pi }{2},\frac{3\pi }{4}\right]\mathit{mod}\left(\pi \right)$ , and that the tan() function is negative and increasing on this interval. The “-” sign of the equality 0_3 “transforms” the tan() function into an equivalent of the abs(tan) function on this interval. Or abs(tan( θ ₂ ))≥1 on $\left[\frac{\pi }{2},\frac{3\pi }{4}\right]\mathit{mod}\left(\pi \right)$ .

An additional reduction in size of the balun 10 can be obtained if the value of θ ₁ is chosen less than 45° and if the value of θ ₂ is chosen less than 135°, the impedance and electrical length values being determined at the using the following equalities 0_3 and 0_4.

This additional reduction is obtained in particular if 3 θ ₁ > θ ₂ and if we work with a substrate and impedances which do not generate too big a difference in line width between the impedances Z1 and Z3 (ie if we work with a substrate , which depending on the impedances Z1 and Z3 used, does not cause an increase in the width of the lines which would cause an overall increase in the surface covered by the balun, despite the reduction in the length of the lines); A Example of a standard criterion is that the length must be at least greater than 3 times the width. $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$ where Z _P1P4 is the impedance of the equivalent transmission line section between the adjacent ports P ₁ P ₄ , of physical length 3λ/4 and unloaded. $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left(2{\mathrm{\theta }}_2\right)}$$

This requires compromises to be made between the impedances of the different line sections of the balun: to reduce the size of the balun, it is necessary either to reduce the electrical length of its lines, or to increase the impedance of its lines; however in the case of the 3λ/4 line loaded with a single capacitor, these two parameters are proportional, a compromise is necessary. It is also necessary to take into account the impedance of the λ/4 lines; if it is too different from that of the 3λ/4 line, the impedance break could reduce performance. The opposite is that if they are too close, then this means that θ ₁ is close to 45° and therefore that the reduction of the λ/4 lines is less important.

The values of capacitance C and impedance Z ₁ for each section of length 2 θ ₁ connecting the adjacent points P ₁ , P ₂ , respectively connecting the adjacent points P ₂ , P ₃ , and connecting the points together adjacent P ₃ , P ₄ , remain determined by application of equations 0_1 and 0_2 above.

The shape of a Rat Race balun usually used is circular or square and is therefore not ideal, particularly for use in a push-pull type processing module 10 on a printed circuit, which has a long structure.

In a fourth embodiment, it is therefore proposed to produce the balun 10 by giving it a “bean” shape (in the plane in which the printed circuit extends), as shown in Figure 4 , instead of a ring shape as shown in figure 2 And 3 . This new topology makes it possible to orient the two ports P ₂ , P ₄ towards the transistor HPA 11, while having an input port P ₁ oriented in the opposite direction, via, for example, an impedance transformer.

In one embodiment, with reference to the figure 4 , the bean balun 10 comprises a perimeter 41 made up of transmission line sections. In the trigonometric sense, the section between ports P2 and P4 is concave, then the section between P4 and P2 is convex.

In reference to the Figure 4 , each capacitor of charged line sections is connected on the one hand to the transmission line forming perimeter 41 and on the other hand to ground via one of the vias (represented by small circles in Figure 4 ) in zone 40 which is inside the perimeter of bean balun 10.

In one embodiment, the bean balun 10 is constructed using circular arcs between the 4 consecutive ports and the lengths of these arcs are fixed according to the lengths between ports defined by calculation according to one of the first, second and third embodiments. The combination of this bean shape with the use of loaded lines as described in the second and third embodiments allows the size of the lines to be significantly reduced.

For example, in the case where we wish to implement the bean shape combined with the second embodiment with 6 capacitors, 31, 32, 33, 34, 35, 36, each of capacity C: 12 arcs of circles and their respective lengths are defined, with 2 concentric arcs of circles (delimiting a transmission line) between each pair of consecutive ports: the structure is divided into 12 arcs of circle; the angle of some is increased (those adjacent to ports P2, P3 and P4), without changing their length, so as to obtain the desired shape.

In one embodiment, the sections 52, 54 of the ports P ₂ and P ₄ immediately connected to the body of the bean-shaped balun 10 (extending in the plane of the printed circuit) are parallel to each other and stretch (in the embodiments where their length is non-zero) in the same direction, DE, from the body of the bean-shaped balun 10. In one embodiment, these two parallel sections are identical.

In one embodiment, a section 51 of port P ₁ (extending in the plane of the printed circuit) of balun 10 is parallel to sections of ports P ₂ and P ₄ and extends in one direction from balun 10 in an opposite direction, D0. In one embodiment, it is replaced by a parallel resistor

Thus as described above and in a conventional manner, in this embodiment also, the input signal is supplied at the input of the bean-shaped balun 10, at port P1; the signal transmitted in the balun 10 undergoes a power division and a phase opposition and the signals output from pots P2 and P4 have a power equal to half the power of the input signal and are in phase opposition. Port P3 of balun 10 is isolated (connected by a load to earth), in the processing module shown in figure 1 .

At the output of the balun 10, the impedance is for example 12.5 Ω, then adaptation circuits (length different from λ/4) are arranged between the HPA 11 and the balun 10 to lower the impedance to Z _E if necessary (an impedance transformer in a known manner comprises transmission lines having increasing or decreasing diameters to modify the impedance).

A balun 10 corresponding to embodiment 2 and/or 3 is particularly suitable for narrow band uses.

The embodiments described above can be implemented independently or in combination: for example, in one embodiment of the invention, the bean balun 10 is combined with one of the first, second and third balun embodiments. . Each of the embodiments makes it possible to have a balun with a reduced footprint.

In one embodiment so that the balun can maintain an input impedance of 50 Ω, with reference to the Figure 4 , an impedance transformer 42, which, in one embodiment, is also loaded by a capacitor 37 is inserted between the perimeter 41 of the balun 10 and the port P ₁ , to further reduce the bulk of the processing module 1 Similar to what was explained in relation to the ^2nd embodiment and using the same equalities 0_1 and 0_2, a portion λ/4 of the transmission line of the impedance transformer. is replaced by a line charged by a capacitor, which is shorter than the uncharged equivalent.

The balun 10 according to the invention is therefore a signal splitter, with impedance transformation or not depending on the case, which is miniaturized and optimized with transmission lines loaded by capacitors. The invention advantageously replaces the historical solution associating an impedance transformer $\frac{\lambda }{4}$ associated with a phase shifter $\frac{\lambda }{2}$ . The invention is even more interesting for low permittivity substrates (FR-4 or RO4350b, low-cost substrates), where the bulk of the classic solution is even more significant.

In terms of comparison with the solution, the size is greatly reduced: for an FR4 HP substrate with a dielectric permittivity constant of 4.34 and a height of 0.245mm, we observe, with reference to the table below, a reduction in about 80%, combining embodiments 3 and 4 with loaded transformer. It depends on the minimum width of a line and the power accepted in the lines and in the capacitors. [Table 1] Historical solution Common solution Clutter ε _r = 4.34, ε _r = 4.34, h = 0.245mm h = 0.245mm S = 40 * 40 = 1600 mm ² S = 16.5 * 19.6 = 323 mm ² Almost 80% reduction Means Microstrip lines Microstrip lines and 5 to 7 capacitors where ε _r is the dielectric permittivity associated with the FR4 HP substrate h is the thickness of the substrate, and S is the surface area of the component.

There figure 8 represents a top view of a printed circuit of a push-pull device 1 in one embodiment of the invention. The balun 10, respectively 12 has a bean shape according to the fourth embodiment (see frame 10_1, respectively 12_1). Frame 10_2, respectively 12_2 indicates where the impedance transformer is located (the transformer load is not apparent in this figure).

In reference to the Figure 7 , a method for reducing the bulk of a Rat-Race Balun is now described.

In one embodiment, in a step 101 of designing such a Rat-Race Balun, for example corresponding to the second embodiment, a bulk reduction module comprising a memory storing software instructions and a processor, determines, following the execution of the software instructions on the processor, the values of Z ₁ , θ ₁ and C of the balun 10 verifying the equalities 0_1 and 0_2 such that θ ₁ <45°.

For example, the substrate to be used is known, the dimension of the lines as a function of the impedance and the dielectric length can therefore be anticipated. The operating impedance is known, θ ₁ is chosen arbitrarily (respecting the condition θ ₁ <45°), depending on the values of Z ₁ and C obtained. It is verified that the associated lines are technically feasible and meet the requirements. Depending on this verification, it is decided to keep this θ ₁ or to modify it accordingly. The search is refined at each θ ₁ .

In another embodiment, the congestion reduction module further determines the values of Z ₃ , θ ₂ and C2 verifying the equalities 0_3 and 0_4 such that θ ₂ <135°.

The balun is then manufactured taking these characteristics into account.

In a design step 102, the electrical lengths of the line sections between balun ports being defined, the bulk reduction module determines, based on these lengths and the real impedances of the lines, the definition data of a bean shape for a Rat-Race balun and the ports, to obtain a bean balun as described above for example.

Steps 101, 102 can also be implemented independently of each other.

Such a process makes it possible to obtain a push-pull assembly comprising the Rat-Race Balun constructed under these conditions, and occupying a reduced footprint.

The method may be implemented by executing software instructions on a processor as described. Alternatively, it can be implemented by dedicated hardware, typically a digital integrated circuit, either specific (ASIC) or based on programmable logic (for example FPGA/Field Programmable Gate Array)

Justification for obtaining the equalities 0 3 and 0 4:

• à gauche (section a) : une ligne de transmission classique (i.e non chargée par des condensateurs) de longueur physique 3λ/4 et de longueur électrique électrique θ_q = 270° et
• à droite (section b) : la ligne équivalente de transmission chargée en condensateur, sous la forme de seulement deux sections de ligne, chacun d'impédance Z_cl et de longueur électrique θ_cl, avec un condensateur C en parallèle, disposé entre les deux sections.

In figure 5 are represented:

• on the left (section a): a conventional transmission line (ie not charged by capacitors) of physical length 3λ/4 and electrical electrical length θ _q = 270° and
• on the right (section b): the equivalent transmission line loaded with capacitor, in the form of only two line sections, each of impedance Z _cl and electrical length θ _cl , with a capacitor C in parallel, placed between the two sections.

Matrix (1) below provides the ABCD parameters for the classic transmission line of physical length 3λ/4:
$$\left[\begin{array}{cc}{\mathrm{HAS}}_q& B_q\\ {\mathrm{VS}}_q& D_q\end{array}\right]=\left[\begin{array}{cc}\cos \left(270\right)& {\mathit{jZ}}_q\sin \left(270\right)\\ {{\mathit{jZ}}_q}^{-1}\sin \left(270\right)& \cos \left(270\right)\end{array}\right]=\left[\begin{array}{cc}0& -{\mathit{jZ}}_q\\ -{{\mathit{jZ}}_q}^{-1}& 0\end{array}\right]$$

Then, to have an equivalent, we must have an equality between (1) and the matrix ABCD of a short-circuited shunt (2) multiplied on both sides by the matrix of a trunk loaded with capacitor (3), represented by (4):
$$M_{\mathrm{vs}}=\left[\begin{array}{cc}{\mathrm{HAS}}_{\mathrm{vs}}& B_{\mathrm{vs}}\\ {\mathrm{VS}}_{\mathrm{vs}}& D_{\mathrm{vs}}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ \mathit{j\omega C}& 1\end{array}\right]$$

$$M_{\mathit{cl}}=\left[\begin{array}{cc}{\mathrm{HAS}}_{\mathit{cl}}& B_{\mathit{cl}}\\ {\mathrm{VS}}_{\mathit{cl}}& D_{\mathit{cl}}\end{array}\right]=\left[\begin{array}{cc}\cos \left({\mathrm{\theta }}_{\mathit{cl}}\right)& {\mathit{jZ}}_{\mathit{cl}}\sin \left({\mathrm{\theta }}_{\mathit{cl}}\right)\\ {{\mathit{jZ}}_{\mathit{cl}}}^{-1}\sin \left({\mathrm{\theta }}_{\mathit{cl}}\right)& \cos \left({\mathrm{\theta }}_{\mathit{cl}}\right)\end{array}\right]$$

$$M_q=M_{\mathit{cl}}{M}_{\mathrm{vs}}{M}_{\mathit{cl}}$$

Equality (4) allows us to establish the following equations:
$${\mathrm{HAS}}_q=\cos {\left({\mathrm{\theta }}_{\mathit{cl}}\right)}^2-{\mathit{\omega CZ}}_{\mathit{cl}}\sin \left({\mathrm{\theta }}_{\mathit{cl}}\right)\cos \left({\mathrm{\theta }}_{\mathit{cl}}\right)+{{\mathit{jZ}}_{\mathit{cl}}}^{-1}\sin \left({\mathrm{\theta }}_{\mathit{cl}}\right)$$
$$B_q=\mathrm{j}{Z}_{\mathit{cl}}\sin \left({\mathrm{\theta }}_{\mathit{cl}}\right)\cos \left({\mathrm{\theta }}_{\mathit{cl}}\right)-{\mathit{j\omega CZ}}_{\mathit{cl}}^2\sin {\left({\mathrm{\theta }}_{\mathit{cl}}\right)}^2+\cos {\left({\mathrm{\theta }}_{\mathit{cl}}\right)}^2$$

Thanks to the correspondence between (1) and (5.a), (6) is determined: $$\mathit{\omega C}=\frac{2}{Z_{\mathit{cl}}\tan \left(2{\mathrm{\theta }}_{\mathit{cl}}\right)}$$

Then by substituting (6) into (5.b), it appears (7)
$$Z_{\mathit{cl}}=-\frac{Z_q}{\tan \left({\mathrm{\theta }}_{\mathit{cl}}\right)}$$

Finally, using (6) and (7), the value of the capacitance used in the equivalent loaded line is equal to
$$\mathrm{VS}=-\frac{2\tan \left({\mathrm{\theta }}_{\mathit{cl}}\right)}{{\mathit{\omega Z}}_q\tan \left(2{\mathrm{\theta }}_{\mathit{cl}}\right)}$$

As C > 0, it follows that:
$$\tan \left({\mathrm{\theta }}_{\mathit{cl}}\right)<0\mathit{and}\tan \left({\mathrm{2\theta }}_{\mathit{cl}}\right)>0$$
Or
$$\tan \left({\mathrm{\theta }}_{\mathit{cl}}\right)>0\mathit{and}\tan \left({\mathrm{2\theta }}_{\mathit{cl}}\right)<0$$

Using conditions (9.a) and (9.b), and taking into account that Z _cl > 0, the only possible values for θ _cl are:
$$\begin{array}{cc}{\mathrm{\theta }}_{\mathit{cl}}\in \left]\frac{\pi }{2};\frac{3\pi }{4}\right]& \mathit{mod}\left(\pi \right)\end{array}$$

The goal is to reduce the length of the 3λ/4 transmission line by replacing the three loaded λ/4 lines with one loaded 3λ/4 line as shown in Figure 6 , it is necessary to find the condition for:
$$\frac{3\pi }{2}>6{\theta }_{\mathit{cl}3}>2{\theta }_{\mathit{cl}}$$

To satisfy (11), it is necessary to take into account condition (10). Finally, the loaded 3λ/4 line can present a reduction in size for:
$$\begin{array}{cc}{\mathrm{\theta }}_{\mathit{cl}}\in \left]\frac{\pi }{2};\frac{3\pi }{4}\right[& \mathit{mod}\left(\pi \right)\end{array}$$

By an ADS simulation, it was demonstrated that the miniaturized rat-race couplers present the same performances for three λ/4 lines loaded with capacitors and for one 3λ/4 line loaded with capacitors.

Beyond the miniaturization aspects, these new aspects provide greater flexibility regarding the value of the impedance.

Claims (10)

Rat-Race balun (10), comprising a transmission line loop and 4 input-output ports P ₁ , P ₂ , P ₃ , P ₄ connected to said transmission line loop, said balun (10) being adapted to receive a first signal on port P ₁ , and to divide said first signal into a second signal delivered on port P ₂ and a third signal delivered on port P ₄ , said second signal and said third signal being in phase opposition with each other, in which the ports adjacent to each other among the ports P ₁ , P ₂ , P ₃ , P ₄ are connected by respective sections of the transmission line loop, and at least some of said sections are sections of capacitor-charged transmission lines; said balun being characterized in that :
the respective transmission line section between the adjacent ports P ₁ and P ₄ is of electrical length 2 θ ₂ , of impedance Z ₃ and is a line section charged by a capacitor of capacity C2; where θ ₂ < 135 and the following equalities are verified: $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left(2{\mathrm{\theta }}_2\right)}$$ And $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$ w being equal to 2 πf, with f the operating frequency, and Z _P1P4 being the impedance of the unloaded transmission line section of physical length 3λ/4 equivalent to said loaded line section. Rat-Race balun (10) according to claim 1, in which:
each of the respective transmission line sections between P ₁ and P ₂ , between P ₂ and P ₃ , between P ₃ and P ₄ is a line section of electrical length 2 θ ₁ , of impedance Z ₁ and charged by a capacitor of capacity C and; where θ ₁ < 45° and the following equalities are verified: $$\mathrm{VS}=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_{\mathrm{vs}}\tan \left(2{\theta }_1\right)}$$ And $$Z_1=\frac{Z_{\mathrm{vs}}}{\tan \left({\theta }_1\right)}$$ w being equal to 2 πf, with f the operating frequency, and Z _c being the impedance of the unloaded transmission line section of physical length λ/4 equivalent to said loaded line section. Rat-Race balun (10) according to claim 1 or 2, in which: - the balun has a bean shape and - the ports P ₂ , P ₄ each comprise at least a first section connected to the transmission line, the first section of the port P ₂ being parallel to the first section of the port P ₄ . Rat-Race balun (10) according to claim 3, in which the first section of port P ₂ and the first section of port P ₄ parallel to each other face each other. Balun (10) according to any one of the preceding claims, comprising an impedance transformer loaded by a capacitor between port P ₁ and the transmission line loop. Method for reducing the bulk of a Rat-Race balun comprising a transmission line loop and 4 input-output ports P ₁ , P ₂ , P ₃ , P ₄ connected to said transmission line loop, said balun being adapted to receive a first signal on port P ₁ , and to divide said first signal into a second signal delivered on port P ₂ and a third signal delivered on port P ₄ , said second signal and said third signal being in phase opposition one with the other, in which the ports adjacent to each other among the ports P ₁ , P ₂ , P ₃ , P ₄ are connected by respective sections of the transmission line loop, and at least some of said sections are sections of transmission lines charged by capacitor, said method comprising the following step implemented by an electronic device for determining Rat-Race balun characteristics: - the respective transmission line section between the adjacent ports P ₁ and P ₄ being of electrical length 2 θ ₂ , of impedance Z ₃ and being a line section charged by a capacitor of capacity C2, determination of the impedance Z ₃ and the capacity C2, verifying θ ₂ < 135 and the following equalities: $$\mathrm{VS}2=-\frac{2\tan \left({\mathrm{\theta }}_2\right)}{{\mathit{\omega Z}}_{P1P4}\tan \left(2{\mathrm{\theta }}_2\right)}$$ And $$Z_3=-\frac{Z_{P1P4}}{\tan \left({\mathrm{\theta }}_2\right)}$$ w being equal to 2 πf, with f the operating frequency, and Z _P1P4 being the impedance of the unloaded transmission line section of physical length 3λ/4 equivalent to said loaded line section. Method for reducing the bulk of a Rat-Race balun (10) according to claim 6, according to which, each of the sections of respective transmission lines between P ₁ and P ₂ , between P ₂ and P ₃ , between P ₃ and P ₄ being a section of line of electrical length 2 θ ₁ , of impedance Z ₁ and charged by a capacitor of capacitance C, determination of the impedance Z ₁ and the capacitance C, checking θ ₁ < 45° and the equalities following: $$\mathrm{VS}=\frac{2\tan \left({\theta }_1\right)}{{\mathit{\omega Z}}_{\mathrm{vs}}\tan \left(2{\theta }_1\right)}$$ And $$Z_1=\frac{Z_{\mathrm{vs}}}{\tan \left({\theta }_1\right)}$$ w being equal to 2πf, with f the operating frequency, and
Z _c being the impedance of the unloaded transmission line section of physical length λ/4 equivalent to said loaded line section. Method for reducing the bulk of a Rat-Race balun (10) according to any one of claims 6 or 7, according to which: the balun has a bean shape and the ports P ₂ , P ₄ each comprise at least a first section connected to the transmission line, the first section of the port P ₂ being parallel to the first section of the port P ₄ . Method for reducing the bulk of a Rat-Race balun (10) according to claim 8, in which the first section of port P ₂ and the first section of port P ₄ parallel to each other face each other. Method for reducing the bulk of a Rat-Race balun (10) according to any one of claims 6 to 9, according to which the balun comprises an impedance transformer loaded by a capacitor between port P ₁ and the loop of transmission line.