Rat-race balun and method of reducing rat-race balun footprint therefor

Abstract

The invention relates to a Rat-Race balun comprising a transmission line loop and 4 input-output ports P1, P2, P3, P4 connected to said transmission line loop, the respective transmission line section between the adjacent ports P1 and P4 is of electrical length 2θ2, of impedance Z3 and is a line section loaded by a capacitor of capacitance C2; ​​where θ2 < 135 and the following equalities are verified: C2=−2tanθ2ωZP1P4tan2θ2 and Z3=−ZP1P4tanθ2 w being equal to 2πf, with f the operating frequency, and ZP1P4 being the impedance of the unloaded transmission line section of physical length 3λ / 4 equivalent to said loaded line section.

Description

Technical field:

[0001] The invention lies in the field of Rat-Race type baluns. Previous technique:

[0002] The term balun comes from the English words BALanced and UNbalanced.

[0003] A balun is an electrical circuit used to connect a balanced transmission line (two-wire line or parallel printed lines) to an unbalanced transmission line (coaxial cable or printed line above a ground plane). A balun can be made, for example, using coiled coaxial cable or a small section of two-wire line wound on a ferrite core or a coreless mandrel (air-core 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 half the wavelength. This type of balun is single-frequency; in fact, it only functions correctly over a narrow frequency band, a few percent of the wavelength. Baluns are also implemented on printed circuit boards, using microstrips or striplines, for example.

[0004] A Rat-Race balun is a loop-shaped component, typically ring or square, with four ports (1, 2, 3, 4) such that an incoming signal on port 1 is split between ports 2 and 4 in opposite 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 split 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.

[0005] A Rat-Race type balun can also be used to combine signals: at port 3 is delivered the difference between two signals injected into the input of the balun, after phase correction, one at port 2, the other at port 4 and at port 1 is delivered, after phase correction, their sum.

[0006] US 2022 / 0263212 describes an example of a Rat-Race type balun.

[0007] US 10320049 B2 describes an annular directional coupler, particularly for microwave distance sensors.

[0008] US 7639102 B2 describes reconfigurable duplexing couplers.

[0009] US 8416033 B2 describes a compact, dual-band, metamaterial-based hybrid ring coupler.

[0010] There is a need to reduce the size of Rat-Race type baluns on the electronic media on which they are integrated. Summary of the invention :

[0011] To this end, according to a first aspect, the present invention describes a Rat-Race balun, comprising a transmission line loop and four input / output ports P1, P2, P3, and P4 connected to said transmission line loop. The balun is adapted to receive a first signal on port P1 and to split said first signal into a second signal delivered on port P2 and a third signal delivered on port P4. The second and third signals are out of phase with each other. Adjacent ports P1, P2, P3, and P4 are connected by respective sections of the transmission line loop, and at least some of said sections are capacitor-loaded transmission line sections. The balun is characterized in that the respective transmission line section between adjacent ports P1 and P4 has an electrical length of 2 θ 2, impedanceZ 3 and is a section of line loaded by a capacitor connected to ground with capacitance C2; ​​where θ 2 < 135 and the following equalities are verified: C 2 = − 2 tan θ 2 ωZ P 1 P 4 tan 2 θ 2 And Z 3 = − Z P 1 P 4 tan θ 2 w being equal to 2πf , with f being 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.

[0012] Such a balun makes it possible to reduce the size of Rat-Race type baluns on the electronic media on which they are integrated.

[0013] In some embodiments, such a balun shall further include at least one of the following features: Each of the respective transmission line sections between P1 and P2, between P2 and P3, and between P3 and P4 is a line section of electrical length 2 θ 1, impedance Z 1 and charged by a capacitor of capacitance C and; where θ 1 < 45° and the following equalities are verified: C = 2 tan θ 1 ωZ c tan 2 θ 1 And Z 1 = Z c tan θ 1 w being equal to 2 πf, with f being 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 ports P2, P4 each have at least one first section connected to the transmission line, the first section of port P2 being parallel to the first section of port P4; the first section of port P2 and the first section of port P4 parallel to each other face each other; the balun has an impedance transformer loaded by a capacitor between port P1 and the transmission line loop.

[0014] According to another aspect, the invention describes a method for reducing the size of a Rat-Race balun comprising a transmission line loop and 4 input / output ports P1, P2, P3, P4 connected to said transmission line loop, said balun being adapted to receive a first signal on port P1, and to split said first signal into a second signal delivered on port P2 and a third signal delivered on port P4, said second and third signals being out of phase with each other, wherein the adjacent ports among ports P1, P2, P3, P4 are connected by respective sections of the transmission line loop, and at least some of said sections are capacitor-loaded transmission line sections, said method comprising the following step implemented by an electronic device for determining the characteristics of a Rat-Race balun: the respective transmission line section between adjacent ports P1 and P4 being of electrical length 2 θ 2, impedance Z 3 and given a line section loaded by a capacitor connected to ground with capacitance C2, determination of the impedance Z 3 and the C2 capability, verifying θ 2 < 135 and the following equalities: C 2 = − 2 tan θ 2 ωZ P 1 P 4 tan 2 θ 2 And Z 3 = − Z P 1 P 4 tan θ 2 w being equal to 2 πf, with f being 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.

[0015] In some embodiments, such a process will further include at least one of the following features: each of the respective transmission line sections between P1 and P2, between P2 and P3, and between P3 and P4 being a line section of electrical length 2 θ 1, impedanceZ 1 and loaded by a capacitor of capacitance C, determination of the impedance Z 1 and of capacity C, verifying θ 1 < 45° and the following equalities: C = 2 tan θ 1 ωZ c tan 2 θ 1 And Z 1 = Z c tan θ 1 w being equal to 2 πf, with f being 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 ports P2, P4 each have at least one first section connected to the transmission line, the first section of port P2 being parallel to the first section of port P4; the first section of port P2 and the first section of port P4 parallel to each other face each other; the balun has an impedance transformer loaded by a capacitor between port P1 and the transmission line loop. Brief description of the figures:

[0016] The invention will be better understood and other features, details and advantages will become clearer from the following description, given by way of non-limiting example, and from the accompanying 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 conventional lines with loaded lines; Fig. 3 ] There figure 3 is a functional balun diagram 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 one 3λ / 4 charged line and three equivalent λ / 4 charged lines; Fig. 7 ] There figure 7 represents a method for reducing the size of a balun in one embodiment of the invention; [ Fig. 8 ] There figure 8 represents a top view of a printed circuit board of a push-pull device of the type shown in figure 1 with a bean-shaped balun.

[0017] Identical references may be used in different figures when they refer to identical or comparable elements. Detailed description:

[0018] There figure 1 schematically represents a push-pull type electronic processing module 1 in an embodiment of the invention, for example operating at high frequency and integrated, on a printed circuit board, in the last stage of an emission chain of an electronic radio communication device.

[0019] 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 narrowband, for example less than 20 MHz wide, or even 15 MHz and at powers up to 1.5 kW peak.

[0020] As is well known, power transistors have a low input impedance compared to the standard 50 Ω impedance and are typically composed of two chips (which can be considered equivalent to two transistors), in a push-pull configuration here. This necessitates splitting the input signal and shifting the two signals by 180° before feeding them to the transistor's input. The fact that the input signals to the HPA 11 are out of phase helps reduce interference caused by amplification on two closely spaced chips.

[0021] For this purpose, the processing module 1 includes upstream of the HPA 11 a balun 10 in an embodiment of the invention.

[0022] The input signal of the processing module 1, typically an RF pulse train in the L band (in the example considered with power In 47 dBm, and load rate 2%), is supplied to the input of port P1 of the balun 10. The power of this input signal is P.

[0023] The two output signals from ports P2 and P4, of the same power P / 2 (at + / -0.2 dB % for example) and in opposite phase to each other, are supplied one at the input of one of the two chips of the HPA 11, the other at the input of the other of the two chips of the HPA 11.

[0024] At the output of HPA 11, the two amplified signals, which are out of phase, are supplied to the input of a balun 12, one on its port P2, the other on port P4. The balun 12 realigns these signals with each other and delivers the sum of these two realigned signals at its output on its port P1.

[0025] The input impedance of balun 10 is Z 0 , which is much greater than each of the input impedances ZE and output impedances ZS of HPA 11. For example, Z 0 = 50 Ω and ZE , ZS less than 20 or even 10 Ω (especially if LDMOS transistor), for example here 2.5 Ω.

[0026] Balun 10, here built on a printed circuit board (PCB) with microstrips for example, has transmission line sections between each port P1, P2, P3, P4.

[0027] In a first embodiment, each transmission line section between two adjacent ports, conventionally, has a physical length (in meters) of λ / 4, except for the section between adjacent ports P1 and P4 (i.e., the section that does not include ports P2 and P3), which has a physical length of 3λ / 4, where λ is the wavelength corresponding to the center frequency of the input signal of processing module 1. The electrical length corresponding to the physical length λ / 4 is equal to 90°. As is known, "electrical length" is a theoretical way of expressing wavelength without having to consider the circuit environment: PCB (printed circuit board), etc. In practice, this means that a wavelength λ corresponds to 360°. Theoretically, for a specific application, the same wavelength ratio must be maintained.The propagation of EM waves depends on the medium, therefore depending on the substrate λ (in m) changes, but not its associated length (always 360°).

[0028] The impedance of the unloaded transmission line of physical length λ / 4 is Z c.

[0029] In a second embodiment, each quarter-wave line section considered in the first embodiment is replaced by its equivalent in a transmission line loaded by a capacitor.

[0030] In terms of physical dimensions, these equivalent sections differ, but in terms of behavior (if we study parameters S for example) they are identical, as shown by a narrowband observation.

[0031] 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 In the case of a ring-shaped balun: each transmission line section of length λ / 4 (as shown on the left of the figure 2 ) is thus replaced (as shown to the right of the figure 2 ) by a transmission line section of electrical length 2 θ 1, of impedance Z1 and loaded as a capacitor, i.e. by two transmission line segments each of electrical length θ 1 and impedance Z 1 intersected by a capacitor connected in parallel, of capacitance C, and therefore connected to ground.

[0032] We then have the following equalities: Z 1 = Z c tan θ 1

[0033] And equality 0_2: C = 2 tan θ 1 ωZ c tan 2 θ 1 where w is the angular frequency, i.e. ω = 2 πf , with f the operating frequency of the balun, i.e. the center frequency of the signal.

[0034] A 52% reduction in balun size, corresponding in particular to the choice of a value of θ 1 less than 45° was obtained in one example of implementation.

[0035] The reduction ratio depends on the θ 1 chosen, and also of the PCB (in particular its dielectric permittivity parameter) ε r ) considered. There is a reduction as soon as θ 1 < 45°: there is a reduction in line length, which depends heavily on the PCB used. Furthermore, since Z1 is inversely proportional to tan( θ1), that tan(45°) = 1 and that the tangent 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 line width, which depends heavily on the PCB used, largely on its thickness.

[0036] The capacitance value of the capacitor and the impedance of the loaded line segments can be deduced from the equations above relating them to the electrical length. θ 1 chosen less than 45°. Impedance being a function of the physical width of the microstrip, the latter are determined according to the impedance Z1 (Z1 here designating the impedance of the type impedance characteristic loaded lines, i.e. the impedance that an input line would have if it were of infinite length: it does not depend on the length).

[0037] 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).

[0038] In Shamaileh et al., the impedance change was an effect that is experienced by the authors.

[0039] The proposal here is to exploit this change in impedance: the longer the θ The smaller the loaded sections, the higher their impedance. Therefore, when using a balun operating at low impedance, there is more leeway to reduce line lengths before reaching the manufacturability limits associated with line widths. This allows for a component with very thin, short lines operating at low impedances.

[0040] However, to meet one of the HPA specificities mentioned above, a balun 10 is needed that operates at low output impedances P2, P4.

[0041] In a third embodiment of balun 10, the second embodiment is modified in that the line section 3 λ / 4 between adjacent ports P1, P4 is replaced by its equivalent inline, loaded with a single capacitor this time, of capacitance C2, as shown in the functional diagram of the figure 3 This section of the line then consists of two transmission line segments, each with impedance Z3 and electrical length θ 2, interspersed with a parallel capacitor of capacitance C2, which is also connected to ground.

[0042] This topology is more restrictive than the previous one shown in the second embodiment, because the impedance of the two sections replacing line 3 λ / 4 is then, unlike before, proportional to their electrical length.

[0043] This stems from the fact that θ 2 ∈ π 2 3 π 4 mod π and that the tan() function is negative and increasing on this interval. The minus sign in the equality 0_3 "transforms" the tan() function into an equivalent of the abs(tan) function on this interval. Now abs(tan( θ 2))≥1 on π 2 3 π 4 mod π .

[0044] A further reduction in the size of balun 10 can be achieved 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 using the following equalities 0_3 and 0_4.

[0045] This additional reduction is obtained in particular if 3 θ 1 > θ2 and if we work with a substrate and impedances that do not generate too large a difference in line width between the impedances Z1 and Z3 (i.e. if we work with a substrate, which, depending on the impedances Z1 and Z3 used, does not generate an increase in line width that would cause an overall increase in the area covered by the balun, despite the decrease in line length); an example of a standard criterion is that the length must be at least 3 times the width. Z 3 = − Z P 1 P 4 tan θ 2 Or Z P 1 P 4 is the impedance of the equivalent transmission line section between adjacent ports P1P4, of physical length 3λ / 4 and unloaded. C 2 = − 2 tan θ 2 ωZ P 1 P 4 tan 2 θ 2

[0046] This necessitates compromises between the impedances of the different line segments of the balun: to reduce the size of the balun, one must either decrease the electrical length of its lines or increase their impedance; however, in the case of the 3λ / 4 line loaded with a single capacitor, these two parameters are proportional, so a compromise is necessary. The impedance of the λ / 4 lines must also be considered; if it is too different from that of the 3λ / 4 line, the impedance mismatch could reduce performance. Conversely, if they are too close, then this means that θ 1 is close to 45° and therefore the reduction of the lines λ / 4 is less important.

[0047] The capacitance C and impedance Z values ​​for each segment of length 2 θ1 connecting the adjacent points P 1 , P 2 , respectively connecting the adjacent points P 2 , P 3 , and connecting the adjacent points P 3 , P 4 , remain, themselves, determined by application of the equations 0_1 and 0_2 above.

[0048] The shape of a Rat Race balun commonly used is circular or square and is therefore not ideal, especially for use in a push-pull 10 type processing module on a printed circuit board, which has a long, narrow structure.

[0049] In a fourth embodiment, it is therefore proposed to make the balun 10 in a "bean" shape (in the plane in which the printed circuit board extends), as shown in figure 4 , instead of a ring shape such as that shown in figures 2 And 3. This new topology allows the two ports P 2 , P 4 to be oriented towards the HPA 11 transistor, while having an input port P 1 oriented in the opposite direction, via, for example, an impedance transformer.

[0050] In one embodiment, with reference to the figure 4 The bean-shaped balun 10 comprises a perimeter 41 made up of transmission line sections. In the counter-clockwise direction, the section between ports P2 and P4 is concave, and then the section between P4 and P2 is convex.

[0051] With reference to the figure 4 Each capacitor in the loaded line sections is connected on one side to the transmission line forming perimeter 41 and on the other side to ground via one of the vias (represented by small circles in figure 4 ) in zone 40 which is inside the perimeter of the bean balun 10.

[0052] In one embodiment, the bean-shaped balun 10 is constructed using circular arcs between the four consecutive ports, and the lengths of these arcs are fixed according to the inter-port lengths calculated according to one of the first, second, and third embodiments. Combining this bean shape with the use of loaded lines as described in the second and third embodiments allows for a significant reduction in line size.

[0053] 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 capacitance 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 circles; 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.

[0054] In one embodiment, sections 52, 54 of ports P2 and P4 immediately connected to the bean-shaped body of the balun 10 (extending in the plane of the printed circuit board) are parallel to each other and extend (in embodiments where their length is non-zero) in the same direction, OF, from the bean-shaped body of the balun 10. In one embodiment, these two parallel sections are identical.

[0055] In one embodiment, a section 51 of port P1 (extending in the plane of the printed circuit board) of balun 10 is parallel to the sections of ports P2 and P4 and extends in one direction from balun 10 in an opposite direction, DO. In one embodiment, it is replaced by a parallel resistor

[0056] As described above and in a conventional manner, in this embodiment as well, the input signal is supplied to the input of the bean-shaped balun 10, at port P1; the signal transmitted through the balun 10 undergoes power division and phase inversion, and the signals at the outputs of pots P2 and P4 have a power equal to half the power of the input signal and are in phase inversion. Port P3 of the balun 10 is isolated (connected by a load to ground) in the processing module shown in figure 1 .

[0057] At the output of balun 10, the impedance is for example 12.5 Ω, then matching circuits (length different from λ / 4) are arranged between HPA 11 and balun 10 to lower the impedance to ZE if necessary (an impedance transformer in a known way includes transmission lines having increasing or decreasing diameters to modify the impedance).

[0058] A balun 10 corresponding to embodiment 2 and / or 3 is particularly suitable for narrowband applications.

[0059] The embodiments described above can be implemented independently or in combination: for example, in one embodiment of the invention, the bean-shaped balun 10 is combined with one of the first, second, and third balun embodiments. Each embodiment provides a balun with a reduced footprint.

[0060] 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 size of the processing module 1. Similar to what has been explained with respect 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 loaded by a capacitor, which is shorter than the unloaded equivalent.

[0061] The balun 10 according to the invention is therefore a signal splitter, with or without impedance transformation depending on the case, which is miniaturized and optimized with capacitor-loaded transmission lines. The invention advantageously replaces the historical solution combining an impedance transformer λ 4 associated with a phase shifter λ 2 The invention is even more interesting for low permittivity substrates (FR-4 or RO4350b, low-cost substrates), where the bulk of the conventional solution is even more significant.

[0062] Compared to the standard solution, the footprint is significantly reduced: for an FR4 HP substrate with a dielectric permittivity constant of 4.34 and a height of 0.245 mm, a reduction of approximately 80% is observed, as shown in the table below, when combining embodiments 3 and 4 with a loaded transformer. This depends on the minimum line width and the power rating of the lines and capacitors. [Table 1] Historical solution Common solution Clutter ε r = 4,34, h = 0,245 mm ε r = 4,34, h = 0,245 mm S = 40 * 40 = 1600 mm 2< S = 16,5 * 19,6 = 323 mm 2< Discount of almost 80% Means Microstrip lines Microstrip lines and 5 to 7 capacitors Or 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.

[0063] There figure 8 Figure 1 represents a top view of a printed circuit board of a push-pull device 1 in one embodiment of the invention. The balun 10, or 12 respectively, has a kidney-shaped form according to the fourth embodiment (see frame 10_1, or 12_1 respectively). Frame 10_2, or 12_2 respectively, indicates the location of the impedance transformer (the transformer load is not visible in this figure).

[0064] With reference to the figure 7 , a method for reducing the size of a Rat-Race Balun is now described.

[0065] In one embodiment, in a step 101 of the design of such a Balun Rat-Race, for example corresponding to the second embodiment, a space-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 satisfying the equalities 0_1 and 0_2 such that θ 1 <45°.

[0066] For example, the substrate to be used is known, so the dimensions of the lines based on the impedance and dielectric length can be anticipated. The operating impedance is known, θ 1 is chosen arbitrarily (while respecting the condition θ 1 <45°), depending on the values ​​of Z1 and C obtained. It is verified that the associated lines are technically feasible and meet the requirements. Based on this verification, it is decided to retain this θ1 or modify it accordingly. The search is refined at each θ 1.

[0067] In another embodiment, the space-saving module further determines the values ​​of Z 3, θ 2 and C2 satisfying the equalities 0_3 and 0_4 such that θ 2 <135°.

[0068] The balun is then manufactured taking these characteristics into account.

[0069] In a design step 102, with the electrical lengths of the line sections between balun ports defined, the footprint reduction module determines, based on these lengths and the actual line impedances, the definition data for a bean shape for a Rat-Race balun and ports, to obtain a bean balun as described above for example.

[0070] Steps 101 and 102 can also be implemented independently of each other.

[0071] Such a process makes it possible to obtain a push-pull assembly including the Rat-Race Balun built under these conditions, and occupying a small footprint.

[0072] The process can 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 (e.g., FPGA / Field Programmable Gate Array). Justification for obtaining the equalities 0 3 and 0 4 :

[0073] In figure 5 are represented: on the left (section a): a conventional transmission line (i.e. not loaded by capacitors) of physical length 3λ / 4 and electrical length θ q = 270° and on the right (section b): the equivalent capacitor-loaded transmission line, in the form of only two line sections, each of impedance Z cl and electrical length θ cl, with a capacitor C in parallel, arranged between the two sections.

[0074] Matrix (1) below provides the ABCD parameters for the conventional transmission line of physical length 3λ / 4: A q B q C q D q = cos 270 jZ q sin 270 jZ q − 1 sin 270 cos 270 = 0 − jZ q − jZ q − 1 0

[0075] Next, to have an equivalent, we need to have an equality between (1) and the matrix ABCD of a short-circuited shunt (2) multiplied on both sides by the matrix of a truncated capacitor (3), represented by (4): M c = A c B c C c D c = 1 0 jωC 1 M cl = A cl B cl C cl D cl = cos θ cl jZ cl sin θ cl jZ cl − 1 sin θ cl cos θ cl M q = M cl M c M cl

[0076] Equality (4) allows us to establish the following equations: A q = cos θ cl 2 − ωCZ cl sin θ cl cos θ cl + jZ cl − 1 sin θ cl B q = j Z cl sin θ cl cos θ cl − jωCZ cl 2 sin θ cl 2 + cos θ cl 2

[0077] Thanks to the correspondence between (1) and (5.a), (6) is determined: ωC = 2 Z cl tan 2 θ cl

[0078] Then, by substituting (6) into (5.b), (7) appears. Z cl = − Z q tan θ cl

[0079] Finally, using (6) and (7), the value of the capacity used in the equivalent loaded line is equal to C = − 2 tan θ cl ωZ q tan 2 θ cl

[0080] As C > 0, it follows that: tan θ cl < 0 and tan 2 θ cl > 0 Or tan θ cl > 0 and tan 2 θ cl < 0

[0081] Using conditions (9.a) and (9.b), and taking into account that Z cl > 0, the only possible values ​​for Θ cl are : θ cl ∈ π 2 3 π 4 mod π

[0082] The goal is to reduce the length of the 3λ / 4 transmission line by replacing the three λ / 4 loaded lines with a single 3λ / 4 loaded line as shown in figure 6 It is necessary to find the condition for: 3 π 2 > 6 θ cl 3 > 2 θ cl

[0083] To satisfy (11), it is necessary to take condition (10) into account. Finally, the loaded 3λ / 4 line can exhibit a size reduction for: θ cl ∈ π 2 3 π 4 mod π

[0084] Through an ADS simulation, it was demonstrated that the miniaturized rat-race couplers exhibit the same performance for three λ / 4 lines loaded with capacitors and for one 3λ / 4 line loaded with a capacitor.

[0085] Beyond miniaturization, these new aspects provide greater flexibility regarding impedance value.

Claims

1. Rat-race balun (10), comprising a transmission line loop and 4 input-output ports P1, P2, P3, P4 connected to said transmission line loop, said balun (10) being designed to receive a first signal on the port P1, and to divide said first signal into a second signal that is delivered to the port P2 and a third signal that is delivered to the port P4, said second signal and said third signal being in phase opposition with one another, wherein the ports adjacent to one another from among the ports P1, P2, P3, P4 are connected by respective sections of the transmission line loop, and at least some of said sections are capacitor-loaded transmission line sections; said balun being characterized in that: the respective transmission line section between the adjacent ports P1 and P4 is of electrical length 2θ2, of impedance Z3 and is a line section loaded by a capacitor connected to the ground and of capacitance C2 ; where θ2 < 135 and the following equalities are satisfied: C 2 = − 2 tan θ 2 ωZ P 1 P 4 tan 2 θ 2 and Z 3 = − Z P 1 P 4 tan θ 2 w being equal to 2πf, with f the operating frequency, and ZP1P4 being the impedance of the unloaded transmission line section of physical length 3λ / 4 equivalent to said loaded line section.

2. Rat-race balun (10) according to Claim 1, wherein: each of the respective transmission line sections between P1 and P2, between P2 and P3, between P3 and P4 is a line section of electrical length 2θ1, of impedance Z1 and loaded by a capacitor connected to the ground and of capacitance C and; where θ1 < 45° and the following equalities are satisfied: C = 2 tan θ 1 ωZ c tan 2 θ 1 and Z 1 = Z c tan θ 1 w being equal to 2πf, with f the operating frequency, and Zc being the impedance of the unloaded transmission line section of physical length λ / 4 equivalent to said loaded line section.

3. Rat-race balun (10) according to Claim 1 or 2, wherein: - the balun is kidney-shaped and - the ports P2, P4 each comprise at least a first section connected to the transmission line, the first section of the port P2 being parallel to the first section of the port P4.

4. Rat-race balun (10) according to Claim 3, wherein the mutually parallel first section of the port P2 and first section of the port P4 face one another.

5. Balun (10) according to any one of the preceding claims, comprising an impedance transformer loaded by a capacitor between the port P1 and the transmission line loop.

6. Method for reducing the footprint of a rat-race balun comprising a transmission line loop and 4 input-output ports P1, P2, P3, P4 connected to said transmission line loop, said balun being designed to receive a first signal on the port P1, and to divide said first signal into a second signal that is delivered to the port P2 and a third signal that is delivered to the port P4, said second signal and said third signal being in phase opposition with one another, wherein the ports adjacent to one another from among the ports P1, P2, P3, P4 are connected by respective sections of the transmission line loop, and at least some of said sections are capacitor-loaded 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 P1 and P4 being of electrical length 2θ2, of impedance Z3 and being a line section loaded by a capacitor connected to the ground and of capacitance C2, determining the impedance Z3 and the capacitance C2, satisfying θ2 < 135 and the following equalities: C 2 = − 2 tan θ 2 ωZ P 1 P 2 tan 2 θ 2 and Z 3 = − Z P 1 P 4 tan θ 2 w being equal to 2πf, with f the operating frequency, and ZP1P4 being the impedance of the unloaded transmission line section of physical length 3λ / 4 equivalent to said loaded line section.

7. Method for reducing the footprint of a rat-race balun (10) according to Claim 6, wherein, each of the respective transmission line sections between P1 and P2, between P2 and P3, between P3 and P4 being a line section of electrical length 2θ1, of impedance Z1 and loaded by a capacitor of capacitance C connected to the ground, determining the impedance Z1 and the capacitance C, satisfying θ1 < 45° and the following equalities: C = 2 tan θ 1 ωZ c tan 2 θ 1 and Z 1 = Z c tan θ 1 w being equal to 2πf, with f the operating frequency, and Zc being the impedance of the unloaded transmission line section of physical length λ / 4 equivalent to said loaded line section.

8. Method for reducing the footprint of a rat-race balun (10) according to any one of Claims 6 and 7, wherein: the balun is kidney-shaped and the ports P2, P4 each comprise at least a first section connected to the transmission line, the first section (52) of the port P2 being parallel to the first section (54) of the port P4.

9. Method for reducing the footprint of a rat-race balun (10) according to Claim 8, wherein the mutually parallel first section (52) of the port P2 and first section (54) of the port P4 face one another.

10. Method for reducing the footprint of a rat-race balun (10) according to any one of Claims 6 to 9, wherein the balun comprises an impedance transformer (42) loaded by a capacitor (37) between the port P1 and the transmission line loop (41).

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