диафрагмированные волноводные фильтры / 5f42dc0b-ef40-41f3-9bed-f472ab30a8e1

1. Introduction

For decades, it is well known that rectangular waveguide (RW) technology has been widely used for microwave devices, including filters and dividers [1, 2]. However, its high fabrication cost, bulky size, and heavy weight cannot satisfy the requirements for certain communication systems and integration with planar circuits. About two decades ago, substrate integrated waveguide (SIW) has been proposed, not only offering a high-power capability with reduced processing complexity and cost, but also allowing integration with active components on a single substrate. SIW components could be inspired by their RW counterparts, and power dividers are not an exception. For instance, the configuration of the SIW power divider/combiner in [3] is derived from a five-port waveguide power divider.

Power dividers, extensively used in the microwave and millimetre-wave systems, could be alone to excite an antenna element or other devices [4], or can be cascaded to form a feeding network with multiple branches [5]. The amplitude ratio of the dividing power could also be customized [6, 7]. Furthermore, dividers could be integrated with couplers or phase shifters to build networks with required phase or power distributions [8, 9], or be embedded with filters for out-of-band rejection [10].

Baluns are special cases of dividers, offering two out-of- phase signals with equal amplitudes, for undesired signal cancellation. To obtain out-of-phase signals in an SIW balun, two microstrip lines could be fabricated on opposite sides of a printed circuit board (PCB) panel [11], or the imbalanced signals could be realized by the SIW phase shifters etched on the same side of the panel [12]. Nevertheless, the behaviour of SIW baluns is dominated by the characteristics of the power-dividing part, which in reported designs has limited bandwidth. In addition, the pure TE20 mode could also be utilized for its intrinsic field distribution where the

electric field amplitude in the middle is zero, and such mode could potentially be excited by the wave mode transducer [13]; however, the complex feeding network could deteriorate in-band reflection and increase the insertion loss [14]. For SIW baluns with enhanced bandwidth, wideband dividers are in great demand.

SIW power dividers can be grouped into the T-type and Y-type divider categories [15]. In the reported RF performance, there is a sharp transmission zero in the operational band of the Y-type divider, limiting the available bandwidth. The existence of the transmission zero is also mentioned in [16, 17], but without further details. In [18], with a taper transition, the transmission zero is slightly shifted to a higher frequency range, permitting an improvement in the bandwidth performance. Nevertheless, the transmission zero still remains and has not been sufficiently investigated yet, even if the SIW Y-type divider has become a key passive device.

To improve the isolation, additional resistance is used in a Wilkinson divider [19] or is placed at the E-plane arm of a modified magic-T [20]. For higher isolation, complicated multiport configurations where the extra ports are terminated with resistance or absorbing material are proposed [3, 21]. The half-mode [22] and quarter-mode [23] SIW divider are employed for miniaturization or other purposes, with the disadvantage of increased insertion loss. As a result, the research on SIW dividers focuses on miniaturization, increased isolation between dividing ports and more complex multilayer or vertical structures [24, 25]. There are very few SIW Y-type dividers with improved bandwidth feature in the standard enclosed, lossless and three-port configuration.

In this paper, a wideband SIW balun is presented, which could be fabricated on PCB panels. The proposed broadband SIW balun consists of an improved SIW Y-type divider with a dramatically expanded bandwidth and reversely placed transitions for out-of-phase signals. In Section 2, both

Fig. 1. Configuration of a traditional SIW Y-type divider

contributing parts of the proposed balun are described in detail, followed by the design procedure of the balun. The transmission zero in dividers are analysed for the first time, with the coupling between the TE10 and TE30 modes employed to ‘remove’ the transmission zero. For demonstration, the SIW balun is manufactured by PCB process. Section 3 shows the measured results of the fabricated baluns and a comparison with other reported SIW designs. Finally, a conclusion is drawn in Section 4.

2.Broadband dividing part, reversely placed transitions and design procedure of the balun

2.1. Configuration of the broadband dividing part

In Section 2.1, the SIW Y-type divider is investigated and is improved in bandwidth, serving as the dividing part of the

‘designed balun’ for equal power splitting. Fig. 1 depicts the configuration of a traditional SIW Y-type divider. The entire structure includes three regions along the propagation axis: the region I – the input terminal with one SIW only, the region II – the coupling region with a constant width where the multiple modes may exist simultaneously, and the region III – the output terminal composed of two parallel SIW output ports.

Fig. 2 shows three reported SIW dividers and the proposed SIW divider, along with their corresponding electric field distributions. An SIW divider where the coupling region II has a short length and a constant width, is referred to as ‘divider 1’ [11] in Fig. 2a. An SIW divider where the coupling region II has a long length and a constant width, is referred to as ‘divider 2’ [15] in Fig. 2b. An SIW divider with a taper in the front and a constant

Fig. 3. Simulated S11 of four SIW dividers in Fig. 2

width structure in the back of the coupling region II, is referred to as ‘divider 3’ [18] in Fig. 2c. Finally, the ‘proposed divider’ consisting of an extended width in the front and a constant width in the back of the coupling region II, is illustrated in Fig.2d.

In Fig. 2, ‘divider 1’ has the shortest coupling region and is an extensively used structure, with the electric field distribution shown in Fig. 2a and the simulated S11 shown in Fig. 3. The frequency band of operation is usually between the cut-off frequencies (fc) of the TE10 and TE20 modes of SIW in the region I, and it also depends on the in-band reflection. The electric field distribution in Fig. 2a illustrates that only the TE10 mode propagates in the coupling region II and little space is provided to high order modes. However, the reflection in the operational frequency band deteriorates as shown in Fig. 3, and only in a narrow frequency band, the reflection is better than 20 dB. Due to the multi-reflection, the performance may be improved slightly by the cascaded transitions [11], whereas the behaviour of the powerdividing part takes the dominant role.

In Fig. 2b, the length of the coupling region II in ‘divider 2’ is a little longer than that in ‘divider 1’ and the relevant S11 of ‘divider 2’, shown as a dotted line in Fig. 3, presents a transmission zero in the X-band; this problem is also reported in [15-17, 26], but with no further analyses or no solution. If the equivalent widths of the region I and II are set as a and b (b = 2 × a), respectively, one can calculate the cut-off frequencies of the modes in these two regions. Based on the RW theory and that only TEn0 modes propagate in SIW [27], cut-off frequencies of the first several modes in the region I and the coupling region II of ‘divider 2’ are roughly shown in Fig. 4. Due to its symmetric geometry,

Fig. 4. Cut-off frequencies (fc) of the first several modes in the region I and the coupling region II of ‘divider 2’

only odd modes can be excited when the TE10 mode propagates into the coupling region II from the input port 1, and therefore, we can ignore the even modes in Fig. 4. Since the width b of the coupling region II is twice as wide as the width a of the region I, the cut-off frequency of the TE30 mode in the coupling region II (the corresponding λc is 2b/3) is located between the first two cut-off frequencies in the region I (the corresponding λc are 2a and a, respectively). Given that a < 2b/3 = 4a/3 < 2a, the TE30 mode is possible to be excited in the coupling region II. In the operational frequency band, there is only the TE10 mode propagating in the region I of ‘divider 2’. When the signal propagates into the coupling region II, the wider cross-section allows not only the TE10 mode but also the TE30 mode. The electric field distribution at the transmission zero is illustrated in Fig. 2b. In the front part of the coupling region II, there are two electric field centres off the midline, indicating two coexisting odd modes (the TE10 and TE30 modes). The coupling between these two odd modes cause a TE20-alike mode in each SIW pathway in the region III; however, each SIW pathway in the region III can only support one TE10 mode in the operational frequency band, consequently leading to the transmission zero and splitting the X-band into two sub-bands in Fig. 3.

The coupling region II of ‘divider 3’, given in Fig. 2c, is partly tapered for broadband [18] and the corresponding S11 is shown in Fig. 3. The front width of the taper transition is narrower than the coupling region II of ‘divider 2’, which means a higher cut-off frequency of the TE30 mode in this tapered section. As a result, the position of the transmission zero in Fig. 3 is shifted to the higher frequency range, from 10.54 GHz for ‘divider 2’ to 11.59 GHz for ‘divider 3’.

However, the transmission zero still remains in the X-band, and the maximum fractional bandwidth of 20 dB reflection loss can only be achieved to around 35% [18]. In Fig. 2c, the electric field distribution of ‘divider 3’ at 11.59 GHz shows the co-existence of the two odd modes, and it is similar to that of ‘divider 2’ at 10.54 GHz in Fig. 2b, demonstrating the shift of the transmission zero.

Therefore, before designing an independent SIW divider or a dividing part in a balun, a trade-off between reflection and bandwidth should be taken into consideration.

To reduce the reflection at the transmission zero, the coexistence of the two odd modes is employed. As analysed, the transmission zero is caused by the higher-order mode, rather than the dominant mode alone. Thus, the step impedance matching method preferred in cases of the single mode is not employed in this paper. In Fig. 3, the frequency range of the transmission zero of ‘divider 2’ is narrow and is only noticeable with a small frequency increment in the simulation and measurement. Inspired by a five-port divider using high order modes to affect the TE10 mode [1], a

symmetric structure is presented in Fig. 2d, which is the

‘proposed divider’ of broadband.

By widening the front part of the coupling region II, more space is provided for the excitation of the TE30 mode at the discontinuity. Given that the propagation constants of the TE10 and TE30 modes are different and they are dependent on the width of SIW, the phase difference between these two modes can be adjusted by partly modifying the widths and length of the coupling region II. With proper dimensions, in the back part of the coupling region II, electric fields of the TE10 and TE30 modes will add along the midline and subtract each other at bilateral sides, which is also different from the situation in [1]. Therefore, the corresponding condition can be roughly expressed as

constants in the front and back part of the coupling region II;30 and 30 are the TE30 mode propagation constants in the front and back part of the coupling region II; Lf and Lb are the lengths of the front and back of the coupling region II; and n = 1, 2, 3 …. In practice, the phase difference between the TE10 and TE30 modes in the back part of the coupling region II may not be equal to 2π exactly. The little phase shift is employed to control the electric field powers of these two odd modes at bilateral sides, to ensure the subtraction of these two modes and a single electric field centre at the back. Experimentally, the proper dimensions of the coupling region II are extracted, and the step-by-step design procedure is presented in Section 2.3.

As a result, the electric field distribution of the ‘proposed divider’ in Fig. 2d is similar to that of ‘divider 1’ in Fig. 2a, presenting a single electric field centred at the back of the coupling region II, which is then divided into two identical TE10 modes passing the SIW pathways in the region III. It should be noted that the widened section in the front and the constant-width section in the back of the proposed coupling region II cannot be swapped. Otherwise, the whole coupling region II will be similar to the coupling region II of ‘divider 3’ in Fig. 2c and then would have less impact on the transmission zero. The simulated S11 of the ‘proposed divider’ is presented as a solid line in Fig. 3. With the transmission zero removed, the two sub-bands can be merged in the proposed structure, and the frequency band of 20 dB reflection loss can cover the entire X-band, from 8 to 12 GHz. The typical fractional bandwidth obtained by the

‘proposed divider’ is about 40%, and Fig. 3 illustrates that the ‘proposed divider’ is superior to any other reported divider. Due to its wideband feature, the ‘proposed divider’ is set as the dividing part of the ‘designed balun’.

2.2. Reversely placed transitions

In Section 2.2, a wideband transition from SIW to microstrip line in [28] is used to obtain imbalanced signals. Two identical transitions are connected to the dividing ports of the ‘proposed divider’, but with one transition upside down.

For a stand-alone transition between SIW and microstrip line, the in-band reflection could be better than 25 dB, if the thickness of the PCB panel is under a certain value [28]. Such a transition in [28] is utilized directly and connected to the dividing part from Section 2.1. At the two dividing ports

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Fig. 5. Electric field distribution at the cross-section of the two reversely placed transitions

of the ‘proposed divider’, one transition is etched on the top and the other is etched on the bottom In Fig. 5, a crosssection of the two reversely placed transitions is illustrated with the electric field distribution. The narrow metal represents the signal line of the microstrip line and the wide metal stands for the ground line. The electric field directions in both microstrip lines are the same, while the fact that one microstrip line is placed upside down results in different electric field orientations. With SMA connectors soldered, the electric field in one coaxial line will be terminated at the inner conductor, while the electric field in the other coaxial line on the other side will be terminated at the outer conductor, achieving a 180-degree phase difference. For smooth power transmission from coaxial lines to microstrip lines, grounded pads are added for soldering, and the perspective view of the whole pattern with physical parameters is shown in Section 2.3.

2.3.Design procedure of the proposed ‘designed balun’

b

Fig. 6. Configuration of the ‘designed balun’ composed of the reversely placed transitions and the proposed wideband Y-type divider

(a) Perspective view with each layer, (b) Top view with physical parameters

Fig. 7. Simulated S11 of ‘divider 2’ with different length of the coupling region II (different l2)

In Fig. 6, the ‘designed balun’ utilizing the ‘proposed divider’ and reversely placed transitions are shown. The grey area represents the top metal layer of the PCB panel, and the dashed-line area represents the bottom metal layer; only planar patterns on the PCB panel are illustrated, without SMA connectors soldered. The dividing part is the

‘proposed divider’ in Section 2.1 and has the dominant role in the quality of the entire balun structure. The reversely placed transition part is from Section 2.2, and the electric field distribution at the reference plane A in Fig. 6b is previously illustrated in Fig.5.

The design steps of the proposed wideband balun are as follows:

(i) Calculate the width of the SIW input port 1 (wSIW). By treating SIW as an equivalent RW [27], the value of wSIW

could be computed, based on the frequency of interest and dielectric constant of the PCB material.

(ii)Design the initial dividing part, similar to ‘divider 1’ in

Fig. 2a. In this circumstance, the two dividing SIW ports are placed in parallel and directly follow the SIW input port 1.

w1 and l1 in Fig. 6b are equal to 0. The value of l2 is small, making the dividing part the same as ‘divider 1’, in Fig. 2a.

(iii)Determine the value of l2, making the dividing part similar to ‘divider 2’ in Fig. 2b. In the simulation, l2 should be increased gradually. A transmission zero will show up in the process, leading to two sub-bands. In ‘divider 1’, the length of the coupling region II is 13 mm, and the transmission zero is at 12.74 GHz, beyond the X-band in Fig.

3. In ‘divider 2’, the length of the coupling region II is increased to 16.6 mm, and the transmission zero moves to 10.54 GHz. There is a certain value of l2 achieving a levelling between two sub-bands, like the solid black line in

Fig. 7. Under current conditions, l2 is equal to 16.6 mm. As shown in Fig. 7, when l2 is smaller or larger than this certain value, the reflection in one sub-band will be much better than that in the other sub-band.

(iv)Determine the values of w1 and l1, with the fixed l2. The value of l2 acquired from the previous step should remain. The excited TE30 mode, which is used to eliminate the inband transmission zero, is affected by w1 and l1. Experimentally, w1 = 2.36 × wSIW, and l2 = 2.20 × l1, which could be the initial values for further optimization. Ultimately, there will be a combination assembling two noncontiguous bands together.

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Table 1 Optimized dimensions of the SIW balun (unit: mm)

(v)Obtain a wideband power-dividing part based on the ‘proposed divider’, by following the previous four steps. It could also be used as an independent power divider alone.

(vi)Use the equations and the relevant theory presented in [28] for designing the transition. Such wideband transitions should be placed reversely at the dividing ports of the

‘proposed divider’, as shown in Fig. 6.

In Fig. 6b, d stands for the diameter of via, and pitch is the distance between centres of adjacent via. The values of d and pitch follow the rules to reduce the possible leakage and rely on the tolerance of the PCB process and feature of the PCB panels. The values of the relevant physical parameters in dividing part and reversely placed transitions are listed in Table 1.

3. Fabricated prototypes and measurement

In this paper, simulations are carried out by ANSYS HFSS. Rogers 6002 is used for fabrication, with a thickness of 0.762 mm and a dielectric constant of 2.94. Two kinds of

a b c d Fig. 8. Photographs of fabricated SIW baluns

(a) Top and (b) Bottom of the fabricated balun based on ‘divider 2’, (c) Top and (d) Bottom of the fabricated

‘designed balun’ based on ‘proposed divider’

baluns are fabricated and photographs are shown in Fig. 8.

One is the ‘designed balun’ in Fig. 6, which is based on the ‘proposed divider’; the other is based on ‘divider 2’, with a long coupling region II of constant width, and other dimensions are kept the same as in Table 1. In the measurement, the input port and one output port of the fabricated baluns are connected to a two-port vector network analyser (VNA), with the other output port loaded by a 50 Ohm terminator.

Fig. 9a shows the simulation and measurement of the balun, which has a long coupling region II of constant width and is based on ‘divider 2’ in Fig. 2b. It is obvious that a transmission zero splits the X-band into two sub-bands, constraining the available bandwidth for applications. Due to the multi-reflection, the reflection loss (RL) at the

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Fig. 9b and c show the simulation and measurement of the ‘designed balun’ where the dividing part is based on the

‘proposed divider’ and which is the fabricated prototype of

Fig. 6. Compared with the reflection loss in Fig. 9a, the transmission zero in Fig. 9b is reduced, and the separated bands merge. The measured reflection of the proposed balun at the input port is below -15 dB from 8.23 to 12.89 GHz, achieving a fractional bandwidth of 43.94%. The insertion loss to one balanced port is better than 0.9 dB in the frequency band of interest. In Fig. 9c, the amplitude and phase imbalance between the two imbalanced ports are below 0.7 dB and ±3 degree, respectively. Due to that it is to expand the available bandwidth of the traditional powerdividing part, the isolation between two output ports remains the typical value in the entire band, which is around 6 dB. The discrepancy between measurement and simulation could be mainly attributed to the fabrication tolerance and the soldering condition at each port. In addition, the threeport balun is measured by the two-port VNA and the 50 Ohm terminator could influence the measured imbalance between two output ports. The air gap between SMA connectors and edges of the fabricated prototype could also lead to a slight shift of the frequency band and more reflection loss. On the whole, a good agreement between simulation and measurement is obtained, showing the validity of the proposed configuration.

A comparison is conducted between previously reported SIW designs and the fabricated balun from Fig. 6, as shown in Table 2. Most of these designs are three-port components, except [3], but the dividing parts of them follow a similar pattern, making the comparison reasonable. From the first five rows in Table 2, it can be concluded that the ‘designed balun’ based on the ‘proposed divider’ achieves a wider band and better in-band reflection. In addition, although two baluns in [14] are added for comparison, they are based on transitions between planar transmission lines and SIW, where one port of the power-dividing part in baluns is not SIW. The inherent electric field distribution of the TE20 mode naturally provides wide band and great amplitude imbalance, but the slotline excitation in [14]-type A causes more insertion loss and the aperture coupling excitation in [14]-type B requires multiple layers; therefore, those two types of baluns are difficult to be integrated inside the subsystems. Apart from that, the in-band reflection of the fabricated ‘designed balun’ behaves much better. Therefore, the proposed wideband balun with the improved powerdividing part is superior to other SIW baluns.

4. Conclusion

In this paper, a broadband SIW balun is designed, by improving the bandwidth of the power-dividing section. The main novelty lies in the reduction of the transmission zero, which limits the bandwidths of the previously reported designs. The coupling between the TE10 and TE30 modes is utilized in the proposed dividing part of the balun, and the design procedure of the balun is presented. For verification, the ‘designed balun’ composing of the ‘proposed divider’ and the reversely placed transitions is fabricated on the PCB panel by standard processing, and the measurement agrees well with the simulation. The measured reflection loss of 15 dB is obtained from 8.23 GHz to 12.89 GHz. In the frequency band of interest, the phase imbalance is within ± 3 degree, and the amplitude imbalance is below 0.7 dB. The proposed configuration is promising for broadband applications.

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