As frequency bands became crowded with the arrival of 3G and 4G communication technologies, the need for high-performing filters and diplexers, capable of providing adequate frequency separation became even more prominent. Here, such high performing filters/diplexers were not only required to separate neighboring frequency bands, but, at the same limit the amount of insertion losses as losing even a fraction of dB at high transmit powers results in high power losses and creation of heat. This problem was particularly pronounced at the Base Station TX side, due to high powers that needed to be transmitted. As an example, the loss of 1 dB in a base station rated at 50 dBm (100 W), infers a signal loss of 20 W. The situation at the mobile terminal is less demanding since its TX powers are much lower – usually limited to 30 dBm (1W). In this case, the focus is placed on filter/diplexer miniaturization rather than on electrical performance – this is a direct consequence of the fact that it is more forgiving to lose a fraction of power at 1 W, compared to a fraction of power at 100 W.

Given this perspective, choosing a filter/diplexer is highly dependent on the type of the communications system (FDD vs TDD), their location in the system (TX or RX) and whether the filter is to operate within the base station or the mobile terminal. To meet electrical filter/diplexer specifications, the designer has a palette of different filter/diplexer types at their disposal. Examples include cavity filters/diplexers, ceramic filters/diplexers and Printed Circuit Board (PCB) filters/diplexers, to name but a few. Usually, the highest performing filters/diplexers are ceramic based with unloaded Quality (Q_u) factors of individual resonators up to 5,000. They are closely followed by silver-plated metal cavity filters/diplexers with individual unloaded resonator Q-factors of up to 3,000-3,500. PCB resonators are among the lowest performing resonators with individual resonator Q-factors rarely exceeding 200-300, however, this is strongly dependent on the losses of the PCB substrate.  Traditional 3G, 4G and 5G base stations would almost exclusively make use of cavity filters due to their inherent cost advantages over ceramic filters, while being able to satisfy very stringent performance requirements. In some instances, though, one or several resonators in such a cavity filter/diplexer would be replaced by a ceramic resonator to improve its performance and meet specifications.

In addition to requiring excellent electrical performance, filters/diplexers are also required to operate across a wide temperature range, typically between – 40^o C up to + 90^o C, with a minimal impact on the insertion losses in the passband and with a maximum insertion loss increase of no more than 10%. Furthermore, in addition to the electrical and thermal specifications, filter specifications additionally stipulate the maximum form factor, i.e. space that the filter/diplexer can occupy. This point is of extreme importance, especially if one considers the fact that standard diplexers in a Remote Radio Head (RRH) operating below 6 GHz occupy up to 70% of its total volume and a great deal of effort is dedicated to its minimization. In the following, we will examine typical 5G FR1 filter characteristics and show how these can be met.

5G FR 1 filter design

An example of specifications of a typical 5G FR1 [1] base station TX filter with a maximum average RF power handing of 50 dBm are shown in Fig. 1. The return losses are expected to be, usually, lower than -18 dB in the passband.

Fig. 1 Typical 5G FR 1 sub 6 GHz filter specifications

As can be seen, the specifications not only stipulate the performance of the bandpass filter in its passband (3.4 GHz – 3.6 GHz) and its vicinity (3 GHz – 4 GHz), but its performance up to 30 GHz. This is done so that the bandpass filter does not interfere with the operation of other communications devices. The response of a bandpass filter capable of satisfying the filter specifications of Fig. 1 in the frequency range from 3 GHz to 4 GHz, can be shown to consist of at least 8 resonators with 4 cross-coupling sections and the individual resonator Q_u of at least 2,700, Fig. 2. However, the fact that the specifications extend up to 30 GHz infers the spurious response of the individual resonators that the filter is composed of needs to be considered. Standard coaxial resonators coaxial resonators traditionally offer a spurious-free response up to 3 times the fundamental frequency (3*f₀), which would indicate that the proposed bandpass filter would be capable of meeting the specifications up to 10 GHz, but it would fail to meet the remaining specifications of Fig. 1. Ceramic resonators fare much worse, with a spurious-free window being on average between 1.5*f₀ and 2*f₀ wide. An example of a high-performing resonator with a wide spurious-free window is a mini-coax resonator, offering a spurious free performance over 7 times greater than the

fundamental frequency [2].  However, even with such a wide spurious-free-window resonator, it would be difficult to meet the full specifications as indicated in Fig. 1. In such cases, it is necessary to perform additional filtering – this is usually performed by connecting a wide passband low-pass filter with the designed bandpass filter, Fig. 3. The cut-off frequency of such a low-pass filter is positioned above the passband frequencies of the bandpass filter in order not to induce additional filter losses.

Due to their wideband realization, such lowpass filters have low insertion losses, typically between 0.2 dB to 0.3 dB. However, this commensurately increases the total passband losses of the filter structure obtained in this way, Fig. 3. To be exact, the total insertion loss would now be equal to anywhere between 1.55 dB and 1.65 dB, which does not satisfy the requirements of Fig. 1. To ameliorate the situation, the designed 8-pole bandpass filter needs to be composed of higher Q_u resonators so that the combined insertion losses of the filter structure of Fig. 3 are close to 1.35 dB. This is obtained when the Q_u of individual resonators is increased to 3,500, which is a significant increase compared to 2,700 as originally calculated. The increase in Q_u demands either an increase in the resonator size or use of more expensive technologies.

For the physical realization of the proposed bandpass filter, we used an innovative resonator design which makes optimal use of the available volume and requires little or no post-production tuning. The measured Q_u of the proposed bandpass filter resonators is around 3,500, which in combination with a lowpass filter with an insertion loss of 0.25 dB satisfies the filter requirements of Fig. 1. The response of the fabricated bandpass filter is shown in Fig. 4. The response of the simulated bandpass filter is also shown.

5G FR 2 filter design

The design of mm-wave filters/diplexers follows a similar path to that of its sub 6 GHz counterparts, however, there is one significant difference. For example, while the electrical and thermal performance of such filters/diplexers is still important, post-production tuning of all, but PCB-based filters has now gained a greater level of importance. To be exact, nearly every high performing filter/diplexer operating in the sub 6 GHz frequency range needs to be manually tuned for correct frequency and bandwidth of operation. This was usually performed using tuning and coupling screws – the interested reader can refer to our earlier article on how to design and tune an RF filter. Since filters and diplexers operating at sub 6 GHz are several times physically larger than filters/diplexers operating at mm-wave frequencies, it was relatively easy to perform tuning using frequency and coupling screws. However, performing manual filter/diplexer tuning of mm-wave filter is a much more difficult task and therefore more costly. To reduce the cost of such devices, filter suppliers usually provide their filters “as is”, with a degree of detuning being acceptable. From the point of view of applications this is acceptable as the 5G mm-wave frequency bands are not as congested as their sub 6 GHz counterparts and a degree of signal spillover can be tolerated. However, as we move towards greater usage of the mm-wave bands, this is expected to become a problem that needs to be addressed in a cost-effective manner, preferably by obviating post-production tuning altogether. One notable filter example which requires no, or little post-production tuning is the distributed resonator concept, [3-5], Fig. 5. Here, the individual resonator consists of a matrix of sub-wavelength resonant elements closely coupled to each other. Because the resonant frequency of operation of the proposed resonator is no longer a function of only one resonant element, but of the spatial arrangement of many such elements, this makes the frequency of operation of the proposed resonator less prone to manufacturing inaccuracies, thus obviating the need for post-

production, which leads to sizeable cost reductions. The authors refer to this feature as dimensional averaging.

A 6-pole designed filter operating at a centre frequency of 28 GHz with a bandwidth of 3 GHz is shown in Fig. 6 and its response is shown in Fig. 7. The individual resonator has a size of 5 x 5 x 0.4 mm³, corresponding to an electrical height at 28 GHz of only 13^o. It unloaded Q is about 500, which is adequate to yield a maximum insertion loss of about 1.5 dB at band edges, with a minimum return loss of -16 dB. The filter requires no post-production tuning and is expected to be fabricated using metal stamping.

Conclusion

In this article a compact overview on important 5G filter and diplexer characteristics is presented. The article presented a real-world example characteristics that typical 5G FR 1 base station filters need to satisfy and presented main issues associated with 5G FR 2 filters and diplexers.

References

[1] https://en.wikipedia.org/wiki/5G_NR_frequency_bands

[2] E. Doumanis, S. Bulja and D. Kozlov, “Compact coaxial filters for BTS applications”, in IEEE Microwave and Wireless Components Letters, vol. 27, issue 12, pp.1077-1079, 2017

[3] S. Bulja and D. Kozlov, “Multi-layered PCB distributed filter”, Electronics Letters, vol. 57, no. 3, February 2021

[4] S. Bulja and D. Kozlov, “Low-profile and low-volume distributed-split resonators and filters”, IEEE Access, vol. 8, Oct. 2020, doi:10.1109/ACCESS.2020.3037666

[5] S. Bulja and M. Gimersky, “Low profile distributed cavity resonators and filters,” in IEEE Trans. Microwave Theory and Tech., vol. 65, issue 10, pp.3769-3779, 2017

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Bulk-tuneable materials have been, to an extent, used to enable reconfigurable radio components, even though such efforts are still in technological infancy, despite being around for a very long time. The most widely examined bulk-tuneable materials include Liquid Crystals (LCs)[xii]^{,[xiii], [xiv]} , Ferro-Electrics (FE)[xv]^{, [xvi], [xvii]} and, most recently, the pioneering work on Electro-Chromic (EC) materials[xviii]^{, [xix], [xx], [xxi], [xxii],[xxiii],[xxiv]}, proving the link between optical and electrical characteristics. However, these materials have not yielded a great deal of commercial traction, because electrical and size requirements imposed on commercially available RF and mm-wave hardware are very strict and simply cannot be met using the reconfigurable technologies available today. For example, the loss tangents of LC mixtures still tend to be quite large – of the order of 0.03^xiii, which is considered too large for many applications, while their response time is usually of the order of a few ms^xii. FEs, even though offering larger tuneable ranges than LCs exhibit very high dielectric constants which are of limited use for RF and mm-wave applications. The research on EC materials is still in infancy, however it appears to offer a compromise between the LCs and FEs, with an added benefit of exhibiting a strong memory effect. The devices and architectures that these traditional bulk-tuneable materials can support in the context of future networks is therefore limited to niche devices encompassing phase shifters, attenuators, to name but a few, where the integration with semiconductor technologies is easier.

However, recently there has been a great deal of progress towards the use of Resistive Switching (RS) exhibited by a new type of bulk controllable material, Transition Metal Oxides (TMOs)[xxv]^,[xxvi]. Several TMOs have been investigated, such as VO_x[xxvii]_,   TiO₂[xxviii] , NiO[xxix], SrTiO₃[xxx] to name but a few as bulk switching elements. The oxides of vanadium have been found to offer excellent electrical performance at mm-wave frequencies[xxxi]^{, [xxxii], [xxxiii], [xxxiv], [xxxv]}. As an example,[xxxvi], a 200 nm thick VO₂ layer deposited using reactive laser ablation on a CPW (Coplanar Waveguide) to form series and parallel switch configurations, was characterised from 5 GHz to 35 GHz. The achieved dynamic range observed is of the order of 25 dB with an insertion loss of about 0.8 dB. The switching speed of VO_x is highly dependent on the deposition technique and is reported to be in the range of several ns down to ps[xxxvii]^{, [xxxviii], [xxxix]} . Characterisation of TMOs other than VO_x and their use in the context of RF & mm-wave devices has been virtually unexplored due to technological delay in responding to demands for very low-power, low-cost and very fast non-semiconductor switches, apart from the work by Bulja which reported on the characterisation of amorphous WO₃, TiO₂ and NiO as a function of the dc bias[xl]. In any case, TMOs appear to hold the promise of cost effectiveness while at the same time being able to be deposited on almost arbitrary surfaces, using different printing techniques, such as inkjet printing[xli],[xlii]. It is of further importance to mention the possibility of inducing bulk-material tunability based on bulk-material switches (TMOs), as shown by Bulja[xliii].  From this aspect, a question could be posed as to whether these new materials could be utilized in the context of novel ways of computing? And more specifically, will novel computing ways utilize bulk-material switches or bulk dielectric tunability? How would such a structure look like?

A possible answer to that question lies with Intelligent Surfaces (IS).  To this end, IS have attracted a great deal of attention recently, since they allow the attainment of re-configurability, which is of great importance in the context of 5G and upcoming 6G and beyond specifications. In particular, IS in the form of Intelligent Reflective Surfaces (IRS) have been used to mitigate harmful effects of the wireless environment by their virtue and ability to redirect incoming signals towards a specific path. This ability is usually achieved by controlling some parameters of meta-atoms, such as the phases and amplitudes. The controlling elements can be managed through either a semi-conductor device, Micro-Electro-Mechanical Switch (MEMS) or LCs[xliv], depending on the parameter of the meta-atoms that are being controlled. In turn, this allows the IRS to manipulate the incident wavefront to achieve steering, adjustable absorption, polarisation, filtering and collimation[xlv]. However, the losses and latency times of the constituent materials limit their application range[xlvi]. Given this premise of IS, it is only natural to ask if the combination of new bulk switchable materials (TMOs in this case) and IS, could lead to the creation of new types of reconfigurabilities, namely computation in the natural domains of radio signals? This will sufficiently take advantage of the very nature of IS, create new ways of computation and act as an enabler of 6G technologies. Let us explore how this could possibly be implemented.

Analogue computing – Implementation

To perform spatial computation on a radio signal impinging on an arbitrary surface, it is imperative to have adequate control of the dielectric characteristics of such a medium with granularity that is commensurate with the wavelength at which computation is to be performed. In computational Electro-Magnetics (EM), reasonable accuracy is achieved using at least 10 cells for a given wavelength, with higher accuracies possible with a denser mesh. It was shown that the control of dielectric permittivity and magnetic permeability of a medium allows for control of functionality of such a medium[xlvii], [xlviii]. To this end, the concept of digital metamaterial bits was introduced in[xlix], where it was shown that using two EM

Fig. 1: Schematic depiction of an experimental setup to demonstrate analogue computation on radio waves, realizing a single-frequency, single-antenna object imaging system (in transmission and/or reflection)[i]

metamaterials, one can synthesize an EM metamaterial with desired dielectric properties at a given frequency of operation. This concept opened a new way of perceiving metamaterials, which led to the extension of the concept to variable, coding metamaterials^l, ultimately used to control the radiation characteristics of a smart surface. The realisation that metamaterials with a pre-described dielectric permittivity can be used to perform mathematical operations, was already shown[i], [ii],  however it was only for static cases. For a medium to perform arbitrary mathematical operations, the static case is of little value. To perform an arbitrary mathematical operation, the dielectric permittivity of the medium needs to be externally controllable to a local level and to yield a dielectric permittivity distribution across the entire medium. This is only achievable using bulk reconfigurable materials, such as TMOs mentioned earlier.  The exact physical realizations of such devices are difficult to predict at this stage, however, one possible realization is shown in Fig. 2, which indicates that the radio signal incident on the structure,  will emerge altered on the other end of the structure as . The extent of change of the incident signal is proportional to the distribution of the dielectric characteristics across the structure. As the means of enabling dielectric reconfigurability, TMO inspired structures can be used. As an example, the extent of dielectric reconfigurability can be maximized by interlacing dielectrics and sub-skin depth TMO, as shown in an earlier concept introduced by Bulja^xliii.

Each pixel (cell) of Fig. 2 will consist of such an interlaced dielectric-TMO- dielectric structure, will be individually addressable and be able to change its constituent parameters (composite dielectric permittivity) upon actuation (application of dc bias voltage). The highest frequency of operation, , of structures obtained in this way will be dictated by pixel resolution, i.e. number of cells per wavelength and the dielectric characteristics of the medium obtained using the following formula:

Here, c stands for the velocity of light,  for the composite relative dielectric permittivity and  stands for the number of cells at the upper frequency of operation. Since reasonable accuracy in computational EM is obtained using at least 10 cells per wavelength and that the macroscopic dielectric permittivity of standard dielectrics is around , it becomes possible to estimate the upper frequency of operation of structures obtained in this way. For a resolution of 1 mm, the highest frequency of operation becomes 17.3 GHz, whereas for the case of ultra-precise 3D printing resolution of 5 μm, the highest frequency of operation becomes 3.46 THz. However, these are estimates only and that the final values will be decided upon testing and evaluating the extent of dielectric reconfigurability in interlaced TMO structures. The extent of dielectric reconfigurability will be dependent on the examined TMO, the dielectric carrier substrate and their corresponding thicknesses.

and ON (metallic). Possibilities exist to extend the concept to multi-layered or stacked structures, expected to provide a greater granularity of achievable dielectric permittivities across the surface.

It needs to be understood that the concept this is a concept only and there are many unknowns as to how the proposed solution will work. For example, there exist serious questions regarding how one can bias such structures, the palette of mathematical functions one will be able to perform using the structure and the extent of signal reflections taking place at the boundary of the surface. At present, there are no answers to this, and this article does not intend to provide them in any case.

Summary

This article reviewed analogue computing and presented a vision of how, in the context of advanced 5G and forthcoming 6G applications and advancements in the development of new materials, analogue computing performing mathematical operations directly on radio signals is worth investigating. In doing so, the article provided a brief historical aspect on analogue computing, reviewed the current state-of-the art of bulk-reconfigurable materials, IS and the current structures used to perform “static” computation directly on radio signals. Based on this and through a thought experiment, the article proposed new structures capable, at least in principle, of performing a palette of mathematical functions in a dynamic fashion. In doing so, the article aims to challenge the traditional way of thinking, approaching and solving problems, leading to the ultimate realization that computing can be performed by anything and anywhere.

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The same principles apply to Electro-Magnetic (EM) waves, since light is, effectively, an EM wave. Every radiated EM signal will get partially reflected and partially transmitted at the interface between media with different propagation environments. This also holds true for microwave circuits, where it is imperative to minimize reflections and, hence, maximize transmission.  The extent of reflections in a microwave circuit, Fig. 1, is represented by the reflection coefficient, 𝛤, given by:

(1)  𝛤= (z_in-z_o)/(z_in+z_o)

From (1) it can be seen that the lowest level of reflections are achieved when the input impedance of the microwave circuits, , is identical to . Delivering maximum power to any microwave circuit is not only beneficial from the point of view of maximizing the efficiency of the microwave circuit, but, also, from the point of view that high levels of reflections can incur damage to the signal source. This is particularly true for the case of active devices, where unwanted load reflections lead to device instability, unwanted oscillations and, ultimately, device failure.

The design of impedance matching circuits is a well-covered topic in many RF textbooks, such as in [1] and they mostly cover narrow-band impedance matching. Typically, in such approaches either lumped elements or their distributed element counterparts (for high frequencies) are used. However, there exist applications, especially at mm-wave frequencies, where wideband impedance matching is required.

In the next section, as an example, we will design an impedance matching circuit to reduce reflections in a measurement system required to infer unknown dielectric characteristics of a material.

Design of wideband impedance matching circuit

Measurements of unknown dielectric characteristics of a material is a very important task and is required to determine the suitability of use of such a material in microwave circuits. However, measurements of such characteristics are adversely affected by high reflections since in that case very little RF power reaches the material under test and even less RF power reaches the output.

In this example, we will design a broadband impedance matching network for the measurement of dielectric characteristics of Liquid Crystal (LC) mixtures at mm-wave frequencies, 30 GHz to 60 GHz in particular. To this end, we are interested in using a microstrip line structure similar to the one in [2], where the compartment for the LC mixtures in under the microstrip line, as shown in Fig. 2. The width of the microstrip line exposed to the LC compartment is wider than the width of the microstrip at the input and output. The primary reason for this is two-fold. First, in order to adequately capture the behavior of the unknown dielectric characteristics of the LC mixtures, the microstrip line should not be too narrow as this make dielectric parameter extraction less immune to fabrication imperfections, resulting in reduced accuracy and increased uncertainty of the results. Second, the height of the LC compartment is dictated by

the fact that LC mixtures switching is best observed when substrate heights are not greater than 100 μm, inferring that narrow microstrip lines may not sufficiently well capture the dielectric behavior of the LC mixtures. Due to this, wider microstrip lines are required for the section exposed to LC mixtures, inferring that the corresponding characteristic impedance is quite low. Even though such wide microstrip lines are useful for the characterisation of LC mixtures, the low characteristic impedance and, hence, wide microstrip lines result in impedance mismatch at the input and output, Fig. 3 (a). In the present case, the dielectric permittivity of the bottom and top dielectric materials is  and , respectively. With reference to Fig. 3 (a), where the microstrip line is 1 mm wide, this results in a characteristic impedance of approximately 16 Ω, whereas the termination impedance is 50 Ω. The reflection coefficient obtained this way for the length of the line length of 4 mm, is presented in Fig. 3 (b), in the frequency range from 20 GHz to 60 GHz. As can be seen, the return losses exhibit resonant behavior indicating that the line is not matched in an appropriate termination impedance.

To improve impedance match over a wide frequency range, a tapered microstrip line is used. Tapered  microstrip lines act as wide-band impedance transformers, provided their electrical length is at least half-wavelength at the lowest frequency of operation.  This is depicted in Fig. 4 (a) where one end of the microstrip line is equal to 1 mm, with a characteristic impedance of 16 Ω (wide end) and the other end is narrow with its width equal to 0.19 mm with a characteristic impedance of 50 Ω. The length of the transition section is 2 mm, corresponding to, approximately half-wavelength at a frequency of 30 GHz. The reflection coefficient of the line obtained this way is shown in Fig. 4 (b), in the frequency range from 20 GHz to 60 GHz. As can be seen, excellent impedance matching of lower than -11 dB is achieved over the frequency

range 30 GHz to 60 GHz. This allows for over 90 % of the total input power to reach the LC compartment. Since the measurements are concerned with the extraction of the unknown dielectric parameters of LC mixtures, the effect of the transitions will need to be taken into account. This can be readily performed using the procedure developed in [3]. As a matter of fact, transitions developed in this way are widely used in the broadband characterisation of  unknown dielectric materials. Examples include the measurement of LC mixtures in [3], Electro-Chromic (EC)  materials [4], [5], Transition Metal Oxides, [6] and many others.

References:

[1] D. M. Pozar, “Microwave Engineering”, fourth edition, 2011.

[2] S. Bulja and D. Mirshekar-Syahkal, “Novel wideband transition between coplanar waveguide and microstrip line”, IEEE Trans. Microwave Theory and Tech., vol. 58, issue 7, pp.1851-1857, 2010.

[3] S. Bulja, D. Mirshekar-Syahkal, M. Yazdanpanahi, R. James, F. A. Fernandez and S. E. Day, “Measurement of dielectric properties of nematic liquid crystals at milimeter wavelength”, IEEE Trans. Microwave Theory and Tech., vol. 58, issue 12, 3493-3501, 2010.

[4] S. Bulja, R. Kopf, A. Tate & T. Hu “High frequency dielectric characteristics of Electro-chromic, WO₃ and NiO films with LiNbO₃ electrolyte”, in Nature, Scientific Reports, June 2016.

[5] S. Bulja, R. Kopf, K. Nolan, R. Lundy, A. Tate, T. C. Hu, M. Norooziarab, R. Cahill and W. Templ, “Tuneable dielectric and optical characteristics of tailor-made inorganic electro-chromic materials”, in Nature, Scientific Reports, October 2017.

[6] S. Bulja et al., “High frequency resistive switching behavior of amorphous TiO₂ and NiO”, in Nature Scientific Reports, August 2022, https://doi.org/10.1038/s41598-022-16907-8.

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