RF MEMS as a Potential Boosting Technology to RF System Improvement 8

In 1965, an article entitled “Cramming more components onto integrated circuits”

marks an indelible moment in human history. It was this review that firstly investigate the progress in the semiconductor industry [11]. Moore observed that the number of components per chip was roughly doubling every year since the invention of the first commercial transistor in 1959. Based on this observation, he proposed a bold statement, predicting the exponential growth in circuit density. This trend of the growth of components per chip seems to be “a life without tradeoffs” with the benefits of continuous reduced cost per transistor [12]. With the tremendous efforts of countless engineers, these three factors of advancement completely revolutionized the whole integrated circuit (IC) industry and our daily life. For the past 40 years, the number of transistors on a semiconductor device has doubled approximately every 18–24 months. The cost reduced about 25-30% per year, giving birth to many complex, high performance, and low power products. If you spend $1 to buy a transistor in 1965, you can almost buy 10 million

Fig. 1.8. Prediction of number of components per chip. Historical data from 1959 to

transistors now [13].

With the prosperous success in IC industry, the manufacturing process continued to refine and become mature. In 1982, K. Peterson published a widely-cited paper, analyzing the potential of silicon as mechanical material [14]. There are four important traits of silicon to be used as electronic base material, which greatly facilitates commercial success:

(1) low price/abundance; (2) processing based on thin deposited film amenable to miniaturization; (3) production using photographic techniques capable of high precision and amenable to miniaturization and; (4) able to be fabricated in batch [14]. As a result, silicon processing successfully finds new areas of applications and leads to various useful MEMS commercial products.

The concept of Micro-electromechanical system (MEMS) technology can be traced back to 1954 with the paper by Smith [15]. After the paper by Smith, MEMS technology has been successful used in many sensing devices, such as accelerometers, strain gauges, microphones, air mass flow sensors, pressure sensors, gyroscopes and yaw-rate sensors [15]. In Fig. 1.9, there’re several typical MEMS inertial sensors listed.

Compared to conventional MEMS products, RF passive component with MEMS technology is new. The first one came out in the early 1990 when MEMS accelerometers were valuable commercial products already. Coplanar waveguide (CPW) and microstrip implementations of transmission lines were studies first. Gradually there were more and more RF components added to the list of RF-MEMS applications. MEMS provides the potential to miniaturize RF passive components, such as switches, voltage-tunable capacitors, high-Q inductors, film bulk acoustic resonators (FBARs), dielectric resonators, transmission line resonators and filters, and mechanical resonators and filters, which mostly outperform traditional RF components if the cost is not considered [17]. Hence, it’s likely for RF-MEMS to revolutionize the design of the transceiver systems and be expected to solve the serious challenges for the implementation of 5G systems.

There are quite a few components of RF-MEMS anticipated to empower the 5G potential application scenes, especially for the mmWave band listed in [18]: “(1) Very-Fig. 1.9. Photos of some MEMS inertial sensors. (a)–(e): MEMS acceleration sensors, (a) first type of integrated acceleration sensor (1-axis); (b), (c) 2-axes; and (d), (e) 3-axes sensors. (f)–(h): MEMS gyros (f), (g): 1-axis, (h): 2-3-axes [16].

OFF) and very-low adjacent channels cross-talk, working from 2–3 GHz up to 60–70 GHz; (2) Reconfigurable filters with very good stopband rejection characteristics and extremely low attenuation of the passed band; (3) Very-wideband multi-state impedance tuners; (4) Programmable step attenuators with multiple configurations and very flat characteristics over 60–70 GHz frequency spans; (5) Very-wideband multi-state/analogue phase shifters; (6) Hybrid devices with mixed phase shifting and programmable attenuation; (7) Miniaturized antennas and arrays of antennas, integrated monolithically with one or more of the devices.”

The potential market growth is also discussed in [19]. According to the hype curve behavior proposed by Gartner Inc., the trends of new technologies, including RF-MEMS, are depicted in Fig. 1.10, and the market expectation for RF MEMS market from 2004-2013 is shown in Fig. 1.11. Despite several overestimations occurred before, RF-MEMS still finds its market position gradually. Qorvo made more than quadruple of its RF-MEMS sales from 145 $M to 585 $M from 2014 to 2017. Through integrating RF-RF-MEMS switches within RF front ends to increase re-configurability over Wi-Fi, Bluetooth, and cellular bands belonging to 3G and 4G networks, tremendous commercial success is

Fig. 1.10. Typical hype curve behavior elaborated by Gartner Inc. [20].

achieved. However, antenna is one of the key components which is rarely investigated in the field of RF-MEMS previously. Combined with the trends of 5G development and various applications, which will be discussed later, it can be expected that antenna miniaturization will play more and more important role. Before going into practical applications and design examples, antenna miniaturization theory will be briefly reviewed in the upcoming part.

Fig. 1.11. Evolution of RF-MEMS market forecasts released in: (a) 2004; (b) 2006; (c) 2010; (d) 2012; (e) 2013 [21].

1.3 Brief Review on Antenna Miniaturization Theory

Regarding how the fundamental limits of electrically small antennas were achieved, many theoretical works have been done. The approach to analyze such an issue was firstly investigated in Chu’s pioneer paper published in 1948 and quickly followed by Harrington and Wheeler in [22], [23] and [24]. The limits on electrically small antennas are studied firstly by assuming that the entire antenna structure within a sphere of radius r as shown in Fig. 1.12(a), sometimes known as “Chu sphere.” Based on the concept of

Chu sphere, electrically small antennas (or ESAs) are often defined as an antenna that satisfies the condition kr < 1, where k is the wave number ^2𝜋

𝜆. The space outside the sphere was replaced by a number of independent equivalent circuits as shown in Fig.

Fig. 1.12. Antenna within a sphere of radius r, and its equivalent circuit model [25].

1.12(b). For a lossless antenna, a single network section with a series C and a shunt L is identified as the equivalent circuit of each spherical mode [25]. Hence, the combined circuit can be seen as a ladder network of L − C sections (one for each mode) with a shunt resistive load, as shown in Fig. 1.12(c). The resistive load represents the normalized antenna radiation resistance, and the original antenna space problem can now be simplified as a circuit problem.

In addition to theoretical investigation, there are some works trying to examine the validity and existence of Chu limit. In the paper by Daniel F. Sievenpiper et al., the previous theoretical works are reviewed and measurement results are compared based on specific criteria [26]. To start, Q is defined as the ratio of stored energy W to radiated power P at a particular frequency ω for an otherwise lossless antenna,

Q = ω𝑊

𝑃 1.3.1

where W is defined as

W = 2Max(𝑊_𝑚, 𝑊_𝑒) 1.3.2

𝑊_𝑚 and 𝑊_𝑒 and are the time-average, non-propagating, stored magnetic and electric energy. Hansen [27] and later McLean [28] derived an expression for Q of the lowest order mode in terms of the electrical size of the antenna’s

Q = 1 + 2(𝑘𝑎)²

(𝑘𝑎)³[1 + (𝑘𝑎)²]≅ 1

(𝑘𝑎)³ 𝑤𝑖𝑡ℎ 𝑘𝑎 ≪ 1 1.3.3 Collin and Rothschild [29] calculated the energy associated with radiation from the total energy to find expressions for Q of each mode. The value for the lowest order spherical mode is given by

Q = 1

𝑘𝑎+ 1

(𝑘𝑎)³ 1.3.4

In Fante’s work [30], he investigated gain and Q optimization including numerical results

for maximum G/Q. Yaghjian and Best [31] derived the relationship between B and Q through the maximum allowable voltage standing wave ratio VSWR, or s

Bandwith ≈ 1

𝑄(𝑠 − 1

√𝑠 ) 1.3.5

s = 2, Q = 1

√2𝐵_{−10𝑑𝐵} 1.3.6

Since the radiation efficiency is always smaller than 1 and combined with 1.3.3, we can obtain the theoretical upper bound of the bandwidth-efficiency product

𝜂 ∙ Bandwith_{−10𝑑𝐵} <(𝑘𝑎³)

√2 1.3.7

The bandwidth efficiency products versus the electrical size for various published designs were shown in Fig. 1.13 [26]. The curves represents the theoretical limit that is derived by applying 1.3.5 to 1.3.4 using a VSWR of s = 2 and including efficiency 

B𝜂 = 1

√2( 1

𝑘𝑎+ 1

𝑛(𝑘𝑎)³)⁻¹ 1.3.8

where n = 1 for linearly polarized or single-mode antennas, and n = 2 for circularly polarized or dual-mode antennas. It was found that most of the works follow the Chu limit except the one done by Friedman in [32]. However, it was due to the extra matching circuit and the incomplete measurement data.

From the above discussion, we know that it’s inevitable to face theoretical limit and need to tradeoff between bandwidth and efficiency while trying to miniaturize the antenna.

What makes it worse is that traditional antennas adopted for miniaturized component, such as dipole, loop, or patch, struggle with image current effect as well as excessive storage of reactive energy between the radiating element and ground, not to mention ohmic losses. These effects will increase the radiation Q factor, make the antenna difficult to match and essentially kill the radiation efficiency. Hence, there are several works aiming at proposing innovative structure different from traditional one. They try to use mechanical resonance coupled with multiferroic material as the source of electromagnetic radiation. In 2019, the group of Draper Laboratory in Cambridge coined the name of

“mechanical” and “antenna” as “mechtenna” [33]. The basic concept is that mechanical Fig. 1.13. Measured product for 110 antenna designs published in the IEEE T-AP by the end of 2010 [26].

acoustic wave speed are typically several thousands (m/s). However, the speed of light in free space is in the order of 8 (m/s). Assuming that they’re both operating under the same resonant frequency, the mechanical resonant structure can be miniaturized by about the order of 5, which is fundamentally different from conventional one. Various kinds of

“mechtenna” are proposed based on different operational frequencies, integrating diverse antenna structures listed in Table 1. For example, an design for ULF band (300 Hz to 3000 Hz) was studied in [34] and that for UHF (300 MHz to 3 GHz) was discussed in [35], [36]. For UHF band, Zhi Yao proposed a theoretical framework based on FDTD Multiphysics numerical simulation and calculated theoretical lower bound of quality factor of such an antenna in 2015. It was found that this kind of antenna has the potential to approach the Chu limit even down to the size of ka ≪ 1 at the frequency of 1 GHz [35] － [43]. In [36], they firstly measure the RX/TX behavior based on nanoplate resonators (NPR) at around 60 MHz and circular resonating disk made of FeGaB at around 2.5 GHz with the device diameter of only 200 μm, as shown in Fig. 1.14. They Table 1. Summary of mechanical antenna transmitter experiments [33].

However, in Zhi Yao’s framework, ferromagnetic resonance is used to explain magnetoelectric coupling, which indeed requires an external biased magnetic field.

Related research is still relatively new and in need of further study. In [36], it lacks explicit theoretical framework despite of evidences of experiments. Hence, I will still mainly follow the theoretical framework by Zhi Yao in the next sub chapter. This thesis is essentailly based on Zhi Yao’s structure and firstly tries to achieve polarization control with an innovative structure [41]. Before illustrating the operating principle of such devices, let’s look at several potential applications for such an antenna.

Fig. 1.14. ME FBAR antenna demonstrated in [36]. The longitudinal mode is excited and the radiation at 2.5GHz is detected with comparison of FeGaB to Al material.