Gain Enhancement of On-Chip Electrically Small Slot Antennas Through Monolithically Integrated Piezoelectric Transformers

1. Introduction

The rapid expansion of the Internet of Things (IoT) continues to drive a demand for antennas that can be integrated into increasingly compact systems [1,2,3]. Fortunately, IoT links often tolerate reduced data rates in favor of a longer battery lifetime for wireless devices [4]. This enables the use of electrically small antennas (ESAs) in wireless sensor nodes [5,6,7,8]. Yet, using ESAs in wireless devices often yields reduced read range and increased bit-error-rate (BER) due to the ESAs’ low realized gain ($G_{\mathrm{realized}}$). In practice, this low gain stems from the inability of matching the very small radiation resistance of ESAs to $50\Omega$ with conventional lumped components (i.e., inductors and capacitors) without introducing significant ohmic losses [9,10].

Motivated by this limitation and by the prospect of achieving chip-scale radiofrequency identification (RFID) tags operating in the Ultra-High-Frequency (UHF) range, a significant attention has been paid over the past decade to alternative electrically small antenna systems. Among them, those based on piezoelectric radio-frequency (RF) microelectromechanical systems (MEMS)-based devices have attracted particular interest because they can transform ESAs’ radiation impedances to $50\Omega$ without resorting to lossy inductors and capacitors. Currently, the most pursued RF MEMS-based approach for this purpose focuses on RF magnetoelectric (ME) antennas [11]. These devices, operating in the RF range, embed magnetostrictive (MS) thin films within RF MEMS bulk acoustic wave (BAW) [12,13,14] or surface acoustic wave (SAW) resonators [15,16]. Most RF ME antennas reported to date rely on RF MEMS devices based on Aluminum Nitride (AlN) or Aluminum Scandium Nitride (AlScN), with the latter enabling larger fractional bandwidths than AlN for the same device size [14]. These ESAs exploit the large strain generated when an RF MEMS device is driven at its mechanical resonance frequency to dynamically modulate the magnetization of the embedded MS layer, which enables intrinsic gains ($G_{\mathrm{intrinsic}}$) orders of magnitude higher than those achievable by solely relying on the oscillating electric dipole moment generated by the piezoelectric layer. Moreover, exploiting an acoustic vibration mode naturally provides a pathway to excellent matching to $50\Omega$ without the need for lossy electronic lumped components. Altogether, these features enable RF ME antennas to achieve $G_{\mathrm{realized}}$ two orders of magnitude higher than those of conventional ESAs with comparable dimensions [11]. However, RF MEMS-based ME antennas require the integration of an MS layer, which complicates their fabrication in conventional RF MEMS foundries [17,18,19] and poses a major obstacle to scaling RF ME antenna technology toward large-scale manufacturing. For this reason, researchers have looked for alternative RF MEMS-based ESAs not relying on MS layers.

Recently, a new class of acoustically mediated piezoelectric (AMP) antennas has been reported [20,21,22]. Among them, in 2025, an RF MEMS-based ESA was presented, wherein a ${\mathrm{LiNbO}}_3$ Rayleigh wave resonator built on a ${\mathrm{LiNbO}}_3{64}^{\circ }$Y-cut substrate and fed using an asymmetrical ground-signal-pad structure has shown the ability to boost $G_{\mathrm{realized}}$ in an on-chip electrical dipole antenna by enabling improved matching to $50\Omega$ [21]. While this seminal demonstration has certainly paved a new pathway for RF MEMS devices to enable ESAs with higher $G_{\mathrm{realized}}$ than conventional electromagnetic counterparts without requiring MS layers, the device reported in [21] sees its performance limited by the low $G_{\mathrm{intrinsic}}$ of the electrical dipole. Also, in its current form, it still shows modest matching to $50\Omega$ (it does not present a quantifiable -10 dB $S_{11}$ fractional bandwidth).

In this work, we report an alternative RF-MEMS-based ESA architecture with improved $G_{\mathrm{realized}}$ and smaller form factor than the previous AMP ESA in [21]. The reported architecture consists of a monolithically integrated RF MEMS piezoelectric transformer (TRX) driving an array of two ESAs. The TRX has two purposes: (1) enable good matching to $50\Omega$ and (2) provide a passive voltage amplification that effectively increases $G_{\mathrm{intrinsic}}$ for the slot-array compared to what the slot-array achieves when connected directly to a $50\Omega$ source. From now on, we will refer to this system as TRX-ESA.

We also describe the first prototype of this architecture, built on a YZ $0^{\circ }$ X-cut ${\mathrm{LiNbO}}_3$ substrate through a single-step lithographic fabrication process. The TRX-ESA prototype, operating at 425 MHz and relying on a shear-horizontal ($S{H}_0$) mode transduced by a leaky surface acoustic wave (LSAW) TRX [23,24,25], shows a $G_{\mathrm{realized}}$ of -12.7 dBi, which, to the best of our knowledge, represents the highest gain ever recorded for RF MEMS-based ESAs. Such measured gain level closely matches the value we predicted using a simulation framework that we also present for the first time in this work. Our prototype also shows a large -10 dB $S_{11}$ bandwidth and greatly improved return loss compared to the previous AMP ESA in [21], thanks to the large electromechanical coupling coefficient ($k_t^2\approx 35\%$) of the TRX device.

In the next sections, we describe the principle of operation of the reported TRX-ESA system, the simulation framework we developed to predict its achievable performance, and a study of the impact of the TRX’s quality factor (Q) and $k_t^2$ on the highest achievable gain enhancement. Next, we report on the design of the LSAW device, followed by a discussion on the measured performance of the TRX-ESA prototype designed and built in this work.

2. Principle of Operation

The TRX-ESA presented in this work comprises two on-chip slot antennas on a YZ $0^{\circ }$ X-cut ${\mathrm{LiNbO}}_3$ substrate, driven by the output voltage of a UHF $S{H}_0$-mode LSAW piezoelectric transformer (TRX). The TRX is designed to maximize $G_{\mathrm{realized}}$ at a target frequency ($f_{\mathrm{target}}=425\mathrm{MHz}$). A top-view schematic of the TRX-ESA system, along with its in-plane dimensions, is reported in Figure 1. In the next subsections, we first examine the intrinsic radiation characteristics of the slot array using numerical and analytical methods. We then clarify the role of the LSAW device and show that its inclusion enhances both $G_{\mathrm{intrinsic}}$ and $G_{\mathrm{realized}}$ for the slot array by acting as a piezoelectric transformer [26]. This is done first through a simplified analytical model and then through actual circuit simulations capturing more realistic electromechanical and RF models for the TRX-ESA prototype reported in this work.

2.1. Intrinsic Radiation Characteristics of the Array of Slots

The slot array integrated into the reported TRX-ESA system consists of two electrically small rectangular slots, which are created by opening two gaps in the metallic pad structure normally used to test an LSAW device with a ground–signal–ground (GSG) probe (Figure 1). Each slot has a width ($W_{\mathrm{slot}}$) of $875\mu \mathrm{m}$, accounting for the presence of lateral fringing fields, and a gap ($L_{\mathrm{slot}}$) of $100\mu \mathrm{m}$, resulting in an aperture area per slot ($A_{\mathrm{slot}}$) equal to $8.75\times {10}^{-8}{\mathrm{m}}^2$ and in an estimated capacitance of the slot ($C_{slot}$) of $0.8\mathrm{pF}$. Moving forward, we will model the underside of the ${\mathrm{LiNbO}}_3$ wafer as being backed by a metallic plane acting as a perfect electric conductor (PEC). This assumption reflects our measurement conditions, where the TRX-ESA system operates in close proximity to a conductor (i.e., the metallic chuck of our probe-station).

Following the standard aperture-antenna formalism, we analyze the radiation from each slot by defining an equivalent bounded volume (V) consisting of the ${\mathrm{LiNbO}}_3$ slab within the slot’s aperture. By applying the equivalence principle [27], the tangential component of the electric field across each side of the slab can be replaced by an equivalent magnetic current density. Since the electric field in each slot, ${\mathbf{E}}_{\mathrm{slot}}$, is mainly oriented along $\widehat{\mathbf{x}}$ and $\widehat{\mathbf{y}}$ (i.e., the z-component of ${\mathbf{E}}_{\mathrm{slot}}$ is negligible) and since we are assuming the presence of a PEC under the ${\mathrm{LiNbO}}_3$ chip, the only equivalent magnetic current density that can contribute to the far field radiation is the one corresponding to the top surface of V. This magnetic current density has components along $\widehat{\mathbf{x}}$ and $\widehat{\mathbf{y}}$ with magnitude proportional to the magnitude of the ${\mathbf{E}}_{\mathrm{slot}}$ components along $\widehat{\mathbf{y}}$ (i.e., ${\mathbf{E}}_{\mathrm{slot}}^y$) and $\widehat{\mathbf{x}}$ (i.e., ${\mathbf{E}}_{\mathrm{slot}}^x$) respectively. Now, since the reported TRX-ESA system is symmetric along the y-axis (Figure 1), the equivalent magnetic current densities along $\widehat{\mathbf{y}}$ for the two slots are equal in magnitude but shifted by ${180}^{\circ }$ in phase. This implies that their contribution to the far-field power radiated can be neglected. Consequently, we retain only the x-component of the equivalent magnetic current density for the top surface of each slot, shown in Eq. (1).

$$\mathbf{M}=-2\widehat{\mathbf{z}}\times {\mathbf{E}}_{\mathrm{slot}}^y,$$

(1)

The factor “2” in Eq. (1) comes from the image theorem [27] (i.e., the TRX-ESA system operates above a PEC). For best accuracy, we extract $|{\mathbf{E}}_{\mathrm{slot}}^y|$ for different input voltages ($V_{\mathrm{in}}$) applied to the signal pad of our GSG probing area directly from finite element analysis (FEM) simulations. To this end, we consider an ad-hoc simulated geometry in which the LSAW TRX is electrically replaced by an ideal short. Next, we simulate ${\mathbf{E}}_{\mathrm{slot}}^y$ in each slot for a $V_{in}$ equal to 1 V (see Figure 2) and compute its spatial average (${\overline{\mathbf{E}}}_{\mathrm{slot}}^y$) over the slot area. This allows us to approximate ${\mathbf{E}}_{\mathrm{slot}}^y$ as [Eq. (2)]:

$${\mathbf{E}}_{\mathrm{slot}}^y\approx {\overline{\mathbf{E}}}_{\mathrm{slot}}^y=2\times {10}^4\times V_{\mathrm{in}}·\widehat{\mathbf{y}}[\mathrm{V}/\mathrm{m}]$$

(2)

For each slot, we can then compute an equivalent magnetic moment (${\mathbf{m}}_1$) as [Eq. (3)]:

$${\mathbf{m}}_{\mathbf{1}}={\displaystyle \frac{\mathbf{M}{A}_{\mathrm{slot}}}{\omega {\mu }_0}}$$

(3)

where $\mathbf{M}$ is obtained by substituting Eq. (2) into Eq. (1). In Eq. (3), $\omega$ is the angular frequency and ${\mu }_0$ is the permeability of free space. Given Eq. (2) and the specific slot geometry, $|{\mathbf{m}}_1|$ can be found to be approximately $2\times {10}^{-6}\times V_{\mathrm{in}}\mathrm{A}·{\mathrm{m}}^2$.

Since the two slots are electrically small, have identical equivalent magnetic current densities, and are separated by a distance $\ll {\lambda }_0$ (with ${\lambda }_0$ being the electromagnetic wavelength), their contributions add coherently (in phase). Therefore, the equivalent magnetic dipole moment of the two-slot array (${\mathbf{m}}_{\mathrm{tot}}$) becomes:

$${\mathbf{m}}_{\mathrm{tot}}=2{\mathbf{m}}_1\approx 4\times {10}^{-6}\times V_{\mathrm{in}}·\widehat{\mathbf{x}}[\mathrm{A}·{\mathrm{m}}^2]$$

(4)

We can now use the Larmor formula to compute the far-field power radiated in free space ($P_{\mathrm{rad}}$) by an electrically small magnetic dipole with moment ${\mathbf{m}}_{\mathrm{tot}}$ [Eq. (5)] [27].

$$P_{\mathrm{rad}}={\displaystyle \frac{{\eta }_0{k}^4{\left|{\mathbf{m}}_{\mathrm{tot}}\right|}^2}{12\pi }}$$

(5)

In Eq. (5), ${\eta }_0=377\Omega$ is the free-space wave impedance and $k=2\pi f/c_0$ is the free-space wavenumber. It is important to emphasize that $P_{\mathrm{rad}}$ is proportional to $V_{\mathrm{in}}^2$. Moreover, ${\mathbf{m}}_{\mathrm{tot}}$ (and consequently $P_{\mathrm{rad}}$) is largely independent of $L_{\mathrm{slot}}$ for $L_{\mathrm{slot}}>300\mu \mathrm{m}$ and grows linearly with $W_{\mathrm{slot}}$, as reported in Figure 3 and Figure 4, respectively. This leads to an important design consideration: for a fixed $A_{\mathrm{slot}}$, increasing $P_{\mathrm{rad}}$ requires using larger $W_{\mathrm{slot}}$ values, which can be achieved with minimal changes of $C_{\mathrm{slot}}$ by simultaneously increasing $L_{\mathrm{slot}}$. As will be clear later, the ability to increase $A_{slot}$ without varying $C_{slot}$ permits to decouple the slot design from the design of the TRX, whose achievable voltage gain ($A_v$) depends heavily on $C_{slot}$.

Determining $P_{\mathrm{rad}}$ is the first step required to find the radiation efficiency (${\eta }_{\mathrm{rad}}$) of the slot array. The second and last step consists in computing the power absorbed ($P_{\mathrm{abs}}$) by the two slots under ideal matching to a reference terminal impedance ($Z_0$), here set to $50\Omega$. Under these conditions, $P_{\mathrm{abs}}$ coincides with the available power of a $50\Omega$ generator with Thevenin voltage equal to $V_{\mathrm{in}}$. Its value is reported for completeness in Eq. (6).

$$P_{\mathrm{abs}}={\displaystyle \frac{V_{\mathrm{in}}^2}{8Z_0}},$$

(6)

Eqs. (5)–(6) can now be used to compute ${\eta }_{\mathrm{rad}}$ as [Eq. (7)]:

$${\eta }_{\mathrm{rad}}={\displaystyle \frac{P_{\mathrm{rad}}}{P_{\mathrm{abs}}}},$$

(7)

It is worth mentioning that ${\eta }_{\mathrm{rad}}$ is independent of $V_{\mathrm{in}}$. By using the expression of ${\mathbf{m}}_{\mathrm{tot}}$ in Eq. (4), we can estimate ${\eta }_{\mathrm{rad}}$ for $\omega ={\omega }_{target}$=2$\pi f_{target}$ to be approximately $0.0103\%$ (i.e., $-39.9\mathrm{dB}$ on a logarithmic scale).

The calculated ${\eta }_{\mathrm{rad}}$ value can now be used to quantify $G_{\mathrm{intrinsic}}$ for the slot array at the targeted frequency of operation (i.e., for $\omega ={\omega }_{target}$). To do so, we use the expression reported in Eq. (8).

$$G_{\mathrm{intrinsic}}={\eta }_{\mathrm{rad}}(\omega ={\omega }_{target})·D\approx -32dBi$$

(8)

In Eq. (8), D is the slot array’s directivity, which can be estimated to be six (i.e., four times the directivity of an electrically small dipole). This directivity value considers the presence of two slots operating in close vicinity to a metallic ground plane parallel to the slots’ aperture.

2.2. Impact of the Piezoelectric Transformer on Realized and Intrinsic Gains

Having determined the intrinsic radiation characteristics of the slot array, we move on to quantify the impact of the LSAW TRX on $G_{\mathrm{intrinsic}}$ and $G_{\mathrm{realized}}$. We focus on two key figures of merit: the matching efficiency, ${\eta }_{match}$, between a $50$ source and the TRX-ESA system, and $A_v$ (i.e., the voltage gain achievable when the LSAW device is terminated by a load capacitance, $C_{load}$, equal to 2$C_{slot}$). Together, ${\eta }_{match}$ and $A_v$ set the maximum attainable values of $G_{\mathrm{intrinsic}}$ and $G_{\mathrm{realized}}$ for the TRX-ESA system reported in this work.

We first derive ${\eta }_{match}$ and $A_v$ analytically by modeling the reported TRX-ESA system with the LSAW device’s Butterworth–Van Dyke (BVD) equivalent circuit [28] terminated by $C_{load}$, as reported in Figure 5.

Later, in Section IV, we will extract the same metrics directly from circuit simulations when using the Modified Butterworth–Van Dyke (MBVD) model rather than the BVD model [29]. This allows to more accurately capture the operation of the actual LSAW device embedded in the prototype we built for this work. It is also worth pointing out that the two slots can be modeled by only using $C_{load}$, because the slots’ radiation resistance (in the m$\Omega$-range) is too small to have a significant impact on the achievable ${\eta }_{match}$ and $A_v$.

2.2.1. Calculation of ${\eta }_{match}$

${\eta }_{match}$ is defined as the fraction of the source’s available power that is delivered to the TRX-ESA system. For its analytical derivation, we represent the LSAW TRX in terms of the total admittance of its BVD equivalent circuit, $Y_{\mathrm{BVD}}$ [30]. $Y_{\mathrm{BVD}}$ is the parallel combination of the LSAW device’s motional branch—described by the complex impedance $Z_m$ [Eq. (9)] (or, equivalently, by the admittance $Y_m$ [Eq. (10)])—and the device’s static capacitance $C_0$, with admittance $j\omega C_0$.

$$Z_m=R_m+j\omega L_m+{\displaystyle \frac{1}{j\omega C_m}}$$

(9)

$$Y_m={\displaystyle \frac{1}{R_m+j\omega L_m+\frac{1}{j\omega C_m}}}$$

(10)

In Eqs. (9)–(10), $R_m$, $L_m$, and $C_m$ denote the motional resistance, motional inductance, and motional capacitance, respectively. For any MEMS transformer with resonance angular frequency ${\omega }_{\mathrm{res}}$=$2\pi f_{res}$, quality factor Q, static capacitance $C_0$, and electromechanical coupling coefficient $k_t^2$ [31,32,33], these parameters are given by Eqs. (11)–(13):

$$R_m={\displaystyle \frac{1}{{\omega }_{\mathrm{res}}{C}_{0}Q{k}_t^2}},$$

(11)

$$C_m=C_0{k}_t^2{\displaystyle \frac{8}{{\pi }^2}},$$

(12)

$$L_m={\displaystyle \frac{1}{{\omega }_{\mathrm{res}}^2{C}_m}}.$$

(13)

$Y_{\mathrm{BVD}}$ can be written as [Eq. (14)]:

$$Y_{\mathrm{BVD}}=Y_m+j\omega C_0.$$

(14)

Eq. (14) can thus be rewritten by substituting Eq. (10) into Eq. (14) and then replacing $R_m$, $L_m$, and $C_m$ with their expressions from Eqs. (11)–(13). This yields the expression for $Y_{\mathrm{BVD}}$ in Eq. (15):

$$\begin{array}{c}{Y}_{\mathrm{BVD}}=\hfill \\ \hfill {\displaystyle \frac{C_0\omega \left[{\pi }^{2}Q(\omega -{\omega }_{\mathrm{res}})(\omega +{\omega }_{\mathrm{res}})-8{\omega }_{\mathrm{res}}\left(k_t^{2}Q{\omega }_{\mathrm{res}}+i\omega \right)\right]}{-8\omega {\omega }_{\mathrm{res}}-i{\pi }^{2}Q(\omega -{\omega }_{\mathrm{res}})(\omega +{\omega }_{\mathrm{res}})}}.\end{array}$$

(15)

Next, we compute the return loss of the whole TRX-ESA system, which is equivalent to the $S_{11}$ of the LSAW device when terminated on the total capacitance of the slot-array ($C_{load}$=2$C_{slot}$, see Figure 5). To this end, we can write the TRX-ESA system’s input reflection coefficient (i.e., its $S_{11}$) as [Eq. (16)]:

$$S_{11}={\displaystyle \frac{Y_0-Y_{\mathrm{in}}}{Y_0+Y_{\mathrm{in}}}},$$

(16)

where $Y_0$ is the reference admittance and $Y_{in}$ is the TRX-ESA system’s input admittance (Figure 5); with regards to $Y_0$, we use $Y_0=1/(50\Omega )=20\mathrm{mS}$, in line with what is typically done for $50$-matched electronic components. $Y_{\mathrm{in}}$ can be computed as shown in Eq. (17), where $Y_{load}$=$j\omega C_{\mathrm{load}}$.

$$Y_{\mathrm{in}}={\displaystyle \frac{Y_{\mathrm{BVD}}{Y}_{\mathrm{load}}}{Y_{\mathrm{BVD}}+Y_{\mathrm{load}}}}$$

(17)

Its complete, fully developed expression is reported in Eq. (18). We can now use the computed expression for $Y_{\mathrm{in}}$ to evaluate the $S_{11}$ of the circuit in Figure 5 via Eq. (16). Then, from the computed $S_{11}$, we can calculate ${\eta }_{match}$ via Eq. (19).

$${\eta }_{match}=1-{\left|S_{11}\right|}^2$$

(19)

As a numerical example, Figure 6 reports ${\eta }_{match}$ as a function of $C_0$ and of the TRX’s resonance frequency $f_{res}$ (i.e., ${\omega }_{res}/2\pi$), evaluated at $\omega ={\omega }_{target}$ when using experimentally extracted parameters for the LSAW device (i.e., $Q=260$ and $k_t^2=35\%$) (refer to Section IV for more information on our experimental data). Evidently, the maximum ${\eta }_{match}$ value occurs when the LSAW transformer is designed with a $f_{res}$ value slightly below $f_{\mathrm{target}}$. This trend is expected because a capacitive load produces a stiffening effect that shifts the resonance of $Y_{\mathrm{BVD}}$ upward, with a shift proportional to $k_t^2$ and inversely proportional to $C_{load}$ [34,35]. Accordingly, selecting a slightly lower $f_{res}$ maximizes ${\eta }_{match}$ for $\omega ={\omega }_{target}$.

2.2.2. Calculation of $A_v$

Having completed the extraction of ${\eta }_{match}$, we now turn to the extraction of $A_v$. To this end, we analyze the two-port network in Figure 7, which includes the input generator’s reference impedance, $Z_0$. This formulation is convenient because $A_v$ can be obtained directly from the coefficients of the network’s Y-matrix reported in Eq. (20).

$$\mathbf{Y}=\left[\begin{array}{cc}{y}_{12}& -y_{12}\\ -y_{12}& y_{12}+j\omega C_{\mathrm{load}}\end{array}\right]$$

(20)

The complete, fully-developed expression for $y_{12}$ is reported in Eq. (21). From Eq. (20), we can compute $A_v$ as [Eq. (22)]:

$$A_v={\displaystyle \frac{V_2}{V_1}}={\displaystyle \frac{Y_{21}}{Y_{22}}}$$

(22)

$$Y_{in}\left(\omega \right)={\displaystyle \frac{(C_0+C_{\mathrm{load}}){\pi }^{2}Q{\omega }^2-8i(C_0+C_{\mathrm{load}})\omega {\omega }_{\mathrm{res}}-\left[8C_0{k}_t^2+(C_0+C_{\mathrm{load}}){\pi }^2\right]Q{\omega }_{\mathrm{res}}^2}{i{C}_0{C}_{\mathrm{load}}\omega \left[8{\omega }_{\mathrm{res}}\left(i\omega +k_t^{2}Q{\omega }_{\mathrm{res}}\right)+{\pi }^{2}Q\left(-{\omega }^2+{\omega }_{\mathrm{res}}^2\right)\right]}}$$

(18)

$$y_{12}\left(\omega \right)={\displaystyle \frac{{\pi }^{2}Q\left(-i+C_0{Z}_{e0}\omega \right)(\omega -{\omega }_{\mathrm{res}})(\omega +{\omega }_{\mathrm{res}})-8\omega {\omega }_{\mathrm{res}}\left[1+C_0{Z}_{e0}\left(i\omega +k_t^{2}Q{\omega }_{\mathrm{res}}\right)\right]}{C_0\omega \left[8{\omega }_{\mathrm{res}}\left(i\omega +k_t^{2}Q{\omega }_{\mathrm{res}}\right)+{\pi }^{2}Q\left(-{\omega }^2+{\omega }_{\mathrm{res}}^2\right)\right]}}$$

(21)

$$A_v\left(\omega \right)={\displaystyle \frac{i{C}_0\left[{\pi }^{2}Q({\omega }_{\mathrm{res}}^2-{\omega }^2)+8{\omega }_{\mathrm{res}}\left(k_t^{2}Q{\omega }_{\mathrm{res}}+i\omega \right)\right]}{C_{\mathrm{load}}\left[8\omega {\omega }_{\mathrm{res}}+i{\pi }^{2}Q({\omega }^2-{\omega }_{\mathrm{res}}^2)\right]-C_0\left(C_{\mathrm{load}}\omega Z_{e0}-i\right)\left[{\pi }^{2}Q({\omega }^2-{\omega }_{\mathrm{res}}^2)-8{\omega }_{\mathrm{res}}\left(k_t^{2}Q{\omega }_{\mathrm{res}}+i\omega \right)\right]}}$$

(23)

We also show the extended derivation for $A_v$ as a function of $\omega$ in Eq. (23). As we did for ${\eta }_{match}$ in Figure 6, Figure 8 reports $A_v$, numerically evaluated for $\omega ={\omega }_{target}$ as a function of $f_{res}$ and $C_0$, when assuming the same Q and $k_t^2$ of the LSAW device in our built prototype (as we will discuss in Section IV). Evidently, a $C_0$ equal to $C_{load}$ maximizes $A_v$, which is found to be 6.51. This voltage amplification arises because a two-port LSAW resonator, even with identical transducer geometries at both ports, behaves as a TRX when one port is terminated with a capacitive load [26]. Thus, the LSAW device can passively step-up the voltage level applied at its input port. Such step-up increases $|{\overline{\mathbf{E}}}_{\mathrm{slot}}^y|$ relative to the case without the LSAW device and, consequently, increases the radiated power by a factor equal to $A_v^2$. In other words, the radiated power of the slot array is significantly enhanced when the array is driven through a TRX rather than being directly connected to a power source.

This enhancement can be interpreted as a boost in the slot array’s radiation efficiency: $A_v$ increases the electric-field distribution across the slots and, consequently, increases ${\mathbf{m}}_{\mathrm{tot}}$. An expression of the power radiated by the slot-array when using a TRX to drive it ($P_{\mathrm{rad}}^{w.t}$) is reported in Eq. (24), followed by the corresponding modified expression for the radiation efficiency (${\eta }_{\mathrm{rad}}^{w.t}$) in Eq. (25).

$$P_{\mathrm{rad}}^{w.t}=A_v^2{P}_{rad}$$

(24)

$${\eta }_{\mathrm{rad}}^{w.t}={\displaystyle \frac{P_{\mathrm{rad}}^{w.t}}{P_{\mathrm{av}}}}={\displaystyle \frac{A_v^2{P}_{rad}}{P_{\mathrm{av}}}}={\eta }_{\mathrm{rad}}·A_v^2$$

(25)

Evidently, both the power radiated and the radiation efficiency of the slot-array are enhanced by a factor equal to $A_v^2$ when driven by a piezoelectric transformer.

2.2.3. Calculation of $G_{\mathrm{realized}}$

Having determined both ${\eta }_{match}$ and $A_v$, we are now ready to compute $G_{\mathrm{realized}}$, which we can do by using the following equation [27]:

$$G_{\mathrm{realized}}={\eta }_{\mathrm{rad}}^{w.t}\left(\omega \right){\eta }_{\mathrm{match}}\left(\omega \right)·D=G_{\mathrm{intrinsic}}\mathcal{G}\left(\omega \right),$$

(26)

where

$$\mathcal{G}=|A_v{|}^2·\left|{\eta }_{match}\right|.$$

(27)

Evidently, $G_{\mathrm{realized}}$ is proportional not only to $G_{\mathrm{intrinsic}}$, as expected, but also to $|A_v{|}^2\left|{\eta }_{\mathrm{match}}\right|$. It is worth emphasizing that, for any targeted operating frequency, $|A_v{|}^2$ and ${\eta }_{match}$ are maximized for different combinations of $f_{res}$ and $C_0$ values. It is therefore important to numerically identify the optimal $f_{res}$ and $C_0$ values to maximize $G_{\mathrm{realized}}$. As an example, Figure 9 reports $\mathcal{G}$, numerically computed under the same assumptions used to generate Figure 6 and Figure 8. Evidently, an LSAW device with $f_{res}$=425 MHz and a $C_0$ close to $C_{load}$ is ideal for maximizing $G_{\mathrm{realized}}$ at $\omega ={\omega }_{target}$. The maximum $\mathcal{G}$ value identified in this study shows that the adoption of an optimized design for the TRX can lead to a $G_{\mathrm{realized}}$ almost 36 times larger than $G_{\mathrm{intrinsic}}$, hence enabling a strong improvement of $G_{\mathrm{realized}}$ over $G_{\mathrm{intrinsic}}$ when considering the actual slot-array geometry used in this work. Such optimal operating conditions correspond to a ${\eta }_{match}$ value equal to 0.8, thus approaching ideal matching conditions. Finally, we report a $G_{\mathrm{realized}}$ vs. frequency trend extracted using the analytical model discussed across this Section in Figure 10, along with the trend of $G_{\mathrm{intrinsic}}$ for the slot-array when no TRX is used. Evidently, our reported TRX-ESA architecture enables a large boost of $G_{\mathrm{realized}}$ compared to $G_{\mathrm{intrinsic}}$ when operating in the proximity of the resonance frequency of $Y_{in}$, allowing us to estimate a maximum gain of -15.9 dBi at $f_{\mathrm{target}}$. As mentioned earlier, $f_{\mathrm{target}}$ is different from $f_{res}$ because of the presence of $C_{load}$ stiffening the TRX.

2.2.4. Impact of Q and $k_t^2$ on $\mathcal{G}$

It is also useful to study how the gain enhancement brought by the adoption of the TRX is related to its electromechanical performance. To do so, we conducted an additional analytical investigation where we searched for the maximum $\mathcal{G}$ value for varying Q and $k_t^2$ values. The results of this analysis are plotted in Figure 11. Evidently, both the increases in Q and $k_t^2$ generally lead to enhanced $\mathcal{G}$ values. However, beyond certain Q and $k_t^2$ values, a plateau emerges in the achievable enhancement, with a maximum $\mathcal{G}$ value still attained for $C_0$ approaching $C_{load}$. Our study also finds that adopting much smaller $C_0$ values [i.e., values for which $1/\left(\omega C_0{Z}_0\right)\gg 1$] can yield substantially larger $\mathcal{G}$ when the slots are designed such that $C_{\mathrm{slot}}$ approaches $C_0$, as reported in Figure 12. Consequently, $\mathcal{G}$ can amplify the sensitivity of $G_{\mathrm{realized}}$ to increases in $A_{\mathrm{slot}}$ compared to the quadratic dependence on $A_{\mathrm{slot}}$ exhibited by $G_{\mathrm{intrinsic}}$. To this end, the weak dependence of $m_{tot}$ on $L_{slot}$ makes it possible to reduce $C_{slot}$ by increasing $L_{slot}$ without reducing $m_{tot}$ at the same time. It is also worth pointing out that the enhancement in $G_{\mathrm{realized}}$ attained by using the TRX inevitably comes with a reduced fractional bandwidth. Finally, we note that we did not pursue low-$C_{slot}$ designs in this work. Although such designs could yield higher $G_{\mathrm{realized}}$, the optimal TRX (with $C_0$ approaching $C_{load}$) would be substantially smaller than the device we fabricated. This size reduction would likely increase the mismatch between the measured and simulated LSAW resonance frequency (see Section III) and could also add more spurious modes and reduce Q (i.e., a smaller active region typically leads to larger anchor dissipations compared with larger-area devices [36]).

3. LSAW TRX Design and Optimization

As mentioned earlier, the LSAW TRX was fabricated on a bulk YZ $0^{\circ }$ X-cut ${\mathrm{LiNbO}}_3$ substrate. The choice of this ${\mathrm{LiNbO}}_3$ cut allows to excites the $S{H}_0$-mode, which is characterized by an in-plane displacement perpendicular to the wave propagation direction, as confirmed by FEM simulations (Figure 13a). This mode exhibits an inherently large $k_t^2$ [25,37], making the proposed LSAW architecture highly attractive for achieving large $A_v$ and, consequently, strong enhancements in $G_{\mathrm{realized}}$ of chip-scale slot-arrays. Yet, the highly dispersive nature of the $S{H}_0$ modes exploited by LSAW devices implies that the $k_t^2$ strongly depends on $t_{el}/{\lambda }_{ac}$, with $t_{el}$ being the thickness of the metal electrodes and ${\lambda }_{ac}$ the acoustic wavelength. Since the associated mass loading concentrates the acoustic energy beneath the surface and reduces substrate leakage, denser electrode materials are preferred [38]. In this work, we select Gold (Au) as metal, as it offers an optimal combination between high density and low electrical resistivity, which minimizes the ohmic loading of the transducer [25]. In the limit of very thin electrodes ($t_{el}/{\lambda }_{ac}\to 0$), the acoustic field is poorly confined beneath the interdigitated transducer electrodes (IDTs), resulting in significant energy leakage into the substrate. However, as $t_{el}/{\lambda }_{ac}$ increases, the acoustic energy is progressively concentrated in the region near the surface, improving $k_t^2$.

To identify the optimal electrode thickness for the present design, we performed 3D FEM simulations on a unit cell of the YZ $0^{\circ }$ X-cut ${\mathrm{LiNbO}}_3$ substrate with a pair of its Au IDTs. We used a section with thickness $5{\lambda }_{ac}$ beneath the electrodes to approximate the semi-infinite bulk substrate, with periodic boundary conditions applied along the propagation direction of the acoustic wave and a perfectly matched layer (PML) at the bottom of the substrate, in order to absorb bulk-radiated energy. We simulate the behavior of $k_t^2$ as function of the $t_{el}/{\lambda }_{ac}$ ratio of the metal in Figure 13b. As evident, $k_t^2$ can be maximized when working at $t_{el}/{\lambda }_{ac}$ ratios between 0.025 and 0.05. For this reason, we designed our TRX with a $t_{el}/{\lambda }_{ac}$ ratio of 0.0375, aiming to a $k_t^2$ close to 35%.

The finalized TRX consists of 20 pairs of gold IDTs surrounded by electrically grounded reflectors, and the aperture of the IDTs is set to $100$m for impedance matching purposes. The $f_{res}$ of the LSAW TRX is set by the IDT period $p=\lambda /2$, according to:

$$f_{res}={\displaystyle \frac{v_{\mathrm{SH}}}{\lambda }}={\displaystyle \frac{v_{\mathrm{SH}}}{2p}}$$

(28)

where $v_{\mathrm{SH}}$ is the phase velocity of the ${\mathrm{SH}}_0$ LSAW mode on X-cut ${\mathrm{LiNbO}}_3$. This term depends on the electrode material, on its thickness and on the chosen $t_{el}/{\lambda }_{ac}$ ratio, and can be obtained from FEM simulations.

4. Experimental Section

4.1. Fabrication Process

The one-mask fabrication process of the LSAW TRX is illustrated in Figure 14a. A 300 nm thick layer of Au was deposited on a YZ 0° X-cut ${\mathrm{LiNbO}}_3$ wafer through e-beam evaporation. Subsequently, the Au-coated wafer was patterned via UV-photolithography and an ion beam etching (IBE) process to minimize fencing effects on the edges of the electrodes. The wafer was then diced in chips, from which we finally sub-diced a 2.5 by 2.5 mm chip hosting the fabricated TRX-ESA. Figure 14b,c show an optical micrograph of the chip hosting the device and a scanning electron microscope (SEM) close-up picture of the TRX’s IDT region. We could not acquire a single SEM image of the full device, because the charging effects under electron-beam exposure on bulk ${\mathrm{LiNbO}}_3$ become prohibitive when imaging the entire chip area [39].

4.2. S-Parameters Characterization and MBVD Fitting

The fabricated TRX-ESA was characterized through on-chip S-parameter measurements using a Keysight N5221A Vector Network Analyzer and a $150$m-pitch GSG probe. The measured $S_{11}$ response around the $S{H}_0$ LSAW $f_{res}$ is reported in Figure 15. As evident, the TRX-ESA shows a good impedance matching at 425 MHz, showcasing a maximum return loss of 23 dB and a -10 dB bandwidth of 0.53%.

The measured $S_{11}$ vs. frequency trend was fitted by using a two-mode MBVD model [40]. The $S_{11}$ retrieved from our MBVD fitting is superimposed to the measured one in Figure 15. It is important to point out that the MBVD model used here considers an additional mode beyond the main one to better match the $S_{11}$ behavior. Also, the model considers two additional resistances ($R_s$ and $R_0$) and a capacitor ($C_{par}$). $R_s$ and $R_0$ capture the effect of the ohmic losses in the IDT and GSG probing pads, as well as dielectric dissipations in the ${\mathrm{LiNbO}}_3$ film. $C_{par}$, on the other hand, models the capacitance between the slots’ top metal strips and the signal pad. A schematic representation of the final MBVD circuit we used to match the measured response is reported in the inset of Figure 15. The various MBVD parameters that best fit the measured electrical response of our reported TRX-ESA system are reported in the caption of Figure 15. The $k_t^2$ fitted for the main mode of our LSAW TRX is $35\%$.

Using the extracted MBVD parameters, we retrieved the experimental values of $A_v$ and ${\eta }_{match}$, and computed $G_{\mathrm{realized}}$ based on the simulated $G_{\mathrm{intrinsic}}$ of the slots. As seen in Figure 10, we expect a maximum $G_{\mathrm{realized}}$ of -15.9 dBi. This value is achieved at a frequency that is higher than $f_{res}$ due to the stiffening effect produced by $C_{load}$.

4.3. Experimental Characterization of $G_{\mathrm{realized}}$ and Comparison with Other RF-MEMS ESA Systems

The value of $G_{\mathrm{realized}}$ for the fabricated TRX-ESA system was measured using the gain-comparison method [12,27]. The experimental setup for gain extraction is illustrated in Figure 16. We first placed a transmitting Log Periodic antenna (Aaronia HyperLOG® 4025) at a fixed distance $h=75\mathrm{cm}$ from the device under test, and connected it to port 1 of the VNA. Port 2 was connected to the on-chip TRX-ESA via GSG probes. Then, we replaced the on-chip device with a reference antenna with fully characterized gain, $G_{REF}$. $G_{\mathrm{realized}}$ was computed as follows:

$$\begin{array}{cc}\hfill G_{\mathrm{realized}}& =G_{REF}+20{log}_{10}\left(\left|S_{21,TRX}\right|\right)\hfill \\ \hfill & -20{log}_{10}\left(\left|S_{21,REF}\right|\right)\hfill \end{array}$$

(29)

In Eq. (29), $S_{21,TRX}$ and $S_{21,REF}$ are the transmission coefficients in linear scale measured with the TRX-ESA system and the reference antenna in place, respectively.

The resulting $G_{\mathrm{realized}}$ trend versus frequency is reported in Figure 17. We measured a maximum gain of -12.7 dBi, which, to the best of our knowledge, is the highest gain ever reported for RF MEMS based ESAs, and is in close agreement with the prediction of our analytical model shown in Figure 10. We believe that the ∼3 dB discrepancy between measured and analytically predicted gain values arises from slight underestimations of $G_{\mathrm{intrinsic}}$, which may stem from radiation contributions of secondary apertures, as well as from unmodelled variations in the dielectric characteristics of the ${\mathrm{LiNbO}}_3$ substrate. In this regard, it is worth emphasizing that a 30% reduction of ${\mathbf{m}}_{\mathrm{tot}}$ would be enough to cause an underestimation of $G_{\mathrm{intrinsic}}$ (and consequently $G_{\mathrm{realized}}$) by 3 dB.

We finally compare the proposed TRX-ESA against previously reported on-chip antenna systems in Table 1. Our TRX-ESA architecture demonstrates exciting advantages across all key performance metrics. First, it shows a clear size reduction compared to its SAW-based counterparts in the same frequency range [15,21]. Even more importantly, the TRX-ESA architecture shows an improvement in the realized gain of approximately 4.5 dBi over the highest previously reported gain for an acoustically actuated device [21]. It is worth adding that the AMP-ESA reported in [21] operates at approximately the same frequency while being nearly two times larger in area, thus representing an ideal benchmark for our device. Our prototype also shows a -10 dB $S_{11}$ bandwidth of 0.53%.

Altogether, the high gain and wide fractional bandwidth of our TRX-ESA leads to a gain-bandwidth product of 28.${\mathrm{5\times 10}}^{-5}$, which is almost an order of magnitude higher than the highest previously reported one for RF MEMS based ESAs [41].

5. Conclusion

In this work, we presented and experimentally characterized a TRX-ESA system, formed by the monolithic integration of an LSAW piezoelectric transformer with an ESA. The proposed architecture shows a significant gain enhancement, excellent impedance matching to $50\Omega$ and the highest gain-bandwidth product among previously demonstrated RF MEMS-based ESAs. The reported TRX-ESA architecture leverages for the first time the passive voltage amplification provided by an LSAW TRX, which increases the tangential electric field across an array of two slot antennas, thus boosting their radiated power and guaranteeing impedance matching despite their small electrical size. To model the acoustic and radiation behavior of the LSAW TRX, we built an ad-hoc simulation framework combining analytical and finite-element methods simulations, which reliably predicts the realized gain of the TRX-ESA system and provides a basis for design optimization.

Our findings demonstrate that monolithically integrated piezoelectric transformers offer a scalable and foundry-compatible route to UHF chip-scale ESAs with substantially improved performance, paving the way towards miniaturized passive wireless sensor tags for IoT applications.