This paper reports on a new type of high-frequency mode-matched gyroscope with significantly reduced dependencies on environmental stimuli such as temperature, vibration, and shock. A novel stress-isolation system is used to effectively decouple an axis-symmetric bulk-acoustic wave (BAW) vibratory gyro from its substrate, minimizing the effect that external sources of error have on the offset and scale factor of the device. Substrate-decoupled (SD) BAW gyros with a resonance frequency of 4.3 MHz and Q values near 60 000 were implemented using the high aspect ratio poly and single-crystal silicon (HARPSS) process to achieve ultra-narrow capacitive gaps. Wafer-level packaged sensors were interfaced with a customized application-specific integrated circuit (ASIC) to achieve low variations in the offset across temperature (±26°s − 1 from − 40 to 85°C), supreme random-vibration immunity (0.012°s − 1 g RMS − 1 ) and excellent shock rejection. With a scale factor of 800 μV (°s, the SD-BAW gyro system attains a large full-scale range (±1250°s) with a non-linearity of less than 0.07%. A measured angle-random walk (ARW) of 0.39°/√h and a bias instability of 10.5°h − 1 are dominated by the thermal and flicker noise of the integrated circuit (IC), respectively. Additional measurements using external electronics show bias-instability values as low as 3.5°h INTRODUCTIONMicromachined gyroscopes have enabled a myriad of applications that range from basic motion detection for gaming to safety control systems in automobiles 1 . More recently, an increased interest in the use of microelectromechanical system inertial sensors for dead reckoning and pedestrian navigation in handheld electronics has placed stringent requirements on the die size, power consumption, and overall performance of this type of device. To date, most commercially available rate sensors have been designed as low-frequency flexural tuning-fork gyroscopes (TFGs), which are typically sensitive to random vibrations and prone to linear accelerations, such as those experienced under shock. These limitations complicate the use of TFG technology in large-volume, high-end applications, particularly in personal navigation, for which dependencies on fluctuations in the environment translate into long-term drift in the output of the system. Additionally, in recent months, concerns about the high sensitivity of consumer-grade gyroscopes in response to lowfrequency pressure signals that can be used to recover audio have increased as a potential threat for eavesdropping 2 , justifying the need for more environmentally robust rotation sensors.Acceleration suppression mechanisms can be implemented in TFGs to alleviate part of this problem using redundant proof masses that reject shock and vibration as common-mode signals 3 .

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Fig. 2. "Average power models" of step-up, step down and "indirect" (or buck-boost) converters The "direct average current" (is the maximum possible common current, that would transfer the maximum possible "direct power" in a loop including the source and the load. That is, the minimum value of input and output currents, as illustrated in 0.b. Then, the "direct power" is the product of this current by the minimum of input and output voltages, as illustrated in (1). Consequently, P diff may be expressed as (2). The internal power (P int) processed by all the components of a power converter is in general higher than P diff (3), especially in isolated converters and most hybrid and SC converters. In general, the internal power is processed by inductors and capacitors, though the power processed by transformers need to be included in any design and optimization process, and in some cases, the power processed by capacitors is transferred in a resonan fashion, so it may be accounted for separately, as illustrated in (4).

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In this paper, we present a highly efficient and compact voltage doubler based on a resonant S'\\itched-capacitor converter implemented with GaN FF.Ts. Two possible approad1es for its implementation are analy:red and compared. In the first approach, the resonant inductor is placed in series with a resonant capacitor, conducting a sinusoidal current, while in the second, it is placed in series with the input source, conducting rectified sinusoidal current Roth resonant converters have the same voltage gain, and although the change in the position of the resonant inductor is, at the first glance, of minor importance, the analysis and results show that it has huge impact on the capability to achieve zero-voltage switching (ZVS) transitions at low output power. The experimental results dearly show that at low loads when the resonant inductor is in series with the resonant capacitor, the S'\\itching frequency can be significantly higher than the resonant frequency and that it is, practically, impossible to achieve ZVS transitions, forcing the implementation of cycle skipping. The prototype implemented for the experiments can provide up to 4.5-kW losing between 20 and 22 W. In the case of tight load (500 W), the power losses were only 2-3 W. Its power density ls higher than 6S kW/dm 3 . The same resonant converter was tested '\\ith Si CoolMOS devices as well and the impact of the semiconductor tedmology on the overall power losses was verified. Due to higher Coss capacitance, the Si-based converter has 40% higher power losses at full power than its GaN-based counterpart. The components of the GaN-based converter occupy only 65 cm 3 , which opens a possibility to obtain a design '\\ith extremely high power density. Index Ten11s-Resonant converters, switched capacitors, zero voltage S'\\itching (ZVS ).

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