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ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 57 (2009), Nr. 3 17 Circuit Models for Anti-Series and Anti-Parallel Connections of Power Bulk Acoustic Wave Resonators Alexandru G. GHEORGHE, Miruna NITESCU, Florin CONSTANTINESCU ∗ Abstract The new anti-series and anti-parallel connections of power bulk acoustic wave resonators have been reported to reduce the second harmonic component. In this paper, New nonlinear we propose circuit models of these connections. A class D power amplifier together with a bulk acoustic wave power filter, using these models, were simulated leading to results agreeing with common expectations. Keywords: power bulk acoustic wave resonator, power amplifiers, anti-serie connection,nonlinear circuit model 1. Introduction The actual microelectronic technology uses digital radio type solutions in mobile communications as a challenge. Next several years, the analog RF front end will be integrated together with the digital part as a SiP/SoC system. At this end, the Bulk Acoustic Wave (BAW) resonators with AlN like piezoelectric material are one of the best solutions, being compatible with silicon substrate and processing and significantly cheaper than surface acoustic wave [1, 2]. The most robust variant of a BAW resonator, the solidly mounted resonator (SMR), contains, besides the AlN piezoelectric layer and electrodes, some additional layers positioned between the bottom electrode and the substrate (Fig. 1). These last layers form the so-called Bragg mirror, which prevents useless energy dissipation in the substrate. produces two nonlinear effects, namely: the amplitude-frequency effect, and the intermodulation effect. The amplitude-frequency effect leads to a shift of the series resonance frequency modifying the filter characteristic. The intermodulation effect produces unwanted harmonic components which can disturb the mobile phone operation. To simulate these nonlinear effects, some nonlinear circuit models have been developed [3, 4]. Unlike the other known models, these models reproduce the amplitude-frequency effect and the intermodulation effect, and can be implemented in time domain and frequency domain circuit simulators [5]. The first model is based on the BVD circuit [2] in which the nonlinear resistor. The inductor and capacitor are implemented as nonlinear controlled sources (Fig. 2). Figure 2. Controlled source implementation of the first nonlinear circuit model Figure 1. Solidly mounted resonator (SMR) A high power fed into the BAW resonator ∗ Alexandru G. GHEORGHE, asist., Miruna NITESCU, prof.dr., Florin CONSTANTINESCU, prof.dr. – Universitatea Politehnica din Bucureşti, Facultatea de inginerie electrică. Recently the anti-series and anti-parallel connections of power BAW resonators proved to be very efficient for the reduction of the intermodulation effect [6]. These connections are shown in Fig. 3, together with the series and parallel connections, and are used by INFINEON 18 ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 57 (2009), Nr. 3 and EPCOS to build low distortion power BAW filters. Series connection or the anti-parallel connection, the second order coefficients have different signs, whilst for the series connection or the parallel connection the coefficients have the same sign. The anti-series connection model was validated by SPECTRE RF simulation of the circuit in Fig. 4. The input source is sinusoidal with a 2.025 GHz frequency (the series resonance frequency) and 4V amplitude. The output magnitude is the source current. Parallel connection Anti-series connection Anti-parallel connection Figure 3. Connections of two power BAW resonators Experimentally, in case of anti-serie connection, a significant reduction of the second harmonic was observed compared to series connection. A similar effect was observed for the anti-parallel connection in comparison with the parallel connection. Even though some measurements results for two anti-series and anti-parallel resonators are not known, these design solutions have been used for power BAW filters, a significant reduction of the distortions at the output of the filter being measured. This reduction of the 2f frequency components has been explained by the polarization-frequency effect. This effect means the series resonance frequency modification by introducing a DC component of about 50 volts in the excitation signal. This explanation suggests that a continuous voltage could stress the piezoelectric material changing its behavior, but probably has no connection with the real phenomenon on which this reduction of certain harmonic components is based. This phenomenon has not been identified yet. Figure 4. Circuit for the anti-series connection model validation For the series connection both capacitors C1 have the characteristic: c1 (3 out) cap1 c = 88.29e-15 model cap1 capacitor coeffs = [6e-5] In case of anti-serie connection one of C1capacitors had the same characteristic as the previous case, and the other one had a quadratic term with the opposite sign, namely: c1 (3 out) cap1 c = 88.29e-15 model cap1 capacitor coeffs = [-6e-5] The PSS analysis results are presented in Table 1. A significant second harmonic component reduction was obtained in case of anti-series connection, whilst the third harmonic had nearly the same amplitude. Table 1 BAW filter structure 2f1 3f1 Series connection 10.58uA 5.387nA Anti-series connection 812.9aA 5.392nA The anti-parallel connection model was validated by SPECTRE RF simulation of the circuit in Fig. 5. 2. Nonlinear circuit models A simple circuit model is proposed in order to reproduce this reduction of 2f frequency components. Only one element of the model is nonlinear, namely the capacitor of the mechanical branch, and is characterized by a second order polynomial q-u characteristic. For the anti-series Figure 5. Circuit for the anti-parallel connection model validation connection N.B. The quadratic coefficients of the anti-parallel resonator models connection have opposite signs. ELECTROTEHNICA, ELECTRONICA, AUTOMATICA, 57 (2009), Nr. 3 The input source is sinusoidal with a 2.025 GHz frequency (the series resonance frequency) and 4V amplitude. The output magnitude is the source current. The resonators models for the parallel connection are the same as the models for series The PSS analysis results are presented in the Table 2. A significant second harmonic component reduction is obtained in the case of the anti-parallel connection whilst the third harmonic has nearly the same amplitude. Table 2 BAW filter structure 2f1 3f1 Parallel connection 1.671uA 427.7pA Anti –parallel connection 5.344aA 425.7pA 3. Example In a D class power amplifier, the transistor has a switch behavior. The output of the amplifier is switched between the cut-off and saturation regions. The efficiency of this amplifier is close to 100% because the active operating region is swept only during the transitions between the cutoff and saturation regions. 19 The frequency characteristic of this circuit for the input voltage range [1mV, 5V] doesn’t significantly change, so the amplitude-frequency effect is negligible for this circuit. In order to analyze the intermodulation effect the second and third harmonic components have been computed for an input voltage of 1V. Replacing each of X2, X4, and X6 by an antiseries connection of two resonators the second harmonic was diminished, while the third harmonic remained unchanged. The results are given in Table 3. Table 3 Harmonic component f1 2f1 3f1 BAW filter structure As in Figure 6 3.822V 7.572uV 2.321uV X2, X4, and X6 replaced by two resonators in anti- 3.822V series connection 1.541uV 2.321uV These simulation results agree with the measurement results reported in [6]. 4. Conclusions New nonlinear circuit models for the antiseries and anti-parallel connections of two power BAW resonators have been proposed. The reduction of the second harmonic component has been pointed out by simulation of simple test circuits, according to the reported measurement results. A D class amplifier together with a BAW filter has been simulated obtaining results which agree with common expectations. References [1] [2] Figure 6. A D class amplifier with a power BAW filter The simulated circuit is a D class power amplifier together with a LC low-pass filter [7] and a power BAW pass-band filter built with six resonators (Fig. 6). The power amplifier is driven by a sinusoidal signal with frequency f1=2.025GHz which is applied at the „+” entry of a comparator. A triangular signal with frequency 100f1 is applied at the „-” entry of the comparator. The components in the range 100f1 and higher of the amplified signal are eliminated by a LC low pass filter. The final filtering is made by the power BAW filter in which each resonator has been replaced with the nonlinear circuit model as described in Section 1. [3] [4] [5] [6] [7] HIGH LEVEL GROUP, Vision 2020 – Nanoelectronics at the centre of change - A far-sighted strategy for Europe (Report), June 2004. CAMPBELL C. K., Surface Acoustic Wave Devices for Mobile and Wireless Communications. Academic Press: Boston, 1998. CONSTANTINESCU F., M. NIŢESCU, A. G. GHEORGHE, „Circuit models for power baw resonators – set-up and implementation”, in IEEE AFRICON 2007, Windhoek, Namibia, September 26-28. CONSTANTINESCU F., M. NIŢESCU, A. G. GHEORGHE, “New Nonlinear Circuit Models for Power BAW Resonators”, in Proceedings of IEEE ICCSC 2008, 26-28 mai 2008, Shanghai, China CONSTANTINESCU F., A. G. GHEORGHE, M. NIŢESCU, ”New Circuit Models of Power BAW Resonators”, in Revue Roumaine des Sciences Technique – Electrotechnique et Energetique, no.1, 2008, pp.67-73. AIGNER R., M. HANDTMANN, US Patent No. US 2006/0290446 A1, December 28 2006. http://www.eng.warwick.ac.uk