AdvancedMicrowaveandMillimeterWave Technologies:SemiconductorDevices,CircuitsandSystems352 (c) Responses of the theoretical prediction and measurement Fig. 8. Three-ordered 2/5.3 GHz dual-passband bandpass filter whose first passband’s bandwidth is smaller  b and the impedances Z 11 , Z 12 , Z 21 , Z 22 and Z 1 are then obtained as 47.1 o , 11.89, 11.2, 11.28, 13.69 and 74.59 , respectively. According to these calculated parameters, theoretical predictions of the dual-passband bandpass filter are shown in Fig. 8c. The multilayered 2/5.3 GHz bandpass filter is fabricated on 10 substrates of 0.09 mm, and its overall size is 4.98 mm  3.6 mm  0.9 mm. Figures 8a and 8b show the 3D architecture and the photograph of this fabricated filter; Fig. 8c also presents the measured results. On the one hand, within the first passband (1.85-2.22 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 20 dB. On the other hand, within the second passband (5.14-5.62 GHz), the measured insertion loss is < 2.5 dB, whereas the return loss is > 18 dB. 4. Multi-passband filter fabrication The multi-passband filter can be obtained from (1) to (4). The fabricated examples of triple- and quadruple-passband filters are introduced below. 4.1 Triple-passband filter Figure 9 shows the architecture of the three-ordered triple-passband filter. The central frequencies of three passbands are set as 2, 5 and 8 GHz. The bandwidths of the first, second and third passband are chosen as 200, 300 and 200 MHz, respectively, which are 10%, 15% and 10% of the first passband’s central frequency. Moreover, the selected ripple for the prototypical Chebyshev lowpass filter is 0.01 dB. With the electrical length  a as 35.5 o , the electrical length  b and the impedances Z 11 , Z 12 , Z 13 , Z 21 , Z 22 , Z 23 and Z 1 are then obtained as 37.2 o , 20.3, 17.51, 20.34, 29.89, 13.21, 29.84 and 67.7 , respectively. According to these calculated parameters, theoretical predictions of the triple-passband bandpass filter are shown in Fig. 10c. Fig. 9. Architecture of the three-ordered triple-passband filter whose passbands have unequal bandwidths The multilayered 2/5/8 GHz bandpass filter is fabricated on 10 substrates of 0.09 mm, and its overall size is 4.72 mm  3.7 mm  0.9 mm. Figures 10a and 10b show the 3D architecture and the photograph of this fabricated filter; Fig. 10c also presents the measured results. (a) 3D architecture (b) Photograph DesignofMulti-PassbandBandpassFiltersWith Low-TemperatureCo-FiredCeramicTechnology 353 (c) Responses of the theoretical prediction and measurement Fig. 8. Three-ordered 2/5.3 GHz dual-passband bandpass filter whose first passband’s bandwidth is smaller  b and the impedances Z 11 , Z 12 , Z 21 , Z 22 and Z 1 are then obtained as 47.1 o , 11.89, 11.2, 11.28, 13.69 and 74.59 , respectively. According to these calculated parameters, theoretical predictions of the dual-passband bandpass filter are shown in Fig. 8c. The multilayered 2/5.3 GHz bandpass filter is fabricated on 10 substrates of 0.09 mm, and its overall size is 4.98 mm  3.6 mm  0.9 mm. Figures 8a and 8b show the 3D architecture and the photograph of this fabricated filter; Fig. 8c also presents the measured results. On the one hand, within the first passband (1.85-2.22 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 20 dB. On the other hand, within the second passband (5.14-5.62 GHz), the measured insertion loss is < 2.5 dB, whereas the return loss is > 18 dB. 4. Multi-passband filter fabrication The multi-passband filter can be obtained from (1) to (4). The fabricated examples of triple- and quadruple-passband filters are introduced below. 4.1 Triple-passband filter Figure 9 shows the architecture of the three-ordered triple-passband filter. The central frequencies of three passbands are set as 2, 5 and 8 GHz. The bandwidths of the first, second and third passband are chosen as 200, 300 and 200 MHz, respectively, which are 10%, 15% and 10% of the first passband’s central frequency. Moreover, the selected ripple for the prototypical Chebyshev lowpass filter is 0.01 dB. With the electrical length  a as 35.5 o , the electrical length  b and the impedances Z 11 , Z 12 , Z 13 , Z 21 , Z 22 , Z 23 and Z 1 are then obtained as 37.2 o , 20.3, 17.51, 20.34, 29.89, 13.21, 29.84 and 67.7 , respectively. According to these calculated parameters, theoretical predictions of the triple-passband bandpass filter are shown in Fig. 10c. Fig. 9. Architecture of the three-ordered triple-passband filter whose passbands have unequal bandwidths The multilayered 2/5/8 GHz bandpass filter is fabricated on 10 substrates of 0.09 mm, and its overall size is 4.72 mm  3.7 mm  0.9 mm. Figures 10a and 10b show the 3D architecture and the photograph of this fabricated filter; Fig. 10c also presents the measured results. (a) 3D architecture (b) Photograph AdvancedMicrowaveandMillimeterWave Technologies:SemiconductorDevices,CircuitsandSystems354 (c) Responses of the theoretical prediction and measurement Fig. 10. Three-ordered 2/5/8 GHz triple-passband bandpass filter whose second passband’s bandwidth is greater Within the first passband (1.66-2.11 GHz), the measured insertion loss is < 1.4 dB, whereas the return loss is > 16.8 dB. Moreover, within the second passband (4.6-5.35 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 16 dB. Furthermore, within the third passband (7.84-8.14 GHz), the measured insertion loss is < 3 dB, whereas the return loss is > 15 dB. 4.2 Quadruple-passband filter Figure 11 shows the architecture of the three-ordered quadruple-passband filter. The central frequencies of four passbands are set as 2, 5, 8 and 11.3 GHz. The bandwidth of four passbands is all chosen as 180 MHz, which is 9% of the first passband’s central frequency. Moreover, the selected ripple for the prototypical Chebyshev lowpass filter is 0.01 dB. As a result, the electrical length  0 and the impedances Z 11 , Z 12 , Z 13 , Z 14 , Z 21 , Z 22 , Z 23 , Z 24 and Z 1 are obtained as 26.8 o , 21.79, 19.61, 22.74, 14.54, 27.49, 16.01, 14.04, 19.84 and 71.5 , respectively. According to these calculated parameters, theoretical predictions of the quadruple-passband bandpass filter are shown in Fig. 12c. Fig. 11. Architecture of the three-ordered quadruple-passband filter whose passbands have equal bandwidth (a) 3D architecture (b) Photograph DesignofMulti-PassbandBandpassFiltersWith Low-TemperatureCo-FiredCeramicTechnology 355 (c) Responses of the theoretical prediction and measurement Fig. 10. Three-ordered 2/5/8 GHz triple-passband bandpass filter whose second passband’s bandwidth is greater Within the first passband (1.66-2.11 GHz), the measured insertion loss is < 1.4 dB, whereas the return loss is > 16.8 dB. Moreover, within the second passband (4.6-5.35 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 16 dB. Furthermore, within the third passband (7.84-8.14 GHz), the measured insertion loss is < 3 dB, whereas the return loss is > 15 dB. 4.2 Quadruple-passband filter Figure 11 shows the architecture of the three-ordered quadruple-passband filter. The central frequencies of four passbands are set as 2, 5, 8 and 11.3 GHz. The bandwidth of four passbands is all chosen as 180 MHz, which is 9% of the first passband’s central frequency. Moreover, the selected ripple for the prototypical Chebyshev lowpass filter is 0.01 dB. As a result, the electrical length  0 and the impedances Z 11 , Z 12 , Z 13 , Z 14 , Z 21 , Z 22 , Z 23 , Z 24 and Z 1 are obtained as 26.8 o , 21.79, 19.61, 22.74, 14.54, 27.49, 16.01, 14.04, 19.84 and 71.5 , respectively. According to these calculated parameters, theoretical predictions of the quadruple-passband bandpass filter are shown in Fig. 12c. Fig. 11. Architecture of the three-ordered quadruple-passband filter whose passbands have equal bandwidth (a) 3D architecture (b) Photograph AdvancedMicrowaveandMillimeterWave Technologies:SemiconductorDevices,CircuitsandSystems356 (c) Responses of the theoretical prediction and measurement Fig. 12. Three-ordered 2/5/8/11.3 GHz quadruple-passband bandpass filter The multilayered 2/5/8/11.3 GHz bandpass filter is fabricated on 12 substrates of 0.09 mm, and its overall size is 4.72 mm  3.7 mm  1.08 mm. Figures 12a and 12b show the 3D architecture and the photograph of this fabricated filter; Fig. 12c also presents the measured results. Within the first passband (1.77-2.3 GHz), the measured insertion loss is < 1 dB, whereas the return loss is > 17 dB. Moreover, within the second passband (5.14-5.48 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 16 dB. In addition, within the third passband (8.06-8.4 GHz), the measured insertion loss is < 3 dB, whereas the return loss is > 15 dB. Furthermore, within the fourth passband (11.05-11.85 GHz), the measured insertion loss is < 4 dB, whereas the return loss is > 12.5 dB. 5. Conclusion A novel structure of the multi-passband bandpass filters has been proposed in this article. Multi-sectional short-circuit transmission lines shunted with transmission lines are utilized. By properly choosing the proposed structure’s electrical lengths and impedances, multiple passbands can be easily controlled. In addition, the design procedures have been described in detail, and 3D architectures are provided. Because of the parasitic effect among capacitors for a physical 3D circuit, there is some slight difference between the theoretical predictions and measured results. However, generally speaking, the measured results match well with the theoretical predictions. Therefore with high integration and compact size, the proposed multi-passband filter is suitable for implementation in a multi-chip module. By the way, because insertion loss measurement is related to the degree and bandwidth of a filter, the performance of a filter with resonators can be well indicated by translating the measurement into an unloaded Q of a resonator. 6. References [1] Bell, H. C. (2001). Zolotarev bandpass filters, IEEE Trans. Microw. Theory Tech., Vol. 49, No. 12, pp. 2357-2362 [2] Miyake, H.; Kitazawa, S.; Ishizaki, T.; Yamada, T. & Nagatomi, Y. (1997). A miniaturized monolithic dual band filter using ceramic lamination technique for dual mode portable telephones, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 789-792 [3] Quendo, C., Rius, E. & Person, C. (2003). An original topology of dual-band filter with transmission zeros, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 1093- 1096 [4] Chang, C. H.; Wu, H. S.; Yang, H. J. & Tzuang, C. K. C. (2003). Coalesced single-input single-output dual-band filter, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 511-514 [5] Tsai, C. M.; Lee, H. M. & Tsai, C. C. (2005). Planar filter design with fully controllable second passband, IEEE Trans. Microw. Theory Tech., Vol. 53, No. 11, pp. 3429-3439 [6] Yim, H. Y. & Cheng, K. K. M. (2005). Novel dual-band planar resonator and admittance inverter for filter design and applications, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 2187-2190 [7] Lee, J.; Uhm, M. S. & Yom, I. B. (2004). A dual-passband filter of canonical structure for satellite applications, IEEE Microw. Wireless Comp. Lett., Vol. 14, No. 6, pp. 271-273 [8] Kuo, J. T.; Yeh, T. H. & Yeh, C. C. (2005). Design of microstrip bandpass filters with a dual-passband response, IEEE Trans. Microw. Theory Tech., Vol. 53, No. 4, pp. 1331- 1337 [9] Chen, C. C. (2005). Dual-band bandpass filter using coupled resonator pairs, IEEE Microw. Wireless Comp. Lett., Vol. 15, No. 4, pp. 259-261 [10] Rong, Y.; Zaki, K. A.; Hageman, M.; Stevens, D. & Gipprich, J. (1999). Low temperature cofired ceramic (LTCC) ridge waveguide bandpass filters. Proceedings of IEEE MTT- S Int. Microw. Symp. Dig., pp. 1147-1150 [11] Heo, D.; Sutono, A.; Chen, E.; Suh, Y. & Laskar, J. (2001). A 1.9 GHz DECT CMOS power amplifier with fully integrated multilayer LTCC passives, IEEE Microw. Wireless Comp. Lett., Vol. 11, No. 6, pp. 249-251 [12] Leung, W. Y.; Cheng, K. K. M. & Wu, K. L. (2001). Design and implementation of LTCC filters with enhanced stop-band characteristics for bluetooth applications. Proceedings of Asia-Pacific Microw. Conf., pp. 1008-1011 [13] Tang, C. W.; Sheen, J. W. & Chang, C. Y. (2001). Chip-type LTCC-MLC baluns using the stepped impedance method, IEEE Trans. Microw. Theory Tech., Vol. 49, No. 12, pp. 2342-2349 [14] Tang, C. W.; Lin, Y. C. & Chang, C. Y. (2003). Realization of transmission zeros in combline filters using an auxiliary inductively-coupled ground plane, IEEE Trans. Microw. Theory Tech. , Vol. 51, No. 10, pp. 2112-2118 [15] Tang, C. W. (2004). Harmonic-suppression LTCC filter with the step impedance quarter- wavelength open stub, IEEE Trans. Microw. Theory Tech., Vol. 52, No. 2, pp. 617-624 [16] Tang, C. W.; You, S. F. & Liu, I. C. (2006). Design of a dual-band bandpass filter with low temperature co-fired ceramic technology, IEEE Trans. Microw. Theory Tech., Vol. 54, No. 8, pp. 3327-3332 DesignofMulti-PassbandBandpassFiltersWith Low-TemperatureCo-FiredCeramicTechnology 357 (c) Responses of the theoretical prediction and measurement Fig. 12. Three-ordered 2/5/8/11.3 GHz quadruple-passband bandpass filter The multilayered 2/5/8/11.3 GHz bandpass filter is fabricated on 12 substrates of 0.09 mm, and its overall size is 4.72 mm  3.7 mm  1.08 mm. Figures 12a and 12b show the 3D architecture and the photograph of this fabricated filter; Fig. 12c also presents the measured results. Within the first passband (1.77-2.3 GHz), the measured insertion loss is < 1 dB, whereas the return loss is > 17 dB. Moreover, within the second passband (5.14-5.48 GHz), the measured insertion loss is < 1.8 dB, whereas the return loss is > 16 dB. In addition, within the third passband (8.06-8.4 GHz), the measured insertion loss is < 3 dB, whereas the return loss is > 15 dB. Furthermore, within the fourth passband (11.05-11.85 GHz), the measured insertion loss is < 4 dB, whereas the return loss is > 12.5 dB. 5. Conclusion A novel structure of the multi-passband bandpass filters has been proposed in this article. Multi-sectional short-circuit transmission lines shunted with transmission lines are utilized. By properly choosing the proposed structure’s electrical lengths and impedances, multiple passbands can be easily controlled. In addition, the design procedures have been described in detail, and 3D architectures are provided. Because of the parasitic effect among capacitors for a physical 3D circuit, there is some slight difference between the theoretical predictions and measured results. However, generally speaking, the measured results match well with the theoretical predictions. Therefore with high integration and compact size, the proposed multi-passband filter is suitable for implementation in a multi-chip module. By the way, because insertion loss measurement is related to the degree and bandwidth of a filter, the performance of a filter with resonators can be well indicated by translating the measurement into an unloaded Q of a resonator. 6. References [1] Bell, H. C. (2001). Zolotarev bandpass filters, IEEE Trans. Microw. Theory Tech., Vol. 49, No. 12, pp. 2357-2362 [2] Miyake, H.; Kitazawa, S.; Ishizaki, T.; Yamada, T. & Nagatomi, Y. (1997). A miniaturized monolithic dual band filter using ceramic lamination technique for dual mode portable telephones, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 789-792 [3] Quendo, C., Rius, E. & Person, C. (2003). An original topology of dual-band filter with transmission zeros, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 1093- 1096 [4] Chang, C. H.; Wu, H. S.; Yang, H. J. & Tzuang, C. K. C. (2003). Coalesced single-input single-output dual-band filter, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 511-514 [5] Tsai, C. M.; Lee, H. M. & Tsai, C. C. (2005). Planar filter design with fully controllable second passband, IEEE Trans. Microw. Theory Tech., Vol. 53, No. 11, pp. 3429-3439 [6] Yim, H. Y. & Cheng, K. K. M. (2005). Novel dual-band planar resonator and admittance inverter for filter design and applications, Proceedings of IEEE MTT-S Int. Microw. Symp. Dig., pp. 2187-2190 [7] Lee, J.; Uhm, M. S. & Yom, I. B. (2004). A dual-passband filter of canonical structure for satellite applications, IEEE Microw. Wireless Comp. Lett., Vol. 14, No. 6, pp. 271-273 [8] Kuo, J. T.; Yeh, T. H. & Yeh, C. C. (2005). Design of microstrip bandpass filters with a dual-passband response, IEEE Trans. Microw. Theory Tech., Vol. 53, No. 4, pp. 1331- 1337 [9] Chen, C. C. (2005). Dual-band bandpass filter using coupled resonator pairs, IEEE Microw. Wireless Comp. Lett., Vol. 15, No. 4, pp. 259-261 [10] Rong, Y.; Zaki, K. A.; Hageman, M.; Stevens, D. & Gipprich, J. (1999). Low temperature cofired ceramic (LTCC) ridge waveguide bandpass filters. Proceedings of IEEE MTT- S Int. Microw. Symp. Dig., pp. 1147-1150 [11] Heo, D.; Sutono, A.; Chen, E.; Suh, Y. & Laskar, J. (2001). A 1.9 GHz DECT CMOS power amplifier with fully integrated multilayer LTCC passives, IEEE Microw. Wireless Comp. Lett., Vol. 11, No. 6, pp. 249-251 [12] Leung, W. Y.; Cheng, K. K. M. & Wu, K. L. (2001). Design and implementation of LTCC filters with enhanced stop-band characteristics for bluetooth applications. Proceedings of Asia-Pacific Microw. Conf., pp. 1008-1011 [13] Tang, C. W.; Sheen, J. W. & Chang, C. Y. (2001). Chip-type LTCC-MLC baluns using the stepped impedance method, IEEE Trans. Microw. Theory Tech., Vol. 49, No. 12, pp. 2342-2349 [14] Tang, C. W.; Lin, Y. C. & Chang, C. Y. (2003). Realization of transmission zeros in combline filters using an auxiliary inductively-coupled ground plane, IEEE Trans. Microw. Theory Tech. , Vol. 51, No. 10, pp. 2112-2118 [15] Tang, C. W. (2004). Harmonic-suppression LTCC filter with the step impedance quarter- wavelength open stub, IEEE Trans. Microw. Theory Tech., Vol. 52, No. 2, pp. 617-624 [16] Tang, C. W.; You, S. F. & Liu, I. C. (2006). Design of a dual-band bandpass filter with low temperature co-fired ceramic technology, IEEE Trans. Microw. Theory Tech., Vol. 54, No. 8, pp. 3327-3332 AdvancedMicrowaveandMillimeterWave Technologies:SemiconductorDevices,CircuitsandSystems358 [17] Sun, S. & Zhu, L. (2006). Novel design of microstrip bandpass filters with a controllable dual-passband response: description and implementation, IEICE Trans. Electron., Vol. E89-C, No. 2, pp.197-202 [18] Quendo, C.; Manchec, A.; Clavet, Y.; Rius, E.; Favennec, J. F. & Person, C. (2007). General Synthesis of N-Band Resonator Based on N-Order Dual Behavior Resonator, IEEE Microw. Wireless Comp. Lett., Vol. 17, No. 5, pp. 337-339 [19] Matthaei, G.L.; Young, L. & Jones, E.M. (1980). Microwave filters, impedance-matching network, and coupling structures, Artech House, Norwood, MA TheSwitchedModePowerAmpliers 359 TheSwitchedModePowerAmpliers ElisaCipriani,PaoloColantonio,FrancoGianniniandRoccoGiofrè x The Switched Mode Power Amplifiers Elisa Cipriani, Paolo Colantonio, Franco Giannini and Rocco Giofrè University of Roma Tor Vergata Italy 1. Introduction The power amplifier (PA) is a key element in transmitter systems, aimed to increase the power level of the signal at its input up to a predefined level required for the transmission purposes. The PA’s features are mainly related to the absolute output power levels achievable, together with highest efficiency and linearity behaviour. From the energetic point of view a PA acts as a device converting supplied dc power (P dc ) into microwave power (P out ). Therefore, it is obvious that highest efficiency levels become mandatory to reduce such dc power consumption. On the other hand, a linear behaviour is clearly necessary to avoid the corruption of the transmitted signal information. Unfortunately, efficiency and linearity are contrasting requirements, forcing the designer to a suitable trade-off. In general, the design of a PA is related to the operating frequency and application requirements, as well as to the available device technology, often resulting in an exciting challenge for PA designers, since not an unique approach is available. In fact, PAs are employed in a broad range of systems, whose differences are typically reflected back into the technologies adopted for PAs active modules realisation. Moreover, from the designer perspective, to improve PAs efficiency the active devices employed are usually driven into saturation. It implies that a PA has to be considered a non-linear system component, thus requiring dedicated non linear design methodologies to attain the highest available performance. Nevertheless, for high frequency applications it is possible to identify two main classes of PA design methodologies: the trans-conductance based amplifiers with Harmonic Tuning terminations (HT) (Colantonio et al., 2009) or the Switching-Mode (SM) amplifiers (Grebennikov & Sokal, 2007; Krauss et al., 1980). In the former, the active device acts as a nonlinear current source controlled by the input signal (voltage or current for FET or BJT devices respectively). A simplest schematic view of such an amplifier for FET is reported in Fig. 1a. Under this assumption, the high efficiency condition is achieved exploiting the device nonlinear behaviour through a suitable selection of both input and output harmonic terminations. More in general, the trans-conductance based amplifiers are identified also as Class A, AB, B to C considering the quiescent active device bias points, resulting in different output current conduction angles from 2 to 0 respectively. The most famous solution of HT PA is the Class F approach (Gao, 2006; Colantonio et al, 2009), while for high frequency applications and taking into account practical limitations on 18 AdvancedMicrowaveandMillimeterWave Technologies:SemiconductorDevices,CircuitsandSystems360 the control of harmonic impedances, several solutions have been successfully proposed (Colantonio et al., 2003). Conversely, in the SM PA, the active device is driven by a very large input signal to act as a ON/OFF switch with the aim to maximise the conversion efficiency reducing the power dissipated in the active devices also. A schematic representation of a SM amplifier is depicted in Fig. 1b. When the active device is turned on, the voltage across its terminals is close to zero and high current is flowing through it. Therefore, in this part of the period the transistor acts as a very low resistance, ideally short circuit (switch closed) minimising the overlap between the current and voltage waveforms. In the other part of the period, the active device is turned off acting as an open circuit. Therefore, the current is theoretically zero while high voltage is present at the device terminals, once again minimising the overlap between voltage and current waveforms. If the active device shows a zero on resistance and an infinite off resistance, a 100% efficiency is theoretically achieved. The latter is of course an advantage over Class A or B, where the maximum theoretical efficiencies are 50 % and 78 % respectively. On the other hand, Class C could achieve high efficiency levels, despite a significant reduction in the maximum output power level achievable (theoretically 100% of efficiency for zero output power). Nevertheless, the HT PAs are intrinsically able to amplify the input signal with higher fidelity, since the active device is basically represented by a controlled current source (FET case) whose output current is directly related to the input voltage. Instead, in SM PAs the active device is assumed to be ideally driven in the ON and OFF states, thus exhibiting a higher nonlinear behaviour. However, this characteristic does not represent a trouble when signals with constant-envelope modulation are adopted. On the basis of their operating principle, SM amplifiers are often considered as DC to RF converter rather than RF amplifiers. V DD L RFC R L Output Matching Input Matching i DS V DD L RFC R L Output Resonator Input Matching i DS v DS HT PA SM PA Fig. 1. Simplified view of a simple single ended HT (left) and SM (right) PA. Different SM PA classes of operation have been proposed over the years, namely Class D, S, J, F -1 (Cripps, 2002; Kazimierczuk, 2008), while the most famous and adopted is the Class E PA (Sokal & Sokal, 1975; Sokal, 2001) that will be described in deep detail in the following. As will be shown, these classes are based on the same operating principle while their main differences are related to their circuit implementation and current-voltage wave shaping only. The applications of SM PAs principles have initially been limited to amplifiers at lower frequencies in the megahertz range, due to the active device and package parasitics practically limiting the operating frequencies (Kazimierczuk, 2008). They have also been applied to DC/DC power converters that also operate at lower switch frequencies (Jozwik & Kazimierczuk, 1990; Kazimierczuk & Jozwik, 1990). Recently, their principles of operation have been extended and applied to RF and microwave amplifier design, made possible by the high-performance active devices nowadays available based on silicon (Si), gallium arsenide (GaAs), silicon germanium (SiGe), silicon carbide (SiC), and gallium nitride (GaN) technologies (Lai, 2009). 2. Switching mode generic operating principle The operating principle of every SM PA is based on the idea that the active device operates in saturation, thus it can be represented as a switch and either voltage or current waveforms across it are alternatively minimized to reduce overlap, so minimizing power dissipation in the device itself. If the transistor is an ideal switch, a 100% of efficiency can be achieved by the proper design of the output matching network. As reported in Fig. 1b, the output resonator can be assumed, in the simplest way, as an ideal L-C series resonator at fundamental frequency, terminated on a series load resistance (R L ). The role of the resonator is to shape the voltage and current waveforms across the switch in order to avoid power dissipation at higher harmonics. In fact, an ideal L-C series resonator shows zero impedance at resonating frequency ( 0 =(LC) -1/2 ) and infinite impedance for every ω≠ω 0 . It follows that fundamental current only is flowing into the output load and fundamental voltage only is generated at its terminals. Consequently, 100% of efficiency is obtained (being zeroed the overlap between voltage and current waveforms over the transistor, thus being nulled the power dissipated in it) and no power is delivered at harmonic frequencies in the load, being the latter not allowed to flow into the load R L . In actual cases, several losses mechanisms, such as ohmic and capacitive discharge or leakage, cause an unavoidable overlapping between the voltage and current waveforms, together with power dissipation at higher harmonics, thus limiting the maximum achievable efficiency levels. The most relevant losses in SM PA are represented by:  parasitic capacitors, such as the device drain to source capacitance C ds . The presence of such capacitance causes a low pass filter behaviour at the output of the active device, affecting the voltage wave shaping with a consequent degradation in the attainable power and efficiency levels. In fact, considering the active device as the parallel connection of a perfect switch and the parasitic capacitance C ds , the higher voltage harmonics are practically shorted by C ds and only few harmonics can be reasonably controlled by the loading network.  parasitic resistance, such as the drain-to-source resistance when the transistor is conducting R ON (ON state). In fact, due to the non zero resistance when the switch is closed, a relevant amount of active power will be dissipated in the transistor causing a lowering in the achievable efficiency.  non-zero transition time, due to the presence of parasitic effects, which increase the voltage and current overlap.  implementation losses due to the components (distributed or lumped elements) employed to realise the required input and output matching networks. [...]... Power Transistors, IEEE MTT-S Int Microwave Symp Dig., Orlando, FL, June 1995, pp .103 7 -104 0 386 Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems Cipriani, E.; Colantonio, P.; Giannini, F & Giofré, R (2008) Optimization of Class E Power Amplifier Design above Theoretical Maximum Frequency, Proceedings of 38th European Microwave Conference, EuMC 2008, pp... continuous wave excitation, Class E behavior is achieved only at a certain level of compression, i.e when the large input sinusoidal waveform implies a “square-shaping” effect on the output current, due to active device physical limits, thus Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 368 approaching a switching behavior The output current and voltage waveforms... the same results as the classical formulation: they have been widely investigated in (Grebennikov, 2003) and are commonly referred as parallel circuit Class E and their main characteristic is the presence of Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 372 a finite parallel inductor in the output network, required for the output device biasing supply,... transmission line can be obtained: tan   0.732 R Z0 (37) Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 374 4 The inverse Class E amplifier The Inverse Class E amplifier, or voltage drive Class E amplifier, is commonly considered as the dual version of the Class E amplifier, in which current and voltage waveforms are interchanged, as shown in Fig 13 It is... time, due to the presence of parasitic effects, which increase the voltage and current overlap  implementation losses due to the components (distributed or lumped elements) employed to realise the required input and output matching networks Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 362 The entity of the parasitic components as well as the associated... output capacitance of the active device is not taken into account and set to zero in the ideal analysis: in real world circuit, this is clearly not true Hence, some actions have to be taken in order to compensate its presence (e.g a shunt inductance) Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 376 Circuit component or electrical value VMax Class E... scheme (i.e short circuiting all the harmonic terminations) Conversely, short circuit condition for even harmonics and open circuit for odd ones have to be synthesized, as schematically depicted in Fig 17 Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 378 VGG Zmatch @f0 VDD Bias TEE IN Bias TEE + @f0 @nf0 n>1 @nf0 n odd Id Vds @nf0 n even OUT - Z1 Zodd=�... given by (27) and depicted in Fig 7a as a function of normalized frequency k=f/fMax, defined as the ratio between the assumed operating frequency f and the maximum Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 370 allowed one fMax, defined in (27) The plot shown in Fig 7a can be considered as a “design chart” for high frequency Class E development,... value Finally, the inductance L is computed taking into account that its reactive energy is exchanged, at every cycle, with the capacitance C1 Thus it follows: Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 366 2 1 1  1  I DC  I M  sin      d     L  I M 2   2   C1 0  2  (22) where the expression in the integral represents the voltage... amplifier performance as compared to higher order ones (Raab, 2001) Therefore, accounting for the reduced number of harmonics can be effectively controlled, new Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems 380 terminating impedance values have been inferred not only at fundamental but also at harmonics, resulting in a different voltage harmonic ratio also . thus Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems3 68 approaching a switching behavior. The output current and voltage waveforms and load. Photograph Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems3 54 (c) Responses of the theoretical prediction and measurement Fig. 10. Three-ordered. architecture (b) Photograph Advanced Microwave and Millimeter Wave Technologies: Semiconductor Devices, Circuits and Systems3 56 (c) Responses of the theoretical prediction and measurement Fig.