Design of Class-E Oscillator With Second Harmonic ... - IEEE Xplore
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Design of Class-E Oscillator With Second Harmonic Injection Ryosuke Miyahara, Xiuqin Wei, Student Member, IEEE, Tomoharu Nagashima, Student Member, IEEE, Takuji Kousaka, Member, IEEE, and Hiroo Sekiya, Senior Member, IEEE
Abstract—This paper presents the class-E oscillator with the second-harmonic injection current, along with its design procedure, design curves, and design example. In the proposed oscillator, the output frequency of the proposed oscillator is locked with the input frequency of the injection circuit. Additionally, the switch-voltage and switch-current waveforms in the main circuit achieve the class-E zero-voltage switching, zero-voltage-derivative switching, zero-current switching, and zero-current-derivative switching (ZVS/ZVDS/ZCS/ZCDS) conditions and the switch voltage waveform in the injection circuit satisfied the class-E ZVS/ZDS conditions. In the laboratory experiment, the oscillator achieved 92.0% power-conversion efficiency at 34.8 W output power and 1 MHz operating frequency. The experimental results agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. Index Terms—Class-E amplifier, efficiency enhancement, freerunning class-E oscillator, injection-locked class-E oscillator, zerocurrent-derivative switching, zero-current switching, zero-voltagederivative switching, zero-voltage switching.
I. INTRODUCTION
T
HE class-E oscillator [1]–[7] offers high efficiency at high frequencies because it satisfies the class-E zero-voltage switching and zero-voltage-derivative switching (ZVS/ZVDS) conditions [8]–[14]. The class-E oscillator can be classified into two categories. One is the free-running oscillator and the other is the injection-locked oscillator. The injection-locked techniques allow the class-E oscillators to achieve a high overall efficiency and a high stability of oscillation frequency [5]–[7]. In many applications, the class-E oscillators can perform the same functions as the class-E amplifiers. They are applicable to FM oscillators, AM transmitters, electric ballast, the inverter part of Manuscript received September 16, 2011; revised December 26, 2011; accepted January 31, 2012. Date of publication April 04, 2012; date of current version September 25, 2012. This work was supported in part by the Scholarship Foundation and Grant-in-Aid for Scientific Research (No. 23760253) of JSPS, the Support Center for Advanced Telecommunications Technology Research, and the Telecommunications Advancement Foundation, Japan. This paper was recommended by Associate Editor Eduard Alarcon. R. Miyahara was with the Graduate School of Advanced Integration Science, Chiba University, Chiba, 263-8522 Japan. He is now with Ricoh Company, Tokyo 143-8555, Japan. X. Wei is with the Department of Electronics Engineering and Computer Science, Fukuoka University, Fukuoka 814-0180, Japan. T. Nagashima and H. Sekiya are with the Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan (e-mail: sekiya@ faculty.chiba-u.jp). T. Kousaka is with the Department of Mechanical and Energy Systems Engineering, Oita University, Oita 870-1192, Japan. Digital Object Identifier 10.1109/TCSI.2012.2188936
dc/dc converters, and more. The switch-current waveform of the class-E oscillator, however, includes a jump at the switch turn-off instant, which deteriorates the power conversion efficiency and increases the circuit-implementation cost. power amplifier [15]–[20] is an improved The classversion of the class-E amplifier [8]–[13], which has the main and injection circuits. By injecting the second-harmonic current to the switch, the main circuit satisfies not only the class-E ZVS/ZVDS conditions at the transistor turn-on instant but also zero-current switching (ZCS) and zero-current-derivative switching (ZCDS) conditions at the transistor amplifier enhances turn-off instant. Therefore, the classthe power-conversion efficiency even if the transistor has a amplifier needs long turn-off-switching time. The classtwo input signals, which drive the switching elements in the main and injection circuits. In circuit implementations, the phase-shift should be fixed at a certain value. However, it is complicated to design the driver circuit with a halfway value of the phase-shift. The design of the driving circuit is one of the amplifier. problems for the classThis paper, which was previously presented in part at ECCE 2009 [20],1 presents the classoscillator with the second-harmonic injection. In the proposed oscillator, the output frequency of the proposed oscillator is locked with the input frequency of the injection circuit. Additionally, the switch-voltage and switch-current waveforms in the main ZVS/ZVDS/ZCS/ZCDS condicircuit achieve the classtions and the switch voltage waveform in the injection circuit satisfied the class-E ZVS/ZDS conditions. The proposed circuit is regarded as an improvement version not only of the class-E amplifier for the fixed freoscillator but also of the classquency and the fixed dc-supply voltage applications. Because there is one input signal in the proposed oscillator, it is not necessary to adjust the phase shift between the main and injection circuits. Therefore, the driver circuit of the proposed oscillator amplifier. The numerical is simpler than that of the classdesign procedure is presented for the proposed oscillator designs. The design curves and the design example, considered with the MOSFET body junction diode nonlinear capacitances and equivalent series resistances (ESRs) of each component, are shown. In the laboratory experiment, the oscillator achieved 92.0% power-conversion efficiency at 34.8-W output power and 1-MHz operating frequency. The experimental results 1In this paper, the proposed circuit is mainly explained from the oscillator point of view. The injection circuit achieves the class-E ZVS/ZVDS conditions though only ZVS condition is achieved in [20]. Additionally, the effect of MOSFET body junction diode nonlinear capacitance is considered in the design. The design curves and design example are newly given.
1549-8328/$31.00 © 2012 IEEE
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Fig. 2. Nominal waveforms of the class-E oscillator for Fig. 1. Circuit topology of the class-E oscillators. (a) Free-running class-E oscillator. (b) Injection-locked class-E oscillator.
agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. II. RELATED WORKS A. Class-E Oscillator Fig. 1(a) shows the circuit topology of the free-running class-E oscillator [1]–[4]. The class-E oscillator consists of the class-E amplifier [8]–[14] and feedback network , and . and give the bias voltage, which equals to the threshold voltage for the gate of the MOSFET. Fig. 2 shows an example of the nominal waveforms of the class-E oscillator. The MOSFET of the class-E oscillator is driven by the feedback voltage , which is from the output voltage . The feedback voltage is a sinusoidal waveform because the feedback current flow through the resonant filter, which consists of , gate-source parasitic capacitance, and gate-source parasitic resistance. By adjusting , , and , the amplitude and phase shift between the output voltage and the feedback voltage are adjusted. The switch voltage achieves the class-E zero-voltage switching and zero-voltage-derivative switching (ZVS/ZVDS) conditions at turn-on instant, which are (1) Because of the class-E ZVS/ZDS, the class-E oscillator achieves high power-conversion efficiency at high frequencies. Fig. 1(b) shows an example topology of the injection-locked class-E oscillator [5]–[7]. When the injection voltage has proper frequency and amplitude, the feedback current is synchronized with the and the feedback-current frequency is locked with the frequency of injection voltage. The synchronization occurs even when the injection power is much lower
.
than the driving power for the MOSFET. Therefore, the injection-locked class-E oscillator offers a stable frequency output with low power injection. In the class-E oscillator, the switch-voltage waveform is smooth because of the class-E ZVS/ZDS conditions. The switch-current waveform, however, includes jumps at every turn-off instant as shown in Fig. 2. When current fall time cannot be negligible, these jumps cause the power dissipations [19]. To avoid this problem, a fast-speed MOSFET or high driving power is required. The fast-speed MOSFET suffers from the implementation cost. The high-driving power deteriorates the power-added efficiency. B. Class-
Amplifier
Fig. 3(a) shows a circuit topology of the classpower amplifier [15]–[20]. The classamplifier has the main and injection circuits. Each circuit has a similar topology to the class-E amplifier. Fig. 3(b) shows the example waveforms of the classamplifier in the nominal operation when the switch-off duty ratio of the main circuit is 0.5. The switch is driven by the input signal as shown in Fig. 3(b). The switch voltage satisfies the class-E ZVS/ZVDS conditions at transistor turn-on instant. Additionally, the switch current achieves the zerocurrent switching (ZCS) and zero-current-derivative switching (ZCDS) conditions simultaneously at the transistor turn-off instant. Because of the ZCS/ZCDS conditions, the waveforms of both the switch voltage and current at the transistor turn-off are also smooth. These switching conditions are expressed as (2) (3)
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Fig. 4. Proposed oscillator topology.
circuit is necessary [15], [21]. The injection circuit should provide the second-harmonic current with the proper phase-shift and the proper amplitude for achieving the ZCS/ZCDS conditions in the main-circuit switch. The switch voltage is transformed into the sinusoidal output voltage through the resonant filter . The classamplifier needs two input signals and , which drive the switching elements in the main and injection circuits, respectively. The phase-shift between the two input signals is an important and useful parameter for adjusting the phase shift of the second-harmonic injection current. In circuit implementations, the phase-shift , which is determined by the other design specifications, should be fixed at a certain value. However, it is complicated to design the driver circuit with the halfway value of the phase-shift. Therefore, was specified in [19] and the injection circuit achieved only the ZVS condition. The design of the driver circuit is one of the problems for the classamplifier. III. CLASSOSCILLATOR WITH SECOND HARMONIC INJECTION Fig. 3. Classand
amplifier. (a) Circuit topology. (b) Nominal waveforms for .
where is the phase shift between two input signals as shown in Fig. 3(b). Because of the switching conditions in (2) and (3), which are called the classZVS/ZVDS/ZCS/ZCDS conditions in this paper, there are no jumps on the switch-voltage and switch-current waveforms in the main circuit. Therefore, the classamplifier enhances high power conversion efficiency even if the main-circuit transistor has a long turn-off-switching time and lowers the implementation cost [15]. To achieve the ZCS/ZCDS conditions in the classamplifier, the injection
Fig. 4 shows a circuit topology of the proposed oscillator, which is composed of the main circuit and the injection circuit. The main circuit is the free-running class-E oscillator and the injection circuit is the class-E frequency doubler [22]–[24]. The nominal waveforms of the proposed oscillator are shown in Fig. 5. The main circuit is driven by the feedback voltage from the output voltage. The switch voltage of the main circuit achieves the classZVS/ZVDS/ZCS/ZCDS conditions by injecting the second-harmonic current to the main switch. The injection circuit is driven by the input signal whose fundamental frequency is the same as the output voltage. In other words, the output frequency is locked with the input frequency. In this sense, the proposed oscillator is regarded as one of the injection-locked oscillators. From the above explanations, it can
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Unstable behaviors, however, appear in the proposed oscillator when the input frequency is changed from the nominal due to the feedback topology. In the classamplifier, the operation can be always stable regardless of the input frequency. This is because the ratio of the input frequency between the main and injection circuits can be kept and the classamplifier is an open-loop circuit. Additionally, it is necessary to consider the additional cost compared with the classamplifier. For example, the bias voltage for driving the main-circuit MOSFET is supplied by using and as shown in Fig. 4, which is based on the assumption of the fixed supply voltage. For example, if the proposed oscillator is applied to the Envelope Elimination and Restoration (EER) systems for wireless-communication amplifiers [25], the control circuit for supplying the main-circuit-MOSFET bias voltage should be newly designed. IV. CIRCUIT DESIGN
Fig. 5. Nominal waveforms of the proposed oscillator without MOSFET drain-to-source capacitances.
be stated that the injection circuit has multiple roles in the proposed oscillator. First, it offers the classZVS/ZVDS/ZCS/ ZCDS conditions, which enhance the power-conversion efficiency and allow to use a slow switching MOSFET. Following the same logic in [15], it is possible to reduce the circuit-implementation cost, especially, the main-circuit-MOSFET cost. Second, the output-voltage frequency is locked with the inputsignal frequency, which is half as high as the injection-current frequency. If we apply the class-E amplifier, whose operating frequency is twice as high as the main circuit, instead of the class-E doubler as injection circuit, it looks like the frequency divider. Finally, the output power becomes high by adding the injection circuit, which is useful for high-power applications. The proposed circuit is also regarded as an improved version of the classamplifier [20]. By reducing the number of input signals from two to one, the driver-circuit design of the proposed circuit is much simpler than that of the classamplifier for the fixed frequency and the fixed dc-supply voltage applications. For example, it is unnecessary to specify the phase-shift between the main and injection circuits. Therefore, one more adjacent parameter can be obtained. As a result, one more switching condition can be specified for the injection circuit design. Therefore, it is possible to apply the class-E ZVS/ZDS conditions to the injection circuit, which improves the power-conversion efficiency of the injection circuit compared to the injection circuit of the classamplifier in [19]. The total driving power can be reduced by using the feedback network at the main circuit, which improves the power-added efficiency. From the above discussions, it can be stated that the proposed oscillator has some features from not only the class-E oscillator point of view but also the classamplifier point of view.
The proposed oscillator is a high-dimensional circuit. Moreover, the proposed oscillator has four switching conditions in the main circuit, two switching conditions in the injection circuit, phase-matching condition for the feedback voltage, and output-power condition. Therefore, it is difficult to obtain analytical design equations for achieving all the conditions. In this paper, the numerical design procedure proposed in [11] is applied to the design of the proposed oscillator. By using this design procedure, it is possible to obtain the element values for achieving multiple restrict conditions. A. Assumptions First, the following assumptions are given. 1) The switching devices and have non-zero on-resistances and and MOSFET body junction diode nonlinear capacitances . Additionally, has the equivalent gate-to-source capacitance and the equivalent gate-to-source resistance . 2) Shunt capacitances and are the sum of the MOSFET body junction diode nonlinear capacitance and the external linear capacitance . The body junction diode nonlinear capacitances of the MOSFET are expressed as (4)
is the built-in potential, is the capacitance where at , and is the grading coefficient of the diode junction [13], [26]. 3) The equivalent series resistances (ESRs) of the inductors are considered. The ESRs of all the capacitors are negligible since they are much smaller than the ESRs of the inductors. 4) All the passive elements except the MOSFET body junction diode capacitances work as linear elements. 5) For simplicity, the following equations are addressed for only the case of . The switch of the injection
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TABLE I SWITCHING PATTERN OF THE MAIN CIRCUIT THE PROPOSED OSCILLATOR FOR
9) IN
10) 11) 12)
SWITCHING
TABLE II PATTERN OF THE INJECTION CIRCUIT THE PROPOSED OSCILLATOR
IN
13) 14)
15) 16) 17)
: the ratio of the resonant frequency in the feedback network to the operating frequency. : the loaded quality factor in the main circuit. : the loaded quality factor in the injection circuit. : the loaded quality factor in the feedback network. : the ratio of the dc-supply voltages. : the phase-shift of the driving signals between the main and the injection circuits, which is in the range of . : the ESR of . : the ESR of . : the ESR of .
C. Circuit Equations We consider the operations for to design the proposed oscillator, where represents the angular time. Using the parameters, the circuit equations are expressed as
Fig. 6. Equivalent circuit of the proposed oscillator.
circuit turns off at and the switching patterns are given in Tables I and II. According to the above assumptions, the equivalent circuit of the proposed oscillator is obtained as shown in Fig. 6. B. Parameters In order to express the circuit equations, the following parameters are defined. The subscripts and 2 mean the main and injection circuits, respectively. 1) : The operating angular frequency. 2) : the resonant frequency. 3) : the resonant frequency in the feedback network. 4) : the ratio of the resonant frequency to the operating frequency. 5) : the ratio of the resonant capacitance to the shunt capacitance for switch voltage . 6) : the ratio of the resonant inductance to the dc-feed inductance. 7) : the ratio of the resonant capacitance in the main circuit to the feedback network capacitance. 8) : the ratio of the capacitances in the feedback network.
(5) In (5), and are the equivalent drain-to-source resistances of the MOSFETs and , which are given as for for for for
and , .
(6)
When we express
(5) can be rewritten as (7)
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For achieving the specified output power relation should be valid:
where
, the following
(14)
D. Conditions for the Design We assume (5) has a solution defined on condition and every of the oscillator is expressed by
with every initial . The steady state (8)
Therefore, (9) is given as the boundary conditions between and . In order to design the proposed oscillator, we have to consider switching conditions, phase-matching condition for the feedback voltage, and output-power condition. As the switching conditions on , (2) and (3) should be considered. The softswitching conditions in the injection circuit improve the whole power conversion efficiency. Therefore, the class-E ZVS/ZVDS conditions at the transistor turn-on are applied in the injection circuit. As a result, we obtain the six switching conditions as
For the calculations of the integration in (14), we apply the trapezoidal method in this paper. From the above considerations, we recognize that the design of the proposed classoscillator reduces to derive the resolutions of the algebraic equations (9)–(11), (13), and (14). There are 21 algebraic equations with 12 unknown initial values. Therefore, nine parameters can be set as the design parameters from . The other parameters should be given as the design specifications. The algebraic equations are solved by the Newton’s method, whose detailed algorithms are described in [11]. For solving the algebraic equations by using Newton’s method, the initial values for iterative calculations are important [19]. First, by using certain values of the variations and , e.g., which are assumed from [1] and [19], the values of are obtained as . Second, the algebraic equations are solved by using the Newton’s method with and as the initial values, where , and is an integer value. The algebraic equaare solved by using the Newton’s tions and . After itmethod with the initial values of erations, we can obtain the solution of the algebraic equations . V. DESIGN CURVE
(10)
The phase matching for the feedback voltage means that the feedback voltage is equal to when the main-circuit switch turns off. Therefore, the equation (11) is given. Since the switch of the main circuit turns off at , the condition (12) is added. If the gate-source voltage of the MOSFET is larger than the maximum gate-source voltage in FET manuals, the MOSFET may be broken. For avoiding this, the feedback voltage should be smaller than the maximum gate-source voltage. When the maximum value of the feedback voltage is defined as , we have (13) is given as a design specification for
.
In this section, the design curves of the proposed oscillator are shown. The design specifications are , , , , and . The parameters of the MOSFETs are assumed as: , , , , , and . For solving the algebraic equations, , , , , , , , , and are set as unknown parameters. The design curves are obtained from the design algorithm in Section IV. Fig. 7 shows the design parameters , , , , , , , , normalized maximum switch voltages, and normalized output power for fixed as a function of the ratio of the dc-supply voltages . It is seen from Fig. 7(a)–(e) that , , , , and have similar characteristics to those of the classoscillator [18], which means that the existence of the feedback network does not affect the element values of the main and injection circuits. From Fig. 7(d), goes infinity as decreases. The infinite means that the external shunt capacitance of the injection circuit becomes zero. Therefore, the lower limit of is governed by , which are 0.214, 0.216, and 0.193 for 5, 3, and 1, respectively. On the other hand, from Fig. 7(e), goes infinity as increases. The infinite appears because the injected power should be limited in spite of high for achieving the ZCS/ZCDS conditions. Therefore, the upper limit of is governed by , which are , 0.566, and 0.557 for 5, 3, and 1, respectively. From Fig. 7(g) and (h), the feedback-network parameters and are changed as varies. These plots show that the
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Fig. 8. Design parameters of normalized output power . of dc-supply voltages as a function of
and ratio
parameters of the main and injection circuits affect the element values of the feedback network. From Fig. 7(i), the normalized maximum switch voltage of is almost constant regardless of and the normalized maximum switch voltage of increases in proportion to the increase in . From Fig. 7(j), it is seen that the normalized output power has the maximum value for variations. From this figure, it can be stated that the maximum output power depends on . Fig. 8 shows the maximum normalized output power and the ratio of the dc-supply voltages for achieving the maximum normalized output power as a function of . For , the maximum normalized output power is almost constant. This is because the output current is pure sinusoidal for . For , however, the maximum normalized output power varies significantly because the dc component of the output current increase as decreases. VI. DESIGN EXAMPLE In this section, the design example of the proposed oscillator is shown. The design specifications are , , and , which follow the specifications in [12]. Additionally, we also specify , , and . A. Selection of MOSFET First, the MOSFETs should be selected. From Fig. 8, the maxis 1.74. As a result, imum normalized output power for the minimum dc-supply voltage of the main circuit for achieving the specified output power is obtained as (15) We choose power is calculated as
. Therefore, the normalized output (16)
Fig. 7. Design parameters of the proposed oscillator as a function of . (a) De. (b) Design parameters of . (c) Design parameters sign parameters of . (d) Design parameters of . (e) Design parameters of . (f) Design of . (g) Design parameters of . (h) Design parameters of . parameters of (i) Design parameters of normalized maximum switch voltages and . (j) Design parameters of .
From the normalized output power and , the value of is obtained as from Fig. 7(j). Therefore, the maximum switch voltages are obtained from Fig. 7(i), which are and . In this design, IRF740 MOSFET
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TABLE III PARAMETERS FOR IRF740 MOSFET
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TABLE IV EXPERIMENTAL RESULTS
is selected for and . Table III gives the parameters for the IRF740 MOSFET. In this table, , , , and drain-tosource break down voltage are obtained from the FET manual, and were measured values by LCR meter of HP 4284A, and , , and are obtained from the Spice model [27]. From and , and are given. B. Approximate ESR Values Using MOSFET parameters, the element values without considering ESR values can be calculated from the design algorithm in Section III. The calculated inductor values are , , , , and . The current waveforms through the inductors can be also obtained from the design algorithm. For the resonant inductor implementations, Micrometals toroidal cores of T200-2, T130-2, and T94-2 are used for , , and , respectively. For the dc-feed inductor implementations, TDK EI30 cores with TDK BE-30-5112 bobbin are used for and . Following the calculations in [28] and [29], we can obtain the approximate ESR values of the inductors as , , , , and , respectively. C. Derivation of the Element Values Finally, we obtain the element values taking into account the MOSFET parameters and ESR values from the design algorithm in Section III. The element values are obtained as given in Table IV. All element values including ESR values were measured by the HP 4284A LCR meter. The maximum switch voltage of the injection-circuit switch increases to 262 V. This is because the nonlinearity of the MOSFETs and ESRs of the inductors are considered in the oscillator design. D. Experimental Result Fig. 9 depicts the numerical waveforms and the experimental waveforms for the obtained design parameters. Note that . Because we consider the MOSFET drain-to-source capacitances, namely , are not zero when the switch is in off state. In Fig. 9, it is confirmed that the experimental oscillator satisfied all the switching conditions, namely, ZVS/ZVDS conditions at the main-circuit transistor turn-on, ZCS/ZCDS conditions at the main-circuit transistor turn-off, and ZVS/ZVDS conditions at the injection-circuit transistor turn-on. Table IV gives the calculated element values from the design algorithm in Section III and the measured values in the labora-
Fig. 9. Waveforms of the proposed oscillator. (a) Calculated waveforms. : 5 V/div, , : (b) Experimental waveforms. Vertical: : 20 V/div, : 2 A/div, : 200 V/div. Horizontal: 200 nS/div. 200 V/div,
tory experiment. In this table, dc-supply voltages and dc-supply currents were measured by the Iwatsu VOAC7532 digital multimeter. Additionally, the measured output power was obtained from
(17)
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where was measured by the Agilent 3458A digital multimeter. The input power was measured by the Textronix TDS3014B oscilloscope. Power-conversion efficiency, poweradded efficiency, and total harmonic distortion (THD) were calculated by (18) (19) and Fig. 10. Normalized output power as a function of output
.
(20) is a root-mean-square value of the th harmonic in where the output voltage . To obtain the measured THD values, we used the waveform data of the output voltage from the Textronix TDS3014B oscilloscope. The output-voltage waveform is not a pure sinusoidal waveform because of low as shown in Fig. 9. The measurement THD value given in Table IV and the experimental output-voltage waveforms shown in Fig. 9 agreed with the numerical predictions well. These results show that the design procedure can be applied to the proposed oscillator designs at any . From Table IV, we can also confirm that the experimental circuit satisfied the maximum feedback-voltage condition and the output-power condition. Additionally, the measurement results agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. In the laboratory measurement, the oscillator achieved 92.0% power conversion efficiency at 34.8-W output power and 1-MHz operating frequency. VII. COMPARISONS WITH CLASS-E OSCILLATOR The comparisons between the classamplifier and the class-E amplifier were discussed in [15] and [19]. Therefore, it is very important to compare the proposed oscillator with the class-E oscillator. The fair comparisons, however, are very difficult because the proposed oscillator is a different class of the oscillator compared with the class-E oscillator. In this section, the classand class-E oscillators are discussed from several points of view. For comparisons, we give and as specifications for both the proposed oscillator and the class-E oscillator and for the proposed oscillator. A. Output Power and Switch Stress Fig. 10 shows the normalized output powers as a function . It is seen from this figure that the of output dc-supply voltage of the proposed oscillator is lower than that of the class-E oscillator under the identical output-power condition. The dc-supply power of the injection circuit is about 1/3 of the main-circuit dc-supply power [15]. The output power of the proposed oscillator is, however, about twice as large as that of the class-E oscillator for the same load resistance and dc-supply voltage. Fig. 11 shows the normalized peak switch voltages and currents as a function of output . It can be stated that the peak
Fig. 11. Normalized peak switch voltages and currents as a function of output . (a) Normalized peak switch voltages. (b) Normalized peak switch currents.
switch voltage of the proposed converter is lower than that of the class-E oscillator under the identical output-power condition because the dc-supply voltage of the proposed oscillator is lower than that of the class-E oscillator. The switch current through the classoscillator is also usually lower than the class-E oscillator in spite of the low dc-supply voltage. Generally, MOSFET cost becomes low as the permissible maximum drain-to-source voltage decreases. Therefore, low MOSFET stress is an additional reason why the switching-device cost can be reduced. B. Total Harmonic Distortion Fig. 12 shows the THD values as a function of output . Usually, THDs increase as the output- value decreases because the resonant filter passes the harmonic components for low . In both the classand the class-E oscillators, however, the THD values for low decrease with the decrease in the output as shown in Fig. 12. It is also seen from this figure that the THD of the classoscillator is lower than that of the class-E amplifier for high . Conversely, it is higher for low . C. Power Conversion Efficiency For power-conversion efficiency comparisons, we carried out another type of the proposed and the class-E oscillators. The common specifications are , , , and . By using these specifications, the dc-feed and resonant inductances of the classoscillator are equal to those of the class-E oscillator. IRF530 MOSFETs were used for all the switching devices. Therefore, , , , ,
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D. Power-Added Efficiency
Fig. 12. Total harmonic distortions as a function of output
TABLE V NUMERICAL PREDICTIONS FOR CLASS-
AND
.
CLASS-E OSCILLATORS
For example, the driving power for IRF740 MOSFET in Fig. 9 was 29.8 mW, which was 0.09% of the output power. In [19], the driving power for the injection-circuit IRFZ24N MOSFET was 0.44% of the output power. It is seen from these results that the power-added efficiency depends on the design specifications and device selection. The driving power of the proposed oscillator is much higher than the injection-signal power of the injection-locked class-E oscillator. It is difficult to conclude which oscillator is better from the power-added efficiency point of view when the drain-current-fall-time effect can be ignored. This is because there are possibilities that the difference between the driving power and injection-locked signal cover with the power-conversion efficiency improvement. Obviously, the proposed oscillator has the complexity compared with the class-E oscillator. Therefore, it is necessary for designers to consider whether the advantages of the proposed oscillator appear for the application requirements. The advantages of the proposed oscillator appear clearly when the drain-current-fall-time problems yield. The analytical evidences are mandatory for explaining the benefits, which are one of the important problems. E. Comparisons With Class-E Amplifier
, and , which were obtained from [3] and [26]. Table V gives the numerical predictions for the classand class-E oscillators. Note that the drain-current-fall-time effect due to the switchcurrent jumps is not included in the numerical calculations. Additionally, the ESRs of the inductors are also not considered in the numerical predictions because they can be controlled by the inductor core-material and wire-type selections. It is seen from Table V that the power-conversion efficiency of the proposed oscillator is little higher than the class-E oscillator in the numerical prediction. This is due to the current-division effects. The similar effects appear in the interleaving topologies of converters [30]. Therefore, it is expected that the power-conversion efficiency of the proposed oscillator is the same as or higher than that of the class-E oscillator even if both the oscillators use the fast-switching devices. Additionally, it is expected that the power-conversion-efficiency improvement appears clearly when the slow-switching devices are used to oscillators. We confirmed that the power conversion efficiency of the proposed oscillator was little higher than that of the class-E oscillator by circuit experiments. It is necessary to use the high-speed switching device in the injection circuit because there are current jumps in the injection-switch current. The injection-circuit power is a quarter of the output power. Therefore, the power dissipations due to the drain-current-fall time of the proposed oscillator, which are caused by overlaps between the injection-switch voltage and current, are narrower than those of the class-E oscillator. When we consider the peak-switch-voltage reduction effect, the injection-circuit switching-device cost can also be reduced. The reduction level depends on design specifications.
The power-added efficiency of the class-E amplifier is the same as the class-E oscillator if the driving power if the amplifier is the same as the feedback power of oscillator. Conversely, the power conversion efficiency of the class-E amplifier is a little higher than the class-E oscillator. This is because the dc-supply power of the class-E oscillator is divided into the output power and the feedback power. From these points of view, the power conversion efficiency of the proposed oscillator is almost the same as the class-E amplifier if the drain-current-fall-time effect is ignored. Additionally, the power-added efficiency relationship between the classoscillator and the class-E oscillator is the same as the classoscillator and the class-E amplifier. VIII. CONCLUSION This paper has presented the classpower oscillator with the second harmonic injection. The injection circuit of the proposed oscillator has some roles. The main circuit achieves the classZVS/ZVDS/ZCS/ZCDS conditions, which enhances the power-conversion efficiency and reduces the implementation cost. The output frequency can be locked with the inputsignal frequency of the injection circuit. Additionally, it is possible to increase the output power. The proposed circuit is regarded as not only the improvement version of the class-E oscillator but also that of the classamplifier. The numerical design procedure is presented for the proposed oscillator design, which can be applied to the design of the proposed oscillator at any set of specifications. The design curves, considered with the MOSFET body junction diode nonlinear capacitances and ESRs of each component, are shown. The design example is also shown in this paper. In the laboratory experiment, the proposed oscillator achieved 92.0% power-conversion efficiency at
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34.8-W output power and 1-MHz operating frequency. The experimental results agreed with the numerical predictions quantitatively, which denotes the validities of the design procedure. This paper has focused on designs of the proposed oscillator for nominal operation. The proposed oscillator behaviors outside nominal operation including the synchronization band between the main and injection circuits should be addressed in the future.
REFERENCES [1] J. Ebert and M. Kazimierczuk, “Class E high-efficiency tuned power oscillator,” IEEE J. Solid-State Circuits, vol. SC-16, no. 2, pp. 62–66, Apr. 1981. [2] M. K. Kazimierczuk, V. G. Krizhanovski, J. V. Rassokhina, and D. V. Chernov, “Class-E MOSFET tuned power oscillator design procedure,” IEEE Trans. Circuits Syst. I, vol. 52, no. 6, pp. 1138–1147, Jun. 2005. [3] H. Hase, H. Sekiya, J. Lu, and T. Yahagi, “Novel design procedure for MOSFET class-E oscillator,” IEICE Trans. Fund., vol. E87-A, no. 9, pp. 2241–2247, Sep. 2004. [4] V. G. Krizhanovski, D. V. Chernov, and M. K. Kazimierczuk, “Lowvoltage electronic ballast based on class E oscillator,” IEEE Trans. Power Electron., vol. 22, no. 3, pp. 863–870, May 2007. [5] M. K. Kazimierczuk, V. G. Krizhanovski, J. V. Rassokhina, and D. V. Chernov, “Injection-locked class-E oscillator,” IEEE Trans. Circuits Syst. I, vol. 53, no. 6, pp. 1214–1222, Jun. 2006. [6] H.-S. Oh, T. Song, S.-H. Baek, E. Yoon, and C.-K. Kim, “A powerefficient injection-locked class-E power amplifier for wireless sensor network,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 4, Apr. 2006. [7] H. R. Bae, C. S. Cho, and J. W. Lee, “Efficiency enhanced class-E power amplifier using the second harmonic injection at the feedback loop,” in Proc. Eur. Microwave Conf. (EuMC2010), Paris, France, Sep. 2010, pp. 1042–1045. [8] N. O. Sokal and A. D. Sokal, “Class E-A new class of high-efficiency tuned single-ended switching power amplifier,” IEEE J. Solid-State Circuits, vol. SC-10, pp. 168–176, Jun. 1975. [9] M. Albulet and R. E. Zulinski, “Effect of switch duty ratio on the performance of class E amplifiers and frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. 45, no. 4, pp. 325–335, Apr. 1998. [10] N. O. Sokal, “Class-E RF power amplifiers,” QEX, no. 204, pp. 9–20, Jan./Feb. 2001. [11] H. Sekiya, T. Ezawa, and Y. Tanji, “Design procedure for class E switching circuits allowing implicit circuit equations,” IEEE Trans. Circuits Syst. I, vol. 55, no. 11, pp. 3688–3696, Dec. 2008. [12] J. Ribas, J. Garcia, J. Cardesin, M. Dalla-Costa, A. J. Calleja, and E. L. Corominas, “High frequency electronic ballast for metal halide lamps based on a PLL controlled class E resonant inverter,” in Proc. Power Electronics Specialists Conf, PESC ’05, Recife, Brazil, Jun. 2005, pp. 1118–1123. [13] A. Mediano, P. Molina-Gaudò, and C. Bernal, “Design of class E amplifier with nonlinear and linear shunt capacitances for any duty cycle,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 3, pp. 484–492, Mar. 2007. [14] X. Wei, H. Sekiya, S. Kuroiwa, T. Suetsugu, and M. K. Kazimierczuk, “Design of class-E amplifier with MOSFET linear gate-to-drain and nonlinear drain-to-source capacitances,” IEEE Trans. Circuits Syst. I, vol. 58, no. 10, pp. 2556–2565, Oct. 2011. [15] A. Telegdy, B. Molnár, and N. O. Sokal, “Class-E switching-mode tuned power amplifier—High efficiency with slow-switching transistor,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1662–1676, Jun. 2003. [16] A. Grebennikov and N. O. Sokal, Switchmode RF Power Amplifiers. Burlington, MA: Elsevier, 2007. [17] A. AlMuhaisen, P. Wright, J. Lees, P. J. Tasker, S. C. Cripps, and J. Benedikt, “Novel wide band high-efficiency active harmonics injection power amplifier concept,” in Proc. 2010 IEEE MTT-S Int. Microwave Symp., Anaheim, CA, May 2010, pp. 664–667.
[18] R. Miyahara, H. Sekiya, and M. K. Kazimierczuk, “Design of class-E power amplifier taking into account auxiliary circuit,” in Proc. IEEE Ind. Electron. Conf. (IECON’08), Orland, FL, Nov. 2008, pp. 679–684. [19] R. Miyahara, H. Sekiya, and M. K. Kazimierczuk, “Novel design procedure for class-E power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3607–3616, Dec. 2010. [20] R. Miyahara and H. Sekiya, “Design of class-E power amplifier with one input signal,” in Proc. Energy Conversion Congress and Exposition, (ECCE’09), San Jose, CA, Sep. 2009, pp. 3859–3864. [21] M. K. Kazimierczuk, “Generalization of conditions for 100-percent efficiency and nonzero output power in power amplifiers and frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. 33, no. 8, pp. 805–807, Aug. 1986. [22] R. E. Zulinski and J. W. Steadman, “Performance evaluation of Class E frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. TCSI-33, no. 3, pp. 343–346, Mar. 1986. [23] R. E. Zulinski and J. W. Steadman, “Idealized operation of Class E frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. TCSI-33, no. 12, pp. 1209–1218, Dec. 1986. [24] M. Albulet, “Analysis and design of the Class E frequency multipliers with RF choke,” IEEE Trans. Circuits Syst. I, vol. 42, no. 2, pp. 95–104, Feb. 1995. [25] W. Feipeng, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. Lie, P. M. Asbeck, and L. E. Larson, “An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4086–4099, Dec. 2006. [26] H. Sekiya, T. Watanabe, T. Suetsugu, and M. K. Kazimierczuk, “Analysis and design of class DE amplifier with nonlinear shunt capacitances,” IEEE Trans. Circuits Syst. I, vol. 56, no. 10, pp. 2362–2371, Oct. 2009. [27] International Rectifier. [Online]. Available: http://www.irf.com/ product-info/models/ [28] K. W. E. Cheng and P. D. Evans, “Calculation of winding losses in high-frequency toroidal inductors using single strand conductors,” IEE Proc.—Electric Power Applications, vol. 141, no. 2, pp. 52–62, 1994. [29] H. Sekiya and M. K. Kazimierczuk, “Design of RF-choke inductors using core geometry coefficient,” presented at the Electrical Manufacturing Coil Winding & Coating Expo (EMCW2009), Nashville, TN, Sep. 2009. [30] M. T. Zhang, M. M. Jovanovic, and F. C. Y. Lee, “Analysis and evaluation of interleaving techniques in forward converters,” IEEE Trans. Power Electron., vol. 13, no. 4, pp. 690–698, Jul. 1998.
Ryosuke Miyahara was born in Nagano, Japan, on October 8, 1985. He received the B.E. and M.E. degrees in information and image science from Chiba University, Chiba, Japan, in 2008 and 2010, respectively. Since April 2010, he has been with Ricoh Company, Tokyo, Japan. When he was a student, his interests were high-frequency high-efficiency dc/ac inverters.
Xiuqin Wei (S’10) was born in Fujian, China, on December 7, 1983. She received the B.E. degree from Fuzhou University, China, in 2005, and the Ph.D. degree from Chiba University, Japan, in 2012. Since April 2012, she has been with Fukuoka University, where she is currently an Assistant Professor in the Department of Electronics Engineering and Computer Science. Her research interests include high-frequency power amplifier.
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OSCILLATOR WITH SECOND HARMONIC INJECTION
Tomoharu Nagashima (S’11) was born in Saitama, Japan, on February 4, 1989. He received the B.E. degree from the Department of Information and Image Sciences, Chiba University, Chiba, Japan, in 2011. He is currently working toward the M.E. degree at Chiba University. His current research interest is in high-frequency high-efficiency tuned power amplifiers.
Takuji Kousaka (S’99–M’00) received the B.E., M.E., and D.E. degrees from Tokushima University, Tokushima, Japan, in 1994, 1996, 1999, respectively. He is currently an Associate Professor of Mechanical and Evergy Systems Engineering at Oita University, Oita, Japan. His research interest is in qualitative properties of nonlinear systems with interrupted characteristics.
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Hiroo Sekiya (S’97–M’01–SM’11) was born in Tokyo, Japan, on July 5, 1973. He received the B.E., M.E., and Ph.D. degrees in electrical engineering from Keio University, Yokohama, Japan, in 1996, 1998, and 2001, respectively. Since April 2001, he has been with Chiba University, Chiba, Japan, where he is currently an Assistant Professor in the Graduate School of Advanced Integration Science. From February 2008 to February 2010, he was also with the Department of Electrical Engineering, Wright State University, Dayton, Ohio, as a visiting scholar. His research interests include high-frequency high-efficiency tuned power amplifiers, resonant dc/dc power converters, dc/ac inverters, and digital signal processing for wireless communications. Dr. Sekiya is a member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan, the Information Processing Society of Japan (IPSJ), and the Research Institute of Signal Processing (RISP), Japan.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 59, NO. 10, OCTOBER 2012
Design of Class-E Oscillator With Second Harmonic Injection Ryosuke Miyahara, Xiuqin Wei, Student Member, IEEE, Tomoharu Nagashima, Student Member, IEEE, Takuji Kousaka, Member, IEEE, and Hiroo Sekiya, Senior Member, IEEE
Abstract—This paper presents the class-E oscillator with the second-harmonic injection current, along with its design procedure, design curves, and design example. In the proposed oscillator, the output frequency of the proposed oscillator is locked with the input frequency of the injection circuit. Additionally, the switch-voltage and switch-current waveforms in the main circuit achieve the class-E zero-voltage switching, zero-voltage-derivative switching, zero-current switching, and zero-current-derivative switching (ZVS/ZVDS/ZCS/ZCDS) conditions and the switch voltage waveform in the injection circuit satisfied the class-E ZVS/ZDS conditions. In the laboratory experiment, the oscillator achieved 92.0% power-conversion efficiency at 34.8 W output power and 1 MHz operating frequency. The experimental results agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. Index Terms—Class-E amplifier, efficiency enhancement, freerunning class-E oscillator, injection-locked class-E oscillator, zerocurrent-derivative switching, zero-current switching, zero-voltagederivative switching, zero-voltage switching.
I. INTRODUCTION
T
HE class-E oscillator [1]–[7] offers high efficiency at high frequencies because it satisfies the class-E zero-voltage switching and zero-voltage-derivative switching (ZVS/ZVDS) conditions [8]–[14]. The class-E oscillator can be classified into two categories. One is the free-running oscillator and the other is the injection-locked oscillator. The injection-locked techniques allow the class-E oscillators to achieve a high overall efficiency and a high stability of oscillation frequency [5]–[7]. In many applications, the class-E oscillators can perform the same functions as the class-E amplifiers. They are applicable to FM oscillators, AM transmitters, electric ballast, the inverter part of Manuscript received September 16, 2011; revised December 26, 2011; accepted January 31, 2012. Date of publication April 04, 2012; date of current version September 25, 2012. This work was supported in part by the Scholarship Foundation and Grant-in-Aid for Scientific Research (No. 23760253) of JSPS, the Support Center for Advanced Telecommunications Technology Research, and the Telecommunications Advancement Foundation, Japan. This paper was recommended by Associate Editor Eduard Alarcon. R. Miyahara was with the Graduate School of Advanced Integration Science, Chiba University, Chiba, 263-8522 Japan. He is now with Ricoh Company, Tokyo 143-8555, Japan. X. Wei is with the Department of Electronics Engineering and Computer Science, Fukuoka University, Fukuoka 814-0180, Japan. T. Nagashima and H. Sekiya are with the Graduate School of Advanced Integration Science, Chiba University, Chiba 263-8522, Japan (e-mail: sekiya@ faculty.chiba-u.jp). T. Kousaka is with the Department of Mechanical and Energy Systems Engineering, Oita University, Oita 870-1192, Japan. Digital Object Identifier 10.1109/TCSI.2012.2188936
dc/dc converters, and more. The switch-current waveform of the class-E oscillator, however, includes a jump at the switch turn-off instant, which deteriorates the power conversion efficiency and increases the circuit-implementation cost. power amplifier [15]–[20] is an improved The classversion of the class-E amplifier [8]–[13], which has the main and injection circuits. By injecting the second-harmonic current to the switch, the main circuit satisfies not only the class-E ZVS/ZVDS conditions at the transistor turn-on instant but also zero-current switching (ZCS) and zero-current-derivative switching (ZCDS) conditions at the transistor amplifier enhances turn-off instant. Therefore, the classthe power-conversion efficiency even if the transistor has a amplifier needs long turn-off-switching time. The classtwo input signals, which drive the switching elements in the main and injection circuits. In circuit implementations, the phase-shift should be fixed at a certain value. However, it is complicated to design the driver circuit with a halfway value of the phase-shift. The design of the driving circuit is one of the amplifier. problems for the classThis paper, which was previously presented in part at ECCE 2009 [20],1 presents the classoscillator with the second-harmonic injection. In the proposed oscillator, the output frequency of the proposed oscillator is locked with the input frequency of the injection circuit. Additionally, the switch-voltage and switch-current waveforms in the main ZVS/ZVDS/ZCS/ZCDS condicircuit achieve the classtions and the switch voltage waveform in the injection circuit satisfied the class-E ZVS/ZDS conditions. The proposed circuit is regarded as an improvement version not only of the class-E amplifier for the fixed freoscillator but also of the classquency and the fixed dc-supply voltage applications. Because there is one input signal in the proposed oscillator, it is not necessary to adjust the phase shift between the main and injection circuits. Therefore, the driver circuit of the proposed oscillator amplifier. The numerical is simpler than that of the classdesign procedure is presented for the proposed oscillator designs. The design curves and the design example, considered with the MOSFET body junction diode nonlinear capacitances and equivalent series resistances (ESRs) of each component, are shown. In the laboratory experiment, the oscillator achieved 92.0% power-conversion efficiency at 34.8-W output power and 1-MHz operating frequency. The experimental results 1In this paper, the proposed circuit is mainly explained from the oscillator point of view. The injection circuit achieves the class-E ZVS/ZVDS conditions though only ZVS condition is achieved in [20]. Additionally, the effect of MOSFET body junction diode nonlinear capacitance is considered in the design. The design curves and design example are newly given.
1549-8328/$31.00 © 2012 IEEE
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Fig. 2. Nominal waveforms of the class-E oscillator for Fig. 1. Circuit topology of the class-E oscillators. (a) Free-running class-E oscillator. (b) Injection-locked class-E oscillator.
agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. II. RELATED WORKS A. Class-E Oscillator Fig. 1(a) shows the circuit topology of the free-running class-E oscillator [1]–[4]. The class-E oscillator consists of the class-E amplifier [8]–[14] and feedback network , and . and give the bias voltage, which equals to the threshold voltage for the gate of the MOSFET. Fig. 2 shows an example of the nominal waveforms of the class-E oscillator. The MOSFET of the class-E oscillator is driven by the feedback voltage , which is from the output voltage . The feedback voltage is a sinusoidal waveform because the feedback current flow through the resonant filter, which consists of , gate-source parasitic capacitance, and gate-source parasitic resistance. By adjusting , , and , the amplitude and phase shift between the output voltage and the feedback voltage are adjusted. The switch voltage achieves the class-E zero-voltage switching and zero-voltage-derivative switching (ZVS/ZVDS) conditions at turn-on instant, which are (1) Because of the class-E ZVS/ZDS, the class-E oscillator achieves high power-conversion efficiency at high frequencies. Fig. 1(b) shows an example topology of the injection-locked class-E oscillator [5]–[7]. When the injection voltage has proper frequency and amplitude, the feedback current is synchronized with the and the feedback-current frequency is locked with the frequency of injection voltage. The synchronization occurs even when the injection power is much lower
.
than the driving power for the MOSFET. Therefore, the injection-locked class-E oscillator offers a stable frequency output with low power injection. In the class-E oscillator, the switch-voltage waveform is smooth because of the class-E ZVS/ZDS conditions. The switch-current waveform, however, includes jumps at every turn-off instant as shown in Fig. 2. When current fall time cannot be negligible, these jumps cause the power dissipations [19]. To avoid this problem, a fast-speed MOSFET or high driving power is required. The fast-speed MOSFET suffers from the implementation cost. The high-driving power deteriorates the power-added efficiency. B. Class-
Amplifier
Fig. 3(a) shows a circuit topology of the classpower amplifier [15]–[20]. The classamplifier has the main and injection circuits. Each circuit has a similar topology to the class-E amplifier. Fig. 3(b) shows the example waveforms of the classamplifier in the nominal operation when the switch-off duty ratio of the main circuit is 0.5. The switch is driven by the input signal as shown in Fig. 3(b). The switch voltage satisfies the class-E ZVS/ZVDS conditions at transistor turn-on instant. Additionally, the switch current achieves the zerocurrent switching (ZCS) and zero-current-derivative switching (ZCDS) conditions simultaneously at the transistor turn-off instant. Because of the ZCS/ZCDS conditions, the waveforms of both the switch voltage and current at the transistor turn-off are also smooth. These switching conditions are expressed as (2) (3)
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Fig. 4. Proposed oscillator topology.
circuit is necessary [15], [21]. The injection circuit should provide the second-harmonic current with the proper phase-shift and the proper amplitude for achieving the ZCS/ZCDS conditions in the main-circuit switch. The switch voltage is transformed into the sinusoidal output voltage through the resonant filter . The classamplifier needs two input signals and , which drive the switching elements in the main and injection circuits, respectively. The phase-shift between the two input signals is an important and useful parameter for adjusting the phase shift of the second-harmonic injection current. In circuit implementations, the phase-shift , which is determined by the other design specifications, should be fixed at a certain value. However, it is complicated to design the driver circuit with the halfway value of the phase-shift. Therefore, was specified in [19] and the injection circuit achieved only the ZVS condition. The design of the driver circuit is one of the problems for the classamplifier. III. CLASSOSCILLATOR WITH SECOND HARMONIC INJECTION Fig. 3. Classand
amplifier. (a) Circuit topology. (b) Nominal waveforms for .
where is the phase shift between two input signals as shown in Fig. 3(b). Because of the switching conditions in (2) and (3), which are called the classZVS/ZVDS/ZCS/ZCDS conditions in this paper, there are no jumps on the switch-voltage and switch-current waveforms in the main circuit. Therefore, the classamplifier enhances high power conversion efficiency even if the main-circuit transistor has a long turn-off-switching time and lowers the implementation cost [15]. To achieve the ZCS/ZCDS conditions in the classamplifier, the injection
Fig. 4 shows a circuit topology of the proposed oscillator, which is composed of the main circuit and the injection circuit. The main circuit is the free-running class-E oscillator and the injection circuit is the class-E frequency doubler [22]–[24]. The nominal waveforms of the proposed oscillator are shown in Fig. 5. The main circuit is driven by the feedback voltage from the output voltage. The switch voltage of the main circuit achieves the classZVS/ZVDS/ZCS/ZCDS conditions by injecting the second-harmonic current to the main switch. The injection circuit is driven by the input signal whose fundamental frequency is the same as the output voltage. In other words, the output frequency is locked with the input frequency. In this sense, the proposed oscillator is regarded as one of the injection-locked oscillators. From the above explanations, it can
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Unstable behaviors, however, appear in the proposed oscillator when the input frequency is changed from the nominal due to the feedback topology. In the classamplifier, the operation can be always stable regardless of the input frequency. This is because the ratio of the input frequency between the main and injection circuits can be kept and the classamplifier is an open-loop circuit. Additionally, it is necessary to consider the additional cost compared with the classamplifier. For example, the bias voltage for driving the main-circuit MOSFET is supplied by using and as shown in Fig. 4, which is based on the assumption of the fixed supply voltage. For example, if the proposed oscillator is applied to the Envelope Elimination and Restoration (EER) systems for wireless-communication amplifiers [25], the control circuit for supplying the main-circuit-MOSFET bias voltage should be newly designed. IV. CIRCUIT DESIGN
Fig. 5. Nominal waveforms of the proposed oscillator without MOSFET drain-to-source capacitances.
be stated that the injection circuit has multiple roles in the proposed oscillator. First, it offers the classZVS/ZVDS/ZCS/ ZCDS conditions, which enhance the power-conversion efficiency and allow to use a slow switching MOSFET. Following the same logic in [15], it is possible to reduce the circuit-implementation cost, especially, the main-circuit-MOSFET cost. Second, the output-voltage frequency is locked with the inputsignal frequency, which is half as high as the injection-current frequency. If we apply the class-E amplifier, whose operating frequency is twice as high as the main circuit, instead of the class-E doubler as injection circuit, it looks like the frequency divider. Finally, the output power becomes high by adding the injection circuit, which is useful for high-power applications. The proposed circuit is also regarded as an improved version of the classamplifier [20]. By reducing the number of input signals from two to one, the driver-circuit design of the proposed circuit is much simpler than that of the classamplifier for the fixed frequency and the fixed dc-supply voltage applications. For example, it is unnecessary to specify the phase-shift between the main and injection circuits. Therefore, one more adjacent parameter can be obtained. As a result, one more switching condition can be specified for the injection circuit design. Therefore, it is possible to apply the class-E ZVS/ZDS conditions to the injection circuit, which improves the power-conversion efficiency of the injection circuit compared to the injection circuit of the classamplifier in [19]. The total driving power can be reduced by using the feedback network at the main circuit, which improves the power-added efficiency. From the above discussions, it can be stated that the proposed oscillator has some features from not only the class-E oscillator point of view but also the classamplifier point of view.
The proposed oscillator is a high-dimensional circuit. Moreover, the proposed oscillator has four switching conditions in the main circuit, two switching conditions in the injection circuit, phase-matching condition for the feedback voltage, and output-power condition. Therefore, it is difficult to obtain analytical design equations for achieving all the conditions. In this paper, the numerical design procedure proposed in [11] is applied to the design of the proposed oscillator. By using this design procedure, it is possible to obtain the element values for achieving multiple restrict conditions. A. Assumptions First, the following assumptions are given. 1) The switching devices and have non-zero on-resistances and and MOSFET body junction diode nonlinear capacitances . Additionally, has the equivalent gate-to-source capacitance and the equivalent gate-to-source resistance . 2) Shunt capacitances and are the sum of the MOSFET body junction diode nonlinear capacitance and the external linear capacitance . The body junction diode nonlinear capacitances of the MOSFET are expressed as (4)
is the built-in potential, is the capacitance where at , and is the grading coefficient of the diode junction [13], [26]. 3) The equivalent series resistances (ESRs) of the inductors are considered. The ESRs of all the capacitors are negligible since they are much smaller than the ESRs of the inductors. 4) All the passive elements except the MOSFET body junction diode capacitances work as linear elements. 5) For simplicity, the following equations are addressed for only the case of . The switch of the injection
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TABLE I SWITCHING PATTERN OF THE MAIN CIRCUIT THE PROPOSED OSCILLATOR FOR
9) IN
10) 11) 12)
SWITCHING
TABLE II PATTERN OF THE INJECTION CIRCUIT THE PROPOSED OSCILLATOR
IN
13) 14)
15) 16) 17)
: the ratio of the resonant frequency in the feedback network to the operating frequency. : the loaded quality factor in the main circuit. : the loaded quality factor in the injection circuit. : the loaded quality factor in the feedback network. : the ratio of the dc-supply voltages. : the phase-shift of the driving signals between the main and the injection circuits, which is in the range of . : the ESR of . : the ESR of . : the ESR of .
C. Circuit Equations We consider the operations for to design the proposed oscillator, where represents the angular time. Using the parameters, the circuit equations are expressed as
Fig. 6. Equivalent circuit of the proposed oscillator.
circuit turns off at and the switching patterns are given in Tables I and II. According to the above assumptions, the equivalent circuit of the proposed oscillator is obtained as shown in Fig. 6. B. Parameters In order to express the circuit equations, the following parameters are defined. The subscripts and 2 mean the main and injection circuits, respectively. 1) : The operating angular frequency. 2) : the resonant frequency. 3) : the resonant frequency in the feedback network. 4) : the ratio of the resonant frequency to the operating frequency. 5) : the ratio of the resonant capacitance to the shunt capacitance for switch voltage . 6) : the ratio of the resonant inductance to the dc-feed inductance. 7) : the ratio of the resonant capacitance in the main circuit to the feedback network capacitance. 8) : the ratio of the capacitances in the feedback network.
(5) In (5), and are the equivalent drain-to-source resistances of the MOSFETs and , which are given as for for for for
and , .
(6)
When we express
(5) can be rewritten as (7)
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For achieving the specified output power relation should be valid:
where
, the following
(14)
D. Conditions for the Design We assume (5) has a solution defined on condition and every of the oscillator is expressed by
with every initial . The steady state (8)
Therefore, (9) is given as the boundary conditions between and . In order to design the proposed oscillator, we have to consider switching conditions, phase-matching condition for the feedback voltage, and output-power condition. As the switching conditions on , (2) and (3) should be considered. The softswitching conditions in the injection circuit improve the whole power conversion efficiency. Therefore, the class-E ZVS/ZVDS conditions at the transistor turn-on are applied in the injection circuit. As a result, we obtain the six switching conditions as
For the calculations of the integration in (14), we apply the trapezoidal method in this paper. From the above considerations, we recognize that the design of the proposed classoscillator reduces to derive the resolutions of the algebraic equations (9)–(11), (13), and (14). There are 21 algebraic equations with 12 unknown initial values. Therefore, nine parameters can be set as the design parameters from . The other parameters should be given as the design specifications. The algebraic equations are solved by the Newton’s method, whose detailed algorithms are described in [11]. For solving the algebraic equations by using Newton’s method, the initial values for iterative calculations are important [19]. First, by using certain values of the variations and , e.g., which are assumed from [1] and [19], the values of are obtained as . Second, the algebraic equations are solved by using the Newton’s method with and as the initial values, where , and is an integer value. The algebraic equaare solved by using the Newton’s tions and . After itmethod with the initial values of erations, we can obtain the solution of the algebraic equations . V. DESIGN CURVE
(10)
The phase matching for the feedback voltage means that the feedback voltage is equal to when the main-circuit switch turns off. Therefore, the equation (11) is given. Since the switch of the main circuit turns off at , the condition (12) is added. If the gate-source voltage of the MOSFET is larger than the maximum gate-source voltage in FET manuals, the MOSFET may be broken. For avoiding this, the feedback voltage should be smaller than the maximum gate-source voltage. When the maximum value of the feedback voltage is defined as , we have (13) is given as a design specification for
.
In this section, the design curves of the proposed oscillator are shown. The design specifications are , , , , and . The parameters of the MOSFETs are assumed as: , , , , , and . For solving the algebraic equations, , , , , , , , , and are set as unknown parameters. The design curves are obtained from the design algorithm in Section IV. Fig. 7 shows the design parameters , , , , , , , , normalized maximum switch voltages, and normalized output power for fixed as a function of the ratio of the dc-supply voltages . It is seen from Fig. 7(a)–(e) that , , , , and have similar characteristics to those of the classoscillator [18], which means that the existence of the feedback network does not affect the element values of the main and injection circuits. From Fig. 7(d), goes infinity as decreases. The infinite means that the external shunt capacitance of the injection circuit becomes zero. Therefore, the lower limit of is governed by , which are 0.214, 0.216, and 0.193 for 5, 3, and 1, respectively. On the other hand, from Fig. 7(e), goes infinity as increases. The infinite appears because the injected power should be limited in spite of high for achieving the ZCS/ZCDS conditions. Therefore, the upper limit of is governed by , which are , 0.566, and 0.557 for 5, 3, and 1, respectively. From Fig. 7(g) and (h), the feedback-network parameters and are changed as varies. These plots show that the
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Fig. 8. Design parameters of normalized output power . of dc-supply voltages as a function of
and ratio
parameters of the main and injection circuits affect the element values of the feedback network. From Fig. 7(i), the normalized maximum switch voltage of is almost constant regardless of and the normalized maximum switch voltage of increases in proportion to the increase in . From Fig. 7(j), it is seen that the normalized output power has the maximum value for variations. From this figure, it can be stated that the maximum output power depends on . Fig. 8 shows the maximum normalized output power and the ratio of the dc-supply voltages for achieving the maximum normalized output power as a function of . For , the maximum normalized output power is almost constant. This is because the output current is pure sinusoidal for . For , however, the maximum normalized output power varies significantly because the dc component of the output current increase as decreases. VI. DESIGN EXAMPLE In this section, the design example of the proposed oscillator is shown. The design specifications are , , and , which follow the specifications in [12]. Additionally, we also specify , , and . A. Selection of MOSFET First, the MOSFETs should be selected. From Fig. 8, the maxis 1.74. As a result, imum normalized output power for the minimum dc-supply voltage of the main circuit for achieving the specified output power is obtained as (15) We choose power is calculated as
. Therefore, the normalized output (16)
Fig. 7. Design parameters of the proposed oscillator as a function of . (a) De. (b) Design parameters of . (c) Design parameters sign parameters of . (d) Design parameters of . (e) Design parameters of . (f) Design of . (g) Design parameters of . (h) Design parameters of . parameters of (i) Design parameters of normalized maximum switch voltages and . (j) Design parameters of .
From the normalized output power and , the value of is obtained as from Fig. 7(j). Therefore, the maximum switch voltages are obtained from Fig. 7(i), which are and . In this design, IRF740 MOSFET
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OSCILLATOR WITH SECOND HARMONIC INJECTION
TABLE III PARAMETERS FOR IRF740 MOSFET
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TABLE IV EXPERIMENTAL RESULTS
is selected for and . Table III gives the parameters for the IRF740 MOSFET. In this table, , , , and drain-tosource break down voltage are obtained from the FET manual, and were measured values by LCR meter of HP 4284A, and , , and are obtained from the Spice model [27]. From and , and are given. B. Approximate ESR Values Using MOSFET parameters, the element values without considering ESR values can be calculated from the design algorithm in Section III. The calculated inductor values are , , , , and . The current waveforms through the inductors can be also obtained from the design algorithm. For the resonant inductor implementations, Micrometals toroidal cores of T200-2, T130-2, and T94-2 are used for , , and , respectively. For the dc-feed inductor implementations, TDK EI30 cores with TDK BE-30-5112 bobbin are used for and . Following the calculations in [28] and [29], we can obtain the approximate ESR values of the inductors as , , , , and , respectively. C. Derivation of the Element Values Finally, we obtain the element values taking into account the MOSFET parameters and ESR values from the design algorithm in Section III. The element values are obtained as given in Table IV. All element values including ESR values were measured by the HP 4284A LCR meter. The maximum switch voltage of the injection-circuit switch increases to 262 V. This is because the nonlinearity of the MOSFETs and ESRs of the inductors are considered in the oscillator design. D. Experimental Result Fig. 9 depicts the numerical waveforms and the experimental waveforms for the obtained design parameters. Note that . Because we consider the MOSFET drain-to-source capacitances, namely , are not zero when the switch is in off state. In Fig. 9, it is confirmed that the experimental oscillator satisfied all the switching conditions, namely, ZVS/ZVDS conditions at the main-circuit transistor turn-on, ZCS/ZCDS conditions at the main-circuit transistor turn-off, and ZVS/ZVDS conditions at the injection-circuit transistor turn-on. Table IV gives the calculated element values from the design algorithm in Section III and the measured values in the labora-
Fig. 9. Waveforms of the proposed oscillator. (a) Calculated waveforms. : 5 V/div, , : (b) Experimental waveforms. Vertical: : 20 V/div, : 2 A/div, : 200 V/div. Horizontal: 200 nS/div. 200 V/div,
tory experiment. In this table, dc-supply voltages and dc-supply currents were measured by the Iwatsu VOAC7532 digital multimeter. Additionally, the measured output power was obtained from
(17)
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where was measured by the Agilent 3458A digital multimeter. The input power was measured by the Textronix TDS3014B oscilloscope. Power-conversion efficiency, poweradded efficiency, and total harmonic distortion (THD) were calculated by (18) (19) and Fig. 10. Normalized output power as a function of output
.
(20) is a root-mean-square value of the th harmonic in where the output voltage . To obtain the measured THD values, we used the waveform data of the output voltage from the Textronix TDS3014B oscilloscope. The output-voltage waveform is not a pure sinusoidal waveform because of low as shown in Fig. 9. The measurement THD value given in Table IV and the experimental output-voltage waveforms shown in Fig. 9 agreed with the numerical predictions well. These results show that the design procedure can be applied to the proposed oscillator designs at any . From Table IV, we can also confirm that the experimental circuit satisfied the maximum feedback-voltage condition and the output-power condition. Additionally, the measurement results agreed with the numerical predictions quantitatively, which denotes the validity of the design procedure. In the laboratory measurement, the oscillator achieved 92.0% power conversion efficiency at 34.8-W output power and 1-MHz operating frequency. VII. COMPARISONS WITH CLASS-E OSCILLATOR The comparisons between the classamplifier and the class-E amplifier were discussed in [15] and [19]. Therefore, it is very important to compare the proposed oscillator with the class-E oscillator. The fair comparisons, however, are very difficult because the proposed oscillator is a different class of the oscillator compared with the class-E oscillator. In this section, the classand class-E oscillators are discussed from several points of view. For comparisons, we give and as specifications for both the proposed oscillator and the class-E oscillator and for the proposed oscillator. A. Output Power and Switch Stress Fig. 10 shows the normalized output powers as a function . It is seen from this figure that the of output dc-supply voltage of the proposed oscillator is lower than that of the class-E oscillator under the identical output-power condition. The dc-supply power of the injection circuit is about 1/3 of the main-circuit dc-supply power [15]. The output power of the proposed oscillator is, however, about twice as large as that of the class-E oscillator for the same load resistance and dc-supply voltage. Fig. 11 shows the normalized peak switch voltages and currents as a function of output . It can be stated that the peak
Fig. 11. Normalized peak switch voltages and currents as a function of output . (a) Normalized peak switch voltages. (b) Normalized peak switch currents.
switch voltage of the proposed converter is lower than that of the class-E oscillator under the identical output-power condition because the dc-supply voltage of the proposed oscillator is lower than that of the class-E oscillator. The switch current through the classoscillator is also usually lower than the class-E oscillator in spite of the low dc-supply voltage. Generally, MOSFET cost becomes low as the permissible maximum drain-to-source voltage decreases. Therefore, low MOSFET stress is an additional reason why the switching-device cost can be reduced. B. Total Harmonic Distortion Fig. 12 shows the THD values as a function of output . Usually, THDs increase as the output- value decreases because the resonant filter passes the harmonic components for low . In both the classand the class-E oscillators, however, the THD values for low decrease with the decrease in the output as shown in Fig. 12. It is also seen from this figure that the THD of the classoscillator is lower than that of the class-E amplifier for high . Conversely, it is higher for low . C. Power Conversion Efficiency For power-conversion efficiency comparisons, we carried out another type of the proposed and the class-E oscillators. The common specifications are , , , and . By using these specifications, the dc-feed and resonant inductances of the classoscillator are equal to those of the class-E oscillator. IRF530 MOSFETs were used for all the switching devices. Therefore, , , , ,
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D. Power-Added Efficiency
Fig. 12. Total harmonic distortions as a function of output
TABLE V NUMERICAL PREDICTIONS FOR CLASS-
AND
.
CLASS-E OSCILLATORS
For example, the driving power for IRF740 MOSFET in Fig. 9 was 29.8 mW, which was 0.09% of the output power. In [19], the driving power for the injection-circuit IRFZ24N MOSFET was 0.44% of the output power. It is seen from these results that the power-added efficiency depends on the design specifications and device selection. The driving power of the proposed oscillator is much higher than the injection-signal power of the injection-locked class-E oscillator. It is difficult to conclude which oscillator is better from the power-added efficiency point of view when the drain-current-fall-time effect can be ignored. This is because there are possibilities that the difference between the driving power and injection-locked signal cover with the power-conversion efficiency improvement. Obviously, the proposed oscillator has the complexity compared with the class-E oscillator. Therefore, it is necessary for designers to consider whether the advantages of the proposed oscillator appear for the application requirements. The advantages of the proposed oscillator appear clearly when the drain-current-fall-time problems yield. The analytical evidences are mandatory for explaining the benefits, which are one of the important problems. E. Comparisons With Class-E Amplifier
, and , which were obtained from [3] and [26]. Table V gives the numerical predictions for the classand class-E oscillators. Note that the drain-current-fall-time effect due to the switchcurrent jumps is not included in the numerical calculations. Additionally, the ESRs of the inductors are also not considered in the numerical predictions because they can be controlled by the inductor core-material and wire-type selections. It is seen from Table V that the power-conversion efficiency of the proposed oscillator is little higher than the class-E oscillator in the numerical prediction. This is due to the current-division effects. The similar effects appear in the interleaving topologies of converters [30]. Therefore, it is expected that the power-conversion efficiency of the proposed oscillator is the same as or higher than that of the class-E oscillator even if both the oscillators use the fast-switching devices. Additionally, it is expected that the power-conversion-efficiency improvement appears clearly when the slow-switching devices are used to oscillators. We confirmed that the power conversion efficiency of the proposed oscillator was little higher than that of the class-E oscillator by circuit experiments. It is necessary to use the high-speed switching device in the injection circuit because there are current jumps in the injection-switch current. The injection-circuit power is a quarter of the output power. Therefore, the power dissipations due to the drain-current-fall time of the proposed oscillator, which are caused by overlaps between the injection-switch voltage and current, are narrower than those of the class-E oscillator. When we consider the peak-switch-voltage reduction effect, the injection-circuit switching-device cost can also be reduced. The reduction level depends on design specifications.
The power-added efficiency of the class-E amplifier is the same as the class-E oscillator if the driving power if the amplifier is the same as the feedback power of oscillator. Conversely, the power conversion efficiency of the class-E amplifier is a little higher than the class-E oscillator. This is because the dc-supply power of the class-E oscillator is divided into the output power and the feedback power. From these points of view, the power conversion efficiency of the proposed oscillator is almost the same as the class-E amplifier if the drain-current-fall-time effect is ignored. Additionally, the power-added efficiency relationship between the classoscillator and the class-E oscillator is the same as the classoscillator and the class-E amplifier. VIII. CONCLUSION This paper has presented the classpower oscillator with the second harmonic injection. The injection circuit of the proposed oscillator has some roles. The main circuit achieves the classZVS/ZVDS/ZCS/ZCDS conditions, which enhances the power-conversion efficiency and reduces the implementation cost. The output frequency can be locked with the inputsignal frequency of the injection circuit. Additionally, it is possible to increase the output power. The proposed circuit is regarded as not only the improvement version of the class-E oscillator but also that of the classamplifier. The numerical design procedure is presented for the proposed oscillator design, which can be applied to the design of the proposed oscillator at any set of specifications. The design curves, considered with the MOSFET body junction diode nonlinear capacitances and ESRs of each component, are shown. The design example is also shown in this paper. In the laboratory experiment, the proposed oscillator achieved 92.0% power-conversion efficiency at
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34.8-W output power and 1-MHz operating frequency. The experimental results agreed with the numerical predictions quantitatively, which denotes the validities of the design procedure. This paper has focused on designs of the proposed oscillator for nominal operation. The proposed oscillator behaviors outside nominal operation including the synchronization band between the main and injection circuits should be addressed in the future.
REFERENCES [1] J. Ebert and M. Kazimierczuk, “Class E high-efficiency tuned power oscillator,” IEEE J. Solid-State Circuits, vol. SC-16, no. 2, pp. 62–66, Apr. 1981. [2] M. K. Kazimierczuk, V. G. Krizhanovski, J. V. Rassokhina, and D. V. Chernov, “Class-E MOSFET tuned power oscillator design procedure,” IEEE Trans. Circuits Syst. I, vol. 52, no. 6, pp. 1138–1147, Jun. 2005. [3] H. Hase, H. Sekiya, J. Lu, and T. Yahagi, “Novel design procedure for MOSFET class-E oscillator,” IEICE Trans. Fund., vol. E87-A, no. 9, pp. 2241–2247, Sep. 2004. [4] V. G. Krizhanovski, D. V. Chernov, and M. K. Kazimierczuk, “Lowvoltage electronic ballast based on class E oscillator,” IEEE Trans. Power Electron., vol. 22, no. 3, pp. 863–870, May 2007. [5] M. K. Kazimierczuk, V. G. Krizhanovski, J. V. Rassokhina, and D. V. Chernov, “Injection-locked class-E oscillator,” IEEE Trans. Circuits Syst. I, vol. 53, no. 6, pp. 1214–1222, Jun. 2006. [6] H.-S. Oh, T. Song, S.-H. Baek, E. Yoon, and C.-K. Kim, “A powerefficient injection-locked class-E power amplifier for wireless sensor network,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 4, Apr. 2006. [7] H. R. Bae, C. S. Cho, and J. W. Lee, “Efficiency enhanced class-E power amplifier using the second harmonic injection at the feedback loop,” in Proc. Eur. Microwave Conf. (EuMC2010), Paris, France, Sep. 2010, pp. 1042–1045. [8] N. O. Sokal and A. D. Sokal, “Class E-A new class of high-efficiency tuned single-ended switching power amplifier,” IEEE J. Solid-State Circuits, vol. SC-10, pp. 168–176, Jun. 1975. [9] M. Albulet and R. E. Zulinski, “Effect of switch duty ratio on the performance of class E amplifiers and frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. 45, no. 4, pp. 325–335, Apr. 1998. [10] N. O. Sokal, “Class-E RF power amplifiers,” QEX, no. 204, pp. 9–20, Jan./Feb. 2001. [11] H. Sekiya, T. Ezawa, and Y. Tanji, “Design procedure for class E switching circuits allowing implicit circuit equations,” IEEE Trans. Circuits Syst. I, vol. 55, no. 11, pp. 3688–3696, Dec. 2008. [12] J. Ribas, J. Garcia, J. Cardesin, M. Dalla-Costa, A. J. Calleja, and E. L. Corominas, “High frequency electronic ballast for metal halide lamps based on a PLL controlled class E resonant inverter,” in Proc. Power Electronics Specialists Conf, PESC ’05, Recife, Brazil, Jun. 2005, pp. 1118–1123. [13] A. Mediano, P. Molina-Gaudò, and C. Bernal, “Design of class E amplifier with nonlinear and linear shunt capacitances for any duty cycle,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 3, pp. 484–492, Mar. 2007. [14] X. Wei, H. Sekiya, S. Kuroiwa, T. Suetsugu, and M. K. Kazimierczuk, “Design of class-E amplifier with MOSFET linear gate-to-drain and nonlinear drain-to-source capacitances,” IEEE Trans. Circuits Syst. I, vol. 58, no. 10, pp. 2556–2565, Oct. 2011. [15] A. Telegdy, B. Molnár, and N. O. Sokal, “Class-E switching-mode tuned power amplifier—High efficiency with slow-switching transistor,” IEEE Trans. Microw. Theory Tech., vol. 51, no. 6, pp. 1662–1676, Jun. 2003. [16] A. Grebennikov and N. O. Sokal, Switchmode RF Power Amplifiers. Burlington, MA: Elsevier, 2007. [17] A. AlMuhaisen, P. Wright, J. Lees, P. J. Tasker, S. C. Cripps, and J. Benedikt, “Novel wide band high-efficiency active harmonics injection power amplifier concept,” in Proc. 2010 IEEE MTT-S Int. Microwave Symp., Anaheim, CA, May 2010, pp. 664–667.
[18] R. Miyahara, H. Sekiya, and M. K. Kazimierczuk, “Design of class-E power amplifier taking into account auxiliary circuit,” in Proc. IEEE Ind. Electron. Conf. (IECON’08), Orland, FL, Nov. 2008, pp. 679–684. [19] R. Miyahara, H. Sekiya, and M. K. Kazimierczuk, “Novel design procedure for class-E power amplifiers,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3607–3616, Dec. 2010. [20] R. Miyahara and H. Sekiya, “Design of class-E power amplifier with one input signal,” in Proc. Energy Conversion Congress and Exposition, (ECCE’09), San Jose, CA, Sep. 2009, pp. 3859–3864. [21] M. K. Kazimierczuk, “Generalization of conditions for 100-percent efficiency and nonzero output power in power amplifiers and frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. 33, no. 8, pp. 805–807, Aug. 1986. [22] R. E. Zulinski and J. W. Steadman, “Performance evaluation of Class E frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. TCSI-33, no. 3, pp. 343–346, Mar. 1986. [23] R. E. Zulinski and J. W. Steadman, “Idealized operation of Class E frequency multipliers,” IEEE Trans. Circuits Syst. I, vol. TCSI-33, no. 12, pp. 1209–1218, Dec. 1986. [24] M. Albulet, “Analysis and design of the Class E frequency multipliers with RF choke,” IEEE Trans. Circuits Syst. I, vol. 42, no. 2, pp. 95–104, Feb. 1995. [25] W. Feipeng, D. F. Kimball, J. D. Popp, A. H. Yang, D. Y. Lie, P. M. Asbeck, and L. E. Larson, “An improved power-added efficiency 19-dBm hybrid envelope elimination and restoration power amplifier for 802.11g WLAN applications,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 12, pp. 4086–4099, Dec. 2006. [26] H. Sekiya, T. Watanabe, T. Suetsugu, and M. K. Kazimierczuk, “Analysis and design of class DE amplifier with nonlinear shunt capacitances,” IEEE Trans. Circuits Syst. I, vol. 56, no. 10, pp. 2362–2371, Oct. 2009. [27] International Rectifier. [Online]. Available: http://www.irf.com/ product-info/models/ [28] K. W. E. Cheng and P. D. Evans, “Calculation of winding losses in high-frequency toroidal inductors using single strand conductors,” IEE Proc.—Electric Power Applications, vol. 141, no. 2, pp. 52–62, 1994. [29] H. Sekiya and M. K. Kazimierczuk, “Design of RF-choke inductors using core geometry coefficient,” presented at the Electrical Manufacturing Coil Winding & Coating Expo (EMCW2009), Nashville, TN, Sep. 2009. [30] M. T. Zhang, M. M. Jovanovic, and F. C. Y. Lee, “Analysis and evaluation of interleaving techniques in forward converters,” IEEE Trans. Power Electron., vol. 13, no. 4, pp. 690–698, Jul. 1998.
Ryosuke Miyahara was born in Nagano, Japan, on October 8, 1985. He received the B.E. and M.E. degrees in information and image science from Chiba University, Chiba, Japan, in 2008 and 2010, respectively. Since April 2010, he has been with Ricoh Company, Tokyo, Japan. When he was a student, his interests were high-frequency high-efficiency dc/ac inverters.
Xiuqin Wei (S’10) was born in Fujian, China, on December 7, 1983. She received the B.E. degree from Fuzhou University, China, in 2005, and the Ph.D. degree from Chiba University, Japan, in 2012. Since April 2012, she has been with Fukuoka University, where she is currently an Assistant Professor in the Department of Electronics Engineering and Computer Science. Her research interests include high-frequency power amplifier.
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OSCILLATOR WITH SECOND HARMONIC INJECTION
Tomoharu Nagashima (S’11) was born in Saitama, Japan, on February 4, 1989. He received the B.E. degree from the Department of Information and Image Sciences, Chiba University, Chiba, Japan, in 2011. He is currently working toward the M.E. degree at Chiba University. His current research interest is in high-frequency high-efficiency tuned power amplifiers.
Takuji Kousaka (S’99–M’00) received the B.E., M.E., and D.E. degrees from Tokushima University, Tokushima, Japan, in 1994, 1996, 1999, respectively. He is currently an Associate Professor of Mechanical and Evergy Systems Engineering at Oita University, Oita, Japan. His research interest is in qualitative properties of nonlinear systems with interrupted characteristics.
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Hiroo Sekiya (S’97–M’01–SM’11) was born in Tokyo, Japan, on July 5, 1973. He received the B.E., M.E., and Ph.D. degrees in electrical engineering from Keio University, Yokohama, Japan, in 1996, 1998, and 2001, respectively. Since April 2001, he has been with Chiba University, Chiba, Japan, where he is currently an Assistant Professor in the Graduate School of Advanced Integration Science. From February 2008 to February 2010, he was also with the Department of Electrical Engineering, Wright State University, Dayton, Ohio, as a visiting scholar. His research interests include high-frequency high-efficiency tuned power amplifiers, resonant dc/dc power converters, dc/ac inverters, and digital signal processing for wireless communications. Dr. Sekiya is a member of the Institute of Electronics, Information and Communication Engineers (IEICE) of Japan, the Information Processing Society of Japan (IPSJ), and the Research Institute of Signal Processing (RISP), Japan.
