Suppression of a Long-Term Instability of a Commercial Magnetron with Low-Ripple DC Power Supply for Heater

Compact but powerful and efficient magnetrons are in service for various high-power microwave applications owing to their additional superiority of low-cost mass production. However, the magnetron’s inherent instability in frequency and phase over a relatively wide spectrum limits the versatile availability of the magnetron for possible advanced applications, including a long-distance wireless power transfer system (WPTS) that employs the magnetron as a unit source of a phased array system. The authors present a methodology suppressing a long-term instability of the S-band commercial magnetron harnessed by the phase-locking-loop (PLL) injection controlling and fixing the phase and frequency of the magnetron to the extent of the precision for a WPTS. The long-term drift of the phase exactly replicating the anode voltage fluctuations is successfully suppressed by the implementation of a DC power supply to compensate the cooling effects of the heater, which contributes to extreme stabilization of the phase (peak to peak 0.2°) for high-power (1kW). And eligibility for the unit source of a phase-arrayed WPTS is proven by varying the output power while maintaining the phase at a constant.


I. INTRODUCTION
Magnetron is a diode tube that generates a high-power microwave using the interaction of spokes of rotating electrons under a magnetic field with a series of cavity resonators. Compact but powerful and efficient magnetron has provided radars since World War II with operational improvements in resolution and range. There are even today thousands of magnetron aviation and marine radar units in service. However, the magnetron's inherent instability in frequency and phase over a relatively wide spectrum limits the availability of the magnetron for possible advanced applications. Instead, industrial implementation of magnetrons flourishes in consumer microwave ovens and commercial ovens for baking and drying, generation of processing plasmas, industrial heating, and chemical process intensification [1]- [5] owing to additional superiority of lowcost mass production.
In recent years, an intensive search for a high-power microwave module capable of (a) a few grams per unit power in the weight-power ratio and (b) 70% or higher in the DC-RF power conversion ratio, has been conducted to realize long-distance wireless power transfer systems, including the space solar power system (SSPS) that transfers electric power wirelessly via microwave to the earth after the sunlight generation on the geostationary orbit targeting from the 36,000 km above to the diameter of 100m [6]- [12]. A magnetron is a competitive source satisfying both of the requirements, (a) to reduce launch costs and (b) to maximize energy utilization and to minimize thermal loss, among various microwave modules [13]- [15]. To employ the magnetron as a unit source of a phased array system forming a spatially confined energy beam and controlling the direction of the beam precisely, researchers including the authors have studied methodologies controlling and fixing the phase and frequency of a magnetron to the extent of the precision required for a phased array antenna or a linear accelerator overcoming the critical and inherent shortcomings of magnetrons [16]- [22].
Previous studies on the noise in high-power microwave tubes [23]- [25] concluded that the noises on the electron beam play an important role, which is mainly attributed to the technical parameters such as beam current and voltage near their nominal values. Fluctuations in the beam parameters can be caused by the finite stabilization of the switching mode power supply (SMPS) for high acceleration voltage and the power supply for heating the electron emitter. Compared to the gyrotron, so-called, electron cyclotron resonance maser [26], [27], the magnetron is not highly resonant device so that the frequency and phase of a magnetron are more strongly influenced by the driving power supplies. In the previous study [28], however, the noises in the frequency and phase of a commercial 2.45GHz magnetron were successfully suppressed with the low pass filter installed to the output of the SMPS driving the magnetron and the phase-locking-loop (PLL) assisted injection. As a microwave power module [29]- [32], the PLL injection harnesses the magnetron on the basis of noise suppression of the driving power supply when the power supply heating the emitter is off to remove the noise. The authors, however, could not but report the long-term drift of the voltage from the phase detector and the anode voltage, where the voltage from the phase detector is the exact replication of the anode voltage. Such a long-term drift may be attributed to emission cooling of the cathode surface [33]- [39] or the conduction cooling of the cathode due to insufficient thermal insulation of the heater.
In Sec. II, we report details of the analysis, design, and implementation of the driving power supplies, which include a DC heater power to compensate the cooling effects on the cathode emitter and a high-voltage source with the combination of a high switching frequency and a low pass filter to reduce ripple and switching noise effectively. Longterm stabilization of the phase and frequency of the magnetron harnessed by the PLL and driven by the developed power supplies is demonstrated in Sec. III. Eligibility for the unit source of a phase-arrayed powertransfer system is proven by varying the output power with the driver while maintaining the phase at a constant. Conclusion follows in Section IV. Figure 1 shows a schematic configuration of the magnetron system harnessed by the PLL and driven by the power supplies. Table I shows specifications of (a) the cathode power supply (CPS) to extract and accelerate electrons from the cathode to the anode and (b) the heater power supply (HPS) to warm up the cathode to the temperature for thermionic emission of electrons. As aforementioned, decreasing output voltage ripple and switching noise of the power supplies improve phase stability of the magnetron. These requirements can be met by increasing switching frequency of the power supplies and applying an output low pass filter (LPF). In this paper, resonant converter, widely used in high frequency applications due to zero voltage switching (ZVS) characteristic, is adapted [40]- [42]. Reduced switching losses enable power supplies to operate at high switching frequency and to decrease switching noise. Considering the output voltage ripples at a small-power condition, we employed the continuous conduction mode (CCM), where switching frequency increases at light load operation, in design instead of the discontinuous conduction mode (DCM). Among various types of resonant converters, a series-parallel resonant converter (SPRC), which can take benefits of a series resonant and a parallel resonant converter, is employed [43]. An LLC resonant converter capable of achieving high efficiency, has been widely used. However, designing an LLC converter with high efficiency for dynamic loads requiring high voltage is difficult as discussed in [44], [45]. (For high voltage applications, high step-up transformers are essential. However, parasitic components of high step-up transformers cause difficulties in designing the  LLC resonant converter and its light load operation.) Therefore, an LCC resonant converter utilizing parasitic components as a resonant tank is employed instead of the LLC converter. In addition, by shaping resonant current as a trapezoid in the LCC, the RMS value of the resonant current decreased, which contributes to reducing conduction losses of the entire circuit [46], [47]. With mentioned advantages of the LCC resonant converter, the developed CPS achieved a maximum efficiency of 96% and the output voltage ripple of 0.4%. In the case of the HPS, a full-bridge inverter (S1-S4) for low stresses of switches and a center-tapped transformer (TR2) rectifier are applied. Since the HPS has low output voltage, the center-tapped structure reduces forward voltage drops compared with the one by a full-wave rectifier. In the case of the full-wave rectifier, there are two diodes in the current path. On the other hand, only one diode induces the forward voltage drop in the center-tapped full-wave rectifier.

1) COMPOSITION OF EACH POWER SUPPLIES
To operate the CPS safely, an interlock control method is applied to controlling the power. Since the interlock control enables to gradually release the control voltage (Vcont) by comparing reference signals (Iref, Vref), the CPS can avoid rapid change of the dynamic load, i.e. magnetron [48,49]. The HPS that employs the same control strategy maintains rated power operation (43W) until the CPS reaches to required output. After that, the output power of the HPS is controlled and kept low (3W) by the power control loop to compensate the cathode cooling effect. As a result, increased switching frequency due to the small power operation improves output voltage ripple.

2) OUTPUT LOW PASS FILTER
Output LPFs are implemented for both the CPS and the HPS to reduce the output voltage ripples and the switching noises. In the case of the CPS, high output voltage makes it hard to increase the capacitance of the filter capacitor. Therefore, the LPF of the CPS consists of a 230μH inductor and a 240nF capacitor. In the case of the HPS, 50μH and 6.6μF are used. Cut-off frequencies of each LPFs are designed to be less than one-twentieth. To shape the resonant current as a trapezoid, the parallel resonant frequency (fop2, determined by Lr2, Cr2, and Cp2) much faster than the series resonant frequency (fos2, determined by Lr2 and Cr2) is chosen. Therefore, the value of Cp2 is much less than Cr2. Operating modes and design of resonant parameters are briefly explained as follows.

1) LCC WITH TRAPEZOIDAL APPROXIMATION
-Mode 1 With switches S1 and S4 on, the input voltage (Vin) is applied to the resonant tank. Then, the resonant current (iLr2) rises until the voltage of Cp2 is clamped by output voltage referred to the primary side of the transformer (Vo,pri). Since the value of Cp2 is much less than Cr2, it can be assumed that the resonant frequency is almost equal to fop2. During M1, no charge is transferred to a load.
-Mode 2 The resonant current in M2 is maintained as a flat form due to (a) lower applied voltage (Vin -Vo,pri) to the resonant tank and (b) higher characteristic impedance than M1. Hence, the voltage of Cr2 (VCr2) linearly increases during M2. To minimize an effect of the voltage of the series resonant capacitor (VCs1) to the shape of the resonant current, the value of Cs1 is chosen to be enormously high.
-Mode 3 After turning off S1 and S4, the resonant current still flows in the positive direction through the anti-parallel diodes of S2 and S3. Therefore, a large negative voltage is applied to the resonant tank, which results in the rapid decrease of the current. In addition, S2 and S3 are capable of soft-switching during M3 because their anti-parallel diodes are conducting. As the direction of the current changes, M4 starts. Analyses from M4 to M6 are the same as those from M1 to M3.

2) DESIGN OF RESONANT PARAMETERS
Resonant parameters must be designed in consideration of a change of load. Since fop1 is relevant to a loaded quality factor, deciding this value affects the light load operating range as well as a peak value of the resonant current and the relation is shown in Fig. 4. In this paper, fop2 is designed to be double the value of fsw2, which makes power supplies cover 10% of the rated load operation at 3 times the switching frequency [46]. By referring to [46], a relationship between ILr2,peak, fop2, and power coverage for the light load can be expressed as (1). 2 2, 2 Due to the assumption that Cr2 is much larger than Cp2, a characteristic impedance during M1 (Zop2) can be approximated by just using Lr2 and Cp2. With the obtained value of ILr2,peak in (1), Zop2 is calculated as (2).
As aforementioned, the value of Cr2 can be chosen to be quite large value to make the resonant current during M2 flat. The value also can be derived as (5) by calculating VCr2,peak for the exactly required output power.   Calculated Cp1 is the required value from primary side. To apply it in the secondary side, the turns ratio and structure of the rectifier circuit should be considered. Similarly, for Cr1, the structure of the inverter should be taken into consideration. In a half-bridge structure like the CPS, half value of Cr1 is applied to each of the capacitors. Furthermore, in designing low voltage power supplies such as HPS, turns ratio (NTR2) needs to be adjusted by considering forward voltage drops of rectifying diodes. Calculated design parameters based on the equations above are shown in Table II.

3) SIMULATION RESULT AND ACTUAL PERFORMANCE
Calculated parameters are shown in Table II. PSpice simulation is conducted and waveforms of resonant current and resultant output voltage for each power supply are shown in Fig. 4. Waveforms of each resonant current follow the trapezoidal approximation. At the same voltage (4.3kV) for the resistive load, the developed CPS achieved lower output voltage ripple (< 45V) than the one (< 85V) with a commercial magnetron power supply, SM445 from MKS [30], [31] as shown in Table III.

III. STABILIZATION OF A COMMERCIAL MAGNETRON A. FREE-RUNNING CHARACTERISTICS OF THE MAGNETRON DRIVEN BY THE POWER-SUPPLIES
A commercial S-band magnetron (National Electronics YJ1540) is driven by the developed power supplies. Figure  6 shows a waveform of the cathode voltage under freerunning condition with a forward power of 1kW. The voltage ripple of CPS is 0.2%, which is better than the result predicted from the PSpice simulation. Since the operating voltage (4kV) driving the magnetron load is lower than the designed voltage (5kV), a higher switching frequency (650kHz) inversely proportional to the voltage contributes to the enhancement. The switching frequency of 650kHz is observed in Fig. 6 where the voltage ripples of 13 periods are monitored during 20us. Figure 7 shows magnetron spectrum under the free-running condition with DC heater, where the resolution bandwidth (RBW) and the video bandwidth (VBW) are set to 1kHz. A black line of Fig. 7 (b) is a spectrum from the magnetron (driven at the output power of 1kW) by the CPS with the heater off after warming up the cathode. When the heater is off (filamentoff), the spectral purity of the magnetron is improved for s h o r t , b u t t h e t e m p e r a t u r e o f t h e c a t h o d e becomes lower because of the cooling mechanisms and the output frequency becomes unstable in the long term for the CPS to compensate for the reduced emission current from the cooler cathode. A DC heater was introduced to stabilize the output frequency of the magnetron and minimize noise caused by the heater. The cathode is heated at 4V and 10.5A, then the heater power is reduced to 1V and 3A after the driving condition is stabilized (in a few minutes). Figure  7 (a) and (b) show the spectrum according to the heater power. The heater power was reduced from 42W to 3W, and the noise from the magnetron was reduced accordingly [50]. When the heater power is decreased to 3W, the linewidth is almost the same as the heater-off condition. A temperature of the magnetron filament with respect to the heater current is divided into two regions, (1) pre-heating (over-heating) region where the filament temperature increase as the filament current increase, and (2) selfheating region where the filament temperature maintains regardless of the heater current [51]. In the (1) pre-heating region, smoothing effect of anode current dominates the noise: The feedback system of the DC stabilized power supply is unstable to control the anode current because the filament temperature is high enough for space charge limited operation, which results in the noise as a function of the anode current owing to the pushing effect [51]. In the (2) self-heating region, the back-bombardment energy of electrons is the main source of heating so that the filament temperature remains at a constant even without the filament current. The conduction cooling and/or the emission cooling accompany axial asymmetry of the filament temperature along the cathode axis, which results in the change of the circulating frequency of the electron spoke synchronized with the RF field by the EｘH drift along the axis as discussed in [52], [53]. Non-uniform emission along the cathode may produce spurious noise, as experimentally demonstrated in the paper by applying cathode shield in [53]. The filament-off technique has a difficulty in maintaining the magnetron operation due to the excessive falloff of the filament temperature owing to cooling mechanisms. When the filament temperature is cooled down below the stable operation condition, the feedback system of the power supply is unstable to make up the anode current, which may attribute to the long-term drift of the phase of the magnetron in our previous study [28]. Therefore, in this study, the DC power supply is employed for the filament and optimize condition to compensate for the cooling of the filament. In Fig. 7(b), the lower the heater power moves from 12W to 3W, the narrower the linewidth at -50 dBc follows at -50dBc follows. The linewidth with the heater power of 3W is comparable to the one when the heater is off.

B. FURTHER STABILIZATION WITH A PLL INJECTION
A PLL injection was applied to the magnetron driven by the developed CPS and HPS to demonstrate further improvements in frequency and phase control. The injection signal is generated from a signal generator (Keysight N5171B) and amplified by a power amplifier (KRF KAH2453-40TS-UNF), then fed into the magnetron through a three-port circulator terminated with a load (National Electronics 2722-162-10311). The PLL mainly consists of a double-balanced mixer (Mini-Circuits SYM-25DLHW) detecting the phase difference between the reference signal and the sampled microwave from th e magnetron, and the control circuit producing the voltage to adjust the phase of the phase shifter accordingly. The phase shifter (Analog Devices HMC928) in front of the balanced mixer is used to compensate the phase of the magnetron output [28]. Figure 8 shows spectral characteristics of the injectionlocked magnetron with the PLL at the output of 1kW at the span of (a) 10MHz and (b) 100kHz, respectively, under the same measurement conditions. The spectral purity of the magnetron is improved to the extent of the linewidth at 60dBc less than 13kHz as depicted in Fig. 8 (b), which is comparable to the one of the reference signals itself injected through the PLL [54].
The phase of the magnetron is monitored by a phase detector (Analog Devices AD8302) with the sensitivity of 10mV/°. To minimize the effect of random thermal noises, the measured signals are averaged over ten times. Figure 9 shows the extreme phase-stability of around 0.2° peak to peak. When the free running case is compared with the PLL injection case, the spectral purity is dramatically improved through the PLL injection and various noise components of the magnetron is eliminated. Consequently, the negative voltage of the cathode extracting electrons becomes more stable than that of the free-running case as shown in Fig. 9.
Owing to the precise HPS-control, the long-term drift of the phase is stabilized as presented in Fig. 10, where the variation of the phase is further restricted within ±0.8° even without the averaging to filter out the effect of random thermal noises owing to DC HPS. Consequently, the cooling mechanisms of the magnetron are effectively compensated, and long-term stabilization of the phase is realized. Systematic fluctuation found in Fig. 10 is about 60Hz, which implies the signal from the magnetron driven by the power supplies is irrelevant because three-phase inputs of 380V AC provide the power to the supplies. The enhanced stability contributes to realizing a power-variable phase-controlled magnetron (PVPCM). Figure 11 demonstrates the stability of the phase during the variation of the magnetron output, which is an essential characteristic for magnetrons to be eligible for unit sources constituting a phased-array power-transfer system. The cathode voltage of the magnetron is fixed at -4.1kV and the beam current is swept from 250mA to 380mA to adjust the output power (blue point) of the magnetron from approximately 700W to 1050W. The phase (magenta point) remains at a constant value while the output power is swept. Owing to the successful suppression of a long-term instability of the magnetron in cooperation with the well-stabilized driving power supply and the heater power supply minimizing the cooling effects, the performance of the magnetron is further stabilized and the feasibility of the magnetron is verified satisfying the main characteristics required as the unit source constituting a phase-arrayed power-transfer system.

IV. CONCLUSION
Long-term stabilization of the phase (peak to peak 0.2°) of an S-band magnetron for high-power (1kW) was achieved by the driving with the DC HPS to compensate the cooling effects of the heater, in cooperation with the PLL assisted injection harnessing the magnetron along with the highvoltage CPS developed using an LCC (Inductor-Capacitor-Capacitor) resonant converter. And eligibility for the unit source of a phase-arrayed power-transfer system is proven by varying the output power while maintaining the phase at a constant. Compact but powerful and efficient magnetrons became promising for advanced high-power microwave applications including a long-distance WPTS and replacement of the bulky klystrons for linear accelerators, by overcoming the inherent instability in frequency and phase.