Frequency-Selective MHz Power Amplifier for Dielectric Barrier Discharge Plasma Generation

Plasma-assisted nitrogen fixation at atmospheric pressure is a clean and decentralized method for fertilizer production. Among many different plasma discharge types, dielectric barrier discharge (DBD) is one of the few that can generate high output of nitrogen compounds at atmospheric conditions for fertilizer usage. Most DBD generators operate at kHz switching frequencies, however, previous research has found that discharge activities occur at the intervals of the greatest voltage slew rate. The finding implies that operating at higher frequencies can lead to more discharge activities and higher plasma generation. This paper presents a MHz Class E power amplifier with frequency selection to generate DBD plasma at two distinct frequencies. The power amplifier achieves a peak efficiency of 91.5% and outputs 600 W at frequencies of 12.4 MHz and 15.5 MHz.


I. INTRODUCTION
The Haber-Bosch process is one of the most impactful chemical reactions in history. This process improves agricultural yield by increasing ammonia fertilizer production, helping in feeding the world's growing population. In 2020, global ammonia production was around 144 million metric tons [1], and more than 95% of ammonia is produced through the Haber-Bosch process [2]. Between 75% to 90% of the ammonia produced is used in making fertilizer, benefiting 50% of the world's food production [3]. The Haber-Bosch process fixes nitrogen with hydrogen to produce ammonia with the feedstock of natural gas (50%), oil (31%) or coal (19%) [2]. Burning these fossil fuels during the process leads to more than 1% of the world's total CO 2 emission. The process requires a centralized plant for high-temperature and highpressure reactions. After the production, the ammonia then needs to be transported to local farms. The transportation not only has environmental and cost concerns, it is also dangerous since ammonia is highly toxic and flammable when exposed to high temperatures [4].
Recently, Non-Thermal Atmospheric Pressure Plasma (NTAPP) has gained attention as a sustainable replacement for conventional nitrogen fixation process [5]. With the development of low-temperature plasma science, the minimum theoretical energy consumption of non-thermal plasmaassisted fixation is lower than that of the Haber-Bosch process [6]. The fixation process applies plasma at the surface of air and water to form soluble reactive oxygen and nitrogen species (RONS). The species include nitrate (NO − 3 ) and other forms of nitrogen compounds, which can all be used as fertilizers [5], [7]. Plasma-assisted nitrogen fixation works under atmospheric conditions without emission of green house gases. Localized production due to the reduced system size and simplified process also eliminates potential cost and hazards during transportation.
The literature has discussed different discharge types for nitrogen fixation, including microwave plasma, spark discharge, gliding arc discharge, and dielectric barrier discharge (DBD) [6]. Among these alternatives, both the gliding arc discharge and DBD have high output of NO x compounds and can operate under atmospheric pressure. This work focuses on designing a power amplifier to produce DBD plasma. Most DBD systems use power supplies that generate a low-frequency (in the range of 50 Hz to a few tens of kHz) multi-kV output at the plasma load [8]. Previous research has shown that the discharge activities occur during the zero crossings of the applied voltage, corresponding to the intervals of the greatest voltage slew rate and maximum current [9]. The finding implies that increasing the frequency can lead to more discharge activities and higher plasma production rate, motivating the design of a MHz power amplifier to drive a DBD plasma load. Conventionally, RF system manufacturers use linear power amplifiers in high-frequency applications, including plasma generation. The linear power amplifiers have the advantages of linearity but low efficiencies. The switch-mode power amplifiers such as Class D, Class E, and Class 2 can achieve much higher efficiencies under zero-voltage-switching (ZVS) operations. However, due to their resonant nature, these switch-mode power amplifiers maintain high efficiencies only at a fixed frequency and constant load condition. Previous research has introduced different methods to extend the frequency and load range, including reactance compensation [10], impedance compression [11], phase-switched impedance modulation [12], and load-independent power amplifier design [13]. The power delivered to a plasma load at MHz can be much higher than that at kHz due to higher plasma generation rate. As a result, it is necessary to operate the power amplifier at a low burst rate to reduce the average power delivered to the DBD reactor. This paper presents a wideband Class E power amplifier using the reactance compensation technique and combined with frequency selection networks to drive multiple DBD loads sequentially. The frequency selection networks allow the power amplifier to operate for longer time within each burst period while each DBD reactor only receives a fraction of the total average power.
One challenge before designing the power amplifier is to measure the plasma load impedance. Before the plasma breakdown, the load is almost entirely reactive. To start the plasma, one requirement is to carefully tune the matching network to minimize the reflective power. After the plasma breakdown, the load has an additional resistive part, and the resistance varies significantly with the operating conditions. Depending on the reactor design and operating conditions, the plasma load after the breakdown can still be very reactive, making it hard to measure precisely. Section II describes the DBD electrode design and plasma impedance measurement in details. The rest of the paper is organized as follows. Section III explains the design of the frequency-selective power amplifier; Section IV shows the experimental results; and Section V concludes the paper.

II. ELECTRODE DESIGN AND PLASMA LOAD MEASUREMENT
A DBD reactor has two electrodes located on the opposite sides of a dielectric barrier [8]. The electrode on the front side is exposed to air, and the electrode on the back side is covered by a layer of dielectric material. Generating DBD plasma at MHz frequencies requires a careful selection of the dielectric material for the board to produce a certain capacitance with low loss. Previous research has used mica at 13.56 MHz [14]. In this work, Rogers 4003C [15] is used because of its low dissipation factor at high frequencies and the possibility of it being integrated into a PCB to keep the costs low. Figure 1(a) shows the electrode on the front side of the Rogers board made by a thin line of copper tape, and Figure 1(b) shows the grounded electrode on the back made by a copper plane covered by a layer of Kapton tape. After experimenting with several different widths of the front electrode and thicknesses of the Rogers board, the designs with low capacitance (narrow copper lines on the front side) and small board thickness are found to break down at lower voltages. The electrodes used in this work has a board thickness of 0.2 mm, a front electrode width of 1 mm, and a length of 100 mm. The plasma strikes when the voltage across the electrodes of this DBD reactor exceeds 700 V rms . After the plasma strikes, a plasma sheath forms only around the top electrode without a breakdown of the dielectric. The detailed measurement procedure will be described later in this section.
Plasma load impedances are sensitive to the operating conditions, such as temperature, pressure, and power delivered [9]. Before the plasma generation starts, the load is nearly purely reactive; after the plasma breakdown, the load impedance changes with the increased applied voltage, especially for the resistive part. A commercial linear power amplifier is used to drive the plasma load for impedance measurement. When the power amplifier drives a highly reactive load, most of the power gets reflected, which makes it hard to reach the voltage for plasma breakdown. Therefore, it is necessary to match the plasma load to 50 using a tunable matching network and actively adjust the network as the plasma impedance changes. Calibration of the probes is also essential for accurate measurements, especially the phase angle between the voltage and current. Even after the breakdown, the plasma load can still have a relatively high quality factor (Q), and a small skew can result in a large error in the measured impedance. Knowing the caveats above, the measurement of the load impedance in a DBD plasma system includes the following steps:

1) VOLTAGE AND CURRENT PROBE CALIBRATION
The voltage measurement requires a capacitor divider by connecting a high-voltage C0G capacitor between the load and the probe because of the high breakdown voltage of the plasma load. The current probe used in the measurement setup is Pearson current monitor 2878. Before connecting to the DBD load, it is important to calibrate the probes. The calibration includes measuring the voltage and current across a 50 radio-frequency (RF) load driven by a linear power amplifier (ENI A1000) at the desired frequency and power level. During this measurement, it is important to adjust the skew time between the two probes to make the phase angle between them 0 • . The measured V r I r is a reference for 50 .

2) SMALL SIGNAL IMPEDANCE MATCHING OF THE DBD LOAD TO 50
After calibrating the probes, the next step is to connect them to the DBD load and measure the small signal impedance with a tunable matching network connected to the load. The tunable matching network can be adjusted until the measured impedance is 50 . Taking the measurements with the probes connected allows for better matching, since the capacitance of the DBD load can be small (on the order of a few pF to hundreds of pF depending on the electrode design). The small signal measurement sets the initial matching conditions before the system is powered on, which accelerates the impedance matching in the next step.

3) MEASUREMENT OF THE DBD PLASMA LOAD
The DBD load and the matching network are then connected to the linear power amplifier and a power meter (Keysight N1914 A). Figure 2 illustrates the overall measurement setup. Figure 3 shows the setup of the voltage and current probes (V & I Probes) in Figure 2. The voltage probe connects to a capacitor divider to measure the high output voltage. The Pearson current monitor 2878 is used to measure the current. The input terminal connects to the tunable matching network, and the output terminal connects to the DBD load. As the applied voltage increases, the matching network can be adjusted when the reflected power becomes significant. Finally at the desired output power after the plasma breakdown, the voltage and current measurements are taken along with the phase angle between them (V m , I m ).

4) CALCULATE THE PLASMA LOAD IMPEDANCE
Using the V r I r reference for 50 in step 1) and the voltage and current measurements in step 3), the following equation calculates the plasma impedance: (1) Figure 4 shows the measured plasma impedance at 13.56 MHz in terms of the parallel resistance and capacitance as modeled in Figure 5. The plasma breakdown starts at an input power of around 200 W and an output voltage of 700 V rms . As the power increases after the breakdown, the output voltage stays relatively unchanged, but the length of  the plasma strip generated at the front electrode gradually extends, causing a decrease in the resistance. The plasma strip reaches the full length of the front electrode at about 600 W. The measured load impedance has a parallel capacitance of 33 pF (including 13 pF of the connectors and the board) and a resistance of 758 with a phase angle of approximately -70 • . Because of its significant real part, the measured impedance provides a relatively reasonable estimate of the plasma load impedance. However, depending on the plasma type, electrode design, and the operating conditions, the load impedance can have a close-to-±90 • phase angle. In those cases, it can be challenging to measure the plasma impedance accurately using voltage and current probes. In step 4), it is also possible to use the input power and output voltage measurements to calculate the plasma impedance. However, the input power measurement includes the power lost in the matching network, which can make the impedance measurement less accurate.

III. DESIGN OF THE FREQUENCY-SELECTIVE POWER AMPLIFIER
Most of the DBD plasma generators operate at low switching frequencies. However, [9] has shown that most of the discharge activities occur during the intervals of the greatest voltage slew rate and maximum current, implying a higher plasma generation rate at a higher frequency. As the frequency increases into MHz, the amount of the plasma generated can result in a much higher power delivery to the load. Even with the high-frequency dielectric materials, it is still hard for the  DBD reactor to dissipate all the power. Therefore, the need to operate the power amplifier at a low burst rate arises to avoid such high power dissipation in the load, as illustrated in Figure 6. However, operating at a low burst rate is not a good utilization of the power amplifier's high power delivering capability. A better operation of the power amplifier is to drive multiple loads sequentially. As illustrated in Figure 7, within each pulsing period, the power amplifier is delivering power selectively to only one of the DBD reactors, which is labeled by the same color as the input signal. As a result, the power amplifier is able to operate longer, while each DBD reactor only receives a fraction of the total average power. The literature has introduced a few techniques for selective power delivery, including using switch selection [16], and frequency selection [17]. Both techniques require active switches to either selectively connect to the load or be used in the switched capacitor banks to change the resonant frequency.
Depending on the applications, these switches may require high voltage blocking and fast switching capabilities, as well as auxiliary gate drive circuitry, which could be complicated for the non-ground-referenced switches. In contrast, this paper proposes to use the similar idea of frequency selection but without any additional switches. Table 1 compares the selective power delivery technique presented in this work with the two mentioned above. Using only passive elements makes the design less expensive and less complicated. Similar to the frequency selection technique using switched capacitor banks, the design presented in this work also requires a wide bandwidth so that selective power delivery can be achieved by setting different switching frequencies. Figure 8 shows the proposed frequency-selective power delivery system. The LC resonant networks connecting to the loads are resonating at different frequencies, and all of these resonant frequencies are within the bandwidth of the designed wideband power amplifier. The prototype design of a frequency-selective Class E power amplifier to drive two DBD loads follows the design procedure below.    Figure 9 shows the Class E power amplifier with finite DC-feed inductance that is able to maintain efficient ZVS operations when driving a variable load [13].

1) DESIGN THE CLASS E POWER AMPLIFIER
L F and C F are the main design components to meet ZVS, while the output network of L S -C S -L P -C P filters out higher harmonics. Following the design steps in [13], L F and C F can be calculated: where f IN = 1.4× f S ( f S is the switching frequency, 13.56 MHz in this case) and k f = 1. The input voltage is 200 V and the power is 600 W based on the measurements from Figure 4.

2) EXTEND THE BANDWIDTH OF THE POWER AMPLIFIER
The conventional switch-mode power amplifiers only operate at a single frequency. When shifting away from the designed frequency, both the efficiency and output power degrade significantly. Extending the bandwidth for the frequencyselective power amplifier is necessary to ensure efficient operations at different frequencies and same power delivery to all of the loads. The literature proposes different methods to extend the bandwidth of these power amplifiers, including tunable and switchable matching networks and reactance compensation techniques [10], [18], [19], [20], [21]. This work uses reactance compensation because it only requires two sets of LC resonant tanks (L S -C S and L P -C P ), which are already in the design. The first step is to design L S and C S based on the output filtering requirement and the targeted bandwidth. A larger Q S makes the output more sinusoidal with less harmonics but the trade-off is a smaller bandwidth. In this design, Q S is selected to be 2.5 to provide a bandwidth that covers the targeted operating frequencies. Next, L P and C P are calculated based on the reactance compensation requirement following the equations below: [22] C F + 1 where Q P = ωRC P , Q S = ωL S R , ω is the the center frequency, and R is the output resistance of the Class E power amplifier determined in the previous step. Substituting the C F and L F calculated from the previous step, Q S = 2.5, and ω = (2π )13.56 MHz into the equation results in a Q P of 1.48.

3) DESIGN THE OUTPUT RESONANT NETWORKS FOR THE TWO LOADS
Selective power delivery to one of the two loads requires two output resonant networks, resonating at different frequencies. Figure 10 shows the schematic of the output networks.
The first design requirement is to deliver the same amount of power to the active plasma load at the corresponding frequency. Specifically, which leads to where Q 2 = 2π f 2 (C 2 + C load )R load , where f 1 is the operating frequency to deliver power to the plasma load Z 1 , f 2 is the frequency to deliver power to Z 2 , and C load and R load are defined in Figure 5. At f 1 , and at f 2 , The second requirement is to make the voltage across the active plasma load to be significantly larger than the other load voltage: so that only one load at a time is receiving power and generating plasma. Designing for a minimum voltage ratio of 2 A high Q allows the two designed frequencies to be close together; however, it also makes the network hard to tune and sensitive to component variations, including the variation in  the plasma capacitance. A low Q requires the two frequencies to be farther apart, but at the same time, both f 1 and f 2 need to be within the bandwidth of the designed power amplifier. For a plasma load of C load = 20 pF and R load = 758 , Q = 5 is selected for both output networks with f 1 = 12 MHz and f 2 = 15.5 MHz. The third requirement is to make sure the output impedance (Z out ) at f 1 and f 2 are equal. If Z out at the two frequencies are not the same due to the interaction of the two close resonances, additional tuning of the component values as well as the designed frequencies can help to achieve equal Z out .

4) MATCH THE OUTPUT RESISTANCE TO THE PLASMA LOAD
The last step is to match the output resistance of the designed Class E power amplifier to the total impedance of the load (Z out ). Figure 11 shows the impedance transformation of the power amplifier's output resistance by a factor of 1 m 2 using Norton transform [23], [24], where m = L S L Fa + 1 (11)   and L Fa is part of L F in Figure 9, where The reactive part of Z out can be combined to L P or C P , so that

TABLE 2. Design Parameters of the Frequency-Selective Class E Power Amplifier
One of the advantages of this technique is that the impedance waveform across frequency is exactly the same after the transformation. Therefore, the transformation step does not change the bandwidth of the designed power amplifier. Figure 12 shows the overall schematic of the design, and Table 2 lists the design parameters.

IV. EXPERIMENTAL RESULTS
This section discusses the experimental results of the design presented, including the small-signal impedance, power, and efficiency measurements. First, it is necessary to measure the small-signal output impedances (Z out ) of the designed power amplifier (Figure 13) at f 1 and f 2 to ensure that they match at the two frequencies. Figure 14 shows the modified front side of the electrode design to include two DBD loads, where each top electrode has the same dimensions as the one in Figure 1(a). Figure 15 shows the dummy loads to measure the impedance and efficiency. The dummy loads are designed using high-voltage resistors and capacitors to emulate the DBD loads with and without plasma generated. The measured output impedances shown in Figure 16 confirm that Z out at f 1 = 12.4 MHz roughly equals Z out at f 2 = 15.5 MHz.
The next step is to test the design with the dummy loads and calculate the system efficiency using the voltage measurements V 1 and V 2 and the dummy load resistance. Figure 17 shows the waveforms of V 1 , V 2 , and V drain at 12.4 MHz and 15.5 MHz. The drain voltage waveforms show ZVS switching behaviors at the two frequencies. V 1 at f 1 = 12.4 MHz and V 2 at f 2 =15.5 MHz are significantly larger than the voltage across the no-plasma load in each case, ensuring the power delivery and plasma generation only at the selected load. The ratios of V 1 V 2 at f 1 and V 2 V 1 at f 2 are not the same, because otherwise,  which contradicts Equation 5 for f 1 = f 2 . Ensuring the same power delivery to each load is more critical than keeping V 1 V 2 at f 1 and V 2 V 1 at f 2 equal as long as the voltages across the no-plasma loads are much lower than the plasma breakdown voltage. Figure 18 shows the power and efficiency plots at both of the designed frequencies. The design achieves a peak efficiency of 91.5% at 15.5 MHz. Finally, it is ready to test the design with the DBD loads as shown in Figure 19. The function generator is programmed to output a series of 12.4 MHz gate pulses followed by an idle period (setting gate to low), and then output a series of 15.5 MHz gate pulses followed by another idle period. The 12.4 MHz and 15.5 MHz operations are both set to 1000 cycles with a burst frequency of 100 Hz. At 12.4 MHz, plasma is generated on the left electrode (Figure 20(a)), and at 15.5 MHz, plasma is generated on the right electrode ( Figure 20(b)). Figure 21 shows the measured output voltages and input power when the designed power amplifier drives the DBD loads. At both frequencies, the plasma starts at an input voltage of around 60 V and an input power of around 100 W. After the breakdown, the measured voltage across the plasma load remains at about 720 V rms regardless of the input power. Since the plasma load is variable and difficult to measure precisely, the measurements of the output power and efficiency when directly driving the DBD loads are neglected.    Table 3 compares this design with the other high-frequency wideband power amplifiers in the literature. By using the reactance compensation technique, the design presented in this work does not require any additional switches, which simplifies the control and reduces cost. The design is able to maintain its high efficiency at two distinct frequencies, 12.4 MHz and 15.5 MHz, with an output power of 600 W. In addition to bandwidth extension, the frequency selection network also allows the designed power amplifier to deliver power to multiple loads selectively, which is an additional feature to all of the previous work in this table.

V. CONCLUSION
As an alternative for the Haber Bosch process, the plasmaassisted nitrogen fixation using the dielectric barrier discharge is able to achieve much cleaner and decentralized fertilizer production. This paper presents a frequency-selective Class E power amplifier that is able to drive DBD plasma loads sequentially at MHz frequencies by using the reactance compensation and frequency-selective resonant networks. The designed power amplifier is able to output 600 W at frequencies of 12.4 MHz and 15.5 MHz with a peak efficiency of 91.5%.