Equivalent circuit and numerical analyses of an inductively coupled plasma torch with a tapped induction coil

Recently, high-powered radio-frequency (RF) inductively coupled plasma (ICP) torch systems have been adopted in various scientific and industrial applications, such as a plasma wind tunnel for aerodynamic heating study,^1,2 ion sources for nuclear fusion research^3,4 and an advanced synthesis reactor for mass production of nano-materials.^5,6 In order to efficiently transmit the RF power required for each application purpose, it is necessary to match the impedances between the RF power supply and ICPs that are generated at the targeted power level.

For this purpose, some ICP torch systems with a 50 Ω RF source employ an impedance matcher that primarily consists of variable capacitors to tune the load resistance to the value of 50 Ω.^7,8 By adjusting the load resistance, i.e. the real part of the load impedance, to the internal resistance of a 50 Ω, it facilitates an effective power transfer from the RF power supply to the plasma. However, most of the free running RF oscillators, widely adopted as a high-powered RF source, are equipped with a tank circuit mainly consisting of the capacitors and the working coil of an ICP torch, instead of an impedance matcher.^9–14 Since the tank circuit determine the oscillation frequency of an ICP torch system,^9,10 the capacitances of the tank circuit are fixed together with the inductance of the working coil. Thus, a tank circuit normally has no variable parts available for tuning the load resistance. On the other hand, the load resistance of an ICP torch system can be varied widely by operation parameters, in particular, such as gas composition and plasma power level.^15,16 Even though the free running oscillators allow the oscillation frequency to be automatically changed to match the load resistance, the variation of the frequency is limited strictly within the range to keep the stable electrical oscillation, and consequently, an ICP torch system with a free running RF oscillator can experience a difficulty in increasing RF power and changing the gas composition. When employing a free running RF oscillator for an ICP torch system, accordingly, the variation of the load resistance needs to be controlled to ensure the stable electrical oscillation at the targeted power level and the designed gas composition.

An ICP torch with a tapped induction coil can be suggested to control the load resistance in the frequency variation range of the free running RF oscillator. As used in induction heating applications, the grounded tap on the coil can be expected to reduce the load resistance of an ICP torch by dividing the coil turn numbers and rearranging the electrical parameters in the tank circuit. For a cylindrical conductor inserted into the coil coaxially, this effect can be mathematically described from the basic circuit theory as will be shown in this work. In an ICP torch system, however, the secondary load of the working coil is in the form of the complicated MHD (Magneto-Hydrodynamic) flow structures, thus, basic circuit theory has a limitation in predicting precisely the effects of a grounded tap. In order to overcome this limitation and clarify the effects of a grounded tap, the equivalent circuit analysis for a tank circuit was combined with the numerical analysis for an ICP in this paper. For this purpose, first, we conducted a numerical analysis of Ar-N₂ ICPs that was generated by the ICP torches with or without a center-tapped induction coil at a plasma power level of 50 kW. Then, the load resistances of a tank circuit were calculated for various N₂ content by applying the equivalent circuit theory to the numerical results and the influences of the tapped induction coil on ICP were discussed from the calculation results. Finally, plasma generation tests using a vacuum tube oscillator were conducted for both of ICP torches with and without the grounded tap in order to clarify the effects of the tapped induction coil.

Figures 1(a) and (b) show a conceptual diagram of an ICP torch system and its equivalent circuit representation, respectively. In these figures, an ICP torch system consists of a tank circuit and a free running oscillator. A tank circuit is composed of an ICP torch connected to a capacitor in parallel, making the R-L-C resonance circuit. Connecting this tank circuit to a free running oscillator, the electrical oscillation can occur at a resonance frequency of the R-L-C tank circuit. In order to enhance the electrical understandings of a free running oscillator for ICP systems, the potential-source equivalent circuit of a tuned-plate vacuum tube oscillator is illustrated in Fig. 1(b). In this figure, the coupling network between a grid circuit and a tank circuit is skipped for simplified representation of the whole equivalent circuit. In addition, the terms of $μ$ and r_p mean the amplification factor and the internal resistance of a vacuum tube, respectively.

In the tank circuit of Fig. 1(b), first, the equivalent electrical parameters and the electrical oscillation frequency can be obtained from the transformer theory for an ICP torch^17,18 and the R-L-C resonance circuit theory,^9,10 respectively. From the transformer theory for an ICP torch,^17,18 for example, the equivalent resistance R_eq and inductance L_eq in Figure 1(b) can be written in terms of the electrical parameters for an ICP:

Here, N_C indicates the turn numbers of the induction coil. R_p and L_p refer to the resistance and inductance of an ICP, respectively, with an assumption of a cylindrical conductor having a turn number of 1. Combined with the resistance R_coil and the inductance L_coil of the induction coil, respectively, those equivalent parameters consist of the torch resistance R_torch and the torch inductance L_torch as the following:

Next, the oscillation frequency can be determined approximately from the resonance frequency of the R-L-C circuit in Figure 1(b), which is defined as:

In the above equation, ω and C_tank indicate the angular frequency of the electrical oscillation and conductance of a tank circuit, respectively. In addition, the load impedance Z₀ of the equivalent tank circuit can be expressed from the basic circuit theory as:

and the load resistance R_load can be obtained by taking the real part of the load impedance Z₀ as the following:

Figures 2(a) and (b) present a conceptual diagram of an ICP torch system with a tapped induction coil and its equivalent circuit representation, respectively. In these figures, the induction coil is cut in half by a grounded center tap. For the equivalent circuit analysis of an ICP torch system with a center-tapped induction coil, it is necessary to examine how the grounded center tap divides the electrical parameters in Fig. 1(b) into two branches of an equivalent circuit in Fig. 2(b). Normally, the self-inductance of an induction coil with small turn numbers can be calculated relatively accurately by summing the self-inductances of each coil segment and the mutual inductances of each coil segment on all others.¹⁹ For example, the inductance L_coil of N_C = 4 can be expressed as:

where, L₁ is the self-inductance of a single turn, M₁₂ is the mutual inductance of any two adjacent turns, M₁₃ is the mutual inductance of any two turns separated by one, and M₁₄ is the mutual inductance of the first and last turns.¹⁹ Considering the relatively short coil length and small turn numbers of 4, we used Rayleigh and Niven’s formula for L₁ and a simplified Maxwell’s series formula for M_1n (n = 2,3,4)¹⁹ in this work, which are expressed as the following equations (9) and (10), respectively,

In the above equations, R_c and d_c are the radius of induction coil and the distance between coil segments, respectively. In addition, $ρc$ refers to the cross-sectional radius of the coil conductor, which was assumed to be 3.175 mm in this work. As demonstrated in Fig. 2(a), the grounded center tap departs a single coil with 4 turns into the two coils with 2 turns. However, the departed two coils are still magnetically coupled by the coil current, and consequently, each coil, which is symmetrically cut by the center tap, will take half the coil inductance of L_coil from Equations (8), (9) and (10). In addition, it is obvious that the center tap will bisect the coil resistance R_coil into each split coil.

In the equivalent circuit analysis of a conventional ICP torch based on transformer theory, the induction coil and the generated ICP are regarded as the primary and the secondary windings of a transformer, respectively.¹⁷ In addition, the ICP is normally assumed as a cylindrical conductor with not only the length equal to the coil but also turn number of 1.¹⁷ In the same way, the center-tapped induction coil and the generated ICP can be regarded as the primary and the secondary windings of a center-tapped transformer, respectively. Moreover, the ICP can be assumed as a cylindrical conductor with not only a symmetry about the center-tapped segment of the coil but also turn number of 1. In this case, the counter electromotive force in the induction coil is divided equally into each split coil according to the center-tapped transformer theory, and consequently, the equivalent components in Fig. 1(b) are reflected evenly into each branch of Fig. 2(b). In other words, the electrical parameters in Fig. 2(b) can be rearranged as R_eq,1 = R_eq,2 = 0.5 R_eq, L_eq,1 = L_eq,2 = 0.5 L_eq and L_coil,1 = L_coil,2 = 0.5 L_coil, and then, the load impedance Z_0,tap of the redrawn equivalent tank circuit can be expressed as:

Considering that the resistance component is very low compared with the inductive one in an ICP torch system, i.e., $ωLtorch≫Rtorch$⁠,¹¹ the above equation can be rewritten as:

The above equation indicates that the load resistance R_load of the tank circuit for the center-tapped induction coil can be reduced to about 1/4 compared with the load resistance of Fig. 1(b). In addition, one can see that the load impedance Z_0,tap has no reactance component in equation (11) and (12), i.e., Z_0,tap = R_load. These effects of a center-tapped induction coil can be used to control the impedance matching condition between a vacuum tube oscillator and a tank circuit. In a conventional ICP torch system, a tank circuit with the load impedance Z₀ is normally connected in series to a vacuum tube with the internal resistance of r_p as shown in Fig. 1(b). Accordingly, the plate current I_b that flows through the load impedance of Z₀ can be written as:

Then, the electrical power dissipated in the load is expressed as the following:

which implies that maximum power can be delivered to the plasma when Z₀ is equal to r_p according to maximum power transfer theorem. Accordingly, if Z₀ is larger than r_p, an ICP torch with a tapped induction coil can be helpful in delivering maximum power to the load by reducing the magnitude of the load impedance Z₀. Finally, it should be noted that the oscillation frequency ω is unchanged as can be proved from the resonance circuit theory for Fig. 2(b).

Figure 3 presents a schematic diagram of an ICP torch employed for numerical analysis on electrical and thermal flow characteristics of ICPs. In this figure, plasma forming gases are injected at the flow rates of Q₁, Q₂ and Q₃ through the injection ports and assumed to be an Ar-N₂ mixture with a given content of N₂. The physical properties of the mixture were calculated by applying the simplified mixing rules to the data of pure Ar and N₂ gases.²⁰ In addition, an induction coil with a turn number of N_C = 4 is located at a distance of z = z_c from the torch inlet of z = 0. The radius of the induction coil and the oscillation frequency are fixed at R_C = 45 mm and f = 2 MHz, respectively. The details of other torch dimensions and operating conditions are summarized in Table I for the present numerical work. The computational domains are divided into rectangular grids, and the number of mesh cells generated by these grids is 1800 (45$×$40) inside the RF torch. All governing equations are discretized by the finite volume method (FVM) and calculated using the SIMPLE algorithm.²¹ In addition, the following assumptions were employed for the present numerical model: 1) Negligible displacement current in the plasma, 2) Laminar flow, 3) Optically thin plasma, and 4) Local thermodynamic equilibrium (LTE).

Tables II and III present a full set of the governing equations and boundary conditions used in this study, respectively, which have been widely adopted in thermal plasma science.^15,22,23 For example, the fluid dynamic behaviors of an ICP can be described by the conservation equations of mass, momentum and energy listed in Table II. In these equations, u, and v are the axial and radial components of the velocity vector, respectively, while h means the specific enthalpy. The terms $ρ$⁠, p and $μ$ represent the mass density, pressure and viscosity, respectively. In equation for the conservation of energy, k and C_p are the thermal conductivity and the specific heat at constant pressure of an ICP, respectively, whereas P and R₀ refer to the volumetric Joule heating and radiation in the plasma, respectively. In addition, the mathematical expressions for the magnetic vector potential A that is listed in Tables II and III correspond to a set of governing equations and boundary conditions for the simulation of the electromagnetic fields in an ICP torch. In these equations, the subscripts R and I mean the real and imaginary parts of the magnetic vector potential A, respectively, i.e., A = A_R + j A_I, where j = $−1$⁠. The $σ$ term indicates the electrical conductivity of an ICP. Once the magnetic vector potential A are obtained, the magnetic field components B_z and B_r and electric field E can be calculated according to Ampere’s law and Faraday’s law. Then, the Lorentz force F_z and F_r and Joule heating P can also be computed from the mathematical formulations listed in Table II.

In addition, we used the boundary conditions listed in Table III for both ICPs with or without a center tap. Although the grounded tap divides the coil voltage depending on the split turn numbers together with the polarity inversion, it has no effect theoretically on the magnetomotive force available for producing magnetic fluxes to generate and sustain an ICP. Accordingly, if the plasma power levels are equal, the same equivalent sheet currents at the confinement tube wall can be applied as a boundary condition for the magnetic vector potential A regardless of the grounded tap on the coil. In the expression for this boundary condition, the terms, $σm$ and S_m are the electrical conductivity and conduction area of the m^th plasma cell, respectively in Fig. 4(a). K(k) and E(k) are the complete elliptic integrals of first and second kinds, respectively. z_c,l and z_w mean the axial position of l^th coil and the confinement tube wall, respectively. With all of these governing equations and boundary conditions in Tables II and III, the numerical analysis of Ar-N₂ ICPs with or without the grounded center-tap can be performed for the computational domain presented in Figure 3.

The equivalent electrical parameters for an ICP torch can be calculated by applying Biot-Savart’s law between the coil and plasma currents,^11–14 which can be obtained from the governing equations and boundary conditions in Tables II and III. In order to review this calculation process briefly, Figure 4(a) presents a cross-sectional view of the induction coil segments and plasma cells, carrying the coil current I_c and the induced plasma current I_p,m, respectively. In this figure, the induction coil has no tap, and the term of V_emf refers to the counter electromotive force induced by all kinds of plasma currents. As formulated by Kim et al.,¹¹ the electromotive force V_emf can be expressed as the following equation,

In the above equation, A_l is the magnetic vector potential at the l th coil segment, which is fully calculated by the summation of the contribution terms from the induced plasma currents:

In an induction coil that is grounded by a center tap, however, V_emf in Fig. 4(a) is divided into two voltage drops, V_emf,1 and V_emf,2, depending on the split turn numbers as displayed in Fig. 4(b). In this figure, V_emf,1 and V_emf,2 correspond to the counter electromotive forces that are induced by a plasma current from the first coil segment to the grounded center tap and from the grounded center tap to the last coil segment, respectively. In addition, the grounded tap redefines the electrical polarity in the induction coil as in a center-tapped transformer; thus, each voltage drop can be expressed as the following equations:

Here, N_t refers to the turn numbers from the first coil segment to the grounded center tap. In this study, N_t is of 2 since the turn number of the coil is of 4 and the center tap is assumed to be located at the end of the second coil segment. Once the V_emf,1 and V_emf,2 are obtained, the equivalent impedance for each branch of the equivalent circuit representation in Fig. 2(b) can be calculated from the ratio of V_emf,1/I_c and V_emf,2/(- I_c), respectively. By taking the real and imaginary parts of the complex impedance, the equivalent resistances and inductances represented in the equivalent circuits of Fig. 2(b) can be obtained as the following:

As discussed previously, the coil resistances, R_coil,1 and R_coil,2, can be expressed as half of the coil resistance, R_coil,

where, σ_coil and S_coil are the electrical conductivity of the coil conductor and coil conduction area, respectively. Furthermore, the coil inductance, L_coil, was obtained from equations (8), (9) and (10), then, the half value of L_coil is used for the L_coil,1 and L_coil,2 in Fig. 2(b). Finally, the load resistance, R_load, of a tank circuit with a grounded center-tap can be calculated by substituting these resistances and inductances into Fig. 2(b) together with the value of C_tank that is determined from the oscillation frequency of equation (5).

Theoretically, the grounded tap only serves to redistribute the equivalent electrical parameters of an ICP in a tank circuit as shown in Figs. 1(b) and 2(b). On the other hand, plasma gas composition, such as N₂ content in Ar-ICPs directly affects the equivalent electrical parameters of an ICP^15,16 regardless of a grounded tap by changing significantly the thermal flow fields as well as electromagnetic fields in an ICP torch. Accordingly, the load impedance of Ar-N₂ ICPs can vary widely according to the N₂ content and often range in the values larger than the internal resistance of a commercial vacuum tube oscillator.¹⁶ In order to check these effects of N₂ content, numerical analyses of ICPs were conducted by varying N₂ contents. Since the grounded tap does not require any change in boundary conditions or governing equations for ICP simulation as mentioned previously, not only thermal flow fields but also electromagnetic fields are calculated to be the same regardless of the grounded center-tap. Accordingly, the equivalent resistances and inductances of ICPs can be obtained depending on the presence or absence of the grounded center-tap by selectively applying equations of (17)–(22) to the numerical results. Furthermore, the load resistances of tank circuits can also be computed from the equivalent electrical parameters of ICPs by using the equivalent circuit equations of (1)–(12).

Fig. 5(a), (b) and (c) display the temperature contours of Ar-N₂ ICPs calculated for the N₂ content of 0 mol%, 20 mol% and 40 mol%, respectively, at the plasma power level of 50 kW. From these figures, it can be observed that the highest temperature region of $≥$ 9,000 K is diminished and shifted to the central region for Ar-N₂ ICP with the increase of N₂ content. Normally, the addition of N₂ decreases the electrical conductivity of the Ar-only ICPs. Therefore, the skin depth of ICP can be broadened as confirmed from the comparison between radial distributions of electric field (E_Θ) for N₂ contents of 0 mol%, 20 mol% and 40 mol% in Fig. 6. In addition, the heat capacity of the ICPs increases with the N₂ addition to the Ar-only ICPs. As a result, the highest temperature region of the Ar-N₂ ICPs can be shifted to the central region and diminished compared with that of the Ar only ICPs at the same plasma power level. In Fig. 6, it is interesting that the direction of electric field (E_Θ) reverses in Ar-only ICP near the centerline of the torch while no field reversal happens for Ar-N₂ (20% and 40 %) ICPs. Taking into account relatively large radius of coil (50 mm) and high electrical conductivity of Ar-only ICP at plasma power level of 50 kW, electric fields with reversed direction can be generated in central region according to Lenz’s law to suppress the increase of magnetic fields, which is induced by plasma current concentrated in skin depth^22,24 as shown in Fig 6.

The variations in temperatures and electrical fields by N₂ addition can also affect the electrical parameters of ICPs as observed in Fig. 7(a) and (b), which present the equivalent resistances (R_eq, R_eq,1, R_eq,2) and equivalent inductances (L_eq, L_eq,1, L_eq,2) of ICP torches for the various N₂ contents, respectively, at a plasma power level of 50 kW. As expected in the broadened skin depth, for example, Fig. 7(a) demonstrates that the equivalent resistance R_eq decreases with the increase of N₂ content regardless of the tapping on the coil. In addition, the equivalent inductances are also found to decrease due to the poor linkage of the magnetic fields through the radially diminished hot region.^15,16 In Fig. 7(a) and (b), the effects of the grounded center-tap on the electrical parameters were also found. From the comparison of equivalent resistances and inductances between ICPs with and without grounded center-tap, it is observed that the equivalent resistance R_eq,1 and the inductance L_eq,1 are slightly larger than the R_eq,2 and L _eq,2 for all content levels of N₂. These trends of the partitioned equivalent parameters come from the asymmetric distribution of the plasma current about the center-tap plane of the torch. As shown in Fig. 8(a), (b) and (c) presenting the electric field contours in Ar-N₂ (0 mol%, 20 mol% and 40 mol%) ICPs, respectively, the highest electric fields for the highest plasma currents are concentrated in the upper part of coil region. Consequently, the equivalent resistance R_eq,1 becomes larger than R_eq,2 according to equations (17) and (18). In addition, due to the asymmetric distribution of the electric fields in Fig. 8(a), (b) and (c), the mutual inductance between the plasma current and coil current can be increased in the top part of the tapped coil, which resulted in the L_eq,1 being higher than the L _eq,2 as presented in Fig. 7(b). However, the differences between the divided equivalent parameters are relatively small and decrease gradually with the increase of N₂ content. In Fig. 7(a) and (b), the grounded center-tap is observed to divide the equivalent parameters nearly in half for various N₂ contents as discussed previously in the equivalent circuit analysis. These results indicate that there are little differences between the total contribution of the plasma currents to the counter electromotive forces in the top and bottom parts of the tapped coil. As displayed in Fig. 8(a), (b) and (c) although highest electric fields of blue zone are concentrated in the top part of the induction coil, the remaining high electric fields including yellow zone are shifted to the bottom part of the coil, and then, spread to the lower region of an ICP torch. Accordingly, the counter electromotive forces that are induced by plasma currents can be allotted almost in half to each part of the center-tapped coil despite asymmetrical distributions of high temperature region and electric fields about the center-tapped segment of the coil.

From the results of Fig. 7(a) and (b), the load resistances were calculated. For this purpose, the coil inductance of L_coil = 1.417 $μ$H was obtained by substituting the design parameters in Table I to the Equations (8), (9) and (10). Then, the tank capacitance was determined as C_t = 5000 pF in order to produce the oscillation frequency of near 2 MHz, which was used in the numerical analysis as listed in Table I. Figure 9 compares the obtained results between the tank circuits with or without a grounded center tap. In this figure, first, the load resistances are observed to increase with the increase of the N₂ content for both cases. These increasing load resistances are a result of the decreasing R_eq and L_eq in Figures 7(a) and (b) according to equation (7). As predicted in the equivalent circuit analysis, Figure 9 also demonstrates that the load resistances of the tank circuit with a grounded center-tap are reduced by about 75% compared with that of the tank circuit without a center-tap.

In order to verify these effects of the grounded tap, plasma generation tests were conducted for both of ICP torches with and without the grounded tap. Fig. 10(a) shows a schematic of an ICP torch system used in this test, primarily consisting of a vacuum tube oscillator, a tank circuit, an ICP torch with or without grounded tap in induction coil and a cylindrical quenching chamber connected to a vacuum pump. In this system, we employed a commercial Huth-Kuhn oscillator (Trumpf, TruHeat HF 7100) equipped with a water-cooled triode (Thales, ITK 60-2) as a vacuum tube oscillator. The technical specification of the oscillator is listed in Table IV. As shown in Fig. 10 and 3, the ICP torch has an induction coil with turn numbers of 4 and a Cu-stripe with the thickness of 0.5 mm was attached to the 3rd segment of the coil as a grounded tap. By connecting this induction coil to the capacitors with capacitance, C_tank of 2250 pF in parallel together with the grounded Cu-stripe, a tank circuit for plasma generation test was configured as presented in Fig. 10(b). Finally, the operation conditions for the tests are listed in Table V together with the information on main dimension of an ICP torch.

Fig. 11 illustrates the ratios of plate voltage to plate current measured by varying N₂ content for both of ICP torches with and without grounded tap. In addition, the detailed experimental results for the data in Fig. 11 are listed in Table VI. In our Huth-Kuhn oscillator, the plate voltage and current were indicated as a percentage of each maximum listed in Table IV, thus, it should be noted that the ratios of plate voltage to plate current in Fig. 11 were obtained from these two percentage values. From Fig. 11 and Table IV, first, it was observed that the ratios of E_bb [%] to I_b [%] for an ICP torch without a grounded tap are more than 30% higher than the ratios obtained for an ICP torch with a grounded tap. As expressed in equation (13), the ratio of E_bb/I_b is proportional to the sum of the load resistance and the internal resistance of a vacuum tube. Neglecting the variations of internal resistance in the data points of Fig. 11 due to the relatively narrow ranges of plate current between 20 and 26 %, accordingly, these experimental results support that the load resistance can be reduced by the grounded tap on the induction coil. In addition, the percentage representation of plate voltage and current implies that the impedances between the internal resistance and the load resistance are perfectly matched when the ratio of E_bb [%] to I_b [%] is equal to one, delivering maximum power to the load at the plate power level indicated by E_bb [%] and I_b [%]. At all values of the N₂ content in Fig. 11 and Table VI, one can see that the ratios of E_bb [%] to I_b [%] for an ICP torch with grounded tap are closer to one than the ratios for an ICP torch without tap, indicating that the installation of a grounded tap improved the impedance matching condition.

In this study, we investigated the effect of an induction coil with a grounded tap on the electrical characteristics of an ICP torch system. For this purpose, the equivalent circuit and numerical analyses of the Ar-N₂ ICP torch system were conducted at the plasma power level of 50 kW. First, the equivalent circuit analysis revealed that the induction coil with the grounded center tap can not only remove the reactance component in the tank circuit but also reduce the load resistance of an ICP torch system by dividing the turn numbers and rearranging the impedance components of the tank circuit. In addition, numerical results showed that the grounded center tap can divide the equivalent resistance and inductance of an ICP in almost half into each part of the bisected induction coil despite the asymmetric distributions of the plasma currents in the inside of an ICP torch. Consequently, the load resistances were calculated to be reduced to about 25% compared with that of a tank circuit without a grounded tap as predicted by the equivalent circuit analysis. In order to verify the reduction of load resistance by the grounded tap, we carried out plasma generation tests using Huth-Kuhn oscillator for both of ICP torches with and without the grounded tap. When the grounded tap was installed on the 3^rd segment of an induction coil with 4 turns, for example, the load resistances of Ar-N₂ ICPs were observed to be reduced by more than 30 % for various N₂ contents ranging from 6.3 % to 16.7 %. By providing a way to reduce the load resistance of the tank circuit, accordingly, the induction coil with a grounded tap can help in improving the impedance matching condition of ICPs with the load resistances higher than the internal resistance of a free running RF oscillator.

This research was supported by Technology Innovation Program (no. 10048910) funded by the Ministry of Trade, Industry and Energy (MI, Republic of Korea). This research was also supported by the Technology Development Program to Solve Climate Changes of the National Research Foundation (NRF) funded by the Ministry of Science and ICT (NRF-2016M1A2A2940152).