{'fraction_non_alphanumeric': 0.030753459764223477, 'fraction_numerical': 0.0178463258934812, 'mean_word_length': 4.4988470407378935, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 2, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Development of Control Circuit for Inductive Levitation Micro-Actuators

The control circuit for inductive levitation micro-actuators is developed in this research. The circuit performance and its electrical parameters are discussed . The developed control circuit was fabricated on a 4 layer PCB board having a size of 60×60×25 mm. It consists of a generator based on high speed Flip-Flop components and a current amplifier build on a H-bridge configuration. The circuit is able to generate AC current with squared waveform in a frequency range from 8 to 43 MHz and with a peak-to-peak amplitude up to 420 mA. To demonstrate the efficiency of developed circuit and its compatibility with a micro-actuation system, an inductive levitation micro-actuator was fabricated by using 3D micro-coil technology. The device was composed of two solenoidal coil designs, a levitation and a stabilization coil, with outer diameter being 2 and 3.8 mm respectively. A 25 μm diameter gold wire was used for fabricating the coils, with levitation coil having 20 number of turns and stabilization coil having 12 number of turns, similar to the micro-structure presented previously by our group. Using the developed control circuit, the micro-actuator was successfully excited and it demonstrated the actuation of an aluminium disc shaped micro-objects having a diameter of 2.8 and 3.2 mm and, for the first time, an aluminium square shaped having a side length of 2.8 mm at a frequency of 10 MHz. To characterize the actuation, the levitation height and the current amplitude were measured. In particular, we demonstrated that the square shaped micro-object can lift up to a height of 84 μmwith current of 160 mA. The characterisation is supported by the simulation using a 3D model based on the quasi-FEM approach.


Introduction
Electromagnetic levitation micro-actuators employing remote ponderomotive forces, in order to act on a target environment or simply compensate a gravity force for holding stably a micro-object at the equilibrium without mechanical attachment, have already found wide applications and demonstrated a new generation of micro-sensors and -actuators with increased operational capabilities and overcoming the domination of friction over inertial forces at the micro-scale.
A wide spectrum of physical principles have been utilized and successfully implemented by using different techniques for micro-fabrication. However, recently developed 3D micro-coil technology [21] together with the integration of a polymer magnetic composite material for flux concentration allows announcing inductive levitation micro-actuator systems, firstly, as systems with an established micro-fabrication process in comparison to the other levitation actuator systems and, secondly, as high-performance systems. As a results of this progress, our group demonstrated the inductive levitation actuator system with the record lowest current consumption [7] around tens of mA. This permits to avoid using standard bulky high frequency current amplifiers for exciting the ILMA and to replace them by the integrated control circuit including the signal generator and amplifier and having a size comparable with a size of micro-actuator system. This prompted us to develop a control circuit on a 4 layer PCB board having a size of 60 x 60 x 25 mm. It consists of a generator based on high a speed Flip-Flop and a current amplifier build on a bridge configuration. The circuit is able to generate alternating current with squared waveform in the frequency range from 8 to 43 MHz and with a peak-to-peak amplitude up to 420 mA.
To demonstrate the efficiency of developed circuit, we show its successful application for excitation of an inductive levitation micro-actuator, which was fabricated using 3D micro-coil technology. The device was composed of two solenoidal coil design including levitation and stabilisation coil, having 2 mm and 3.8 mm in diameters, respectively. The levitation coil has 20 turns of a gold wire of a 25 µm diameter, while the stabilization one has 12 turns similar to the micro-structure presented previously by our group. The micro-actuator was successfully excited by the control circuit and it demonstrated the levitation of an aluminium disc shaped micro-objects having a diameter of 2.8 and 3.2 mm and, for the first time, an aluminium square shaped having a side length of 2.8 mm at a frequency of 10 MHz. To characterize the actuation, the levitation height and the current amplitude were measured.In particular, we showed that the square shaped micro-object can lift up on a height of 84 µm with rms current of 160 mA. The characterisation is supported by the simulation using a 3D model based on the quasi-FEM approach. In particular, the simulation shows that the coil design produces the maximum levitation force in order to levitate the presented square shaped proof mass (PM).

Development of control circuit
According to the results of the comprehensive characterization of the ILMA performance in our previous paper [22], namely, a levitation height as a function of the input parameters, i.e., the amplitude and frequency of the excitation currents, as well as the theoretical model to estimate the current versus frequency dependence for a given constant height of the disc shaped proof mass, we showed that the main advantage of using 3D microcoils in the ILMA is the possibility of increasing in the ampere-turn value as a result of an increased number of windings. This increased number of windings can be achieved in a single processing step, as opposed to, for example, the planar coils. As a consequence, the current amplitudes required to achieve similar levitation performance are reduced dramatically compared to the 2D case. However, we have also emphasized the precautions that must be taken in the case of using 3D coil structures. These are related mainly to the range of operating frequencies, which is significantly reduced to a much smaller value for the self-resonant frequency of these 3D structures compared to their 2D counterparts. Due to the reasons above discussed and the results of measurements conducted in [22], the application of 3D microcoils in ILMA requires the following electrical parameters for a voltage suppler, an excitation current, its frequency range, amplitude and waveform, which are summed up below: • High frequency output voltage suppler from 0 to 40 Vpp; • High frequency current (maximum peak to peak) from 0 to 400 mA;  This list of electrical parameters is applied as the requirements for the development of the control circuit. The control circuit consists of two main functional elements as shown in Figure 1, which are a generator (oscillator) and a current amplifier. The generator is responsible for shaping the current waveform with corresponding frequency range and proving the input signal for current amplifier. Finally, the current amplifier delivers shaped AC current with the required electrical parameters to a ILMA device for its successful excitation. Hence, the development process of the control circuit can be split into two main parts, namely, the development of an oscillator and a current amplifier. Then both functional elements are integrated in one control circuit as shown in Figure 1.
The required peak to peak value of AC current up to 400 mA provides a relative high value, and the necessity of high frequency bandwidth with also high levitation coil impedance was the motivation for choosing the H-bridge configuration for building the current amplifier. The H-bridge configuration  ), connected to the voltage regulator (implemented on a chip LM7805 -(a)) having the voltage limit, which is up to 5.5 V. In the output of the frequency oscillator is located the frequency divider (implemented on an chip SN74LVC1G74 -(c)) avoids the usage of a transformer which its disadvantages of bandwidth limitation and enhanced input current consumption. The amplifier was accompanied with an active cooling system to avoid overheating of the electronic components. To realise the proposed configuration and to fulfil the output power and the frequency condition, two high-power output current feedback amplifiers (THS3491) developed by Texas Instruments (Austin, USA) were used. Figure 2 shows the design of electrical circuit of the current amplifier build on the H-bridge configuration by using two chips (THS3491), which are supported by double voltage suppliers of ±15 V. The input voltage for current amplifiers is controlled by the frequency divider flip-flop (please see Figure 3, (c)), which helps providing the symmetrically signals between the output of oscillator and the inputs of the amplifiers. The output frequency given by the frequency oscillator is reduced by a factor of two.
Consequently, the oscillator must provide a frequency range more than 80 MHz. To meet this requirement, the oscillator was realized on the LTC6905 chip, which is easy to use and occupies very little board space. It requires only a single resistor to set the output frequency up to 170 MHz with a typical frequency error 0.5% or less. The designed circuit of the oscillator is shown in Figure 3. It is supplied by a single voltage supplier of 5 V. Voltage regulator (chip LM7805) helps providing   the required supplying voltage . The change in the range of oscillation frequency is performed by a jumper. When the jumper is closed the frequency range is from 7.6 to 26 MHz and when it is opened, the frequency range becomes form 15 to 50 MHz. The jumper connector is located in the frequency oscillator circuit (Jmp1) as shown in Figure 3, (b)).
Finally, the proposed circuit design was fabricated on the 4 layer PCB board having a dimension of 60×60×25 mm. Figure 4 shows the top view of the PCB with the location of the voltage regulator (LM7805), the frequency oscillator (LTC6905), divisor (SN74LVC1G74) and the two amplifiers (THS3491). The cooling system, which is located behind, is not visible on the Figure.

Experimental setup
In order to verify the developed control circuit and demonstrate its successful application to ILMA, we organized the following experimental setup as shown in Figure 5. The fabricated device of ILMA was mounted on the PCB board and fixed on the optical table. The device was composed of two solenoidal coil design including levitation and stabilisation coil, having 2 mm and 3.8 mm in diameters, respectively. The levitation coil has 20 turns of a gold wire of a 25 µm diameter, while the stabilization one has 12 turns similar to the micro-structure presented previously by our group [6].  To control the levitation height of a levitated PM in the vertical direction, the laser sensor (LK-G32) was used. It was mounted on the the optical table, above of the proof mass (PM). Then, the PCB with the developed control circuit was connected to the device as shown in Figure 5, which shows also the location of the cooling system under the circuit PCB.
For the experiment, a set of proof masses, in disc and square shapes were fabricated using an aluminium foil with the thickness ranging from 10 µm to 15 µm. Using the described experimental setup and the developed control circuit, we were able to successfully levitate the disc shaped PM of diameters of 2.8 mm and 3.2 mm and, for the first time, square shaped PM of a side length of 2.8 mm at excitation AC frequency of 10 MHz. In particular, Figure 5 shows the levitation of the disc shaped PM of a diameter 3.2 mm at a height of 90 µm. The results of measurements of levitation heights of listed PM versus the coil current and the applied voltage are shown in Figure 6.

Simulation
The mechanism of stable levitation of the square shape proof mass in the framework of two coil design is similar to one as described in our previous work [23]. The induced eddy currents are distributed along the levitated proof mass in such a way that two circuits having maximum values of eddy current density can be identified. The fact will be also demonstrated by performing the simulation based on quasi-FEM model. The first circuit is corresponded to the eddy current distributed along the edge of square-shaped PM and the second circuit is defined by the levitation coil. The later one has a circular path with radius equal to the radius of the levitation coil. This mechanism can be split into two force interactions. The force interaction happens between the current in the stabilization coil and induced eddy current corresponding to the first circuit, which contributes mainly to the lateral stability of the levitated PM. While, the force interaction between the current in the levitation coil and induced eddy current corresponding the second circuit contributes mainly to the vertical and angular stability of the levitated PM.
The simulation is directed to study the levitation force and to demonstrate that the current coil design produces the maximum levitation force under the keeping the same value of the current in the coils, to levitate the square shaped PM having a side length of 2.8 mm. For such a simulation the method based on a quasi-FEM approach is applied [24,25].

Simulation of induced eddy current within the proof mass
At the beginning, the levitated micro-object is meshed by circular elements of the same radius, R e =2.8025 × 10 −3 m, as shown in Fig. 7, a value of which is defined by a number of elements, where E is the (2500 × 2500) unit matrix, M o is the (2500 × 2500) -symmetric hollow matrix whose elements are L o ks (k = s). The self-inductance of the circular element is calculated by the known formula for a circular ring of circular cross-section where µ 0 is the magnetic permeability of free space, ε = th/(2R e ), th is the thickness of a mashed layer of micro-object (in the particular case, th =13 µm). Accounting for the values of diameters of levitation and stabilization coils, 3D geometrical scheme of the actuator for the eddy current simulation can be build as shown in Fig. 8. The position of the coordinate frame {x k } (k = 1, 2, 3) with respect to the fixed frame {X k } (k = 1, 2, 3) is defined by the radius vector r cm = [0 0 h l ] T , where the levitation height, h l is to be 84 µm. Then, the position of the s-mesh element with respect to the coordinate frame { (j) z k } (k = 1, 2, 3) assigned to the j-coil filament can be found as (s,j) r = r cm + (s) ρ − (j) r c or in a matrix form as (s,j) r z = (j) A zX r X cm where (j) A zX = (j) A zX (j) φ c = (j) e z · e X and (j) A zx = (j) A zX (j) φ c A Xx (ϕ) = (j) e z · e x are the direction cosine matrices, ϕ = [0 0 0] is the vector of the angular generalized coordinates. Because all angles are zero, hence (j) A zx = (j) A zX = E, where E is the (3 × 3) unit matrix. Since the coils are represented by the circular filaments and using the radius vector (s,j) r, the mutual inductance between the jcoil and s-meshed element can be calculated directly by the formula presented in [26]. Thereby, the the (2500 × 32) matrix M c of mutual inductance between coils and finite elements can be formed. The induced eddy current in each circular element is a solution of the following matrix equation where I is the (2500 × 1) matrix of eddy currents and I c = [I c1 I c2 . . . I cN ] T is the given (32 × 1) matrix of currents in coils. It is convenient to present the result of calculation in the dimensionless form. For this reason, the dimensionless currents in the levitation coil and stabilization one are introduced by dividing currents on the amplitude of the current in the levitation coil. Since the amplitudes of the current in both coil are the same. Hence, the input current in the levitation coil filaments is to be one, while in the stabilization coil filaments to be minus one (because of the 180 • phase shift). Now, the induced eddy current in dimensionless values can be calculated [24]. The results of calculation are shown in Fig. 9. Fig. 9(a) shows the 2D plot of the distribution of magnitudes of eddy current along the area of the surface of the PM. While Fig. 9(b) shows the 3D plot. The intensity of the color shown by the bar characterizes the value of dimensionless magnitude of the eddy current. As it was expected, analysis of Fig. 9 depicts that maximum magnitudes of eddy current are concentrated along the edge of the PM and in its central part along the circle having the same diameter as the levitation coil. It is Worth noting that the obtained distribution of the eddy current within the square shaped PM is similar to one obtained by Lu in work [27] for the two coil design and the levitated disc shape PM.

Levitation force
Knowing the law of distribution of eddy current, the levitation dimensionless force can be calculated by using the following equation [24]: where λ = q 3 /h l is the dimensionless displacement along the X 3 axis, which is characterized by the generalized coordinate q 3 , η sj = I s I cj R cj χ, I s = I s /I c1 and I cj = I cj /I c1 are the dimensionless currents, R cj = R cj /R c1 , R c1 is the radius of the first winding of the levitation coil, χ = h l /R e is the scaling factor, ∂M sj /∂λ is the derivative of dimensionless mutual inductance with respect to λ. The derivative of dimensionless mutual inductance is defined as follows: where ν j = R e /R cj , R cj is the radius of the j-coil filament, x 1 , x 2 and x 3 are the components of the radius vector r in base e z (see Eq. (3)), which are defined in dimensionless form as The derivative of dimensionless mutual inductance with respect to x 3 is where Substituting x 3 = λκχ into Eq. (10), the desired equation for the derivative of dimensionless mutual inductance with respect to λ is derived.
Noting that if a diameter of the levitation coil is equal to zero (d l = 0), the levitation force is disappeared. But if a diameter the levitation coil is the same as the stabilization coil (d l = d s ), the levitation force has the minimum value due to the minimization of the magnetic flux generated by both coils. Hence, between these two limit points can be found a particular value of a diameter of the levitation coil, under which the levitation force has its maximum value. To show this, the levitation force is calculated from a following range of radius the levitation coil, which is 0.5 mm to 1.8 mm for the square shaped proof mass with a side length of 2.8 mm and a levitation height of 84 µm. The result of calculation is shown in Fig. 10. The levitation force is presented in the normalized value F n = F m (1)/F m0 (1), where F m0 (1) is calculated for a 0.5 mm radius of the levitation coil. The analysis of Fig. 10 shows the existence of extremum of levitation force and, as a result, confirms the fact that the fabricated two coil design is the optimum for levitation of the square shape PM with a side length of 2.8 mm.

Conclusions
In this paper, we developed the control circuit for application to inductive levitation micro-actuators. The developed control circuit was fabricated on a four layer PCB board having a size of 60×60×25 mm, which is comparable with size of levitation micro-actuators. The developed circuit is able to generate AC current with squared shape in a range of frequency from 8 to 43 MHz and with peak-to-peak amplitude up to 420 mA. The fabricated device of ILMA composed of two solenoidal coil design including levitation and stabilisation coil, having 2 mm and 3.8 mm in diameters, respectively, was exited by using the developed control circuit. We demonstrated successful levitation of disc shaped PM of diameters of 2.8 mm and 3.2 mm and, for the first time, square shaped PM of a side length of 2.8 mm at excitation frequency of 10 MHz. This fact confirmed the efficiency of the proposed circuit design and its compatibility with micro-actuation system.
Applying a quasi-finite element method, we simulated the distribution of induced eddy current within the square shaped PM of a side length of 2.8 mm, which showed that maximum magnitudes of eddy current are concentrated along the edge of the PM and in its central part along the circle having the same diameter as the levitation coil. The numerical analysis of the force interaction between the coils and the levitated proof mass along the vertical direction shows the existence of extremum of levitation force and, as a result, confirms the fact that the fabricated two coil design provides the optimum coil design for levitation of the square shape PM with a side length of 2.8 mm.

Materials
The printed circuit board (PCB) was manufactured by Beta Layout GmbH (Aarbergen, Germany). The basic electronic components such as capacitors, diodes, resistors, switches, etc were acquired in house. The main electronic components for the control circuit are listed below: • Voltage regulator, chip 78L05 IC1 (National Semiconductors, Danbury, United States of America) [28]; • Frequency oscillator, chip LTC6905 (Linear Technology, Milpitas, United States of America) [29]; • Frequency divider, chip D-FF-IC3 (Texas Instruments, Dalas, United States of America) [30]; • High-power output current feedback amplifier THS3491 (Texas Instruments, Dalas, United States of America) [31].

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:

ILMA
Inductive Levitation Micro-Actuator PM Proof Mass MLMA Magnetic Levitation Micro-Actuator ELMA Electric Levitation Micro-Actuator