Patent Publication Number: US-8120259-B2

Title: Impedance matching methods and systems performing the same

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2007-0116023, filed on Nov. 14, 2007, the entire contents of which are hereby incorporated by reference. This application is also a continuation-in-part of and claims priority to U.S. patent application Ser. No. 12/072,991, filed Feb. 29, 2008, which claims priority to Korean Application No. 2007-38209 filed Apr. 19, 2007 the entire contents of both of which are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention disclosed herein relates to an impedance matching, and more particularly, to an impedance matching method used in an electric system such as a plasma system, a nuclear magnetic resonance system, a communication system, and a power transmission line, and a system performing the same. 
     If impedance is mismatched between a power source and a load, supplied power to the load cannot be maximized, and moreover controlling of the supplied power is not precisely carried out. Accordingly, an electric system, such as a plasma system, a nuclear magnetic resonance system, a communication system, a high frequency induction heating device, and a power transmission line, includes an impedance matching network between a power source and a load, in order to overcome the above mismatching impedance. For example, a plasma chamber system for fabricating a semiconductor device includes an RF electrode connected to an RF power source and an impedance matching network between the RF power source and the RF electrode. General contents for impedance matching are disclosed in “Microwave Engineering” (Addison-Wesley publisher) in page. 281-328 written by David M. Pozar, and also techniques relating to impedance matching of a plasma system are disclosed in U.S. Pat. No. 3,569,777, U.S. Pat. No. 4,112,395, U.S. Pat. No. 4,557,819, U.S. Pat. No. 5,187,454, U.S. Pat. No. 5,585,766, U.S. Pat. No. 5,621,331, and U.S. Pat. No. 5,689,215, and International Publication No. WO9724748. 
       FIG. 1  is a flowchart for illustrating a typical impedance matching method. 
     Referring to  FIG. 1 , the typical impedance matching method measures electrical characteristics (e.g., current, voltage, and phase) in operation S 1 , control parameters are extracted from the measured electrical characteristics of a power transmission line to control a matching network in operation S 2 , and then the matching network is controlled through the extracted control parameters in operation S 3 . 
     According to typical methods, a matching network generally includes a plurality of variable capacitors of which capacitances can be controlled through operations of control motors. The extracting of the control parameter in operation S 2  includes extracting information for an impedance magnitude and a phase of the power transmission line from a measured current, voltage, and phase difference of the power transmission line, and then by means of the information, capacitances of the variable capacitors required for impedance matching can be calculated. 
     However, the typical methods cause various technical limitations as follows: 
     (1) convergence failure for a matching state according to brute dependency on an initial state; 
     (2) matching delay according to instability near a matching position; and 
     (3) haunting issue according to high dependency on a load and power transmission line impedance. 
     That is, the above mentioned limitations may not be overcome by a typical matching method because a capacitance magnitude required for matching is determined based on an un-normalized impedance magnitude. This will be described later in more detail. 
       FIGS. 2 and 3  are diagrams of brute dependency on an initial state in typical impedance matching. 
     As described above, a typical impedance matching method includes calculating required capacitances based on a magnitude and a phase of measured impedance. At this point,  FIGS. 2 and 3  are diagrams for illustrating a mapping method in a capacitance space used for calculation according to a typical matching method. More specifically,  FIGS. 2 and 3  are diagrams for illustrating an impedance magnitude and an impedance phase in a power transmission line, respectively, in a capacitance space expressed by coordinates C 1  and C 2 . At this point,  FIGS. 2 and 3  illustrate simulation results when an impedance of a load is 5+50j. C 1  and C 2  represent capacitances of the variable capacitors, respectively. 
     On the other hand, the solid line of  FIG. 2  represents a contour line that connects points of 50 ohm impedance required for matching, and the solid line of  FIG. 3  represents a contour line that connects points of a 0° phase required for matching. Accordingly, point corresponding to matching state is point where the solid lines of  FIGS. 2 and 3  intersect, and the matching point is illustrated as a small rectangle in  FIGS. 2 and 3 . On the other hand, a position corresponding to an asterisk represents an initial state. 
     According to a typical matching method, variations (i.e., ΔC 1  and ΔC 2 ) of the variable capacitors are respectively determined by the magnitude and phase of the measured impedance. That is, as illustrated in  FIG. 2 , when the measured impedance is more than 50 ohm expressed by an arrow A 1 , a corresponding motor is driven to increase C 1 , and when the measured impedance is less than 50 ohm expressed by an arrow A 2  or an arrow A 3 , a corresponding motor is driven to decrease C 1 . According to this matching method, points corresponding to arrows A 1  and A 2  approach the matching state, a point corresponding to arrow A 3  is father away from the matching state. That is, according to the typical matching method, matching convergence is dependent on an initial position of a capacitance space because there may be a region (e.g., FR) not converged into a matching state. A diverging issue of matching may identically occur in an impedance phase. Especially, as illustrated in  FIG. 2 , the matching failure region FR may become excessively broader in a typical method. 
     Additionally, there are two points of 50 ohm impedance magnitude required for matching with respect to one coordinate C 1  in a region R 1  of  FIG. 2 . Like this, when a capacitance space is used, the coordinate C 1  may not be to a point of 50 ohm impedance magnitude require for matching in one-to-one correspondence. Therefore, there may be ambiguity in determining a direction of a matching trajectory. This ambiguity may be another reason causing the divergence of matching. 
       FIG. 4  is a diagram for illustrating instability around a matching point according to typical impedance matching. 
     Referring to  FIG. 4 , as a matching trajectory approaches toward a matching state, variations of variable capacitors required for impedance matching are delicately controlled. However, because the typical matching method determines the direction and speed of a matching trajectory based on un-normalized magnitude and phase of impedance, it is difficult to precisely control C 1  and C 2  around the matching point. As a result, according to the typical matching method, as illustrated in  FIG. 4 , a spiral matching trajectory may occur, which delays a time for reaching impedance matching. If a gradient of impedance in a capacitance space, which will be described below, is large, the time delay for impedance matching is greatly increased. 
       FIG. 5  is a diagram for illustrating high dependency on load impedance in typical impedance matching. In more detail,  FIG. 5  illustrates a simulation result for a magnitude of impedance when impedance of a load is 1+50j. 
     Comparing  FIG. 5  having a load impedance of 1+50j with  FIG. 2  having a load impedance of 5+50j, as a real part in the load impedance is decreased, a matching contour line (a contour line of 50 ohm impedance magnitude required for matching) is shrunken to a narrow region of a capacitance space, and an gradient of a impedance magnitude is drastically increased around the matching contour line. This increase of the gradient value makes a precise capacitance control around the matching point more difficult. Consequently, as illustrated in  FIG. 6 , a matching trajectory may abnormally move around the matching point (i.e., the haunting issue). 
     Another impedance matching method in a continuous wave (CW) mode will be described. That is, impedance is measured or calculated at a measurement point. If impedance of a measurement point and reactance of variable devices in a matching system are known, load impedance can be calculated. Therefore, a matching condition can be found through the above load impedance and thus control parameters can be determined. 
     An RF power source operates as a pulse mode, which is periodically turned on or turned off. In this case, after a matching condition is found by operating an RF power source temporarily in a CW mode, it is typically applied to a pulse mode. However, if a load changes as time elapses, the above typical technique cannot completely remove a reflected wave. Accordingly, the typical CW mode matching method needs to be modified in a pulse mode method or requires a new method in order to deal with pulse matching. 
     SUMMARY OF THE INVENTION 
     The present invention provides an impedance matching method operating stably in a pulse mode. 
     The present invention also provides an impedance matching method operating in a pulse mode where there are several Hz and/or a duty ratio is less than 10 percent. 
     The present invention also provides a matching device operating stably in a pulse mode. 
     The present invention also provides a matching device operating in a pulse mode where there are several Hz and/or a duty ratio is less than 10 percent. 
     Embodiments of the present invention provide matching methods of an electric device including a power source, a load, a power transmission line, and a matching system include: measuring an electrical characteristic of the power transmission line; determining a pulse mode of the power source; extracting a control parameter for impedance matching from the electrical characteristic of the power transmission line; and controlling the matching system through the control parameter, wherein the matching system is controlled differently according to the pulse mode. 
     In some embodiments, the determining of the pulse mode of the power source includes determining an on time interval of when the power source is in an on state and an off time interval of when the power source is in an off state. 
     In other embodiments, the determining of the on time interval and the off time interval uses a power source trigger signal for controlling an operation of the power source or the electrical characteristic. 
     In still other embodiments, the determining of the pulse mode of the power source further includes determining a pulse period that is defined by an interval of when the power source changes from an i th  on time state to an i+1 th  on time state, wherein the matching system is controlled by differently setting the control parameter according to the pulse period. 
     In even other embodiments, the determining of the pulse mode of the power source further includes determining the pulse mode as a slow pulse mode when the pulse period is greater than a predetermined time and determining the pulse mode as a fast pulse mode when the pulse period is less than the predetermined time, wherein the matching system is controlled by differently setting the control parameter according to the pulse mode of the power source. 
     In yet other embodiments, when the pulse mode is the slow pulse mode, the power source allows the matching system to be in an idle state during the off time interval. 
     In further embodiments, when the pulse mode is the fast pulse mode, the power source controls the matching system through the control parameter during the off time interval. 
     In still further embodiments, if the off time interval of the power source lasts more than a critical off time, the matching system is controlled by setting the control parameter in a preset state. 
     In even further embodiments, the determining of the pulse mode of the power source further includes progressing a continuous wave mode of a predetermined time before the pulse mode of the power source is determined. 
     In yet further embodiments, the measuring of the electrical characteristic of the power transmission line further includes removing the noise of the power transmission line. 
     In yet further embodiments, the removing of the noise of the power transmission line uses lock-in detection. 
     In yet further embodiments, the extracting of the control parameter for impedance matching from the electrical characteristic of the power transmission line includes: converting the electrical characteristic of the power transmission line into a normalized characteristic vector; extracting a displacement vector by analyzing the characteristic vector in an analytic coordinate; converting the displacement vector into a converted device vector; and converting the converted device vector into a driving vector. 
     In yet further embodiments, the extracting of the control parameter for impedance matching from the electrical characteristic of the power transmission line includes: extracting a control parameter by comparing an absolute value of impedance with characteristic impedance; and extracting a control parameter by comparing a phase of impedance with a reference value. 
     In yet further embodiments, the extracting of the control parameter for impedance matching from the electrical characteristic of the power transmission line includes: calculating an impedance of a load through impedance; and extracting a control parameter through the impedance of the load. 
     In other embodiments of the present invention, matching devices of an electric device including a power source, a load, a power transmission line, and a matching system include: a sensing unit measuring an electrical characteristic of the power transmission line; a measurement result analyzing unit processing the electrical characteristic; a pulse mode processing unit processing a pulse mode according to the power source; a control parameter extracting unit extracting a control parameter for impedance matching from the electrical characteristic of the power transmission line; and a controller controlling the matching system through the control parameter according to the pulse mode. 
     In some embodiments, the pulse mode processing unit is configured to determine an on time interval of when the power source is in an on state and an off time interval of when the power source is in an off state. 
     In other embodiments, the pulse mode processing unit is configured to determine the pulse mode as a slow pulse mode when a pulse period is greater than a predetermined time and as a fast pulse mode when the pulse period is less than the predetermined time, and differently set a control parameter according to the pulse mode of the power source. 
     In still other embodiments, the measurement result analyzing unit further includes a noise removing unit removing noise from the electrical characteristic of the power transmission line. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying figures are included to provide a further understanding of the present invention, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments of the present invention and, together with the description, serve to explain principles of the present invention. In the figures: 
         FIG. 1  is a flowchart for illustrating a typical impedance matching method; 
         FIGS. 2 and 3  are diagrams of brute dependency on an initial state in typical impedance matching; 
         FIG. 4  is a diagram for illustrating instability around a matching point according to typical impedance matching; 
         FIG. 5  is a diagram for illustrating high dependency on load impedance in typical impedance matching according to a typical method; 
         FIG. 6  is a diagram for illustrating haunting issue when a matching trajectory moves abnormally around a matching point according to a typical method; 
         FIG. 7  is a circuit diagram of an electric device including a matching system according to one embodiment of the present invention; 
         FIGS. 8 to 11  are circuit diagrams of various types of a matching system according to one embodiment of the present invention; 
         FIGS. 12 to 15  are circuit diagrams of various types of a modified matching system according to one embodiment of the present invention; 
         FIG. 16  is a flowchart of an impedance matching method according to one embodiment of the present invention; 
         FIGS. 17 and 18  are diagrams of an analytic coordinate system for illustrating displacement vector extraction according to one embodiment of the present invention; 
         FIG. 19  is a flowchart of a matching method according to a modified embodiment of the present invention; 
         FIG. 20  is a flowchart of a detailed matching method according to a modified embodiment of the present invention; 
         FIGS. 21 and 22  are diagrams of a matching state test method according to one embodiment of the present invention; 
         FIG. 23  is a graph of a gain factor according one embodiment of the present invention; 
         FIGS. 24 through 26  are diagrams of impedance matching results according to embodiments of the present invention; 
         FIG. 27  is a view of a matching system according to the present invention; 
         FIG. 28  is a view of a plasma chamber device including an impedance matching system according to one embodiment of the present invention; 
         FIG. 29  is a flowchart illustrating an impedance matching method according to one embodiment of the present invention; 
         FIG. 30  is a flowchart illustrating a pulse mode processing operation according to one embodiment of the present invention; 
         FIG. 31  is a flowchart illustrating a control parameter extracting operation according to one embodiment of the present invention; 
         FIG. 32  is a flowchart illustrating a pulse mode matching method according to one embodiment of the present invention; 
         FIG. 33  is a flowchart illustrating a pulse mode matching method according to one embodiment of the present invention; 
         FIGS. 34 through 38  are timing diagrams illustrating a fast or slow mode pulse matching method according to one embodiment of the present invention; and 
         FIGS. 39 through 41  are views of a matching system according to the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention relates to a matching method of a pulse mode and a continuous wave (CW) mode. The matching method of a pulse mode may be combined with matching methods of all typical continuous wave (CW) modes. Additionally, a new CW mode matching method described below may be combined with the matching method of a pulse mode. 
     When an RF power source operates in a pulse mode, an operating method of a matching system in an on time interval where the RF power source is turned on is different from that in an off time interval where the RF power source is turned off. Specifically, the pulse mode can be classified into a slow pulse mode and a fast pulse mode in order to perform matching. 
     That is, in a case of the slow pulse mode (e.g., less than about 500 Hz), values of variable devices in a matching network are changed only at the on time interval of the RF power source and are not changed at the off time interval of the RF power source. Accordingly, since the values of the variable devices of the matching network at the off time interval does not significantly deviate from a matching condition of the next on time interval, fast matching can be realized. 
     In a case of the fast pulse mode (e.g., more than about 500 Hz), values of variable devices in a matching network are changed at an on time interval and may can be continuously changed with information of the on time interval at the off time interval. In a case of short pulse period, if the variable devices are in an idle state at the off time interval, a life cycle of a motor is reduced and a fast speed control is cannot be accomplished at the next on time due to frequent speed increase and decrease. According to the present invention, if a pulse period is short, there is no great change for a matching condition between the on time and the next on time. Therefore, fast matching can be achieved by continuously changing values of variable devices at the off time interval. 
     Technical ideas, other objects, features and advantages of the present invention will be described below in more detail with reference to preferred embodiments below. The present invention may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present invention to those skilled in the art. 
       FIG. 7  is a circuit diagram of an electric device including a matching system according to one embodiment of the present invention. 
     Referring to  FIG. 7 , an electric device  100  according to the present invention includes a power source  102 , a load  101 , a power transmission line  103  between the power source  102  and the load  101 , and a matching system  104 . The power source  102  is connected to input terminals N 1  and N 2  on the power transmission line  103 , and the load  101  is connected to load terminals N 3  and N 4  on the power transmission line  103 . An input impedance to be described later means an impedance of a system including the matching system  104  and the load  101 , which is measured at the input terminal N 1 . At this point, the load  101  may be one a plasma system, a nuclear magnetic resonance system, a communication system, a high frequency induction heating device, and a power transmission line. 
     The matching system  104  includes at least one variable reactive element that variably controls its reactance. According to one embodiment of the present invention, the matching system  104  further includes passive elements providing a fixed reactance besides the variable reactive element. On the other hand, the matching system  104  is configured to resolve typical limitations such as brute dependency on an initial state, instability around a matching point, and high dependency on a load and transmission impedance. These technical effects can be accomplished through impedance matching methods according to the present invention that will be described in more detail later. The matching system  104  further includes a processing unit  200  of  FIG. 27  performing operations of an impedance matching method according to the present invention. The processing unit  200  will be described in more detail with reference to  FIG. 27 . 
     According to the present invention, a variable reactive element may be one of a variable capacitor providing a variable capacitance, a variable inductor providing a variable inductance, and a variable resistance providing a variable resistance. Below, for concise description, technical features of the present invention will be described based on embodiments using a variable capacitor as a variable reactive element. However, it is apparent to those skilled in the art that technical features of the present invention are easily realized without unnecessary efforts in embodiments including different kinds of variable reactive elements, according to a well-known electromagnetic theory. Furthermore, for succinct description, technical features of the present invention will be described based on embodiments including two variable reactive elements. However, it is apparent to those skilled in the art that technical features of the present invention are easily realized without unnecessary efforts in embodiments including the more number of variable reactive elements and including the additional passive elements, according to a well-known electromagnetic theory. 
     Various Types of Matching Systems 
     On the other hand, the matching system  104  may be classified into various types according to methods in which the variable reactive element or the passive elements are connected to the power transmission line  103 . For example, according to the above-mentioned premises for concise description, if the matching system  104  includes first and second variable capacitors  111  and  112 , it may be classified into an L-type, an inverted L-type, a T-type and a π-type according to the way the first and second variable capacitors  111  and  112  are connected to the power transmission line  103 . 
       FIGS. 8 to 11  are circuit diagrams of various types of the matching system  104 . 
     Referring to  FIG. 8 , according to the L-type matching system, the first variable capacitor  111  is connected to a predetermined point P of the power transmission line  103 , and the second variable capacitor  112  is disposed between the load  101  and the point P. Referring to  FIG. 9 , according to the inverted L-type matching system, the first variable capacitor  111  is connected to a predetermined point P of the power transmission line  103 , and the second variable capacitor  112  is disposed between the power source  102  and the predetermined point P. 
     Referring to  FIG. 10 , according to the T-type matching system, the first and second variable capacitors  111  and  112  connect the power source  102  and the load  101  in series on the power transmission line  103 . According to one embodiment of the present invention, a predetermined passive element (e.g., an inductor  115 ) may be connected to the power transmission line  103  (i.e., the point P) between the first and second variable capacitors  111  and  112 . Referring to  FIG. 11 , according to the π-type matching system, the first and second variable capacitors  111  and  112  are respectively connected to the power transmission line  103  in parallel. According to one embodiment of the present invention, a predetermined passive element (e.g., an inductor  115 ) may be connected to the power transmission line  103  (i.e., the point P) between the first and second variable capacitors  111  and  112 . 
     Elements connected to the point P of the power transmission line  103 , as illustrated in  FIGS. 8 through 12 , may be connected to another grounded power transmission line. On the other hand, the matching system of the present invention may have various modified structures. For example, as illustrated in  FIGS. 12 through 13 , at least one passive element can be further included, which is connected in parallel or series to the power transmission line  103 . To be more specific, the matching system of the L-type matching system further includes passive elements (i.e., a capacitor  116 ) or inductors ( 117  and  118 ), which are additionally provided, as illustrated in  FIGS. 14 and 15 . 
     On the other hand,  FIGS. 8 through 15  are circuit diagrams of the matching system, and the kinds and number, and positions of the variable reactive elements and passive elements in the matching system  104  may vary according to other embodiments of the present invention. 
     Matching Method 
       FIG. 16  is a flowchart of an impedance matching method according to one embodiment of the present invention. 
     Referring to  FIG. 16 , the impedance matching method includes measuring electrical characteristics of a power transmission line in operation S 20 , extracting control parameters from the measured electrical characteristics of the power transmission line for impedance matching in operation S 30 , and then controlling the matching system by using extracted control parameters in operation S 40 . 
     According to the present invention, the electrical characteristics may include a current, a voltage, and a phase difference therebetween of the power transmission line, and their physical quantities can be measured periodically or in real time through a predetermined sensor. The phase difference can be calculated by analyzing a measurement result of the current and voltage of the power transmission line. 
     On the other hand, before the measuring of the electrical characteristics, predetermined matching parameters can be set in operation S 10 . The matching parameters are various parameters used in an impedance matching process of the present invention, and may include physical/electrical parameters related to the corresponding electric device, parameters for the measuring of the electrical characteristics in operation S 20 , parameters for the extracting of the control parameters in operation S 30 , and parameters for controlling of the system in operation S 40 . Additionally, the matching parameters may be set in other operations, and also a part of the matching parameters may be changed if necessary while performing impedance matching, as illustrated below. 
     According to one embodiment of the present invention, the extracting of the control parameter in operation S 30  includes converting the measured electrical characteristic of the power transmission line into a characteristic vector in operation S 31 , extracting a displacement vector for impedance matching by analyzing the characteristic vector in a predetermined analytic coordinate system in operation S 32 , and converting the displacement vector into a control parameter for the controlling of the matching system of operation S 40  in operation S 33 . 
     At this point, the analytic coordinate system is selected to express a predetermined phase space that quantitatively relates the electrical characteristic of the matching system to the electrical characteristic of the power transmission line. That is, a quantitative relationship between the electrical characteristic of the matching system and the electrical characteristic of the power transmission line can be expressed through the analytic coordinate system. The displacement vector includes magnitude of a coordinate change as an element, which is required for moving the characteristic vector toward a point corresponding to a matching state in the analytic coordinate system. The analytic coordinate system and the displacement vector will be described in more detail. 
     Pulse Matching Method 
       FIG. 29  is a flowchart illustrating an impedance matching method according to one embodiment of the present invention. 
     Referring to  FIG. 29 , the impedance matching method includes measuring an electrical characteristic of a power transmission line in operation S 120 , determining a pulse mode of a power source in operation S 130 , extracting a control parameter for impedance matching from the electrical characteristic of the power transmission line in operation S 150 , and controlling a matching system through the control parameter in operation S 160 . The matching system is differently controlled according to the pulse mode. 
     According to the present invention, the electrical characteristic may be a current, a voltage, and a phase difference therebetween of the power transmission line, and these physical amounts are measured in real time or periodically through a predetermined sensing device. The phase difference can be calculated by analyzing the measurement result of a current and voltage of the power transmission line. 
     On the other hand, before the measuring of the electrical characteristic in operation S 120 , predetermined matching parameters can be set in operation S 110 . The matching parameters are various parameters used during an impedance matching process according to the present invention. The matching parameters may include physical/electrical parameters related to a corresponding electric device, parameters for the measuring of the electrical characteristic in operation S 120 , parameters for the extracting of the control parameter in operation S 150 , and parameters for the controlling of the matching system in operation S 160 . Additionally, the matching parameters may be set in another operation, and a portion of matching parameters may be changed during impedance matching if necessary, which will be described later. 
       FIG. 30  is a flowchart illustrating a pulse mode processing operation according to one embodiment of the present invention. 
     Referring to  FIG. 30 , the determining of the pulse mode in operation S 130  includes determining an on time interval of when a power source is turned on and an off time interval of when the power source is turned off in operation S 131 , determining a pulse period in operation S 132 , and determining a slow pulse mode and a fast pulse mode according to the pulse period in operation S 133 . 
     The determining of the on time interval and the off time interval in operation S 131  is accomplished through an power source trigger signal controlling an operation of the power source or the above mentioned electrical characteristic. That is, the on time interval is distinguished from the off time interval by calculating an incident power through the electrical characteristic. Additionally, since the power source operates as a pulse mode, an on time interval can be determined by receiving a power source trigger signal synchronized with a power of the power source. 
     The pulse period is defined by an interval of when the power source changes from an i th  on time state to an i+1 th  on time state. According to the pulse period, the control parameter is differently set to control the matching system. If the pulse period is greater than a predetermined time, it is determined as a slow pulse mode. If the pulse period is less than the predetermined time, it is determined as a fast pulse mode. Additionally, the control parameter is differently set according to the pulse mode of the power source in order to control the matching system differently. The predetermined time may be about 1/500 sec. In more detail, if the pulse mode is the slow pulse mode, it allows the matching system to be in an idle state while the power source is in the off time interval. The idle state may be a state where a value of a variable reactive device of a matching system does not change. That is, a motor connected to the variable reactive device may stop during the off time interval. 
     If the pulse mode is the fast pulse mode, it controls the matching system through the control parameter while the power source is in the off time interval. The control parameter of the off time interval may be the last control parameter used in the on time interval. That is, a value of a variable reactive device of a matching system can change during the off time interval. 
       FIG. 31  is a flowchart illustrating a control parameter extracting operation according to one embodiment of the present invention. 
     Referring to  FIG. 31 , the extracting of the control parameter in operation S 150  includes converting the electrical characteristic of the power transmission line into a characteristic vector in operation S 151 , extracting a displacement vector for impedance matching by analyzing the characteristic vector in a predetermined analytic coordinate system in operation S 152 , and converting the displacement vector into a control parameter for the controlling of the system in operation S 160 . 
     According to another embodiment of the present invention, the extracting of the control parameter in operation S 150  may include extracting a control parameter according to whether an absolute value (or, magnitude) of impedance is greater or less than a predetermined characteristic impedance (usually, 50 ohm) and extracting a control parameter according to whether a phase of the impedance is greater or less than a predetermined value. 
     According to further another embodiment of the present invention, the extracting of the control parameter in operation S 150  includes measuring impedance at a measurement position, calculating an impedance of a load by using the impedance at the measurement position and reactance of variable devices of a matching system, and extracting a control parameter by using the load and impedance. 
     According to further another embodiment of the present invention, the extracting of the control parameter can be accomplished through a reflection coefficient. It is apparent to those skilled in the art that the extracting of the control parameter may be modified. 
     Selection of Characteristic Vector 
     According to the present invention, the characteristic vector is defined based on measured electrical characteristic of the power transmission line, and may be a physical quantity having a normalized magnitude. Like this, because the measured electrical characteristic of the power transmission line is expressed in a normalized physical quantity, the matching method of the present invention can reduce excessive dependency on a gain factor, which will be described layer, and its fine control around the matching point is possible. As a result, the matching method may be contributed to resolve the above-mentioned typical technical limitations. These technical effects will be descried in more detail below. 
     According to one embodiment of the present invention, the characteristic vector may be defined from a reflection coefficient S 11  of the power transmission line. As well-known, the reflection coefficient S 11  of the power transmission line can be defined by characteristic impedance Z 0  of the power transmission line and impedance (i.e., input impedance Z) of the input terminal of the power transmission line, as expressed in a following Equation 1. 
     
       
         
           
             
               
                 
                   
                     S 
                     11 
                   
                   = 
                   
                     
                       Z 
                       - 
                       
                         Z 
                         0 
                       
                     
                     
                       Z 
                       + 
                       
                         Z 
                         0 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ] 
                 
               
             
           
         
       
     
     Its magnitude (i.e., S=|S 11 | is a value between 0 and 1. (at this point, the input impedance Z of the power transmission line represents impedance of a system including the matching system and the load, which is measured at the input terminals N 1  and N 2 .) 
     On the other hand, as described above, the matching system  104  may include at least two variable reactive elements. In this case, to explicitly determine reactance of each variable reactive element, the characteristic vector needs to be a physical quantity including at least two elements. For example the characteristic vector Q can be defined by using a two dimensional vector including a real part Re{S 11 } and an imaginary part (Im{S 11 }) of the reflection coefficient as its elements, as expressed in Equation 2. 
     
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               Q 
                               1 
                             
                           
                         
                         
                           
                             
                               Q 
                               2 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               Re 
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                         
                           
                             
                               Im 
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     Selection of Analytic Coordinate System 
     As described above, the analytic coordinate system is selected to express a predetermined phase space that quantitatively relates the electrical characteristic of the matching system to the electrical characteristic of the power transmission line. For this end, coordinates of the analytic coordinate system are selected from physical quantities related to the electrical characteristics of the power transmission line, and the electrical characteristic of the power transmission line is expressed as one selected point of the analytic coordinate system. According to one embodiment of the present invention, the coordinates (hereinafter, referred to as an analytic coordinates) of the analytic coordinate system can be expressed in a function of an electrical characteristic (e.g., reactance) of variable reactive elements constituting the matching system, and the characteristic vector expressing the measured electrical characteristic of the power transmission line can be expressed as one point of the analytic coordinate system. 
     On the other hand, the analytic coordinate system may be selected for injectively mapping a quantitative relationship between the electrical characteristic of the matching system and the electrical characteristic of the power transmission line (at this point, the meaning of the “injective mapping” in the present invention will be described in more detail with reference to  FIGS. 17 and 18 ). To make the injective mapping possible, the analytic coordinate system may be a physical quantity that can be obtained by converting the measurable electrical characteristic (e.g., reactance) of the matching system through a predetermined conversion matrix T. For example, an analytic coordinate G can be obtained by an inner product of a predetermined conversion matrix T and a predetermined device vector X as expressed in Equation 3 below.
 
 G=TX   [Equation 3]
 
     At this point, the conversion matrix T and the device vector X may be selected to satisfy technical requirements for the analytic coordinates related to the injective mapping. This selection is dependable on a type of the matching system. To be more specific, the device vector X includes physical quantities related to respective electrical characteristics of variable reactive elements constituting the matching system as its elements, and can be selected according to a type of the matching system. Consequently, the analytic coordinate G is also selected according to a type of the matching system. 
     To be more specific, the matching system may include two variable reactive elements. In this case, the analytic coordinates G 1  and G 2  can be obtained by an inner product of physical quantities X 1  and X 2  and a 2 by 2 square matrix T as illustrated in Equation 4 below. The physical quantities X 1  and X 2  are related to the respective electrical characteristics of the variable reactive elements. According to the present invention, elements a 11 , a 12 , a 21 , and a 22  of the conversion matrix T are selected from values between −1 to 1. 
     
       
         
           
             
               
                 
                   
                     
                       ( 
                       
                         
                           
                             
                               G 
                               1 
                             
                           
                         
                         
                           
                             
                               G 
                               2 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       T 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               
                                 X 
                                 1 
                               
                             
                           
                           
                             
                               
                                 X 
                                 2 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                   , 
                   
                     T 
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 a 
                                 11 
                               
                               ⁢ 
                               
                                 a 
                                 12 
                               
                             
                           
                         
                         
                           
                             
                               
                                 a 
                                 21 
                               
                               ⁢ 
                               
                                 a 
                                 22 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
     On the other hand, the conversion matrix T can be prepared through various methods. For example, the conversion matrix T can be obtained using at least one of an empirical data analysis, a theoretical approach analysis, and a computer simulation analysis. These analyses are performed based on a type of the matching system and a physical quantity of the device vector X. Additionally, the form and rank of the conversion matrix T are determined by the number of reactive elements constituting the matching system. That is, if the matching system includes the more number of variable reactive elements, the form and rank of the conversion matrix T may grow. 
     As described above, the matching system may include two variable capacitors, and may be an L-type or an inverted L-type as described with reference to  FIGS. 8 and 9 . In this case, the conversion matrix T and the device vector X may be expressed in a function of capacitances of the variable capacitors. That is, in a case of the L-type matching system illustrated in  FIG. 8 , the device vector X may be given as expressed in Equation 5, and in a case of the inverted L-type matching system, the device vector X may be given as expressed in Equation 6. 
     
       
         
           
             
               
                 
                   
                     X 
                     i 
                   
                   = 
                   
                     1 
                     
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         C 
                         i 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     X 
                     i 
                   
                   = 
                   
                     C 
                     i 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
       FIGS. 17 and 18  are diagrams of an analytic coordinate system for illustrating displacement vector extraction according to one embodiment of the present invention. To be more specific, this embodiment is related to the L-type matching system including two variable capacitors, and also coordinates of the analytic coordinate system are physical quantities obtained by converting capacitances of the variable capacitors through the above Equations 4 and 5. At this point, elements of the characteristic vector are selected by a real part and an imaginary part of a reflection coefficient of the power transmission line, as expressed in Equation 2. 
       FIG. 17  illustrates one element (i.e., the real part of the reflection coefficient) of the characteristic vector, which is mapped into the analytic coordinate system.  FIG. 18  illustrates one element (i.e., the imaginary part of the reflective part) of the characteristic vector, which is mapped into the analytic coordinate system. Additionally, the respective solid lines of  FIGS. 17 and 18  are contour lines (hereinafter, matching lines) showing positions of the characteristic vector that satisfies the requirement of Re{S 11 }=0 and Im{S 11 }=0. In this aspect, a point (hereinafter, referred to as a matching point) corresponding to a matching state is a point where the solid lines of  FIGS. 18 and 19  intersect, and this matching point is illustrated in a small rectangle in  FIGS. 17 and 18 . On the other hand, a point corresponding to an asterisk represents an initial state. 
     Because the analytic coordinates G 1  and G 2  are prepared through Equation 4 to satisfy technical requirements for the analytic coordinate system, points on the matching line can be expressed in a function of the analytic coordinate system. That is, referring to  FIG. 17 , an arbitrary value of a coordinate G 1  corresponds to one point of the matching line in a predetermined region. Similarly, referring to  FIG. 18 , an arbitrary value of a coordinate G 2  corresponds to one point of the matching line in a predetermined region. The term “injective mapping” means that one point of the matching line corresponds to one of the analytic coordinates. In this aspect, as illustrated in  FIG. 17 , the coordinate G 1  is injectively mapped into one element (i.e., the real part of the reflection coefficient) of the characteristic vector. Likewise, as illustrated in  FIG. 18 , the coordinate G 2  is injectively mapped into the other element (i.e., the imaginary part of the reflection coefficient) of the characteristic vector. 
     Through this injective mapping, the matching method of the present invention makes it possible to search an effective matching trajectory in an entire region of the analytic coordinate system. That is, as illustrated in  FIGS. 17 and 18 , through this infective mapping, the effective matching trajectory can be obtained with respect to all points of the analytic coordinate system, and the matching failure region FR of  FIG. 2  according to the typical method is not shown in the analytic coordinate system. That is, ambiguity in determining a direction of the matching trajectory in the typical method does not occur in during a matching trajectory analysis using an analytic coordinate system of the present invention. 
     Determination of Displacement Vector 
     The determining of the displacement vector in operation S 32  includes analyzing a magnitude or a position of the characteristic vector (hereinafter, referred to as a measured characteristic vector) corresponding to a measured state of the power transmission line in the analytic coordinate system. As defined above, the magnitude of the displacement vector expresses the magnitude of coordinate movement required for moving the measured characteristic vector to the matching line in the analytic coordinate system. That is, the length of the displacement vector corresponds to the distance between the position of the measured characteristic vector and the matching point. 
     However, because only the information (i.e., impedance) for a measured electrical state during an actual matching process is known, it is possible to determine whether a current measured state is matching state or not. However, the position of a matching point cannot be accurately determined. As a result, a direction (i.e., a progression direction of a matching trajectory) of the displacement vector can be determined, but the exact magnitude of the displacement vector may not be determined. Due to these technical limitations, capacitances of the variable capacitors are determined based on the measured magnitude of impedance according to the typical method. However, because the impedance is not a normalized physical quantity, it is difficult to precisely control capacitance variations. 
     On the other hand, according to one embodiment of present invention, elements of the displacement vector, as expressed in Equation 7, can be defined by the elements of the characteristic vector, and this definition for the displacement vector also can be contributed to resolve the above-mentioned typical technical limitations. 
     In more detail, referring to  FIG. 17  again, the magnitude of each point, expressed through tone of color, represents a value of a real part Re{S 11 } of a reflection coefficient, and the matching line expressed by a solid line represents points that satisfy the requirement of Re{S 11 }=0. Additionally, a region (hereinafter, referred to as a first region) below the matching line where an arrow of B 2  is disposed represents Re{S 11 }&gt;0. Additionally, a region (hereinafter, referred to as a second region) above the matching line where arrows of B 1  and B 3  are disposed represents Re{S 11 }&lt;0. Likewise, referring to  FIG. 18 , the matching line expressed by the solid line represents points that satisfy the requirement of Im{S 11 }=0. Additionally, the right region B 5  (hereinafter, referred to as a third region) of the matching line where an arrow B 5  is disposed represents a region of Im{S 11 }&gt;0, and the left region (hereinafter, referred to as fourth region) of the matching line where arrows B 4  and B 6  are disposed represents a region of Im{S 11 }&lt;0. 
     Accordingly, to approach the matching point, a value of the coordinate G 2  in the first region needs to be increased, and a value of the coordinate G 2  in the second region needs to be decreased. Additionally, values of the coordinates in the third region need to be decreased, and values of the coordinates in the fourth region need to be increased. For example, the coordinates values G 1  and G 2  needs to be reduced, such that an initial state indicated as asterisk can approach the matching point. Accordingly, if variations dG 1  and dG 2  in the values of the coordinates G 1  and G 2  are defined by −Im{S 11 } and Re{S 11 } respectively, the above-mentioned requirements for approaching the matching point can be satisfied. 
     According to one embodiment of the present invention, based on the above facts, elements dG 1  and dG 2  of the displacement vector dG can be defined as expressed in Equation 7 (however, Equation 7 below is just one example of a method of defining the displacement vector, and according to another embodiment, this definition of the displacement vector can be variously modified based on types of a matching system and kinds of selected analytic coordinate system). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             dG 
                             1 
                           
                         
                       
                       
                         
                           
                             dG 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             
                               - 
                               
                                 Q 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               Q 
                               1 
                             
                           
                         
                       
                       ) 
                     
                     = 
                     
                       ( 
                       
                         
                           
                             
                               
                                 - 
                                 Im 
                               
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                         
                           
                             
                               Re 
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
     According to Equation 1, as it approaches the matching point, the size of a reflection coefficient of the power transmission line approaches to 0. At this point, because elements of the displacement vector dG and the elements of the reflection coefficient S 11  have a quantitative relationship obtained by Equation 7, the matching method of this embodiment can search a trajectory that converges into the matching point at high speed. That is, according to the present invention, as the distance between the position of the measured characteristic vector and the matching point increases, the reflection coefficient increases. Therefore, the magnitude of the displacement vector dG also increases. This allows the matching trajectory to approach fast toward the matching point. Additionally, when the position of the measured characteristic vector is around the matching point, the reflection coefficient is small, and thus, this allows the displacement vector dG to have a small magnitude. Furthermore, this allows a matching trajectory to be accurately controlled around the matching point. Accordingly, the matching time delay described through  FIG. 4  and the haunting issue described through  FIG. 6  can be prevented. 
     Moreover, as described above, because the coordinates G 1  and G 2  are converted to satisfy the requirements for infective mapping, ambiguity related to the selection of the coordinate movement direction according to the typical method described with reference to  FIG. 2  is not shown in the present invention. 
     On the other hand, as described above, when the matching system is the inverted L-type including variable capacitors, differentiation of the coordinate G 1  may be a negative number of the imaginary part of the reflection coefficient, and differentiation of the coordinate G 2  may be a negative number of the real part of the reflection coefficient (i.e., (dG 1 ;dG 2 )=(−Q 2 ;−Q 1 )=(−Im{S 11 };−Re{S 11 })). Moreover, when the matching system is the T-type, the displacement vector may be identical to that of the inverted L-type, and when the matching system is the Z-type, the displacement vector may be identical to that of the L-type. 
     Determination of Control Parameter 
     According to the present invention, the displacement vector dG is a physical quantity that converts reactance or admittance of the variable reactive element for analysis in the analytic coordinate system. Accordingly, to control the matching system, a process is required to convert the displacement vector into a magnitude (i.e., reactance of the variable reactive element) of an electrical characteristic of elements constituting the matching system, or a physical quantity related thereto. The converting of the displacement vector dG into the control parameters in operations S 33  corresponds to the above converting process. 
     For this end, according to one embodiment of the present invention, the operation S 33  may include inverse transforming the displacement vector dG into a reduced device vector dX′ having a dimension of a variable physical quantity of the variable reactive element in operation S 331 , and converting the reduced device vector dX′ into a driving vector V controlling the driving of the variable reactive elements in operation S 332 . 
     When considering the analytic coordinates G 1  and G 2  obtained through the conversion matrix T of Equations 3 and 4, the reduced device vector dX′ may be obtained through an inner product of the inverse matrix T −1  of the conversion matrix and the displacement vector dG, as expressed in Equations 8 and 9 below. 
     
       
         
           
             
               
                 
                   
                     dX 
                     ′ 
                   
                   = 
                   
                     
                       T 
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     dG 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     8 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             dX 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             dX 
                             2 
                             ′ 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       T 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               dG 
                               1 
                             
                           
                         
                         
                           
                             
                               dG 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
     On the other hand, if the matching system is the L-type including a variable capacitor as a variable reactive element, the reduced device vector dX′ can be expressed in Equation 10 below through Equation 5, and if the matching system is the inverted L-type, the reduced device vector dX′ can be expressed as Equation 11 below through Equation 6. 
     
       
         
           
             
               
                 
                   
                     dX 
                     1 
                     ′ 
                   
                   ∼ 
                   
                     - 
                     
                       
                         dC 
                         i 
                       
                       
                         C 
                         i 
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     dX 
                     i 
                     ′ 
                   
                   ∼ 
                   
                     dC 
                     i 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     According to one embodiment of the present invention, reactance of the variable reactive element may be controlled by rotation of a predetermined driving motor. In this case, the driving vector V may have values for a numerical control of the driving motor as its elements, and its magnitude and physical dimension may vary according to kinds of the numerical control methods and the driving motors. For example, the driving vector V may be obtained by a scalar product of the reduced device vector dX′ and a predetermined numerical control factor M as expressed in Equation 12. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             V 
                             1 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     M 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               dX 
                               1 
                               ′ 
                             
                           
                         
                         
                           
                             
                               dX 
                               2 
                               ′ 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     At this point, V 1  and V 2  represent inputted control parameters in order to drive the driving motors that are respectively connected to the first and second variable capacitors. Additionally, the numerical control factor M may be a normalized size (e.g., a standard speed of an operating motor) of the numerical control, and the reduced device vector dX′ is selected to have the same dimension as the driving vector V. 
     On the other hand, by the definition of Equations 5 and 6, the reduced device vector dX′ has a dimension of reactance or admittance. Accordingly, to actually control the variable reactive element, a process may be further required to convert the reduced device vector dX′ into a primary physical quantity (e.g., capacitance or inductance). That is, when the matching system is the L-type, as expressed in Equation 10, because the reduced device vector dX′ has a different dimension than the capacitance, the driving vector V converts the reduced device vector dX′ into a capacitance dimension through Equation 10. In this case, the numerical control factor M can be expressed in a function of current capacitances C i  of the variable capacitors through Equation 10. However, if the matching system is the inverted L-type, as given in Equation 11, because the reduced device vector dX′ has the same dimension as the capacitance, the additional conversion process is not required. 
     On the other hand, according to the above Equation 7 and 9, Equation 12 also can be expressed as Equation 13 below. That is, according to this embodiment, variations (i.e., rotations of the driving motors connected to the first and second variable capacitors) of the first and second variable capacitors in the matching system are determined by the reflection coefficient (to be more specifically, the magnitude of a real part and an imaginary part of the reflection coefficient). 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             V 
                             1 
                           
                         
                       
                       
                         
                           
                             V 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       MT 
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               
                                 - 
                                 Im 
                               
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                         
                           
                             
                               Re 
                               ⁢ 
                               
                                 { 
                                 
                                   S 
                                   11 
                                 
                                 } 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     The controlling of the matching system in operation S 40  includes adjusting reactance of variable reactive elements constituting the matching system by using the driving vector V. 
     According to a modified embodiment of the present invention, if at least one element of the driving vector V is greater than the maximum speed V max  that can be driven in an actual driving motor, a rescale process can be further included in order to maintain a direction of a matching trajectory. In the rescale process, if one element of the driving vector V is greater than the maximum speed V max , the element is set to the maximum speed V max , and another element is reduced to a speed as illustrated below. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 V 1   
                 V 2   
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                   
                 V 1  &gt; V max   
                 V 1  = V max   
                 V 2  = V max  × (V 2 /V 1 ) 
               
               
                   
                 V 2  &gt; V max   
                 V 1  = V max  × (V 1 /V 2 ) 
                 V 2  = V max   
               
               
                   
                   
               
            
           
         
       
     
     Matching State Test 
       FIGS. 19 and 20  are flowcharts of a matching method according to a modified embodiment of the present invention. This embodiment further includes performing a matching state test that determines whether the matching system is within an allowable matching state or not in operation S 22  after the measuring of the electrical characteristic in operation S 20 . Except for the performing of the matching state test in operation S 22 , this embodiment is identical to the above-mentioned embodiments. Therefore, its overlapping description will be omitted for conciseness. 
     Referring to  FIGS. 19 and 20 , after the measuring of the electrical characteristic in operation S 20 , the matching state test that determines whether the matching system is within an allowable matching state or not is further performed in operation S 22 . In this operation S 22 , if the matching system is out of the allowable matching state, the extracting of the control parameters in operation S 30  and the controlling of the matching system in operation S 40  are performed as illustrated in the method of the above embodiment. Moreover, in this operation S 22 , if the matching system is within the allowable matching state, the electrical characteristic of the power transmission line is measured without the extracting of the control parameters in operation S 30  and the controlling of the matching system in operation S 40 . Due to this matching state test in operation S 22 , the matching system reaching a matching state is not disturbed unnecessarily. 
     On the other hand, according to one embodiment of the present invention, this embodiment may further include evaluating whether setting values of the matching parameters are appropriate or not in operation S 23 , and modifying a portion of the matching parameters if the evaluation result is negative in operation S 24 . The evaluating of the setting values in operation S 23  may include determining whether one period process from the measuring of the electrical characteristic of the power transmission line in operation S 10  to the controlling of the system in operation S 40  is repeated or not in the predetermined number of times n. The modifying of the matching parameters in operation S 24  is performed when the electric device  100  does not reach a matching state even if the one period process is repeated in the predetermined number of times n. The kinds of modified matching parameter and modifying methods during the modifying of the matching parameter in operation S 24  will be described in more detail below. 
     Matching State Parameter 
     On the other hand, according to the present invention, the performing of the matching test in operation S 22  may be accomplished using a state parameter P (or, standing-wave ratio (SWR)) defined by Equation 14 below. 
     
       
         
           
             
               
                 
                   P 
                   = 
                   
                     
                       1 
                       + 
                       S 
                     
                     
                       1 
                       - 
                       S 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     where S represents the magnitude (i.e., an absolute value) of a reflection coefficient S 11  of the power transmission line. 
     According to this definition, when the state parameter P is matched (i.e., S=0), it has a unit value 1, and when the state parameter P is extremely mismatched (i.e., S=1), it has an infinite value. Furthermore, as illustrated in  FIG. 21 , a changing rate of the state parameter P is small in a region LR close to the matching state, and is drastically increased in a region HR far from the matching state. That is, if the matching state is determined based on the state parameter defined by Equation 14 rather than the impedance itself, the matching state around a matching point can be more precisely determined. 
     According to one embodiment of the present invention, the performing of the matching state test in operation S 22  may include comparing a state parameter P −  of the previous operation (hereinafter, referred to as a prior parameter) and a current state parameter P 0  (hereinafter, referred to as a current parameter) with the minimum allowable value P 1  (hereinafter, referred to as the minimum level) of the state parameter and the maximum allowable value P 2  (hereinafter, referred to as the maximum level) of the state parameter. To be more specific, referring to Table 2 and  FIG. 22 , if the current parameter P 0  is less than the minimum level P 1  (i.e., a case I), it is determined as a matching state regardless of the prior parameter P − . Additionally, if the current parameter P 0  is between the minimum level P 1  and the maximum level P 2 , and the prior parameter P −  is less than the minimum level P 1  (i.e., a case II), it is determined as a matching state. If the current parameter P 0  is between the minimum level P 1  and the maximum level P 2 , and the prior parameter P −  is more than the minimum level P 1  (i.e., a case III), it is determined as a mismatching state. Additionally, to make the entire system be a matching state, the extracting of the control parameter in operation S 30  and the controlling of the matching system in operation S 40  are performed. Furthermore, if the current parameter P 0  is greater than the maximum level P 2  (i.e., a case IV), it is determined as a mismatching state regardless of the prior parameter P − , to make the electric device  100  be in a matching state, the extracting of the control parameter in operation S 30  and the controlling of the matching system in operation S 40  are performed. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                   
                 Matching 
               
               
                   
                 Current state 
                 Prior State 
                 Determination 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 Case I 
                 P 0  = P 1   
                   
                 Yes 
               
               
                   
                 Case II 
                 P 1  &lt; P 0  &lt; P 2   
                 P −  = P 1   
                 Yes 
               
               
                   
                 Case III 
                 P 1  &lt; P 0  &lt; P 2   
                 P −  &gt; P 1   
                 No 
               
               
                   
                 Case IV 
                 P 0  = P 2   
                   
                 No 
               
            
           
           
               
               
               
            
               
                   
                 P 0   
                 Current state parameter 
               
               
                   
                 P −   
                 Previous state parameter 
               
               
                   
                 P 1   
                 Allowable minimum value in state parameter 
               
               
                   
                 P 2   
                 Allowable maximum value in state parameter 
               
               
                   
                   
               
            
           
         
       
     
     As illustrated above, if the matching state test is performed based on the minimum allowable value P 1  and the maximum allowable value P 2  of the state parameter, unnecessary matching state change can be minimized, such that accurate and effective matching characteristics can be obtained. 
     Rotation Matrix 
     According to one embodiment of the present invention, the characteristic vector Q, as expressed in Equation 15, can be selected by physical quantity that is obtained through rotating a real part Re{S 11 } and an imaginary part (Im{S 11 }) of the reflection coefficient by a predetermined rotation matrix R. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           
                             Q 
                             1 
                           
                         
                       
                       
                         
                           
                             Q 
                             2 
                           
                         
                       
                     
                     ) 
                   
                   = 
                   
                     
                       
                         R 
                         ⁡ 
                         
                           ( 
                           θ 
                           ) 
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 Re 
                                 ⁢ 
                                 
                                   { 
                                   
                                     S 
                                     11 
                                   
                                   } 
                                 
                               
                             
                           
                           
                             
                               
                                 Im 
                                 ⁢ 
                                 
                                   { 
                                   
                                     S 
                                     11 
                                   
                                   } 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                                 - 
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                             
                           
                           
                             
                               
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 θ 
                               
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               
                                 Re 
                                 ⁢ 
                                 
                                   { 
                                   
                                     S 
                                     11 
                                   
                                   } 
                                 
                               
                             
                           
                           
                             
                               
                                 Im 
                                 ⁢ 
                                 
                                   { 
                                   
                                     S 
                                     11 
                                   
                                   } 
                                 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ] 
                 
               
             
           
         
       
     
     At this point, an angle θ of the rotation matrix R may be a value between −90° and 90°. According to one embodiment of the present invention, the angle θ of the rotation matrix R may be set as 0° during the setting of the matching parameter of operation S 10 . On the other hand, if the electric device  100  does not reach the matching state within the predetermined number of times by the performing of the matching state based on the first selected angle, the angle θ of the rotation matrix R may be changed into one value between −90° and 90° during the changing of the matching parameter in operation S 24 . An angle change of the rotation matrix R provides an effect of elongation of the power transmission line. An angle change of the rotation matrix R does not change an absolute value of the reflection coefficient, but only its phase value. Accordingly, the angel change of the rotation matrix R is one method of changing a matching parameter, which can be selected in order to prevent matching failure, and change matching trajectory. 
     Gain Factor 
     According to one embodiment of the present invention, the driving vector V can be obtained by a scalar product of the numerical control factor M, the reduced device vector dX′, and a gain factor g, as illustrated in Equation 16. At this point, the gain factor g may be a product of a standard gain factor g 0  and a first gain factor g 1  as defined in Equation 17.
 
 V=M·g·dX′   [Equation 16]
 
 g=g   0   ·g   1   [Equation 17]
 
     The standard gain factor g 0  may be a constant that is a standard size of the gain factor g. Additionally, the first gain factor g 1  is set to allow the magnitude of the driving vector V to have a dynamic correlation with respect to the measured characteristic vector. That is, the first gain factor g 1  is a variable that depends on the measured characteristic vector, and is defined to have a larger value as the magnitude (i.e., the magnitude of the displacement vector) of coordinate movement in the analytic coordinate system, which is required for matching, is larger. According to one embodiment of the present invention, the first gain factor g 1  is given as expressed in Equation 18 below. 
     
       
         
           
             
               
                 
                   
                     g 
                     1 
                   
                   = 
                   
                     
                       g 
                       min 
                     
                     + 
                     
                       
                         [ 
                         
                           
                             g 
                             max 
                           
                           - 
                           
                             g 
                             min 
                           
                         
                         ] 
                       
                       ⁢ 
                       
                         
                           S 
                           m 
                         
                         
                           
                             S 
                             0 
                             m 
                           
                           + 
                           
                             S 
                             m 
                           
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
             
           
         
       
     
     At this point, S represents the magnitude of the reflection coefficient. Additionally, g max , g min , S 0 , and m are matching parameters determined by considering environmental factors such as physical/electrical characteristics of the matching system, and as described above, can be changed during the modifying of the matching parameter of operation S 24 . To be more specific, g max  and g min  represent the maximum value and the minimum value of the first gain factor, respectively. S 0  represents the standard value of the first gain factor. Additionally, m is a characteristic parameter determining the value of the first gain factor, and also can be modified by a user or a computer during the modifying of the matching parameter of operation S 24 . Furthermore, the above Equation 1 is just one example of methods of defining the first gain factor g 1  and also can be defined through various other methods. 
       FIG. 23  is a graph for illustrating a relationship between a gain factor (esp. the first gain factor g 1 ) and the magnitude S of the reflection coefficient according to one embodiment of the present invention. According to this embodiment, the first gain factor g 1  is defined by Equation 18, and in this case, g max , g min , and S 0  are given with 1, 0.2, and 0.5, respectively. 
     Referring to  FIG. 23 , the first gain factor g 1  has a value close to g min  in a region MR where the magnitude S of the reflection coefficient is small, and has a value close to g max  in a region UMR where the magnitude S of the reflection coefficient is large. A level (i.e., a matching level) in which the electric device  100  is close to the matching state is inversely proportional to the magnitude S of the reflection coefficient. Accordingly, referring to Equations 16 and 18, the first gain factor g 1  defined as  FIG. 23  is contributed to increase the magnitude of the driving vector V when the matching level is low, and also is contributed to decrease the magnitude of the driving vector V when the matching level is high. That is, the first gain factor g 1  can accurately controls a matching trajectory when a matching level is high (i.e., around a matching point), and moves a matching trajectory toward around the matching point within a short time when the matching level is low. These effects due to the first gain factor g 1  are contributed to more enhance technical effects obtained by the displacement vector, defined by Equation 7. 
     On the other hand, according to another embodiment of the present invention, a gain factor g, as defined by Equation 19 below, is a product of a standard gain factor g 0  and a second gain factor g 2 , or is a product of the standard gain factor g 0 , the first gain factor g 1 , and the second gain factor g 2 , as defined by Equation 20 below.
 
 g=g   0   ·g   2   [Equation 19]
 
 g=g   0   ·g   1   ·g   2   [Equation 20]
 
     The second gain factor g 2  may be defined to prevent matching failure in a situation where change of a matching trajectory is required. For example, when reactance or admittance in at least one of the variable reactive elements reaches a feasible extreme value, the matching trajectory needs to be changed to prevent a matching failure. The second gain factor g 2  can be defined to cause a change of this matching trajectory. According to one embodiment of the present invention, a normal case where a change of the matching trajectory is unnecessary is set as 1, and an abnormal case where a change of the matching trajectory is necessary is set as −1.
 
 g   2 =+1(normal)
 
 g   2 =−1(abnormal)  [Equation 21]
 
     On the other hand, after changing the matching trajectory by a certain degree defined by a predetermined condition, the second gain factor g 2  may be set with +1 again in order to perform a normal matching process. At this point, requirements for restoring the second gain factor g 2  may be diversely defined if necessary. For example, after performing the matching process under the conditions where the second gain factor g 2  is defined as −1 within the predetermined number times, the above-mentioned normal matching process can be performed under the conditions where the second gain factor g 2  is defined as +1. 
       FIGS. 24 and 25  are diagrams illustrate results of impedance matching according to embodiments of the present invention. As described above, impedance matching according to theses embodiments is performed through the analytic coordinate system. However, in order to compare this method to the typical method, an impedance matching trajectory according to this embodiment is illustrated in a capacitance space of  FIGS. 24 and 25  like  FIG. 2 . 
     Referring to  FIGS. 24 and 25 , initial states (referring to asterisks at the right lower portion of  FIG. 24  and the left lower portion of  FIG. 25 ) in these embodiments correspond to the cases where two variable capacitors have feasible extreme values. When starting with these initial states, the matching system cannot reach the matching state according to the typical methods. However, even with a extreme initial condition, as illustrated in  FIGS. 24 and 25 , the matching method of the present invention can allow the matching system to be within the matching point. That is, the matching method according to the present invention has less dependency on an initial state. 
     Especially, as illustrated in  FIG. 25 , the matching method of the present invention changes a direction of the matching trajectory at a turning point T in the right lower portion in order to reach the matching state even if a missed matching path is selected first. A change (esp. a change of the second gain factor g 2 ) of the above-mentioned parameter is contributed to change a direction of this matching trajectory. 
       FIG. 26  is a diagram for illustrating a result of impedance matching according to one embodiment of the present invention. 
     Referring to  FIG. 26 , the matching method of the present invention creates a matching trajectory that stably reaches a matching point from around a matching point without a spiral matching trajectory or hunting of the typical method. That is, the matching method of the present invention provides improved matching convergence and enhanced matching characteristic around the matching point. 
     Matching Method of Pulse Mode 
     A matching method according to one embodiment of the present invention can operate as a slow pulse mode or a fast pulse mode. In the slow pulse mode, a frequency of a pulse is less than about 500 Hz and in the fast pulse mode, a frequency of a pulse is more than about 500 Hz.  FIG. 32  is a flowchart illustrating a pulse mode matching method according to one embodiment of the present invention. In this embodiment, a typical matching method of a CW mode is applied to the pulse matching method of the present invention. 
     This embodiment further includes determining a pulse mode if a power operates as the pulse mode after measuring the electrical characteristic. Excepting for the determining of the pulse mode, since this embodiment is identical to those of  FIG. 16 , its overlapping description will be omitted. 
     Referring to  FIG. 32 , measuring of the electrical characteristic in operation  120  may further include removing noise in operation S 112  before the measuring of the electrical characteristic in operation S 120 , calculating impedance of a power transmission line in operation S 121 , and calculating a forward power P_AVG in operation S 122 . The removing of the noise in operation S 112  may use a band pass filter or a lock-in detector. For example, the lock-in detector can extract only a driving frequency component of a power. The calculating of the forward power P AVG (or, an incident power) in operation S 122  can be calculated using the electrical characteristic (e.g., current, voltage, and phase). If the forward power P_AVG is calculated using the electrical characteristic, a power trigger signal P_TRIG can be generated according to whether the forward power P_AVG is more than or less than a threshold power P_th. The threshold power P_th may be set with several percent of the incident power. Accordingly, the matching system may operate being separated from the power. 
     Determining of the pulse mode in operation S 130  may include determining whether it is on time or not in operation S 131 , determining a pulse period in operation S 132 , and determining a fast pulse mode and a slow pulse mode in operation S 133 . The determining of whether it is on time or not in operation S 131  determines whether the forward power is more than a threshold power or the power trigger signal RF_TRIG is high (i.e., on time). 
     In a case of on time, testing a matching state in operation S 140  is performed to determine whether the matching system is in an allowable state or not. If the matching system is not in an allowable state during the testing of the matching state in operation S 140 , extracting a control parameter in operation S 150  and controlling the matching system are performed in operation S 160 . Additionally, if the matching system is in an allowable state during the testing of the matching state in operation S 140 , the removing of the noise in operation  112  and the measuring of the electrical characteristic of a power transmission line in operation S 120  are performed without the extracting of the control parameter in operation S 150  and the controlling of the matching system in operation S 160 . The extracting of the control parameter in operation S 150  includes extracting a control parameter in operation S 150   a  according to whether an amplitude of impedance is more than a specific impedance (usually, about 50 ohm) or not and extracting a control parameter according to whether a phase of impedance is more than 0° or not. The extracting of the control parameter in operation S 150  may vary. 
     The determining of the pulse mode in operation S 130  may include the determining of the pulse period in operation  132 . The pulse period can be calculated through a power trigger signal P_TRIG outputting ‘high’ or the power source trigger signal RF_TRIG when the forward power is more than the threshold power. According to the pulse period, it is classified into a fast pulse mode and slow pulse mode in operation S 133 . According to each pulse mode, a control parameter can be set. The control parameter is used for controlling the matching system during off time. According to a modified embodiment of the present invention, the fast pulse mode and the slow pulse mode can be set from the external. 
     In a case of the fast pulse mode, the matching system operates during off time by using the control parameter of a previous on time state. For example, the control parameter is a variable that controls reactance of variable reactive devices constituting the matching system. The control parameter is an input variable of a motor controlling device for adjusting reactance of the variable reactive devices. In a case of the fast pulse mode, the motor operates during off time such that durability deterioration of the motor due to frequent operating and stopping can be prevented and reliability of the motor can be improved. Additionally, since a matching condition between on time and the next on time is not greatly deviated due to a short pulse period, there is no great difference in the control parameter. Accordingly, the matching condition can be achieved in a shorter time. On the other hand, in a case of the slow mode, the matching system is controlled in an idle state. For example, a control parameter of the matching system is controlled in order to maintain values of the variable reactive devices. In the slow pulse mode, the motor can stop during off time. During off time, values of the variable reactive devices in the matching system do not significantly deviate from a matching point. 
     In operation S 134 , it is determined whether a power source is in an off time state or not during critical off time C_OFF_T. The critical off time C_OFF_T may be set with about 2 sec. If the off time state exceeds the critical off time C_OFF_T, the power source may be continuously regarded as off. That is, the matching system may change into a preset state. The preset state is a state of the matching system when the power source is not supplied. In operation S 135 , the control parameter is set with a preset state, and accordingly, the matching system is controlled. 
       FIG. 33  is a flowchart illustrating a pulse mode matching method according to one embodiment of the present invention. Overlapping description will be omitted. 
     In a case of on time, testing a matching state in operation S 140  is performed in order to determine whether the matching system is in an allowable state or not. If the matching system is not in the allowable state in operation S 140 , extracting the control parameter in operation S 150  and controlling the matching system in operation S 160  are performed. Moreover, if the matching system is in the allowable state in operation S 140 , removing noise in operation S 112  and measuring an electrical characteristic of a power transmission line in operation S 120  are performed without the extracting of the control parameter in operation S 150  and the controlling of the matching system in operation S 160 . The extracting of the electrical characteristic in operation S 150  may include converting the electrical characteristic of the power transmission line into a normalized characteristic vector in operation  151 , extracting a displacement vector by analyzing the characteristic vector in an analytic coordinate in operation S 152 , and converting the displacement vector into a control parameter in operation S 153 . The converting of the displacement vector into the control parameter in operation S 153  may include converting the displacement vector into a converted device vector in operation  1531  and converting the converted device vector into a driving vector in operation S 1532 . 
       FIG. 34  is a timing diagram illustrating a fast mode pulse matching method according to one embodiment of the present invention. 
     A voltage RF_V of a power transmission line is periodically tuned on/off as time elapses. Accordingly, an incident power (or, a forward power P_AVG) is increased as a power source increases and is decreased when the power source is turned off. When the incident power is more than a threshold power P_th, a power trigger signal P_TRIG is generated. A control parameter CP driving a motor of a matching system is generated if the incident power is more than the threshold power P_th. When the control parameter is CP is inputted in a motor driving system, a motor operates. During on time, the control parameter CP may vary as time elapses according to impedance or a reflection coefficient before reaching a matching state. During off time, the control parameter CP continuously maintains the final value of the control parameter of the on time state during off time. Accordingly, the motor of the matching system continuously operates. When it reaches a matching state (MAT=1) through a test, the control parameter CP is reset. Therefore, the motor stops. 
       FIG. 35  is a timing diagram illustrating a fast mode pulse matching method according to one embodiment of the present invention. 
     A voltage RF_V of a power transmission line is periodically tuned on/off as time elapses. Accordingly, an incident power (or, a forward power P_AVG) is increased as a power source increases and is decreased when the power source is turned off. A power source outputs a power source trigger signal RF_TRIG in synchronization with on/off. Through the power source trigger signal RF_TRIG, a pulse period of a power source and on/off time interval can be identified. During off time of the fast pulse mode, a control parameter CP maintains the same value as the control parameter of the previous on time state. If it reaches a matching state (MAT=1) through a test, the control parameter CP is reset. Accordingly, the motor stops. 
       FIG. 36  is a timing diagram illustrating a fast mode pulse matching method according to one embodiment of the present invention. 
     Referring to  FIG. 36 , a voltage RF_V of a power transmission line is periodically tuned on/off as time elapses. Accordingly, an incident power (or, a forward power P_AVG) is increased as a power source increases and is decreased when the power source is turned off. Thus, an input power (or, a forward power P_AVG) is increased when an RF power source increases and is decreased when the RF power is turned off. If the incident power is more than a threshold power P_th, a power trigger signal P_TRIG is generated. If the off time state is maintained more than a critical off time C_OFF_T, it is regarded that the power source is continuously in an off state. Thus, the control parameter is set with a preset state. The critical off time C_OFF_T may be about 2 sec. 
       FIG. 37  is a timing diagram illustrating a fast mode pulse matching method according to one embodiment of the present invention. 
     Referring to  FIG. 37 , a power source may operate in a CW mode during a CW time before a voltage RF_V of a power transmission line is periodically turned on/off as time elapses. An incident power (or, a forward power P_AVG) is increased when a power source is turned on and is decreased when a power source is turned off. If the input power is greater than a threshold power P_th, a power trigger signal P_TRIG is generated. During the CW time, the matching system may or may not reach a matching state. For example, if it does not reach the matching state during the CW time, a control parameter CP may be changed in a pulse mode state. After the CW mode, if the power source operates in a pulse mode, the control parameter CP is reset when it reaches a matching state (MAT=1) through the fast mode. On the other hand, if the power source deviates from the matching state as time elapses after it reaches the matching state (MAT=1), the control parameter CP is changed to reach the matching state again. That is, after the power source reaches the matching state, it reaches a matching state again even when it deviates from a matching state due to characteristic changes. 
       FIG. 38  is a timing diagram illustrating a slow mode pulse matching method according to one embodiment of the present invention. 
     Referring to  FIG. 38 , a voltage RF_V of a power transmission line is periodically turned on/off as time elapses. Accordingly, an incident power (or, a forward power P_AVG) is increased when a power source is turned on and is decreased when a power source is turned off. When the input power is greater than a threshold power P_th, a power trigger signal P_TRIG is generated. A control parameter CP for driving a motor of a matching system is generated when an average input power is greater than the threshold power P_th. Once the control parameter CP is inputted into a motor driving system, a motor operates. The control parameter CP in an on time state is changed as time elapses according to impedance or a reflection coefficient before it reaches a matching state (MAT=1). In an off time state, the control parameter CP is reset. Therefore, the motor of the matching system stops. On the other hand, if it reaches the matching state through a test, the control parameter CP is reset. Accordingly, the motor stops. 
     Matching System 
       FIG. 27  is a view of a matching system according to the present invention. In more detail,  FIG. 27  is provided to further describe the matching system of the electric device  100  referring to  FIG. 7 . 
     Referring to  FIGS. 7 and 27 , the matching system  104  of the present invention includes a processing unit  200  performing each matching operation, and variable reactive elements  301  and  302 . The matching system  104  may further include a sensor  141  measuring an electrical characteristic of the power transmission line  103 . 
     The variable reactive elements  301  and  302  may variably control reactance of the electrical device  100  in order to match impedance of the electric device  100 . For example, a variable capacitor or a variable inductor may be used as the variable reactive elements  301  and  302 . Additionally, as described above, the matching system  104  may further include passive elements providing a fixed reactance besides the variable reactive elements  301  and  302 . According to one embodiment of the present invention, the matching system  104  may be an L-type (described referring to  FIG. 8 ) that uses the variable capacitors as the variable reactive elements. 
     In a functional aspect, the processing unit  200  includes a measurement result analyzer  201 , a characteristic vector extractor  202 , a displacement vector extractor  203 , and a driving vector extractor  204 . In a form aspect, the processing unit  200  may include one chip or one electronic board performing functions of the functional parts  201 ,  202 ,  203 , and  204 . According to another embodiment of the present invention, in a form aspect, the processing unit  200  may be a computer installed with software performing functions of the functional parts  201 ,  202 ,  203 , and  204 . 
     The measurement result analyzer  201  is configured to analyze an electrical characteristic of the power transmission line  103  measured in the sensor  141  in order to create output information, which is used as input information of the characteristic vector extractor  202 . The output information of the measurement result analyzer  201  may be a complex impedance and a complex reflection coefficient of the power transmission line  103 . The electrical characteristic of the power transmission line  103  measured in the sensor  141  may be a current, a voltage, and a phase difference of the power transmission line  103 . 
     The characteristic vector extractor  202  is configured to process the converting of the measured electrical characteristic of the power transmission line into the normalized characteristic vector Q of operation S 31 , which is described referring to  FIGS. 16 ,  19 , and  20 . For this end, the output information of the measurement result analyzer  201  is used as the input information of the characteristic vector extractor  202 . Moreover, the characteristic vector Q includes at least two independent physical quantities related to the electrical characteristic of the power transmission line and having a normalized magnitude as its elements. According to one embodiment of the present invention, the characteristic vector Q, as illustrated in the above [Selection of Characteristic Vector] and also expressed in Equation 2, can be defined as a two-dimensional vector including a real part Re{S 11 } and an imaginary part (Im{S 11 }) of the reflection coefficient as its elements. 
     The displacement vector extractor  203 , as described referring to  FIGS. 16 ,  19 , and  20 , is configured to process the extracting of the displacement vector dG by analyzing the characteristic vector Q in the analytic coordinate system in operation S 32 . For this end, the output information of the characteristic vector extractor  202  is used as the input information of the displacement vector extractor  203 . According to one embodiment of the present invention, the displacement vector dG, as described in the above [Determination of Displacement Vector] and expressed in Equation 7, can be defined as a two-dimensional vector including an imaginary part (−Im{S 11 }) and a real part Re{S 11 } of the reflection coefficient as its elements. On the other hand, comparing to Equation 2 and Equation 7, the characteristic vector Q and the displacement vector dG are the same except for reverse of the element positions and change of sign. Therefore, characteristic vector Q and the displacement vector dG can be obtained by substantially the same process and the same processing unit in a matching system performing the above matching process. 
     The driving vector extractor  204  is configured to process the converting of the displacement vector dG into the reduced device vector dX′ in operation S 331 , and the converting of the reduced device vector dX′ into the driving vector V in operation S 332 , which are described with reference to  FIGS. 19 and 20 . 
     The converting of the displacement vector dG into the reduced device vector dX′ in operation S 331  includes converting the displacement vector dG through a predetermined matrix (i.e., an inverse matrix T −1  of the conversion matrix) as expressed in Equations 8 and 9. At this point, the conversion matrix T provides a phase space dealing with the characteristic vector Q in the predetermined analytic coordinate system, and also can be prepared according to the method described in the above [Selection of Analytic coordinate system]. That is, the analytic coordinate system is selected to express a predetermined phase space that quantitatively relates the electrical characteristic of the matching system to the electrical characteristic of the power transmission line. For this end, the coordinates of the analytic coordinate system are selected from physical quantities related to the electrical characteristic of the matching system, and the electrical characteristic of the power transmission line is expressed as one point in the selected coordinates of the analytic coordinate system. According to one embodiment of the present invention, the coordinates of the analytic coordinate system (hereinafter, referred to as an analytic coordinates) can be expressed in a function of reactance or admittance of variable reactive elements constituting the matching system, and the characteristic vector Q can be expressed as one point in a reactance space or an admittance space, which is prepared using the same process above. The analytic coordinate system is selected to injectively map a quantitative relationship between the electrical characteristic of the matching system and the electrical characteristic of the power transmission line. 
     The converting of the reduced device vector dX′ into the driving vector V in operation S 332  can be obtained by a scalar product of the numerical control factor M and the reduced device vector dX′, or a scalar product of a control factor M, the reduced device vector dX′, and the gain factor g as expressed in Equation 12 or 16. At this point, the gain factor g may be a value that is defined in Equations 17, 19, and 20. 
     The processing unit  200  further includes a controller  205 , an I/O signal processing unit  206 , and a data storage unit  207 . The I/O signal processing unit  206  is configured to process a numerical control signal for controlling the variable reactive elements  301  and  302 . For example, the I/O signal processing unit  206  may include one of typical various I/O interfaces (including a series interface such as RS232C or a parallel interface such as centronics interface). The numerical control signal includes the driving vector V itself or information generated by the driving vector V. The data storage  207  temporarily stores matching parameters used in a series of procedures for generating the numerical control signal or information generated during the procedures. For this end, the data storage  207  may be a memory semiconductor chip such as flash memory or a hard disk. The controller  205  is configured to control the measurement result analyzer  201 , the characteristic vector extractor  204 , the I/O signal processing unit  206 , and the data storage  207 . Besides that, the controller  205  may be configured to control information exchange between them and operations of the variable reactive elements  301  and  302 . 
     Furthermore, the processing unit  200  may further include at least one auxiliary unit that is configured to process the performing of the matching state test in operations S 22  and S 23 , and the modifying of the matching parameter in operation S 24 , which are described with reference to  FIG. 19 . In more detail, this auxiliary unit may be configured to process a calculating of a state parameter for the matching state test, evaluating of appropriateness of the matching parameter, changing of an angle of the rotation matrix, and changing of the gain factors. 
     The elements constituting the matching system  104  or the processing unit  200  are configured to realize one of the above-mentioned matching methods according to the present invention. However, this configuration is not limited to the embodiments described with reference to  FIG. 27 , and can be diversely modified. 
     Pulse Matching System 
       FIG. 39  is a view of a matching system according to the present invention. 
     Referring to  FIG. 39 , a matching system  104  according to the present invention includes a processing unit  200  for performing the above mentioned matching operations and variable reactive devices  301  and  302 . The matching system  104  may further include a sensing unit  141  for measuring an electrical characteristic of a power transmission line  103 . A power source  102  may operate in a pulse mode. 
     The variable reactive devices  301  and  302  may be a device for variably controlling their reactance to match an impedance of the electric device  100 . For example, a variable capacitor or a variable inductor may be used as the variable reactive devices. As mentioned above, the matching system  104  may further include passive devices for providing a fixed reactance in addition to the variable reactive devices  301  and  302 . The variable reactive devices  301  and  302  may include a motor for changing their values and a motor controlling system. 
     According to one embodiment of the present invention, the matching system  104  may be the L type (refer to  FIG. 8 ) using variable capacitors as the variable reactive device. 
     In a functional aspect, the processing unit  200  may include a noise removing unit  210 , a measurement result analyzing unit  201 , a pulse mode processing unit  211 , and a control parameter extracting unit  212 . In a structural aspect, the processing unit  200  may include at least one chip or electronic board, which is manufactured to perform the above functions of the above unit  210 ,  201 ,  211 , and  212 . According to another embodiment of the present invention, in a structural aspect, the processing unit  200  may be a software installed computer for performing the above functions of the above unit  210 ,  201 ,  211 , and  212 . The measurement result analyzing unit  201  is configured to analyze an electrical characteristic of the power transmission line  103  measured in the sensing unit  141  and then generate an output information used as an input information of the control parameter extracting unit  212 . The output information of the measurement result analyzing unit  201  may include complex impedance, complex reflection coefficient, and an incident power P_AVG of the power transmission line  103 . The electrical characteristic of the power transmission line  103  measured in the sensing unit  141  may be current, voltage, and phase difference of the power transmission line  103 . The noise removing unit  210  may use a band pass filter or a lock-in detector. For example, the lock-in detector can extract only a driving frequency component of a power source. 
     According to one embodiment of the present invention, the control parameter extracting unit  212  may include a characteristic vector extracting unit, a displacement vector extracting unit, and a driving vector extracting unit. According to another embodiment of the present invention, the control parameter extracting unit  212  may be a device for extracting a control parameter through an absolute value and a phase of impedance as illustrated in  FIG. 32 . 
     The processing unit  200  may further include a controller  205 , an input/output (I/O) signal processing unit  206 , and a data storage  207 . The I/O signal processing unit  206  is configured to process a numerical value controlling signal for controlling the variable reactive devices  301  and  302 . For example, the I/O signal processing unit  206  may include one of various I/O interfaces (including a serial interface such as RS232C or a parallel interface such as a centronics interface). The numerical value controlling signal may include a driving vector V or a control parameter itself, or information generated from them. The data storage  207  temporarily stores matching parameters used in the series of processes for generating the numerical value controlling signal or information generated during the processes. For this, the data storage  207  may be a memory semiconductor chip such as a flash memory or a hard disk. The controller  205  is configured to control operations of the measurement result analyzing unit  201 , the pulse mode processing unit  211 , the control parameter extracting unit  212 , the I/O signal processing unit  206 , and the data storage  207 . Furthermore, the controlling unit  205  may be configured to control information transmission between the units and operations of the variable reactive devices  301  and  302 . 
       FIG. 40  is a view of a matching system according to the present invention. 
     Referring to  FIG. 40 , a matching system according to the present invention may include a first matching system  104   a  and a second matching system  104   b , connected to one load  101 . Frequencies of a power source connected to the matching systems  104   a  and  104   b  may be respectively different. Additionally, each power source may operate in at least one of a pulse mode and a CW mode. Overlapping description for each matching system will be omitted. 
       FIG. 41  is a view of a matching system according to the present invention. 
     Referring to  FIG. 41 , the matching system may include a first matching system  104   a  connected to a first load  101   a  and a second matching system  104   b  connected to a second load  101   b . Frequencies of a power source connected to the first and second matching systems  104   a  and  104   b  may be respectively different. Additionally, each power source may operate in at least one of a pulse mode and a CW mode. Overlapping description for each matching system will be omitted. 
     Plasma Chamber System 
     As illustrated with reference to  FIG. 7 , the matching system  104  of the present invention may be used for impedance matching of the electric device  100  having one of a plasma system, a nuclear magnetic resonance system, a communication system, a high frequency induction heating device, and a power transmission line as the load  101 . Below, according to one embodiment of the present invention, a plasma chamber device used in the manufacturing process of a semiconductor device among various applicable fields is described with reference to  FIG. 28 . However, the electric device including the matching system of the present invention is not limited to the above. That is, the matching system of the present invention can be used in all kinds of electric devices requiring impedance matching through the impedance matching method or its simple modifications. 
       FIG. 28  is a view of a plasma chamber device including an impedance matching system according to one embodiment of the present invention. 
     Referring to  FIGS. 7 and 28 , the plasma chamber device  900  of this embodiment includes a chamber  901  providing a space to which a semiconductor substrate is loaded, an upper electrode  911  and lower electrode  912  contributed to generate and control plasma in the chamber  901 , and an upper power source  921  and a lower power source  922  providing powers to the upper and lower electrodes  911  and  912 , respectively. An upper power transmission line  931  is disposed between the upper electrode  911  and upper power source  921  for connection therebetween, and a lower transmission line  932  is disposed between the lower electrodes  912  and the lower power source  922  for connection therebetween. An upper sensor  941  and a lower sensor  942  are respectively disposed on the upper and lower power transmission lines  931  and  932  to measure electrical characteristics of them. Furthermore, upper and lower matching systems  951  and  952  are disposed on the upper and lower power transmission lines  931  and  932 , respectively, to maximize electric powers that are applied to the upper and lower electrodes  911  and  912 . Furthermore, the plasma chamber device  900  further comprises a controller  960  for controlling the sensors, the matching systems, and the power sources. 
     At least one of the upper and lower matching systems  951  and  952  may be configured to realize one of the matching methods of the present invention. For example, the upper and lower matching systems  951  and  952  may be the matching system  104  including the processing unit  200  as illustrated with reference to  FIG. 27 . 
     According to one embodiment of the present invention, even if a matching system does not receive an additional trigger signal from an RF power source, it measures an incident power by itself and can operate independently in a pulse mode and/or a CW mode. Therefore, the matching system can operate in the pulse mode where there are several Hz and/or a duty ratio is less than about 10 percent. 
     The above-disclosed subject matter is to be considered illustrative, and not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other embodiments, which fall within the true spirit and scope of the present invention. Thus, to the maximum extent allowed by law, the scope of the present invention is to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing detailed description.