US007839223B2
`
`(12) United States Patent
`Van Zyl et al.
`
`(10) Patent No.:
`(45) Date of Patent:
`
`US 7,839,223 B2
`Nov. 23, 2010
`
`(54) METHOD AND APPARATUS FOR ADVANCED
`FREQUENCY TUNING
`
`(75) Inventors: Gideon Van Zyl. Fort Collins, CO (US);
`Jeff Roberg, Longmont, CO (US)
`
`(73) Assignee: Atassists Industries, Inc., Fort
`Oll1nS,
`
`(*) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 297 days.
`(21) Appl. No.: 12/242,328
`
`(22) Filed:
`(65)
`
`Sep. 30, 2008
`Prior Publication Data
`US 2009/023717OA1
`Sep. 24, 2009
`O
`O
`Related U.S. Application Data
`(60) Provisional application No. 61/038,774, filed on Mar.
`23, 2008.
`
`(2006.01)
`(51) E",/00
`(200 6,015
`H05B 7/8
`(200 6. 01)
`H05H I/24
`331A35315/111.21
`52) U.S. C
`ir grgrrr.
`(52)
`s
`(58) Field of Classification Search ............. r 331/1 R,
`331/34, 35, 126, 127: 315/1 11.21
`See application file for complete search history.
`References Cited
`
`(56)
`
`U.S. PATENT DOCUMENTS
`5,543,689 A * 8/1996 Ohta et al. ............. 315, 111.21
`
`3/2004 Coumou et al.
`6,707,255 B2
`6/2005 Mahoney et al.
`6,902,646 B2
`7,145,398 B2 * 12/2006 Dalton et al. ............... 331 (1 A
`7,476,233 B1* 1/2009 Wiener et al. ............... 606/169
`
`FOREIGN PATENT DOCUMENTS
`O2884.056 B2
`4f1999
`2006-054148
`2, 2006
`
`JP
`JP
`
`OTHER PUBLICATIONS
`Jung, Jong Han, “International Search Report re Application No.
`p
`9.
`9.
`pp
`PCT/US09/037001”, Oct. 16, 2009, Published in: PCT.
`* cited by examiner
`Primary Examiner David Mis
`(74) Attorney, Agent, or Firm Neugeboren O’Dowd PC;
`Sean R. O'Dowd
`
`(57)
`
`ABSTRACT
`
`A method and apparatus fortuning the operational frequency
`of an electrical generator coupled to a time-varying load is
`described. One illustrative embodiment rapidly calculates an
`error (reflection coefficient magnitude) at the current opera
`tional frequency of the electrical generator, adjusts the fre
`quency of the electrical generator by an initial step size so:
`rapidly calculates a second error, and if the magnitude of the
`second error is Smaller than the magnitude of the first error,
`then the step size is increased and the frequency is adjusted by
`the increased step size.
`
`16 Claims, 12 Drawing Sheets
`
`Error
`calculation
`
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`
`
`
`Frequency
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`amplifier
`
`Page 1 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 1 of 12
`
`US 7,839,223 B2
`
`
`
`
`
`Matching
`circuit
`
`4 -
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`FG.
`
`Page 2 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 2 of 12
`
`US 7,839,223 B2
`
`FG.2
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`
`Page 3 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 3 of 12
`
`US 7,839,223 B2
`
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`except in special cases where aprior
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`1 Frequency
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`
`Page 4 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 4 of 12
`
`US 7,839,223 B2
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`Page 5 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 5 of 12
`
`US 7,839,223 B2
`
`FG.9
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`Page 6 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 6 of 12
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`US 7,839,223 B2
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`
`Page 7 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 7 of 12
`
`US 7,839,223 B2
`
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`Page 8 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 8 of 12
`
`US 7,839,223 B2
`
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`
`Page 9 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 9 of 12
`
`US 7,839,223 B2
`
`FG.13
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`Page 10 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 10 of 12
`
`US 7,839,223 B2
`
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`Page 11 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 11 of 12
`
`US 7,839,223 B2
`
`F.G. 17
`
`F.G. 18
`
`
`
`Time (ms)
`
`Page 12 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`

`

`U.S. Patent
`
`Nov. 23, 2010
`
`Sheet 12 of 12
`
`US 7,839,223 B2
`
`F.G. 19
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`Page 13 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
`
`

`

`1.
`METHOD AND APPARATUS FOR ADVANCED
`FREQUENCY TUNING
`
`US 7,839,223 B2
`
`RELATED APPLICATION
`
`This application claims the benefit of priority of U.S. pro
`visional application Ser. No. 61,038,774 entitled “Advanced
`Frequency Tuning filed on Mar. 23, 2008, which is incor
`porated by reference in its entirety herein.
`
`FIELD OF THE INVENTION
`
`5
`
`10
`
`The present invention relates generally to electrical gen
`erators. In particular, but not by way of limitation, the present
`invention relates to methods and apparatuses for tuning (ad
`justing) the operational frequency of a generator.
`
`15
`
`BACKGROUND OF THE INVENTION
`
`Power generators are typically designed for optimal per
`formance into a specific load impedance, typically 50 ohms.
`Operating into a load impedance close to the design value
`typically results in the highest output power capability and the
`lowest stress on the components internal to the generator.
`Typically, but not always, some type of matching network is
`used to match the load to the generator. By correct design of
`the matching network (either internal to the generator or
`external), it is possible to transform the impedance of the load
`to a value close to the desired load impedance at Some fre
`quency in the range of frequencies that the generator can
`produce.
`
`25
`
`30
`
`SUMMARY OF THE INVENTION
`
`35
`
`40
`
`Illustrative embodiments of the present invention are
`shown in the drawings and Summarized below. These and
`other embodiments are more fully described in the Detailed
`Description section. It is to be understood, however, that there
`is no intention to limit the invention to the forms described in
`this Summary of the Invention or in the Detailed Description.
`One skilled in the art can recognize that there are numerous
`modifications, equivalents, and alternative constructions that
`fall within the spirit and scope of the invention as expressed in
`the claims.
`Many embodiments of the present invention provide a
`method and apparatus for rapidly tuning the operational fre
`quency of a generator (e.g., an RF generator) in response to
`changes in load impedance of a nonlinear and/or time-varying
`load coupled to the generator.
`One illustrative embodiment comprises a method of fre
`quency tuning, the method including calculating the load
`reflection coefficient and then adjusting the generator's oper
`ating frequency based on the relative magnitude of the calcu
`lated load reflection coefficient as compared with one or more
`previously calculated load reflection coefficients.
`55
`Another illustrative embodiment comprises a method of
`frequency tuning, the method including calculating the load
`reflection coefficient and then adjusting a frequency step size
`based on the relative magnitude of the calculated load reflec
`tion coefficient as compared with one or more previously
`calculated load reflection coefficients.
`Yet another illustrative embodiment comprises a method of
`calculating the load reflection coefficient (or other metric) in
`a rapid time frame relative to the variability of a time-variant
`load coupled to a generator.
`These and other embodiments are described in further
`detail herein.
`
`45
`
`50
`
`60
`
`65
`
`2
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`Various objects and advantages and a more complete
`understanding of the present invention are apparent and more
`readily appreciated by reference to the following Detailed
`Description and to the appended claims when taken in con
`junction with the accompanying Drawings, wherein:
`FIG. 1 is a system-level block diagram depicting a system
`in which embodiments of the present invention may be real
`ized;
`FIG. 2 is a graphical illustration (Smith chart) of the gen
`eral behavior of the load reflection coefficient as a function of
`frequency for the system depicted in FIG. 1;
`FIG.3 is a graphical illustration of an error (here simply the
`reflection coefficient magnitude) as a function of frequency
`corresponding to FIG. 2;
`FIG. 4 is a block diagram depicting functional components
`that may be implemented in connection with the system
`depicted in FIG. 1;
`FIG. 5 is a graphical illustration of the error and frequency
`as a function of time in the case where an erroris a monotonic
`function of frequency;
`FIG. 6 is a graphical illustration of an error and frequency
`as a function of time for the case where methods in accor
`dance with embodiments of the present invention are benefi
`cial;
`FIG. 7 is a graphical illustration of an error function as a
`function of frequency for a time-invariant (linear or nonlin
`ear) load;
`FIG. 8 is a graphical illustration of another error function as
`a function of frequency for a time-varying (linear or nonlin
`ear) load;
`FIG. 9 is a flowchart of a method for finding a desirable
`frequency in accordance with yet another illustrative embodi
`ment of the disclosed frequency tuning method;
`FIG. 10 is a flowchart of a method for finding a desirable
`frequency in accordance with yet another illustrative embodi
`ment of the disclosed frequency tuning method;
`FIGS. 11 and 12 are graphs depicting a simulation of
`exemplary methods carried out in connection with embodi
`ments exposed to noise;
`FIGS. 13 and 14 are graphs depicting a simulation of
`exemplary methods carried out in connection with embodi
`ments in the absence of noise;
`FIGS. 15 and 16 are graphs depicting a simulation of
`additional exemplary methods carried out in connection with
`embodiments in the absence of noise;
`FIGS. 17 and 18 are graphs that illustrate a failure of a
`stabilized method to tune in the presence of noise;
`FIGS. 19, 20 and 21 are graphs that graphically illustrate
`inter-pulse frequency tuning in accordance with one or more
`embodiments of the disclosed frequency tuning method;
`FIG. 22 graphically illustrates an exemplary frequency
`tuning method which uses a small percentage of time with a
`maximum time slot of duration T to search for a global opti
`mum frequency.
`
`DETAILED DESCRIPTION
`
`Reference is now directed to the drawings, where like or
`similar elements are designated with identical reference
`numerals throughout the several views.
`Frequency tuning in generators (e.g., RF generators) is
`often used to reduce reflected power and thereby obtain effi
`cient operation. Referring to FIG. 1, a block diagram of a
`typical generation system 100 is shown. A generator 102 is
`electrically coupled to a load 106. Typically, but not always,
`
`Page 14 of 19
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`

`3
`some type of matching network 104 is used to match the load
`to the generator. By correct design of the matching network
`(either internal to the generator, or external as shown in FIG.
`1), it is possible to transform the impedance of the load to a
`value close to the desired load impedance of the generator
`(either at the output connector, typically 5092, or at the active
`devices internal to the generator, which is typically some low
`complex impedance like 8+3S2) at Some frequency in the
`range of frequencies that the generator can produce.
`The measure of how close the load impedance is to the
`desired impedance can take many forms, but typically it is
`expressed as a reflection coefficient
`
`10
`
`15
`
`where p is the reflection coefficient of the impedance Z with
`respect to the desired impedance Zo. The magnitude of the
`reflection coefficient (pl) is a very convenient way to express
`how close the impedance Z is to the desired impedance Z.
`Both Zand Z are in general complex numbers.
`Frequency tuning methods and algorithms try to find the
`optimal or desirable frequency of operation. A point of opti
`mization may be defined as the frequency where the magni
`tude of the reflection coefficient with respect to the desired
`impedance is the Smallest, but other measures may be used for
`this purpose. Such other measures, for example, include mini
`mum reflected power or maximum delivered power.
`On a time-invariant linear load, many tuning methods will
`work well. But on time-varying and/or nonlinear loads, it has
`been found that special techniques are required to ensure
`reliable operation of the tuning algorithms. As changes in
`load impedances occur (e.g., as a result of a change in power
`delivered to the load, gas chemistry, pressure etc.), there is
`often a need to dynamically tune the generator to operate at
`the frequency that presently corresponds to a desired (e.g.,
`optimal) frequency, in a time frame that corresponds to the
`dynamics of the time-varying and/or nonlinear load to which
`the generator is coupled.
`In the context of a control problem, it is useful to view an
`error as the indication of an undesirable (e.g., non-optimal)
`operational state. In classical control theory, it is theoretically
`possible to drive an error to zero, but this is rarely the case in
`frequency tuning methodologies.
`Assuming that a desirable frequency of operation is a fre
`quency at which the magnitude of the load reflection coeffi
`cient is at or Substantially close to its minimum, it is noted that
`the relationship between the controlled variable (frequency)
`and the error is not necessarily monotonic. Furthermore, the
`optimum point of operation is at a point where the gain
`(defined as change in error divided by change infrequency) is
`ZO.
`To add to the challenges, it is also possible that local
`minima may exist in an area which a control method can get
`trapped. By way of illustrative example, FIG. 2 shows a plot
`of a load reflection coefficient on a load reflection coefficient
`chart (Smith chart), and FIG. 3 shows the corresponding
`magnitude of the load reflection coefficient used as the error,
`as a function of frequency.
`In Some special cases, where a priori information about the
`load is known, it is possible to arrange for an error function to
`be a monotonic function of frequency, so that a simple linear
`controller may be used. For example, Such a system is dis
`
`25
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`40
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`45
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`50
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`US 7,839,223 B2
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`4
`closed in U.S. Pat. No. 6,472,822, entitled “Pulsed RF Power
`Delivery for Plasma Processing issued to Chen et al., on Oct.
`29, 2002.
`Referring to FIG. 5, it is a graph depicting an error and
`frequency that are both monotonic. Such linear control is
`rarely applicable due to the non-monotonic relationship
`between frequency and error, except in those special cases
`where a priori information about the load is available.
`It has been found that two common problems with plasma
`loads are: (1) the nonlinear nature of the load because the
`plasma load impedance is a function of power level; and (2)
`the load impedance changes over time because of changing
`chemistry, pressure, temperature and other physical charac
`teristics of the non-linear plasma load. Another problem that
`is unique to plasma (or plasma-like) loads is that the plasma
`can extinguish if the delivered power to the plasma falls below
`a minimum value for a long enough time. Thus a frequency
`where insufficient power is delivered to the plasma load can
`not be applied for very long, or the plasma will extinguish.
`If a plasma load changes with time, known tuning tech
`niques are often unsatisfactory and problematic as FIGS. 7
`and 8 help to illustrate. Referring to FIG. 7 for example, an
`error, e.g., the magnitude of the load reflection coefficient, as
`a function of frequency, is assumed to remain fixed. In this
`situation, a frequency tuning algorithm operating at fre
`quency f. and time to and Subsequently at frequency f. at time
`t will correctly determine that f is a better frequency at
`which to operate, and will continue to tune to higher frequen
`cies until the minimum error at f
`is reached.
`In FIG. 8, however, an error, e.g., the magnitude of the load
`reflection coefficient, as a function offrequency, changes over
`time. In this situation, a typical frequency tuning algorithm
`operating at frequency f. and time to and subsequently at
`frequency f. at time t will incorrectly determine that f is a
`worse frequency at which to operate and will tune away from
`the optimal frequency. This incorrect result is because the
`error function itself has changed over time.
`Moreover, when the power (e.g., RF power) to the load is
`pulsed, frequency tuning becomes even more problematic.
`Due to the nonlinear nature of the load and the relatively high
`quality factor (ratio of stored energy to energy delivered per
`cycle (e.g., RF cycle), often denoted by “O'”) that impedance
`matching networks employ, the load impedance changes very
`rapidly during the first few microseconds of the applied pulse
`(e.g., RF pulse).
`Referring first to FIG. 4, it is a block diagram depicting
`functional components of exemplary embodiments, which
`may be implemented in connection with the embodiment
`depicted in FIG.1. It should be recognized that the illustrated
`arrangement of these components is logical and not meant to
`be an actual hardware diagram. Thus, the components can be
`combined or further separated in an actual implementation.
`Moreover, the construction of each individual component,
`which may include hardware, firmware, Software, and com
`binations thereof, is well-knownto those of skill in the art in
`light if this specification.
`Several variations of the controller depicted in FIG. 4 are
`configured to accommodate (e.g., by carrying out control
`methodologies described further herein) circumstances in
`which a non-monotonic relationship between an error and the
`frequency exist (e.g., whena priori information about the load
`is not known). And the error function depicted in FIG. 4 in
`many variations indicates non-desirable operation, and in
`many embodiments indicates non-optimal operation.
`Several embodiments of the present invention address the
`speed required to keep up with a time-varying load. In many
`embodiments, the solution is two-fold. The first is the devel
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`5
`opment of a very fast division methodology that allows the
`calculation of the load reflection coefficient at speeds signifi
`cantly faster (up to one thousand times faster) than what is
`traditionally used. The second part of the solution in these
`embodiments is to allow the frequency step size to increase if
`the error is decreasing step-over-step, and decrease (or stay
`constant) if the error is increasing step-over-step. Taken
`together, the problem of keeping up with a time-varying load
`is solved. It is certainly contemplated, however, that alterna
`tives to the specific fast division methodology disclosed
`herein may be utilized (if sufficiently fast) in connection with
`the above-identified second part of the solution.
`FIG.9 depicts a flow diagram 900 illustrating one embodi
`ment of a frequency tuning method in accordance with the
`present invention, which may be carried out, at least in part,
`by the controller depicted in FIG. 4. The method initiates at
`block 902, typically, but not always, at power up. Next, at
`block 904, the method rapidly calculates the load reflection
`coefficient (e.g., using a very fast division method that allows
`the calculation of the load reflection coefficient at speeds
`significantly faster (e.g., up to one thousand times faster) than
`what is traditionally used). Calculation in this context may be
`in the order of microseconds (depending on the specific
`implementation), which is rapid relative to the rate at which
`the load varies in time, typically in the order of milliseconds.
`Although a specific method for arriving at the load reflection
`coefficient is described in detail herein, other methodologies
`for calculating the load reflection coefficient are certainly
`contemplated.
`At branch906 the method determines whether the error is
`decreasing relative to the previous error (or errors) calculated.
`One skilled in the art will readily appreciate that alternative
`approaches (e.g., ensemble averaging) to comparing the cur
`rent calculated error relative to previously calculated errors
`are within the scope of this embodiment. If the currenterroris
`decreasing relative to the previous calculated error (or errors),
`then the frequency step size (by which the frequency is
`adjusted) is increased, as reflected in block 908. If, on the
`other hand, the current error is not decreasing relative to the
`previous calculated error (or errors), then the method
`branches to block 910, where the frequency step size is
`decreased or (left at the present value). Finally, the method
`progresses to block 912, where the new frequency is set
`(based on the applicable step size) and the method cycles
`through again.
`The rapid division method disclosed herein makes use of
`the fact that the reflection coefficient is a complex number
`with magnitude between 0 and 1. Treating the real and imagi
`nary parts of the reflection coefficient separately, and deter
`mining the sign of the result from the signs of the numerator
`and denominator, or when only calculating the magnitude of
`the reflection coefficient (or, more typically the square of the
`magnitude of the reflection coefficient by dividing reflected
`power by forward power), the problem is reduced to the
`calculation of the ratio of two positive real numbers. When it
`is known that the answer must be between 0 and 1, it allows
`for an iterative solution without ever having to perform mul
`tiplication operations. Note that in the specific application, it
`can be assumed that the denominator is never Zero because
`the denominator is generally proportional to the square root
`of forward power, which is never Zero during operation, when
`this calculation is required.
`The fast division method can be understood by noting that
`R=N7D, where R is the ratio to be calculated, N is the numera
`tor, and D the denominator. R, the ratio to be calculated, is the
`same as N=RxD. The calculation is performed in fixed point
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`US 7,839,223 B2
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`arithmetic, and therefore we assign a power of 2, for example
`2", to represent a ratio of one. With this assignment, we have
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`where N, Rand Dare integers. The calculation of 2"xN can be
`performed inexpensively (in terms of computing resources)
`as a left-shift operation on the binary representation of N.
`The calculation starts by calculating low, middle and upper
`estimates of what Ris. The initiallow estimate is simply 0, the
`initial upper estimate, 2", represents a ratio of 1 and the initial
`middle estimate is 2'". At the same time low, middle and
`high estimates of the product, RxD are calculated as 0, 2"
`1)xD and 2"xD, respectively. Note that the middle and upper
`estimates for the product can again be calculated efficiently as
`left shifts of the binary representations of D by n-1 and n,
`respectively.
`The calculation iterates by comparing the middle estimate
`of the product to the required value, 2"xN. If the middle
`estimate is greater than 2"xN, then the middle estimate
`becomes the new upper estimate; otherwise the middle esti
`mate becomes the new low estimate. A new middle estimate
`is calculated as half the sum of the new low and upper esti
`mates. This calculation is performed as a sum followed by a
`right shift, again using computationally non-intensive
`numerical processing techniques. By maintaining extra frac
`tional bits, rounding errors can be avoided.
`After n iterations, the calculation is complete as the differ
`ence between the upper and lower estimates collapse until
`they are separated by 1 in fixed point arithmetic. The middle
`estimate can then be used to select the lower or upper esti
`mate, which ever is closer.
`One skilled in the art will appreciate that the fast division
`method disclosed herein may be implemented in numerous
`manners, including without limitation, hardware, firmware
`and Software.
`Using this high speed, computationally-efficient division
`method, the reflection coefficient (or its magnitude) is avail
`able for use by the frequency tuning method with sufficient
`accuracy and within a fraction of a microsecond after the new
`values for the forward and reflected signals are available,
`allowing for very fast tuning. For example, when using 8-bit
`estimates of the ratio, and a 64 MHZ clock, the ratio is calcu
`lated in 125 nanoseconds. Typically the noisy nature of the
`plasma load limits the maximum frequency update rate to a
`few microseconds, so this method efficiently provides the
`required calculation in adequate time to deliver a fast and
`effective frequency tuning capability.
`Many variations of the inventive frequency tuning meth
`odologies carried out in connection with several embodi
`ments deviate from the traditional step-halving algorithms in
`use in that the methodologies allow the frequency step to
`increase when it is going in the desired direction (detected by
`a decreasing error). This feature allows these methods to
`follow time-varying loads much more accurately. Although
`these methods may be prone to instability, stability may be
`enhanced by allowing the step size to increase after a fixed
`number of steps after a change in direction (typically 2 to 4
`depending in a complex way on the step-up and step-down
`gains discussed infra). This instability, however, takes the
`form of a limit cycle, and eliminating this limit cycle is not
`necessary for correct operation of the tuning method itself.
`Noise considerations relative to stabilizing the frequency tun
`ing methodologies are discussed infra.
`To facilitate further description of frequency tuning
`method methodologies described herein, the following vari
`ables are defined:
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`ADVANCED ENERGY INDUSTRIES INC.
`Exhibit 1022
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`US 7,839,223 B2
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`threshold as determined in block 1042, a failure to tune timer
`is started and the method is allowed to continue trying to tune
`to the upper threshold until this failure to tune time is
`exceeded as determined in block 1054. If the method failed to
`tune, an error is declared and RF may be turned off depending
`on the user settings.
`The exemplary method depicted in FIG. 10 is augmented
`by conditions for starting and stopping the tuning method. For
`example, as illustrated at branches 1038 and 1042, a lower
`and upper target for the error, as well as a time to get to the
`lower target, are typically set. The tuning method will then
`attempt to get to the lower target in the allotted time. If it
`reaches the lower target the method stops, as illustrated at
`block 1038. If the allotted time is exceeded, the method stops
`if the error is less than the upper target, as illustrated at block
`1042. Once the method is stopped, it is generally re-started
`when the upper target is exceeded. If the method fails to reach
`the upper or lower targets, errors and warnings may be issued
`to the system controller.
`The method can be further augmented by doing an initial
`frequency sweep when power (e.g., RF power) is first turned
`on to find the optimal operating point with some degree of
`accuracy before starting the frequency tuning method. The
`Sweep is generally carried out in both directions because the
`effects of ignition, or failure to ignite, may mask the true
`minimum. For example, the plasma may ignite at one fre
`quency, but once ignited, the plasma may operate at a differ
`ent, higher optimum frequency. If the frequency is swept from
`low to high, the optimum frequency will be found, but not if
`it is swept from high to low, since the plasma will not be
`ignited when the higher, optimal frequency is probed.
`Further enhancements include searching for the desirable
`ignition frequency separately from searching for a desirable
`operating frequency. Sometimes the desirable ignition fre
`quency corresponds to the frequency at which the load reflec
`tion coefficient is minimized with the plasma not ignited. A
`Sweep at very low power where the plasma cannot ignite can
`determine the best ignition frequency under Such conditions,
`which often occur.
`Further enhancements include waypoints for specific sys
`tems and processes. Such waypoints may include a start fre
`quency for ignition, a time to stay at the ignition frequency,
`then a second frequency with a time to stay at that frequency
`(and even more frequency, duration points) before starting the
`regular frequency tuning method. Instead of using a fre
`quency and duration for ignition, ignition may also be
`detected by looking for a sudden change in load reflection
`coefficient, delivered, forward or reflected power, or combi
`nations thereof.
`In connection with many variations of the inventive tuning
`methodologies described herein, a step down gain, g, may be
`generally less than 0.5 for stability reasons, with 0.125 being
`an exemplary value. The step up gain, g, is generally set to 2
`or 4. The minimum frequency is generally set large enough so
`that when comparing two frequencies, the error is signifi
`cantly different, and noise does not influence the decision
`process in the method too much. Correctly setting the Small
`est frequency step helps to optimize the method. The maxi
`mum frequency step is generally set such that the method
`does not jump over minima or extinguish (in the case of
`plasma loads) the plasma. The variables are generally preset,
`but the user may have the ability to change the settings to
`optimize the method in specific applications.
`One solution for simultaneous pulsing and frequency tun
`ing discards information at the start of the pulse while the
`impedance is stil