HYBRID METHOD TO SYNTHESIZE VOLTAGE WAVEFORMS WITH NON-HARMONIC PROFILES

Abstract

Method and apparatus for generating asymmetric high-voltage waveforms with near-rectangular profiles. The method comprises producing selected low-frequency components of the Fourier series for a rectangular waveform explicitly and adding them to the amplified residual of lower-amplitude near-rectangular waveform upon filtering out certain frequencies.

Claims

1. A method to synthesize a desired voltage waveform of other than a harmonic profile, the method comprising the steps of: i. generating an initial voltage waveform of said profile at a lower amplitude than a desired final amplitude; ii. substantially depleting a finite number of lower-frequency components of a Fourier series of said initial waveform in (i) to yield a depleted waveform; iii. amplifying the depleted waveform produced in (ii) to an amplitude wherein non-depleted components have magnitudes approximately equal to the amplitude of the desired voltage waveform; iv. generating said finite number of lower-frequency components as individual harmonics with amplitudes approximately matching those in the desired voltage waveform; and v. superposing all the waveforms obtained in (iii) and (iv).

2. The method of claim 1, wherein said lower-frequency components in (ii) are consecutive lower-order terms of the Fourier series.

3. The method of claim 1, wherein said lower-frequency components are depleted in (ii) using a high-frequency pass filter.

4. The method of claim 3, wherein said filter has an adjustable low-frequency cutoff or slope.

5. The method of claim 1, wherein said lower-frequency components are generated in (iv) using individual resonating circuits.

6. The method of claim 5, wherein said circuits have tunable resonance frequencies.

7. The method of claim 1, wherein said finite number of lower-frequency components depleted in (ii) and generated in (iv) is four.

8. The method of claim 1, wherein said finite number of lower-frequency components depleted in (ii) and generated in (iv) is selected from the group of two, six, and eight.

9. The method of claim 1, wherein the desired voltage waveform comprises two substantially flat segments with equal voltage levels of opposite polarity.

10. The method of claim 9, wherein the desired voltage waveform is employed to implement ion mobility spectrometry with the alignment of dipole direction (IMS-ADD).

11. The method of claim 1, wherein said desired voltage waveform comprises two substantially flat segments with unequal voltage levels of opposite polarity.

12. The method of claim 11, wherein the desired voltage waveform is employed to implement differential ion mobility spectrometry or field asymmetric waveform ion mobility spectrometry (FAIMS) analyses.

13. The method of claim 1, wherein said desired voltage waveform comprises at least three substantially flat segments with unequal voltage levels.

14. The method of claim 13, wherein the desired voltage waveform is employed to implement higher-order differential ion mobility spectrometry (HODIMS) analyses.

15. The method of claim 1, wherein (v) is effected in at least two separate superposition sub-steps.

16. The method of claim 15, wherein the first sub-step is adding all said individual waveforms generated in (iv) and the second sub-step is superposing the result on the amplified depleted waveform formed in (iii).

17. The method of claim 1, wherein said desired voltage waveform of other than harmonic profile is an asymmetric high-voltage waveform with a near-rectangular profile, wherein: said initial voltage waveform in (i) is a rectangular waveform; said lower-frequency components are depleted by filtering the rectangular waveform to remove harmonics below a desired low-frequency cut-off to produce a filtered rectangular waveform that is said depleted waveform in (ii); said depleted waveform is amplified in (iii) by linearly amplifying the filtered rectangular waveform to produce an amplified rectangular waveform; and said superposing in (v) comprises summing the amplified rectangular waveform with the individual harmonic waveforms generated in (iv).

18. The method of claim 17, wherein the asymmetric high-voltage waveform is employed to implement ion mobility spectrometry with the alignment of dipole direction (IMS-ADD).

19. The method of claim 17, wherein the asymmetric high-voltage waveform is employed to implement differential ion mobility spectrometry or field asymmetric waveform ion mobility spectrometry (FAIMS) analyses.

20. The method of claim 17, wherein said lower-frequency components are filtered with a high-frequency pass filter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] FIG. 1a is a graph showing prior art exemplary dependences of ion mobility on the electric field intensity.

[0023] FIG. 1b depicts a prior art scheme of FAIMS device and ion trajectories within its analytical gap during separation.

[0024] FIG. 2 illustrates prior art ideal rectangular asymmetric waveforms for FAIMS and 1.sup.st-order HOD IMS separations.

[0025] FIG. 3 shows the expansion of rectangular FAIMS waveform with 2:1 aspect ratio into a Fourier series.

[0026] FIG. 4 illustrates the concept of present invention, where the four leading harmonics are generated explicitly and added to the rectangular waveforms treated using a high-pass filter and subsequently amplified.

DETAILED DESCRIPTION

[0027] While the present disclosure is exemplified by specific embodiments, the invention is not limited thereto and variations in form and detail may be made without departing from the spirit and scope of the invention. All such modifications as would be envisioned by those of skill in the art are hereby incorporated.

[0028] The production and use of non-harmonic waveforms generated according to the instant invention is illustrated below with respect to the separation and identification of ions by nonlinear IMS methods. In particular, differential ion mobility spectrometry exploits the dependence of mobility (K) on electric field intensity (E), elicited directly using an asymmetric rf waveform loaded on a pair of electrodes [FIG. 1a]. This includes the 1.sup.st-order differential IMS or field asymmetric waveform IMS (FAIMS) based on the difference between K at two E values, i.e., the average 1.sup.st derivative of K(E) function between those values. The invention also applies to higher-order differential (HOD) IMS methods based on the second and higher K(E) derivatives, determined by the coefficients b, c, etc. of eq (1) without the influence of coefficient a with the quadratic term.

[0029] Ions introduced into a gap of any shape between those electrodes are dispersed orthogonally to it and, on top of oscillations with the waveform period, experience net drift to one of the electrodes. This motion for a particular species is offset by equal and opposite drift caused by dc compensation voltage (CV) co-loaded with the waveform, while other species still impinge on the electrodes and are neutralized [FIG. 1b]. Scanning the CV allows different ions to pass the gap and be registered by a detector or further processed by another stage, revealing the spectrum of species present. Alternatively, a fixed CV allows pulling a given species out of a complex mixture for further processing.

[0030] The stage following differential IMS is commonly a mass spectrometer, but may be a differential IMS stage of other separation order or otherwise distinct selectivity, a linear IMS stage, a laser spectrometer such as a photoelectron or photodissociation spectrometer, or a combination of two or more of said stages. Said mass spectrometer may be of the ion trap, Orbitrap, Fourier transform ion cyclotron resonance (FTICR), transmission quadrupole, magnetic sector, or other type, or a combination thereof for tandem MS and MS' analyses, without limitation. Said linear IMS stage may be of the drift tube, traveling wave (TWIMS), funnel trap (TIMS), differential mobility analyzer (DMA), cyclotron IMS, or other type, or a combination thereof for tandem IMS and MS' analyses, without limitation.

[0031] Simulations and experiments have shown that the optimum waveforms for FAIMS and HODIMS of all orders are rectangular, consisting of level segments joined by vertical rises or falls. The number of needed segments equals the order of differential separation plus one, e.g., two for FAIMS, three for 1st-order HODIMS, and four for the 2.sup.nd-order HODIMS.

[0032] For FAIMS, the calculated ratio of voltages in opposite polarities (the aspect ratio, f) for maximum CV is exactly two if eq (1) is truncated at the a(E/N).sup.2 term (FIG. 2) and ranges from 1.24 to 2.6 if truncated at the b(E/N).sup.4 term, depending on the b/a ratio and maximum E/N (Shvartsburg. Differential Ion Mobility Spectrometry. Nonlinear Ion Transport and Fundamentals of FAIMS. CRC Press, Boca Raton, Fla., 2008). Consideration of the c(E/N).sup.6 and further terms of eq (1) may introduce further corrections to the optimum f value. While rigorously optimizing the profile requires a different f for each targeted ion pair, the outcome within 10% of optimum is achievable using just two profilesone (with higher f) for ions of types A and C where the mobility consistently increases or decreases with growing E/N and another (with lower f) for ions of type B where the mobility first increases to a certain maximum and then decreases.

[0033] The aspect ratio also affects the mean field heating and thus the high-field anisotropic diffusion of ions during the waveform cycle, which controls the peak width, w (customarily defined at the half maximum). Hence the FAIMS resolving power, which equals (CV)/w, depends on f through both CV and w and maximizes at a somewhat different f than the CV itself. The optimum f depends on the magnitude of E/N that sets the extent of field heating and, with eq (1) truncated at the quadratic term, varies from 2 to 4 in the low- and high-field limits, respectively. Combination of this diffusion factor with the contribution of 4.sup.th-power and higher terms of eq (1) may modify the optimum f still further.

[0034] The waveform profiles for HODIMS of all orders have thus far been optimized with the eq (1) limited to the appropriate leading term and without accounting for the diffusion factor. The result for 1.sup.st-order HODIMS comprises segments with the relative voltages of 1, 0.809, and 0.309 and durations of , , and of the period, respectively (FIG. 2). The 2.sup.nd-order HODIMS would utilize the voltages of 1; 0.223, 0.623, and 0.901 and durations of 1/7, 2/7, 2/7, and 2/7, respectively. The profiles for yet higher orders can be constructed following the systematic procedure laid out by Shvartsburg et al. (J. Phys. Chem. A 110, 2663, 2006). Consideration of the further terms in eq (1) and high-field diffusion would somewhat modify the above values.

[0035] The waveform profiles for IMS-ADD would be symmetric rectangular, with the maximum voltage allowed by electrical breakdown and electrical engineering limitations.

[0036] These profiles exemplify the options performing well in experiment or simulations in specific circumstances for common analyte classes, but do not limit the scope of invention. Other adjustments to the rectangular waveforms for FAIMS and HODIMS may be desired to reduce the amplitude of ion oscillations during the waveform cycle, to simplify the electrical engineering tasks, and for other practical reasons. The rise and fall times also cannot be null, but should best be within a few percent of the period. Such adjustments are fully envisioned in the art, and all profiles substantially rectangular in full or in part fall within the scope and are deemed rectangular for the purpose of this disclosure.

[0037] According to the invention, the rectangular waveform is blended up by an approach combining the elements of methods to generate harmonic and rectangular waveforms, while sidestepping their deficiencies. The desired profile is decomposed into a Fourier series using well-known mathematical formalisms such as the fast Fourier transform (FFT) and associated software (FIG. 3). A pre-determined finite number n (for example, without limitation, a number of 1-200) of leading harmonics of lowest frequency and highest amplitude is produced directly with requisite phases, employing means known in the art (such as resonating circuits that are tunable within certain ranges) to deliver the sinusoidal waveforms of targeted frequency and amplitude (FIG. 4). Separately, a rectangular waveform of much lower amplitude is produced by key switching (logic levels) and filtered through a high-pass frequency filter to eliminate the low-frequency harmonics up to and including the frequency of the n-th harmonic. The output is amplified to the desired level (for example, using a linear broadband amplifier) and then summed with the individually generated harmonics (FIG. 4).

[0038] The choice of n is governed by the balance between simplicity of electronic implementation (favoring lower n) and advantage of the present hybrid approach (favoring higher n). Of particular interest with respect to FAIMS is n=4, where all higher harmonics encompassed within the rectangular profile have an amplitude under 14% of the dispersion voltage: e.g., just 770 V for the final waveform with DV=5.5 kVthe maximum reported in the art (Shvartsburg et al., Anal. Chem. 82, 7649, 2010). The corresponding fraction would increase to 24% with the minimum n=2 and decrease to 9% with the next n=6. While these embodiments are described by way of example, the invention is not limited to any particular n and another number may be preferred depending on the order of differential IMS separation, aspect ratio of desired rectangular waveform, performance requirements, constraints of generator size, weight, and electrical power, and the availability and cost of hardware options.

[0039] Whereas the utility of present invention is illustrated by application to nonlinear IMS, high-voltage rectangular waveforms are desired in other mass spectrometric and analytical systems and broader electrical engineering contexts. This invention is expressly not limited to its use in a specific analytical device, but extends its scope to all systems employing the presently disclosed hybrid approach to rectangular waveform synthesis.

[0040] Further, while the enablement and benefits of present invention are illustrated for rectangular waveforms, the presently disclosed hybrid synthesis method equally applies to other non-harmonic profiles (such as triangular and trapezoidal) that may be desired in other applications. The extension of essentially the same method to other profiles is within the scope of this invention.