US 20010015644 A1 Abstract A method of operating a high-resolution NMR spectrometer comprising a DDS generator containing an NCO
_{L }for generating an LO frequency, wherein the frequency of the NCO_{L }is defined by inputting a numerical value Z, is characterized in that this numerical value Z may assume only values which satisfy the equation Z=n·N/m, wherein Z, n, N, and m are integer and positive numbers, N is a power of 2 with a positive integer exponent, wherein said exponent represents the maximum number of bits during the calculation process, m is approximately 2·f_{s}/ΔB, n approximately m·f_{out}/f_{s }and m additionally a common integer divisor of n·N and f_{s }is the clock frequency of the NCO_{L}, ΔB is the desired bandwidth with high spectral purity and f_{out }is the output frequency of the NCO_{L}. This method allows the use of a DDS generator even in the case where very high spectral purity is required, wherein in particular quantization noise is largely eliminated over the frequency range relevant for NMR measurements. Claims(14) 1. A method of operating an NMR (nuclear magnetic resonance) spectrometer to obtain a bandwidth ΔB of high spectral purity, the method comprising the steps of:
a) implementing a DDS (direct digital synthesis) generator;
b) incorporating an NCO (numerical controlled oscillator) within said DDS for generating an LO (local oscillation) frequency, said NCO having a clock frequency f
_{s }a numerical input Z, and an output frequency f_{out}; and c) selecting said input Z to satisfy the relationship Z=n·N/m, wherein Z, n, N, and m are positive integers, N being a power of 2 with a positive integer exponent, said exponent representing a maximum number of bits during a calculation process, wherein m is approximately 2·fs/ΔB, n approximately m·f
_{out}/f_{s }and m is a common integer divisor of n·N. 2. The method of claim 1 3. The method of claim 1 _{LO1}. 4. The method of claim 1 5. The method of claim 4 C1) the determining m by means of the equation m=2 ^{RndDwn{log[2fs/ΔB) /log 2]} } wherein RndDwn is a rounding-off process to a next smaller integer value; C2) calculating n following step C1), using the equation n=Rnd(m·f _{out}/f_{s})wherein Rnd is a rounding process to a next integer value; and C3) specifying Z=n·N/m following steps C1) and C2) 6. A DDS (=Direct Digital Synthesis) generator for NMR spectrometers, comprising:
a first NCO (=Numerical Controlled Oscillator) for generating an LO (=Local Oscillator) frequency f _{LO1}; and a least one second NCO, for generating a transmitting frequency. 7. The DDS generator of claim 6 8. The DDS generator of claim 6 _{s }which satisfies the condition f_{s}=2^{k}·f_{0}, wherein k is a positive integer and f_{0 }is a base frequency from which all LO frequencies are derived as integer multiples of f_{0 }with the exception of a frequency F_{LO1 }for a mixing stage and a frequency f_{dqd }for a DQD (=digital quadrature detector). 9. The DDS generator of claim 6 10. The DDS of claim 6 11. The DDS of claim 6 12. The DDS generator of claim 6 13. A method of operating the DDS generator of claim 8 _{Q }in a DQD. 14. A method of operating the DDS generator of claim 6 claim 5 Description [0001] This application claims Paris Convention priority of DE 100 07 679.3 filed Feb. 19, 2000 the complete disclosure of which is hereby incorporated by reference. [0002] The invention concerns a method of operating an NMR (=nuclear magnetic resonance) spectrometer, in particular a high-resolution NMR spectrometer, comprising a DDS (=direct digital synthesis) generator which contains an NCO [0003] An NMR spectrometer comprising such a DDS is disclosed in the company leaflet “AVANCE/Digital NMR” of Bruker AG, Fällanden, Switzerland, dated March 1999, wherein in particular page 11 shows a functional unit “DDS” performing as “frequency and phase control” in the CPU. [0004] Frequency generators which operate with direct digital frequency synthesis, so-called DDS generators (DDS=Direct Digital Synthesis) are described e.g. in “Frequency Synthesizers Design Handbook”, J. A. Crawford, Artech House, Boston, London, 1994, page 346 or in “Digital PLL Frequency Synthesizers. Theory and Design”, U. L. Rohde, Prentice-Hall Inc., Englewood Cliffs, N.J. 1983, page 110. [0005] The DDS generators have the following positive characteristics: [0006] They generate numerical values with a clock rate given by an externally supplied constant clock frequency f [0007] The DDS generators essentially require only digital IC components which keeps their manufacturing costs low. A very advantageous solution consists in that the entire DDS generator is integrated in one single ASIC component (ASIC= Application Specific Integrated Circuit) which can considerably reduce costs when a large number are produced and allows particularly dense packing of the functional digital elements. The latter is particularly advantageous in fast electronic processes which are increasingly required today. [0008] These positive aspects of a DDS generator, however, face the serious drawback that the spectral purity of the output signal is no longer sufficient for today's standards. DDS generators have been successfully used for more than 10 years in NMR (=nuclear magnetic resonance) spectrometers. The demand for spectral purity of the LO signals has increased in such a way that these generators can no longer provide the high performance needed during the receiving phase of the NMR signal. [0009] The insufficient spectral purity of the DDS generator is caused by the so-called quantizising noise which is due to the fact that the signal generated in the DDS generator is quantizised, i.e. represents a stepped approximation to the desired signal, wherein the numerical values of these steps are defined only with a finite accuracy given by the maximum number of available bits. [0010] The quantizising noise decreases the larger the number of steps within one period and the higher the accuracy of the numerical values of said steps. The number of steps cannot be increased arbitrarily. There is a limit given by the maximum clock rate of the digital components. [0011] NMR signals in high-resolution NMR often consist of very strong and at the same time very weak frequency components, wherein the weak components are frequently the significant ones. This means that the NMR signal has a large dynamic range. One of the most sensitive mixing stages in the NMR receiver is the first mixing stage which uses an LO signal (f [0012] During the relatively uncritical transmitting phase in NMR spectroscopy, DDS generators are still used today without any problems. [0013] However, during the critical receiving phase, the demand for spectral purity is very high today such that the DDS generator which provides the variable LO frequency does no longer meet these demands due to the quantization noise described above. Up to now, no practicable method has been available to reduce said quantization noise. Therefore, in all critical experiments which required high spectral purity, one had only the choice to do without this elegant and powerful generator or accept its disadvantages. [0014] It is therefore the underlying purpose of the present invention to present a method comprising the initially mentioned features utilizing a DDS generator even when very high spectral purity is required, wherein particularly the quantization noise is eliminated as much as possible in the frequency range of the NMR spectrum. [0015] In accordance with the invention, this object is achieved in a simple and effective way in that the numerical value Z is selected such that it assumes only values which satisty the equation
[0016] wherein Z, n, N, and m are positive integers, wherein N is a power of 2 with a positive integer exponent, said exponent representing the maximum number of bits during the calculation process, wherein m is approximately 2·f [0017] According to the inventive teaching, it is not allowed to use arbitrary but only selected Z values for the input to the DDS generator. As a result, the lowest occurring disturbing frequency will always be larger than the repetition frequency Δf [0018] In a variant of the inventive method which is particularly easy to carry out and is thus used with particular preference, m is a power of 2 having a positive integer exponent. This considerably simplifies the calculations to be carried out in the inventive method with respect to the general case and as a result the amount of calculations needed is reduced considerably. [0019] The method is particularly facilitated in a further development of the above-mentioned variant, wherein the calculation of Z is carried out in the following three stages. [0020] (a) the value for m is determined by means of the equation m=2 [0021] wherein ΔB is the desired bandwidth of high spectral purity, f [0022] (b) the value for n is determined through equation n=Rnd(m·f [0023] wherein f [0024] (c) the value for Z is determined through equation
[0025] wherein N is defined in claim [0026] The present invention also includes a DDS (=Direct Digital Synthesis) generator for application in NMR spectrometers, in particular high-resolution NMR spectrometers comprising an NCO [0027] A preferred embodiment of the inventive DDS generator is characterized in that the NCO [0028] One further development of the invention is particularly preferred wherein one of the NCOs oscillates continuously and can provide a reference phase for all other NCOs by transferring its actual phase to the other NCOs via switches thereby achieving an exact definition of the initial phase of the FID signal and allowing phase synchronism for several successive FID signals. [0029] A further particularly preferred embodiment of the inventive DDS generator is characterized in that a saw tooth to sinusoidal signal transformer is provided for transforming the saw tooth signal of an NCO into a sinusoidal signal and in that a further saw tooth to cosine signal transformer is provided for transforming the saw tooth signal of this NCO into a cosine signal thereby producing two channels which are in quadrature with one another and can be used in a subsequent frequency synthesizer for a quadrature mixing stage. A quadrature mixing stage produces considerably less undesired mixing components compared to a normal mixing stage. [0030] One embodiment is also preferred which preferably comprises digital multiplicators which are fed with signals from signal transformers and where the desired amplitude dependence is achieved by a numerical calculation process during the transmitting phase. In this way, a digital amplitude modulator can be produced with simple means which has a much higher precision than an analog modulator. [0031] One further embodiment of the inventive DDS generator is also preferred which comprises an attenuator whose phase and attenuation errors can be compensated in that the phase errors are stored as a function of the desired attenuation value in a first memory and that the attenuation errors are stored as a function of the desired attenuation value in a further memory and in that during setting of a desired attenuation value, the associated phase error is added with reverse signs to the current signal in one adding stage, and the corresponding attenuation error with reverse signs is added to the desired attenuation value and supplied to the attenuator. Registration of the attenuation errors can thus allow mathematical pre-compensation of the signals thereby obtaining the desired attenuation values practically without phase and attenuation errors. [0032] One method is also advantageous for operating an inventive DDS generator with DQD which is characterized in that during the receiving phase, exact positioning of the NMR spectrum in the low frequency range is not effected via NCO [0033] Further advantages of the invention can be extracted from the description and the drawing. The features mentioned above and below can be utilized in accordance with the invention either individually or collectively in any arbitrary combination. The embodiments shown and described are not to be understood as exhaustive enumeration but rather have exemplary character for describing the invention. [0034] The invention is shown in the drawing and further explained by means of embodiments. [0035]FIG. 1 [0036]FIG. 1 [0037]FIG. 2 shows the schematic construction of a modern NMR spectrometer according to prior art; [0038]FIG. 3 shows an operational diagram of the main transmitting unit T [0039]FIG. 4 shows a schematic design of a main transmitting unit in accordance with the invention; [0040]FIG. 5 [0041]FIG. 5 [0042]FIG. 6 [0043]FIG. 6 [0044]FIG. 7 [0045]FIG. 7 [0046]FIG. 7 [0047]FIG. 2 shows the block diagram of a modern NMR spectrometer. The individual parts are explained below: [0048] [0049] [0050] [0051] [0052] [0053] [0054] [0055] [0056] [0057] [0058] [0059] [0060] [0061] [0062] [0063]FIG. 3 shows a known circuit of the main transmitting unit T [0064] The individual parts of the main transmitting unit T [0065] [0066] [0067] [0068] [0069] [0070] [0071] [0072] [0073] [0074] [0075] [0076] [0077] [0078] Determination of the numerical value Z at the entry of the NCO in accordance with the invention is described below: [0079] Considering the fact that an NMR spectrum requires only a very limited frequency range, with protons e.g. only approx. 50 to 100 ppm of the mean NMR frequency, it is possible to operate the DDS generator such that its spectrum is very pure in the desired frequency range and outside of this range may generate disturbing components. Under this condition, it is actually possible to use DDS generators which meet the high demands on stability and purity in high-resolution NMR spectroscopy. [0080] The inventive idea combines two findings. Firstly, the DDS generator must have a pure spectrum only within a limited frequency range and secondly, there are possibilities to operate the DDS generator such that its spectrum is very pure within this limited frequency range. [0081] The DDS generator operated in this fashion, provides in addition to the desired frequency, a grid of additional, however much smaller frequency components which appear at identical intervals. The interval is selected such that it can accommodate half the NMR spectrum (halving since quadrature detection is assumed). The desired frequency is then identical to one of the components of the grid and can be shifted in discrete steps from one component of the grid to the next. [0082] How has the DDS generator to be operated in order to show such behavior ? To answer this question, the NCO (=Numeric Controlled Oscillator) in the DDS generator has to be examined more closely in order to explain how the grid components are generated. FIG. 1 [0083] In FIG. 1 [0084] The disturbing components represent a frequency grid having a grid separation of Δf [0085] The output frequency f [0086] The individual terms mentioned in FIGS. 1 [0087] f [0088] f [0089] Δf [0090] ΔB see FIG. 1 [0091] n number of periods of f [0092] m number of periods of f [0093] Z positive integer value which is stored in the input register of the NCO, is integrated therein by the NCO and produces a saw-tooth shaped signal at its output [0094] N numerical value determined by the maximum number of bits used in the NCO. If same is e.g. 34 bit, then N=2 [0095] Moreover, two further terms N [0096] N1=maximum number of bits used in the NCO calculations. This value defines the numerical value N=2 [0097] M1 =positive integer exponent of 2 for the definition of the number m=2 [0098] Four conditions can be derived from FIG. 1 [0099] Condition [0100] Condition [0101] Condition [0102] Condition [0103] The first condition can be derived by means of the function F(t) in FIG. 1 [0104] Since Z must be an integer (see condition [0105] wherein: [0106] n, N and m are integer and positive values [0107] N>m>n [0108] N=power of 2 [0109] m=common divisor of n·N [0110] If m is selected as power of 2 with an positive integer exponent m [0111] N=2 [0112] M=2 [0113] Z=n·N/m=n·2 [0114] Since N>m and thus N1>m1, the above value for Z is always an integer. As a result, the following conditions must be valid: [0115] wherein [0116] n, N and m are integer and positive values [0117] N>m>n [0118] N and m are powers of 2 [0119] To obtain the desired values for the frequency f Δf [0120] entered into condition 2/ΔB=m/f m=2fs/ΔB=2 m1=log(2fs/ΔB)/log 2 [0121] Since m1 should be an integer, the above term must be rounded, and if the resulting bandwidth should not be smaller than the given bandwidth ΔB rounding off to the next lower value is required (=RndDwn): m1=RndDwn{log(2fs/ΔB)/log 2} m=2 [0122] From conditions m/f 2/ΔB=n/f n=m·f [0123] Since n must also be an integer (condition n=Rnd(m·f [0124] Calculation of Z is thus possible in three stages: [0125] Stage 1: m=2 [0126] Stage 2: n'Rnd(m·f [0127] Stage 3: Z=n·N/m [4] [0128] wherein: [0129] RndDwn=round off to the next lower integer number [0130] Rnd=round off or up to the nearest integer number [0131] Given: [0132] N=2 (34 bit calculation accuracy) [0133] f [0134] Desired: [0135] ΔB=9 kHz [0136] f [0137] Calculation result: [0138] m=2 [0139] n=3,347 [0140] Z=3,347·2 [0141] Since rounding off was necessary, the predetermined values for f [0142] fout=n·f [0143] ΔB=2·fs/m=2·80,000/16,384=9.765625 kHz [0144] The output frequency is larger by 1.77 kHz and the bandwidth ΔB is larger by 0.765625 kHz than required. The desired values are thus not met exactly but a frequency band of ΔB is given which allows clear NMR spectroscopy. Exact adjustment of the output frequency is nevertheless required and has to be achieved by other means as will be described later on. [0145] The differences between the transmitting phase and the receiving phase are as follows. [0146] Since the excitation of the NMR signal does not demand high spectral purity of the excitation signal, all DDS generators which generate the required transmitting frequencies, can be designed according to current prior art. Such DDS generators allow easy and fine adjustment of the frequency and thus the positioning of the transmitting frequency in the center of the NMR spectrum. [0147] The case is completely different during the receiving phase. The DDS generator is used for generating the LO frequency f [0148] Fine adjustment of the frequency during the receiving phase is nevertheless possible as described below, in particular how the NMR spectrum is positioned exactly in the desired low frequency range: [0149] Basically it is possible to use each of the LO frequencies for positioning the NMR spectrum exactly in the desired low frequency range. It is not absolutely necessary to use the LO frequency f [0150] The DQD belongs to prior art and is essentially a digital quadrature mixing stage which mixes the NMR spectrum mathematically down such that its center is positioned at the frequency zero. [0151] Finally it is important to note that the quadrature mixing stage [0152] The positioning of the NMR spectrum about the frequency zero is carried out at three different positions by means of rough, fine and finest steps as described below: [0153] 1. The largest frequency steps of fo (e.g. 5 MHz) are generated by the numerical value Z [0154] 2. The NCO [0155] 3. The DQD [0156] The conditions for the LO frequencies for preventing any additional disturbing components are further explained below: [0157] Even if the first LO frequency f [0158] The LO frequencies in the frequency synthesizer [0159] Δf [0160] f [0161] It can be shown that the above condition is automatically met if the clock frequency f f _{0 } 5a
[0162] ====== [0163] This can be easily shown: f f [0164] As long as Δf [0165] In summary, the following conditions must be met to ensure that f [0166] wherein: [0167] k=positive and integer value [0168] Δf [0169] The generation of the quantizing grid at the output of the DDS generator is explained below: [0170] The output signal of the NCO Z Z [0171] These two sinusoidal signals Z [0172] Generation of a completely pure signal is easy to understand taking into consideration that the numerical values of the stepped phase curve (2π/N)·F(t) would be on an exact straight line. The gradient dφ/dt of this straight line would give exactly the desired angular frequency 2π·f [0173] Since the calculation process has a finite accuracy, the values of the steps are rounded off or up values and are not precisely on the exact straight phase curve. Deviations from the exact phase curve are called quantization noise which has nothing to do with noise in the common sense since the phase error repeats itself after each period [0174] The sinusoidal signals therefore also produce a frequency grid just like the saw-tooth shaped signal only with much smaller amplitude values. Therefore, all previous calculations made on the basis of the saw-tooth function are also qualitatively valid for the sinusoidal signal. [0175] As mentioned before, an accuracy of 34 bits would be sufficient to keep the grid components negligibly small. This would lead to a practically ideal DDS generator which would supply a frequency with a pure spectrum which could furthermore be finely adjusted. The above described theory for calculating discrete Z values for VCO would therefore no longer be required any more. [0176] An accuracy of 34 bits however cannot be realized for dynamic reasons. The two sinusoidal functions cannot be calculated directly during the runtime since the digital components today are too slow. The sinusoidal function must therefore be available through discrete numerical values stored in a table and all intermediate values must be calculated through linear interpolation during the runtime. The latter is possible from the dynamic point of view since the linear interpolation is a much more simple calculation process in contrast to the calculation of the sinus function. [0177] Unfortunately, the number of required values of the sinusoidal function increases with increasing calculation accuracy such that with an accuracy of 34 bits, the number of these values would result in an in admissibly large memory requirement for today's standards. The accuracy of the sine calculation has to be reduced to 16 bits for this reason by using only the upper 16 bits of the 34 bit values from the VCO. This reduced accuracy is then no longer sufficient to prevent the quantization effects. [0178] The generation of the transmitting frequency and the first LO frequency by means of NCOs is explained below. [0179] The inventive DDS generator [0180] There are special NMR experiments wherein during the transmitting phase, the frequency has to be switched from one value f [0181] If two NCOs are used for the above-described experiment, namely NCO [0182] The LO frequency f [0183] The entire spectrometer can be again represented by the block diagram in FIG. 2. This is true for prior art and also for the inventive circuit. The individual components have already been described in connection with prior art. [0184] The main transmitting unit T [0185] [0186] [0187] [0188] [0189] [0190] [0191] [0192] [0193] [0194] [0195] [0196] [0197] [0198] [0199] [0200] [0201] [0202] [0203] [0204] [0205] [0206] [0207] [0208] Referenced by
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