W-Band Frequency-Swept EPR（四）
3. Discussion
3.1. Frequency-sweep rate
Prospects for enhancement of peak frequency deviation and frequency sweep rates in a YTO are primarily limited by the FM coil circuit inductance (turns, current, and magnetic field strength tradeoffs). Coils could be redesigned to increase frequency deviation, but then the frequency sweep rate would decrease. The coil driver-circuit bandwidth could be increased, but then the phase-noise performance degrades. One possible approach is to use multiple YTOs with each FM coil designed to reach just the desired peak frequency deviation in order to preserve frequency sweep rate. Likewise, the coil driver circuit could be designed to the peak deviation and frequency sweep rate. In short, engineering tradeoffs within YTO custom designs are possible, but a fundamental increase in high-speed frequency agility performance is not anticipated.
Other frequency-agile microwave sources exist. The varactor-tuned oscillator, for example, utilizes a variable capacitance diode to change the resonant frequency of the oscillator. The frequency-tuning characteristic is highly nonlinear and would necessitate frequency-correction measures (linearizer circuit) to achieve linear frequency sweeps. We utilized a varactor-tuned oscillator in W-band FM and SR EPR experiments [3,6]. The varactor can be modulated at a high rate, often 100 MHz. However, it suffers from frequency-tuning nonlinearity.
The V-band source reported here is superior to a varactor-tuned oscillator in this application. The YTO frequency-tuning characteristic is far more linear than that of the varactor-tuned oscillator. The Q of a varactor-tuned oscillator must be low (on the order of tens) if the varactor diode is to change the oscillator frequency significantly. This low Q degrades phase-noise performance of the oscillator. On the other hand, in the frequency-translation approach in Fig. 2, the frequency agility is now performed by the lower frequency YTO. The 51 GHz Gunn diode oscillator used to translate the 8 GHz (nominal) YTO is a fixed frequency source, with a much lower phase noise relative to a varactor-tuned Gunn diode oscillator. A key feature of the YTO is that the Q of its oscillator circuit is fairly independent of the microwave frequency. The combination of low phase-noise performance of modern YTOs and the low phase noise of the fixed-frequency Gunn diode oscillator results in a low phase-noise frequency-agile V-band source.
Recent advances in digitally based synthesized sources are promising. Arbitrary waveform generators (AWGs) numerically store a programmed waveform in memory and play it back through a D/A converter, often in a continuous loop. The AWG is especially useful for generating rapid frequency sweeps. Commercially available AWGs have reached 500 MHz with a linear frequency tuning speed of 3 MHz/ns. Software can be utilized to account for system nonlinearities through waveform predistortion.
AWGs currently have high performance and have bright prospects for higher performance as digital circuit technology continues to evolve. Higher frequency units with lower spurious content (via software correction) are expected. Software support and user interfaces continue to improve and become commercially available. AWGs clearly have a higher frequency accuracy relative to YTOs.
3.2. Slow wide-range frequency sweep
It is apparent that relatively slow sweep of the microwave frequency across the full nitroxide spectrum coupled with magnetic field offsets that are large enough to achieve baseline stability by subtraction is within reach. The pure absorption spectrum can be obtained with good sensitivity, which is a long sought goal. The YIG-based, frequency-sweep technology used in this paper appears adequate. It is possible that the same goal could be reached by combining a slow sweep of the magnetic field, coupled, as with frequency sweep, with sufficiently large magnetic field offsets to achieve baseline stability by subtraction. It is felt that it would be useful to explore this alternative technology, although homogeneity of the swept magnetic field over the sample, as well as induced eddy current and the accompanying Lorentz forces, may present difficult problems.
We have found that a combination of magnetic field and microwave frequency variation is necessary to achieve flat baselines in frequency-agile experiments. In the work presented here, variation of the resonator microwave reflection coefficient with frequency was a dominant problem, even though the bandwidth of the resonator was very high. It was found necessary to step the magnetic field off-resonance in order to measure the variation of the resonator reflection coefficient with microwave frequency, which then was subtracted from the on-resonance data. Other combinations of magnetic field and microwave frequency variation include sweep of the magnetic field while using sinusoidal frequency modulation [3] and sweep of the microwave frequency while using magnetic field modulation. Since the W-band LGR used here is made from solid silver with no modulation slots, we are limited to rather slow rates of magnetic field variation in order to minimize induced eddy currents and associated Lorentz forces.
3.3. Baseline correction
Baseline issues are significant because the reflected power from the resonator is larger with frequency sweeps than it is in a conventional EPR experiment where the frequency is set at the lowest reflection coefficient point of the sample resonator. Techniques employed for baseline improvement were described in section 2.2. A potential improvement in this technique would be to smooth the off-EPR line data set before subtracting it from the on-line data set. The off-line data sets typically showed no high frequency content other than noise; hence, smoothing reduces the high frequency noise that would otherwise be superimposed onto the on-line data and consequently improves the EPR signal quality.
Another potential improvement would be to implement a larger field modulation increment. The 20 G increment utilized with the modulation coils in these experiments was insufficient to shift off of the EPR line completely. The 50 G increment with the sweep coils of the magnet was utilized in some of the experiments as an additional technique to improve the baseline. We speculate that a larger field modulation increment may render the additional field shift with the magnet sweep coils unnecessary. Removal of the second off-line data collection would allow a larger fraction of on-line data collection time or reduced total collection time. More rapid on/off cycling may also improve the baseline. Another approach is to apply linear or quadratic detrending on the swept frequency spectra. These aspects require further investigation.
Automatic frequency control (AFC) was not utilized in the experiments reported here. If the time constant of the AFC system were set to be much longer than the frequency-sweep waveform period, the AFC would be expected to improve long-term stability. It is expected that the AFC loop gain would be reduced because of the large frequency deviation due to the frequency sweeps.
We have observed that the sample resonator match changes as the experiment progresses, probably due to small temperature changes. Remote automatic matching of the sample resonator would improve long-term baseline stability and allow longer averaging periods.
Balanced path lengths within the bridge in frequency-swept experiments are essential to preserving the phase setting of the bridge for absorption or dispersion. Otherwise, the relative phase of the EPR signal and the reference signal would change as a function of frequency within the frequency sweep, which would generate a changing absorption/dispersion admixture during the sweep.
3.4. High df/dt FT EPR spectroscopy, where f is the microwave frequency
Experiments described here at the highest microwave frequency-sweep rates where FID signals are observed are new in the context of EPR spectroscopy, but have been done before in NMR [4]. Twenty-fold higher sweep rates are available using AWG technology than can be achieved using YIG technology.
The magnetization tip angle, ϕ, in radians, can be estimated by defining an equivalent pulse duration, τ:
ϕ = γH1τ,
(2)
(3)
Here, H1 in the numerator is derived from the half-width of the Rabi transition probability [12,13], which contains, in the denominator a term of the form [(γH1)2 + (Δω)2], where Δω is the difference between the EPR line center and the irradiating frequency. We have:
(4)
Assuming that 1 W is available, that the resonator efficiency parameter, Λ, for the W-band LGR is 10 GW−1/2 as given by Sidabras et al. [1], and that the sweep rate is 3 MHz/ns,
ϕ = 1.6 radians,
(5)
which is close to a π/2 equivalent pulse. It seems within reach to tip the magnetizations of the entire spectrum of a nitroxide radical spin label in less than a tenth of a microsecond using less than a watt of microwave power. Measurements in the motionally narrowed regime as well as the very slow rotational diffusion regime will be possible. At intermediate rotational correlation times, “selection” of subsets of molecules at spectral locations where spectral diffusion is slow may be possible. Because FID rates are determined by the phase-memory time, separation of spectral components with differing phase-memory times may become a principal application of the methodology introduced here. As in NMR correlation spectroscopy, one could also apply the methodology to restricted spectral regions.
A distinguishing characteristic of the work described here is the use of a trapezoidal RF sweep waveform as shown in Fig. 1b. It consists of two characteristic time periods: the sweep period of 250 ns duration and the readout period of 1000 duration. The 44 Hz ramp was centered on the EPR transition of interest, and, thus, a free precession rate of 22 MHz is observed during the readout time (i.e., a period of 45 ns). This is the rate of precession in a rotating frame defined by the readout frequency, which is the W-band microwave frequency during readout. This frequency is translated first to a fixed frequency at Q-band and then to a fixed frequency at L-band, where detection to baseband occurs and 22 MHz oscillations are seen (Fig. 7). In the work of Refs. [4,5] the frequency or field continued to be swept during readout, and solutions of Bloch equations in this more complicated environment were required. The use of a trapezoidal RF sweep waveform with a readout time is analogous to FT NMR where a reference frequency incident on the detector establishes a rotating frame in which FID is observed. If the sweep is across multiple lines, FIDs are superimposed in both FT NMR and, in future work using an AWG, our experiment. Interpretation would be by FT in both cases, yielding frequencies that determine spectral positions of each line. The envelope would determine lineshapes.
In the experiment of Fig. 7, 125 ns was required to sweep from the irradiated line spectral frequency to the readout frequency, and during this time, the free precession rate increased from 0 to 22 MHz. The waveform during this period could, in principle, be modeled following the methodology of Refs. [4,5]. In this scenario, there would be no experimental dead time.
Introduction of trapezoidal frequency sweep with separate ramp and readout times appears to provide for EPR spectroscopy many of the benefits that pulse FT methodology provided for NMR spectroscopy. It also overcomes the enormous technical difficulties in formation of a microwave pulse that is sufficiently intense that the entire EPR spectrum is uniformly irradiated.
Acknowledgments
This work was supported by grants EB002052, EB001980, and EB001417 from the National Institutes of Health.
Footnotes
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References
1. Sidabras JW, Mett RR, Froncisz W, Camenisch TG, Anderson JR, Hyde JS. Multipurpose EPR loop-gap resonator and cylindrical TE011 cavity for aqueous samples at 94 GHz. Rev Sci Instrum. 2007;78:034701.[PubMed]
2. Weger M. Passage effects in paramagnetic resonance experiments. Bell System Tech J. 1960;39:1013–1112.
3. Hyde JS, Froncisz W, Sidabras JW, Camenisch TG, Anderson JR, Strangeway RA. Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator. J Magn Reson. 2007;185:259–263. [PubMed]
4. Dadok J, Sprecher RF. Correlation NMR spectroscopy. J Magn Reson. 1974;13:243–248.
5. Stoner JW, Szymanski D, Eaton SS, Quine RW, Rinard GA, Eaton GR. Direct-detected rapid-scan EPR at 250 MHz. J Magn Reson. 2004;170:127–135. [PubMed]
6. Froncisz W, Camenisch TG, Ratke JJ, Anderson JR, Subczynski WK, Strangeway RA, Sidabras JW, Hyde JS. Saturation recovery EPR and ELDOR at W-band for spin labels. J Magn Reson. 2008;193:297–304. [PMC free article] [PubMed]
7. Camenisch TG, Ratke JJ, Strangeway RA, Hyde JS. A versatile Q-band electron paramagnetic resonance spectrometer. IEEE (Electro/Information Technology Conference, 2004, EIT 2004); 2008. pp. 66–81.
8. Strangeway RA, Ishii TK, Hyde JS. Design and fabrication of a 35 GHz, 100 mW low phase noise Gunn diode oscillator. Microwave J. 1988:107–111.
9. Strangeway RA, Ishii TK, Hyde JS. Low-phase-noise Gunn diode oscillator design. IEEE Trans Microwave Theory Tech. 1988;36:792–794.
10. Bahl I, Bhartia P. Microwave Solid State Circuit Design. John Wiley & Songs; New York: 1988.
11. Hyde JS, Subczynski WK. Simulation of ESR spectra of the oxygen-sensitive spin-label probe CTPO. J Magn Reson. 1984;56:125–130.
12. Rabi II. Space quantization in a gyrating magnetic field. Phys Rev. 1937;51:652–654.
13. Hyde JS. Saturation of the magnetic resonance absorption in dilute inhomogeneously broadened systems. Phys Rev. 1960;119:1492–1495.
