Digitally generated excitation and near-baseband quadrature detection of rapid scan EPR signals

Abstract

The use of multiple synchronized outputs from an arbitrary waveform generator (AWG) provides the opportunity to perform EPR experiments differently than by conventional EPR. We report a method for reconstructing the quadrature EPR spectrum from periodic signals that are generated with sinusoidal magnetic field modulation such as continuous wave (CW), multiharmonic, or rapid scan experiments. The signal is down-converted to an intermediate frequency (IF) that is less than the field scan or field modulation frequency and then digitized in a single channel. This method permits use of a high-pass analog filter before digitization to remove the strong non-EPR signal at the IF, that might otherwise overwhelm the digitizer. The IF is the difference between two synchronized X-band outputs from a Tektronix AWG 70002A, one of which is for excitation and the other is the reference for down-conversion. To permit signal averaging, timing was selected to give an exact integer number of full cycles for each frequency. In the experiments reported here the IF was 5kHz and the scan frequency was 40kHz. To produce sinusoidal rapid scans with a scan frequency eight times IF, a third synchronized output generated a square wave that was converted to a sine wave. The timing of the data acquisition with a Bruker SpecJet II was synchronized by an external clock signal from the AWG. The baseband quadrature signal in the frequency domain was reconstructed. This approach has the advantages that (i) the non-EPR response at the carrier frequency is eliminated, (ii) both real and imaginary EPR signals are reconstructed from a single physical channel to produce an ideal quadrature signal, and (iii) signal bandwidth does not increase relative to baseband detection. Spectra were obtained by deconvolution of the reconstructed signals for solid BDPA (1,3-bisdiphenylene-2-phenylallyl) in air, 0.2mM trityl OX63 in water, ¹⁵N perdeuterated tempone, and a nitroxide with a 0.5G partially-resolved proton hyperfine splitting.

Keywords: Arbitrary wave form generator; Digital EPR; Rapid scan EPR.

Figure 1

Graphical description of the algorithm for f_IF = 5 kHz and K = 8 (Eq. 13), showing only the first two harmonics. (a) Fourier transform of the IF signal (Eq. 15). The Fourier coefficients for negative and positive frequencies are interdependent, so that only positive frequencies are used. Red and blue colored bars represent S_nK+1 and S_nK−1 coefficients in Eq. (17). The black dashed line denotes the position of the strong 5 kHz signal that was filtered out. (b) The complex conjugates of S_nK−1 coefficients are taken and mirror-inverted into the negative half of the frequency domain. (c) All coefficients are shifted in the negative direction by 5 kHz. The result is the Fourier transform of the complex quadrature signal c(t) (Eq. 9).

Figure 2

Block diagram for digital EPR spectrometer. KH refers to a Krohn-Hite 3955 LP Butterworth dual-channel filter. 1) microwave power amplifier: Mini circuits ZX60-14012L-S+; 2) microwave power amplifier: Aydin AWA 8596B; 3) microwave power amplifier: MITEQ AMF 4s 9092-20; 4) low noise amplifier: HD27028, noise figure =1.8dB; 5) amplification in KH filter; 6) low pass filter with a cutoff frequency of 29 kHz; 7) low pass filter with a cutoff of 5 MHz ; 8) 4 pole high pass Butterworth filter (-3dB) at 25 kHz. This proof-of-principle experiment was conducted with available components. The design has not been optimized.

Figure 3

Timing details for AWG outputs. The synchronization of the five outputs from the AWG is sketched for a sampling frequency of 24.135575 Gs/s. The timing is selected to have an integer number of cycles for each output. The lengths of the outputs from channels 1 and 2 differ by 1 cycle, which corresponds to the IF. The output from marker 1 is sent through a low-pass filter with a cutoff of 29 kHz frequency to convert the square wave into a sine wave that generates the sinusoidal rapid scan. The scan frequency is exactly 8 times IF. Marker 2 synchronizes the SpecJet II digitization, and Marker 3 triggers the oscilloscope. The clock output provides the external clock signal for the Specjet II. For the examples shown in this paper, the IF was about 5 kHz. The exact value of IF changes with resonator tuning because that changes the excitation frequency.

Figure 4

Schematic sequence of data analysis as described in the text.

Figure 5

X-band rapid-scan data for solid BDPA in air. a) Experimental data for the time corresponding to one IF cycle obtained with power = 0.6 mW (B₁ ~ 90 mG) and 102400 scans, which required about 20 s. One IF cycle encompasses 16 passages through resonance, including both the up-field and down-field sinusoidal scans. b) Reconstructed quadrature-detected rapid scan spectrum including both up and down scans - real (blue) and imaginary (red). c) Deconvolved field-domain spectrum.

Figure 6

X-band rapid-scan data for 0.2 mM OX63 in water with 0.6 mW power (B₁~7 mG) and 1024000 scans which required 200 s. a) Reconstructed quadrature-detected rapid scan spectrum including both up and down scans - real (blue) and imaginary (red), including the rapid-scan oscillations. b) Deconvolved spectrum.

Figure 7

X-band rapid scans. a) Spectrum of 6 mM ¹⁵N-PDT in superabsorbent polymer obtained with 0.6 mW power (B₁ ~ 15 mG) and 102400 scans, which required 20 s. b) Spectrum of 0.1 mM mHCTPO in 80:20 ethanol:water obtained with 0.6 mW power (B₁ ~ 10 mG) and 2048000 scans, which required 400 s.