An x-band continuous wave saturation recovery electron paramagnetic resonance spectrometer based on an arbitrary waveform generator

Joseph E McPeak; Richard W Quine; Sandra S Eaton; Gareth R Eaton

doi:10.1063/1.5043316

. 2019 Feb 4;90(2):024102. doi: 10.1063/1.5043316

An x-band continuous wave saturation recovery electron paramagnetic resonance spectrometer based on an arbitrary waveform generator

Joseph E McPeak ¹, Richard W Quine ², Sandra S Eaton ¹, Gareth R Eaton ^1,^a)

PMCID: PMC6364795 PMID: 30831717

Abstract

An X-band (ca. 9-10 GHz) continuous wave saturation recovery spectrometer to measure electron spin-lattice relaxation (T₁) was designed around an arbitrary waveform generator (AWG). The AWG is the microwave source and is used for timing of microwave pulses, generation of control signals, and digitizer triggering. Use of the AWG substantially simplifies the hardware in the bridge relative to that in conventional spectrometers and decreases the footprint. The bridge includes selectable paths with different power amplifications to permit experiments requiring hundreds of milliwatts to fractions of nanowatts for the pump and observe periods. The signal is detected with either a single or quadrature-output double balanced mixer. The system can operate with reflection or crossed-loop resonators. The source noise from the AWG was decreased by addition of a Wenzel high-stability clock. The source is sufficiently stable that automatic frequency control is not needed. The spectrometer was tested with samples that contained 1 × 10¹⁵ to 8 × 10¹⁷ spins and have T₁ between a few hundred ns and hundreds of μs. Excellent signal-to-noise ratio was obtained with acquisition times of 2–90 s. Signal-to-noise performance is similar to that of a conventional saturation recovery spectrometer with a solid-state source. The stability and data reproducibility are better than with conventional sources. With replacement of frequency-sensitive components, this spectrometer can be used to perform saturation recovery measurements at any frequency within the range of the AWG.

INTRODUCTION

Saturation recovery electron paramagnetic resonance (EPR) measures the spin-lattice relaxation time (T₁) of paramagnetic species.¹ In a continuous wave (CW) saturation recovery experiment, low-power pulses that are long relative to T₁ are used to saturate the spin system, including transitions that are accessible by spectral diffusion.² Recovery of z axis magnetization is then monitored with lower power continuous microwaves that do not disturb the recovery to equilibrium. Inversion recovery may also be used to measure T₁ if spectral diffusion is negligible. In this approach, a high-power pulse is used to invert the spin magnetization along the z-axis, which is monitored with a two-pulse spin echo sequence. Monitoring the echo intensity as a function of the time between the inverting pulse and the two-pulse sequence gives an estimate of T₁. A disadvantage of inversion recovery is that the short pulses do not saturate spectral diffusion, which results in a recovery curve that contains contributions from both spectral diffusion and T₁. This problem may be partially mitigated by using a train of saturating pulses,^3,4 but this requires careful selection of pulse spacing and may be limited by hardware and software. Variation of the saturating power or “pump” time in CW saturation recovery separates T₁ from spectral diffusion processes. Comparison of recovery times measured by CW saturation recovery and inversion recovery can be used to distinguish between spin-lattice relaxation and spectral diffusion. Inversion recovery experiments require high power amplifiers (typically kW) which makes instrumentation more expensive. In addition, the inversion recovery method requires that T₂ be long enough to detect a spin echo. When T₂ is too short for formation of spin echoes, CW saturation recovery is the method of choice for measuring T₁.

A brief history of early saturation recovery experiments is in the work of Eaton and Eaton.¹ Hyde and co-workers^2,5–8 developed the modern saturation recovery spectrometer, and a range of applications have been performed in the Hyde lab at the Medical College of Wisconsin.^9,10 Purpose-built saturation recovery spectrometers have been reported by Quine et al.,¹¹ Beck et al.,¹² and Mailer et al.¹³ at X-band and by Quine et al. at L-band¹⁴ and 250 MHz.¹⁵ Saturation recovery is available as an option for the Bruker Elexsys E580 spectrometer that uses an electron-electron double resonance (ELDOR) accessory and a 5 W solid state amplifier. Recently, digital components such as arbitrary waveform generators (AWG) and fast digitizers have made it possible to re-envision continuous wave saturation recovery spectrometers. Incorporating an AWG provides high frequency stability, the ability to operate over a much wider (and programmable) frequency range than Gunn diode sources and the ability to control experiment timing with marker functions based on the master clock. The AWG greatly simplifies the spectrometer while expanding capabilities.

SPECTROMETER DESIGN

Excitation and waveform generation

The digital source for the spectrometer is a Tektronix 70002A AWG that has two independent outputs, each with sampling rates up to 25 gigasamples/s. A constant frequency of 12.5 GHz is supplied by an external Wenzel Associates Golden Frequency Source (500-29237 rev C). The output of the Wenzel, multiplied by 2, provides a more stable clock for the AWG than that is available internally. Experiments at frequencies between 9 and 10 GHz can be performed by synthesizing sine waves with approximately 2.5 samples per cycle. The waveforms are designed to repeat infinitely or loop to create a continuous output. To avoid artifacts between loops, the end of one waveform must match exactly with the start of the next waveform.¹⁶ When designing the waveform for a desired X-band frequency, the sampling rate is held constant and the number of points per waveform is adjusted to be the greatest common divisor of both the sampling rate and the desired X-band frequency.¹⁶ This method creates a smooth transition for looping waveforms and avoids discontinuities that create phase noise. The two independent microwave outputs from the AWG provide the X-band source frequency and a reference frequency input to the LO side of a double balanced detection mixer. Each microwave output on the AWG has four event markers that are used to control instrument switches and to trigger the digitizer. A TTL circuit encodes the two marker signals from the AWG into four control states and increases 1.4 V for the high state to 5 V, which is needed to control devices in the bridge.

Bridge

Unlike pulse experiments such as inversion recovery, CW saturation recovery requires source power to be incident on the resonator during the signal detection. For this reason, the microwave bridge consists of three paths. One path is for the pump power that saturates the spin system. A lower power path excites the recovery signal. The AWG event markers allow for fast switching between the saturating power path and the lower power observe path. A third path to bypass amplifiers and other components is available for troubleshooting (Fig. 1). The microwave pump path consists of a 17 dB gain preamplifier followed by a 2-W amplifier to provide sufficient power to saturate the spin system. The 2-W amplifier is output-saturated to produce a constant power output. Variation of the pump pulse length allows the integrated power of the saturating waveform to be increased or decreased to saturate all spins that are interconnected by spectral diffusion processes. The low power observe path has a 24 dB gain amplifier followed by a voltage-controlled attenuator. The amplifier may be bypassed for samples with very long relaxation times for which a low observe power and resulting microwave magnetic field (B₁) are required. The characteristics of major components in the bridge are summarized in Table I.

TABLE I.

Characteristics of key components in the AWG-SR bridge (Fig. 1).

			Gain/loss	Noise	Bandwidth	Max input	Output power^a
Component	Manufacturer	Part number	(dB)	figure (dB)	(GHz)	(dBm)	(dBm)
Preamplifier	HD	HD27028	17	1.9	7-14	5	13
	Communications
2-W amplifier	Pasternack	PE15A4001	35	6	6-12	17	33
RF amplifier	Mini-Circuits	ZX60-24+	24	6.5	5-20	20	18
Detection LNA	L3 Narda Miteq	AFS4-08001200-	34	1.3^b	8-12		23
		20-20P-4
LO amplifier	Mini-Circuits	ZX60-183A+	28	5	6-18	20	18
Quadrature mixer	Marki Microwave	MLIQ-0218L	5^c		2-18	11-18
Low-loss mixer	Marki Microwave	MM1-0626S	1.5^c		6-24	17-23
Voltage	RF-Lambda	RFVAT0812R50	1.2		8-12	30
controlled attenuator
Phase shifter	ARRA	9828A	0.75		0-18
Circulator	UTE Microwave	CP-5444-OT	0.8		7-11
Limiter	Aertech	A9L111B	0.6

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^{^a}

At 1 dB compression point.

^{^b}

The effective noise figure is increased to 4.3 dB by the 3 dB loss of the switches, cabling, and limiter on its input when using about 1 ft of cable to connect to a resonator.

^{^c}

When the double balanced mixer is used as a phase sensitive detector, the estimated loss is about 1.5 dB.¹⁷ When the quadrature mixer is used as a phase sensitive detector, the estimated loss is about 5 dB.

The paths for resonator tuning are shown in the right-hand side of the schematic (Fig. 1). The transfer switch provides options to tune a loop-gap resonator (LGR) or to tune either of the two resonators in a crossed-loop resonator (CLR). Adjustment of the isolation between the two resonators of a CLR is also facilitated by using the transfer switch. The double-throw switches select the appropriate paths for tuning and signal detection. These switches are manually controlled from the front panel of the bridge. Once tuned, normal operation does not require further resonator path selection.

A power limiter in the reflected signal path protects the detection system. After the limiter, the signal is amplified 34 dB to make the signal amplitude appropriate for the mixer. As modeled by the Friis relationship for cascaded amplifiers,^17,18 the first amplifier in a series is the primary determinant of the overall noise figure of the system. The Narda low noise amplifier (LNA) was selected as the first stage amplifier in the detection system due to its high gain and low noise figure. At X-band, microwave loss in signal cables greatly increases overall noise figure. To minimize the loss between the resonator and the first detection amplifier, the length of lossy coax cables was kept to a minimum.

A double balanced mixer (DBM) is used as the phase-sensitive detector to generate a baseband signal that is near DC. A switch on the front panel of the bridge directs the signal and the reference waveforms into either a single output or a quadrature (I/Q) mixer. Although this mixer has a greater microwave loss, quadrature detection permits phase manipulation during post-processing. The AWG reference output is amplified by 28 dB to provide sufficient power for the LO side of either mixer. When using a double balanced mixer as a phase sensitive detector, very little noise in the detected signal is from the LO input.¹⁷ Thus, the noise figure of the amplifier in the LO path has little impact on the overall noise figure of the detection system.

A mechanical phase shifter in the reference path is used to match the reference and signal phase by adjusting the effective path length. The phase adjustment is made by observing the phase of the CW field-swept EPR signal when the output of the video amplifier is directed to the Bruker signal processing unit. It was observed that when the phase is adjusted to maximize the EPR signal in the absorption channel, the noise in the absorption channel is simultaneously minimized. Alternatively a delay line could be used to give equal path lengths and decrease the resultant noise;¹⁴ however, microwave loss at X-band makes this impractical. Saturating the LO side of the double balanced mixer decreases the effect of phase noise due to path length inconsistencies. Neither of the spectrometers to which the new spectrometer is compared in this paper used a delay line to match path lengths.

Video amplifier

Following the mixer, a video amplifier (Fig. 2) in the signal detection path provides bandwidth filtering and DC offset adjustment, as well as signal amplification to match the input range of the digitizer. The circuit is an updated version of a previously reported one.^11,14 During the pump period, the power to the LO side of the mixer is switched off to avoid saturating the video amplifier. This “blanking” was maintained for a short period after the end of the pump to include the resonator ringdown time. The video amplifier is composed of 2 channels of similar construction, of which only one is shown in Fig. 2. Video gain settings are selectable from 34 dB to 54 dB in four increments: 34 dB, 42 dB, 46 dB, and 54 dB. These high gain stages have noise figures on the order of tens of decibels. The video amplifier is preceded by the first-stage Narda LNA, which has high gain and low noise figure. Calculations using the Friis relationship for cascaded amplifiers show that the noise figure of the video amplifier makes a negligible contribution to the overall noise figure when placed after the Narda LNA. Two selectable 4-pole Butterworth filters are also present in the video amplifier, with 10 kHz and 100 kHz cutoff frequencies. These filters may be bypassed, giving an overall video bandwidth of 2 MHz. The digitizer that is used in this spectrometer is a Bruker SpecJet II controlled by Bruker Xepr software, but any digitizer of appropriate bandwidth may be used.

Source noise

The source noise for current models of AWGs is substantially higher than that for traditional electron paramagnetic resonance (EPR) sources such as the klystron or Gunn diode. These traditional sources for EPR spectrometers have single-sideband (SSB) phase noise of less than −140 dBc at 100 kHz offset from the carrier frequency. The microwave power is on during detection of the saturation recovery signal, so source noise may contribute to noise in the detected signal. Saturation recovery uses direct detection instead of the 100 kHz modulation and phase sensitive detection that is routinely used in CW-EPR spectrometers. The effective noise in the detected signal is the integration of the noise over the effective bandwidth of the detection system, which can be adjusted with the selectable filters.

The source noise from the AWG is about −100 dBc at 100 kHz offset. The source noise was decreased by using a 12.5 GHz Wenzel Associates Golden Frequency Source (500-29237 rev C) in place of the internal clock of the AWG. The Wenzel source contains a fundamental crystal oscillator operating at 125 MHz. The constant 12.5 GHz output results from four multipliers within the Wenzel source. The manufacturer specification states that phase noise from the Wenzel source is −136 dBc at 100 kHz offset when operating at 12.5 GHz. This value is much closer to that of typical EPR microwave sources than using the AWG internal clock alone.

Source noise was compared for the internal AWG clock, the AWG with the Wenzel clock, and the Gunn diode source in the bridge of the Bruker Elexys E500t spectrometer. The 24 dB amplifier in the observe path was used for all measurements. A relatively high-Q critically coupled Bruker ER4118X-MD-5 dielectric resonator (Table II) was used. The high Q results in larger phase noise in the detected signal than would be observed with a lower Q resonator. A constant waveform at X-band was generated. The highest available video gain, 54 dB, was used with no filter, which gives a system bandwidth of 2 MHz. The reflected signal was monitored on the SpecJet II digitizer as a function of source power up to about 1 mW and the standard deviation of the signal was calculated in Matlab (Mathworks). For all three sources, noise was independent of source power up to about 1 μW (Fig. 3). At higher powers, the noise increases in the order Bruker source < AWG with the Wenzel clock < AWG internal clock. At 1 mW, the noise from the AWG internal clock is about a factor of 10 higher than from the Bruker source. Addition of the Wenzel clock reduces the noise at 1 mW by about a factor of 6 relative to that from the AWG internal clock. The use of high efficiency loop-gap resonators reduces the impact of source noise because less source power is required to generate sufficient B₁.²¹ The impact of source noise is also reduced by using resonators with lower Q and by using a crossed-loop resonator.²⁰ Samples with faster relaxation rates benefit from the use of higher B₁ and therefore are impacted to a greater extent by source noise.

TABLE II.

Comparison of resonators.

Resonator	Λ = G/√W	Loaded Q	Dead time^a (μs)
ER-4118X-MD-5	3.8	9000	2-3
ER-4118X-MS-5	2	3000	1-1.5
ER4102 ST	1	3000	1-1.5
5-loop-4-gap^b	3.2	1300	0.6-0.8
CLR^c	1	300	0.6-0.8

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^{^a}

See text for the definition of a practical dead time in these experiments.

^{^b}

Described in Ref. 19.

^{^c}

Described in Ref. 20.

FIG. 3. — Dependence of source noise on power incident on the resonator for the Bruker internal source (black triangle), AWG with the internal clock (red circle), and the AWG with the Wenzel clock (blue square). For this test, a critically coupled Bruker ER4118X-MD-5 dielectric resonator was used. A lower Q resonator would shift to higher power the point at which source noise dominates. Values are normalized to 1 at the lowest incident power.

Experimental dead time

The dead time after a pulse is defined as the time in which the signal amplitude cannot be defined with fidelity. Several factors contribute to the experimental dead time, including resonator ringdown after the saturating pulse (Table II), the recovery time of amplifiers after the saturating pulse, switching transients, the intensity of the signal to be detected, and the dynamic range of the digitizer. The EPR signal is superimposed on these interfering signals. Subtraction of an off-resonance signal was used to remove unwanted transients from the EPR signal, which requires that all contributions are well-defined and within the dynamic range of the digitizer. A stronger EPR signal reduces the dead time for a given amplitude of resonator ringdown and switching transients.

The reflected power from a reflection resonator, leakage power through a circulator, or leakage power through a crossed-loop resonator may saturate the detection amplifier if there is no protection of the detection system during the pump pulse. During recovery from amplifier saturation, the signal is not detected accurately. To avoid amplifier damage, a limiter is placed before the first stage amplifier. This has the disadvantage that the limiter introduces loss into the signal path, which degrades the signal-to-noise ratio (S/N) of the detected signal. Shutting off the power to the LO side of the mixer acts as a switch, further decreasing power to the detector during the pump time. In this AWG-SR system, both tactics are employed. A limiter was placed before the first amplifier of the detection system and the input to the LO side of the mixer was disabled during the pump time to both maximize protection of the detection system and minimize dead time.

Higher resonator Q creates a longer ringdown after the saturating pulse. Weak EPR signals require more time before the signal becomes detectable relative to ringdown. For this reason, lower Q resonators are preferable when studying samples with short T₁. Effective dead times after a 20 µs, 800 mW pump pulse are listed in Table II. These values follow the expected trend of decreasing dead time with decreasing resonator Q. When resonator Q is sufficiently low, dead time is limited by the recovery time of the video amplifier after saturation. For inversion recovery measurements of T₁, resonators are often over-coupled to achieve lower Q.¹⁹ However, in saturation recovery, the resonator is critically coupled to reduce reflected power during signal detection. A pulse experiment with an over-coupled resonator has a much larger resonator bandwidth than a CW experiment with a critically coupled resonator. The smaller bandwidth for the CW saturation recovery experiment is consistent with the higher selectivity of long pump times. When other contributions have been minimized, the dead time for the instrument depends on the bandwidth of the video amplifier. Large filter bandwidths in the video amplifier are needed for faster recovery from saturation. However, increasing bandwidth increases the high frequency noise in the collected data, which then requires additional averaging to compensate.

INSTRUMENT PERFORMANCE

Measurements of relaxation times

To test the performance of the spectrometer, relaxation times were measured for samples with a range of T₁ values (Table III). Data were obtained using the Wenzel clock. Samples in fluid solution were deoxygenated. Off-resonance data were subtracted from recovery curves to minimize interfering artifacts such as switching transients and resonator ringdown. A selection of recovery curves obtained for samples presented in Table III are shown in Fig. 4. Some samples had been previously characterized: trityl-CD₃ in water,²² irradiated glycylglycine (9.8 Mrad),²³ and irradiated fused quartz (24.4 Mrad).^25,26 Other samples were 0.4 mM perdeuterated 2,2,6,6-tetramethyl-4-piperidone-1-oxyl (PDT) in heavy mineral oil (Fisher Scientific), amino-acid DICPO immobilized in polyvinylalcohol borate glass,²⁷ and powdered coal. Samples for which T₁ has not been reported previously in the literature were also examined by inversion recovery and/or saturation recovery on a conventional spectrometer.

TABLE III.

T₁ (µs) at X-band^a at 20 °C.

		Spins in the active volume	T₁ measured with	Previously
Sample	Radical	of the resonator^b	a new spectrometer	reported	Reference
0.4 mM PDT in heavy		3 × 10¹⁶	0.54 ± 0.01	0.49 ± 0.01	This work^d
mineral oil^c
Amino-acid DICPO in		8 × 10¹⁷	11.0 ± 0.2	10.9 ± 0.8	This work^e
PVA/borate glass
Trityl-CD₃ in H₂O		1 × 10¹⁵	16.0 ± 0.3	17 ± 1	²²
Coal^c		2 × 10¹⁶	26.2 ± 0.2	26.5 ± 1.5	This work^e
Irradiated glycylglycine^c		1 × 10¹⁷	58.1 ± 0.5	53	^23,24
Irradiated fused quartz		2 × 10¹⁶	182 ± 4	180	²⁵

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^{^a}

Measured at the magnetic field that corresponds to the maximum in the absorption spectrum.

^{^b}

The number of spins in the active volume of the resonator was calculated by comparison of double-integrated signal intensity with a calibration curve for 4-hydroxy-tempo in toluene based on concentrations between 0.1 and 10 mM.

^{^c}

Values in this table are for a single exponential fit, although the fit to the data is better for the sum of two components than for a single exponential, as reported previously.

^{^d}

Measured by inversion recovery on a Bruker E580.

^{^e}

Values on a conventional saturation recovery spectrometer at DU.

FIG. 4. — Data recorded on the AWG-SR spectrometer with 2 MHz detection bandwidth and the Bruker ER4118-MS5 [(a)–(c)] or 5-loop-4-gap (d) resonator. (a) Coal recorded with 19 mG B₁, 4.5 µs trigger delay, and 2 s acquisition time. (b) Irradiated glycylglycine recorded with 3.2 mG B₁, 1 µs trigger delay, and 2 s acquisition time. (c) Trityl-CD₃ recorded with 3.2 mG B₁, 8 µs trigger delay, and 2 s acquisition time. (d) PDT recorded with 150 mG B₁, 0.8 µs trigger delay, and 15 s acquisition time. The traces in each panel are saturation recovery data (blue), exponential fit to data (red), residual (yellow), off resonance data (purple), and continuous-wave spectra (inset, black) with approximate linewidths. Data have been scaled by adjusting the input sensitivity of the digitizer.

Values of T₁ ranging from about 0.5 to 250 µs are in good agreement with the literature (Table III). The accurate measurement of T₁ for PDT in heavy mineral oil demonstrates the performance of the spectrometer for relatively short relaxation times. Data for rapidly tumbling nitroxides with relaxation times of 0.31–7.9 µs were measured with this instrument.²⁸ The relaxation times for immobilized nitroxides²⁹ and irradiated fused quartz²⁵ depend on the position in the line. The observed position dependence of T₁ for irradiated fused quartz (Fig. 5) is in good agreement with prior studies.²⁵ For the same number of scans averaged, uncertainties are larger for data at the outer extremes of the spectrum where the signal is weaker.

FIG. 5. — (a) Rapid scan spectrum of E′ center in irradiated fused quartz (24.4 Mrad). (b) Field dependence of T₁ for irradiated quartz, with error bars based on 5 replicate measurements at each field position with a scan time of 90 s for each measurement. Sample placement was not disrupted during replicate measurements.

Spectral diffusion makes very strong contributions to recovery curves for irradiated glycylglycine,^23,30 so the good agreement between the value of T₁ obtained with the digital SR system and the value obtained previously by ELDOR (Table III) indicates that the power and pulse lengths in the pump path are sufficient to saturate transitions that are connected by spectral diffusion. Longer values of T₁ require the use of lower B₁ for detection without distortion. For the SR experiments reported in this study, the B₁ was 3.2–150 mG, which is much smaller than the spectral widths (Fig. 4). The numbers of spins within the active volume of the resonator for each sample are listed in Table III. The ratio of B₁ to the spectral width ranged from about 6% for trityl-CD₃ to 0.003% for irradiated glycylglycine. Because of the small B₁, only a fraction of the spins in the resonator contribute to the saturation recovery signals. For trityl-CD₃ and irradiated glycylglycine, the numbers of detected spins are estimated to be about 6 × 10¹³ and 3 × 10¹², respectively. For the samples listed in Table III, acceptable S/N was achieved with signal acquisition times of 2 s for coal, 15 s for 0.4 mM PDT, and 90 s for irradiated quartz. S/N is strongly dependent on resonator Q, instrument dead time, B₁, and resonator efficiency.

In some EPR spectrometers, an automated frequency control (AFC) circuit is used to lock the source frequency to the resonator frequency. Prior saturation recovery spectrometers stabilized the source frequency by locking to an auxiliary resonator.^2,6,11 In other cases, the AFC lock was to the sample resonator, but the need to blank the AFC signal during the saturating pulse resulted in drifting of the source frequency.^12,31,32 The AWG provides extremely stable source frequency such that an AFC is not needed. When the T₁ and S/N for a coal sample were measured repeatedly over a period of 16 h, the relative standard deviations were 1% and 8%, respectively. The main instability is the temperature of the sample-containing resonator. In a temperature-controlled room with a temperature-controlled magnet, the microwave pump power is the primary cause of resonator temperature changes. Acquisition times on the order of tens of minutes are considered long for saturation recovery,^13,33,34 although much longer periods of stability may be achieved with the AWG system and proper temperature control. Once a steady-state has been achieved, the overall system stability is sufficient for signal averaging for several hours.

Magneticfield stability also contributes to overall measurement stability. To measure extremely narrow lines, magnetic field stabilization with a teslameter might be required. For most samples for which pulsed saturation recovery is used, T₂ is too short for spin echo measurements. The EPR lines in these cases are generally broad enough that modern Bruker magnets, power supplies, and Hall probe field control systems maintain the field with sufficient stability for long-term signal averaging.

Comparison of gain and noise figure with a conventional saturation recovery spectrometer

The gain and noise figure of the detection system of the AWG-SR were compared with those of the saturation recovery spectrometer described in the work of Quine et al.¹¹ (Table IV). The conventional system has been upgraded by replacing the Varian E3 microwave bridge with a Bruker ER048 bridge and replacing the digital oscilloscope with a Bruker SpecJet fast digitizer. The y-factor method for measuring gain and noise figure in Ref. 35 was used. For these measurements, the input to the detection system for both the AWG-SR and the conventional SR system was a Noisecom, Inc., NC3208A wideband calibrated noise source with a 28 dB excess noise ratio (ENR) noise level. The detected signal was recorded with a LeCroy Waverunner 44Xi-A 400 MHz oscilloscope or monitored with a Fluke 8922A true RMS voltmeter.

TABLE IV.

Comparison of gain and noise figures for the conventional spectrometer and the AWG-SR system.

	Conventional SR		AWG-SR^a
	Detection	End-to-end	Detection	End-to-end
	amplifier (dB)	gain/NF^b (dB)	amplifier (dB)	gain/NF^b (dB)
Gain	32	78	34	84
Noise figure	1.4	5	1.3	7

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^{^a}

The gain and noise figure were measured with the DBM path and the CLR2 input path (Fig. 1), which is the path with lowest microwave loss.

^{^b}

A video gain of 500 (54 dB) was used in these measurements.

The best performance of the AWG-SR is achieved when using the signal path for a CLR and the DBM, with the EPR signal detected via CLR2 (Fig. 1). Results for this configuration are summarized in Table IV. This detection path, which is denoted as “end-to-end,” has an overall gain of 84 dB and noise figure of 7 dB. The conventional system has an overall gain of 78 dB and noise figure of 5 dB for the analogous path. The AWG-SR system has higher gain, but the higher noise figure diminishes overall performance. The Narda LNA used in the AWG-SR provides a small improvement over the detection amplifier in the conventional system. The gain and noise figure of a series of amplifiers are largely determined by the first stage amplifier, which makes its selection critical. The 2 dB higher overall noise figure in the AWG-SR is attributed to the additional microwave loss prior to the Narda LNA. This arises mainly from the components that are not present in the conventional system but are needed to accommodate and tune either a reflection resonator or a CLR. The measured loss between the bridge input and the LNA including the cabling, switches, and limiter is about 2 dB. The addition of coax cable to connect to a resonator adds more loss and increases the effective noise figure of the LNA. The coaxial cable design was chosen to be compatible with Bruker X-band Flexline resonators and cryostats. The measured gain and noise figures for the complete detection system (Table IV) are consistent with the values calculated for the individual components using the Friis relationship for cascaded amplifiers.

For the AWG-SR system, the I/Q mixer splits the signal into two paths, which decreases gain and increases the noise figure of the system. Using a reflection resonator requires addition of a circulator in the detection path (Fig. 1), which introduces 0.8 dB loss, thereby increasing the noise figure. Because the system was designed to have the flexibility of using either an LGR or a CLR, the additional switching introduces more loss than if the system were designed for only one type of resonator. A system designed for a reflection resonator with wave-guide connections could have about 2 dB better noise figure than this system that uses coaxial cable connections, which would make the noise figure equivalent to the Gunn-diode and waveguide-based conventional SR system.

Comparison of S/N with a conventional saturation recovery spectrometer

Three samples (Table III) were used to compare S/N: coal, irradiated glycylglycine, and DICPO. The AWG-SR system utilized a Bruker SpecJet II fast digitizer, which has more data acquisition options than a SpecJet I. The dynamic range and timings were set within the limits of the SpecJet I in the conventional system. Data were acquired on the two systems at the same positions in the spectra. Observe powers were selected to be low enough that the detected signal was not perturbed. A Bruker ER4102 ST TE₁₀₂ cavity resonator was used on both systems, and the reflection mode of the AWG-SR was used. S/N for the three samples measured with both instruments is shown in Table V. The two mixer paths in the AWG-SR were also compared. The S/N with the AWG-SR using the single channel DBM is within the experimental uncertainty of values obtained with the conventional system. The S/N for the AWG-SR system decreased by about square root of two when the quadrature (I/Q) mixer was used, which is attributed to the division of the signal between the two outputs.

TABLE V.

Comparison of S/N for recovery curves.^a

Instrument	Coal	Glycylglycine	DICPO
Standard SR	890 ± 270	380 ± 110	350 ± 110
AWG-SR^b	1100 ± 90	430 ± 40	240 ± 30
AWG-SR, I/Q mixer^c	730 ± 110	280 ± 60	200 ± 30

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^{^a}

Observe power for all 3 samples was 25 μW, which produces a B₁ of 5 mG in the Bruker ER4102 resonator and is sufficiently low such that source noise is negligible. The detection bandwidth was ∼1.3 MHz on the conventional SR and ∼2.1 MHz on the AWG-SR which decreases the S/N for the AWG-SR by about 27%. For both systems, 10 240 transients were co-added, which is much fewer than the number of scans for which coherent digitizer noise has been found to be significant.

^{^b}

Data acquired with the Wenzel source and the single-channel DBM.

^{^c}

Data acquired with the Wenzel source and the quadrature mixer. This path is expected to lower the signal by about 3–3.5 dB, which is a factor of 1.4–1.5, as observed.

The frequency drift in the Wenzel clock is much less than for the conventional sources used for SR, which provides greater reproducibility in values of T₁ (Table III) and smaller estimated uncertainties in the S/N values reported in Table V. The SpecJet II has the capability to sample at 1 ns/pt compared with 4 ns/pt for the SpecJet I used on the conventional system. Collection of a larger number of data points with subsequent smoothing could substantially improve the S/N for the system. No smoothing was applied to the data presented in this work. The new design has the flexibility and the precise timing control of the AWG without sacrificing S/N or accuracy of the measured relaxation times.

Future directions

The overall performance of the AWG-SR could be improved by designing for a single type of resonator rather than for multiple types. Although the amplifiers used in the AWG-SR are specified to operate at X-band, this new design can be implemented at any frequency below the limit of the AWG by replacing frequency-sensitive components. Future improvements in AWGs are expected to result in lower source noise. The use of AWGs with frequency multipliers, such as that employed by the 12.5 GHz Wenzel source, will allow access to higher frequency bridge designs. Measurements reported in this paper were performed at room temperature; however, cryostats could be used to measure T₁ at lower temperatures. Cryostats are readily available for many Bruker resonators, including the three that were used in this work.

CONCLUSION

The flexibility of an AWG to control the timing and switching functions of a saturation recovery spectrometer allows for increased precision of measurements and a greatly decreased physical footprint. The use of an external clock decreases the source noise inherent in AWGs that are commercially available at the time of this publication. A significant source of uncertainty in measurements with the conventional spectrometer is frequency drift and the need for periodic retuning. The frequency drift of the AWG-SR spectrometer is much lower than that for the conventional system. Improved stability is reflected in the higher reproducibility and therefore lower standard deviations in values of T₁ (Table III) and S/N (Table V). Increased reproducibility and flexibility offered by the AWG are valuable features. The AWG design also has the attractive feature that replacement of a relatively small number of narrow-banded components (including the resonator) would permit operation at another microwave frequency. The source noise from the AWG becomes significant at higher powers; however, this is less of a problem for saturation recovery because detection typically is performed at relatively low observe powers. Bridge designs can be simplified relative to previously reported systems by the use of the marker functions from the AWG. As AWGs become commonplace in the EPR laboratory, continuous wave saturation recovery will be more accessible through the implementation of relatively uncomplicated bridge designs such as the one presented here.

ACKNOWLEDGMENTS

Partial support of this work by NIH NCI AIP Grant No. CA177744 and NSF Grant No. CHE-1117992 is gratefully acknowledged.

REFERENCES

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25.Eaton S. S. and Eaton G. R., “Irradiated fused-quartz standard sample for time-domain EPR,” J. Magn. Reson. 102, 354–356 (1993). 10.1006/jmra.1993.1116 [DOI] [Google Scholar]
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29.Du J.-L., Eaton G. R., and Eaton S. S., “Temperature, orientation, and solvent dependence of electron spin-lattice relaxation rates for nitroxyl radicals in glassy solvents and doped solids,” J. Magn. Reson., Ser. A 115, 213–221 (1995). 10.1006/jmra.1995.1169 [DOI] [Google Scholar]
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32.Kundu K. and Das R., “Saturation recovery relaxation studies of benzene anion radical and its derivatives: Application of Kivelson-Orbach mechanism of electron spin relaxation,” Mol. Phys. 112, 1577–1588 (2014). 10.1080/00268976.2013.845701 [DOI] [Google Scholar]
33.Haas D. A., Sugano T., Mailer C., and Robinson B. H., “Motion in nitroxide spin labels: Direct measurement of rotational correlation times by pulsed electron double resonance,” J. Phys. Chem. 97, 2914–2921 (1993). 10.1021/j100114a014 [DOI] [Google Scholar]
34.Bridges M. D., Hideg K., and Hubbell W. L., “Resolving conformational and rotomeric exchange in spin-labeled proteins using saturation recovery EPR,” Appl. Magn. Reson. 37, 363–390 (2010). 10.1007/s00723-009-0079-2 [DOI] [PMC free article] [PubMed] [Google Scholar]
35.See literature.cdn.keysight.com/litweb/pdf/5990-5800EN.pdf for Keysight Application Note 5990-5800EN, High Accuracy Noise Figure Measurements Using the PNA-X Series Network Analyzer; accessed 2014.

[c1] 1.Eaton S. S. and Eaton G. R., “Saturation recovery EPR,” Biol. Magn. Reson. 24, 3–18 (2005). 10.1007/0-306-48533-8_1 [DOI] [Google Scholar]

[c2] 2.Huisjen J. and Hyde J. S., “A pulsed EPR spectrometer,” Rev. Sci. Instrum. 45, 669–675 (1974). 10.1063/1.1686710 [DOI] [Google Scholar]

[c3] 3.Dalton L. R., Kwiram A. L., and Cowen J. A., “Electron spin-lattice and cross relaxation in irradiated malonic acid,” Chem. Phys. Lett. 14, 77–81 (1972). 10.1016/0009-2614(72)87146-x [DOI] [Google Scholar]

[c4] 4.Narath A., “Nuclear magnetic resonance in magnetic and metallic solids,” in Hyperfine Interactions, edited by Freeman A. J. and Frankel R. B. (Academic Press, New York, 1967), p. 297. [Google Scholar]

[c5] 5.Huisjen J. and Hyde J. S., “Saturation recovery measurement of electron spin-lattice relaxation times,” J. Chem. Phys. 60, 1682–1683 (1974). 10.1063/1.1681251 [DOI] [Google Scholar]

[c6] 6.Percival P. W. and Hyde J. S., “Pulsed EPR spectrometer II,” Rev. Sci. Instrum. 46, 1522–1529 (1975). 10.1063/1.1134096 [DOI] [Google Scholar]

[c7] 7.Percival P. W. and Hyde J. S., “Saturation-recovery measurements of the spin-lattice relaxation times of some nitroxides in solution,” J. Magn. Reson. 23, 249–257 (1976). 10.1016/0022-2364(76)90206-7 [DOI] [Google Scholar]

[c8] 8.Hyde J. S., “Saturation recovery methodology,” in Time Domain Electron Spin Resonance, edited by Kevan L. and Schwartz R. N. (John Wiley, New York, 1979), pp. 1–30. [Google Scholar]

[c9] 9.Altenbach C., Froncisz W., Hyde J. S., and Hubbell W. L., “Conformation of spin-labeled melittin at membrane surfaces investigated by pulse saturation recovery and continuous wave power saturation electron paramagnetic resonance,” Biophys. J. 56, 1183–1191 (1989). 10.1016/s0006-3495(89)82765-1 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c10] 10.Mainali L., Sidabras J. W., Camenisch T. G., Ratke J. J., Raguz M., Hyde J. S., and Subczynski W. K., “Spin-label W-band EPR with seven-loop-six-gap resonator, application to lens membranes derived from eyes of a single donor,” Appl. Magn. Reson. 45, 1343–1358 (2014). 10.1007/s00723-014-0578-7 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c11] 11.Quine R. W., Eaton S. S., and Eaton G. R., “Saturation recovery electron paramagnetic resonance spectrometer,” Rev. Sci. Instrum. 63, 4251–4262 (1992). 10.1063/1.1143722 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c12] 12.Beck W. F., Innes J. B., Lynch J. B., and Brudvig G. W., “Electron spin-lattice relaxation and spectral diffusion measurements on tyrosine radicals in proteins,” J. Magn. Reson. 91, 12–29 (1991). 10.1016/0022-2364(91)90403-g [DOI] [Google Scholar]

[c13] 13.Mailer C., Danielson J. D. S., and Robinson B. H., “Computer-controlled pulsed electron-paramagnetic-resonance spectrometer,” Rev. Sci. Instrum. 56, 1917–1925 (1985). 10.1063/1.1138445 [DOI] [Google Scholar]

[c14] 14.Quine R. W., Rinard G. A., Ghim B. T., Eaton S. S., and Eaton G. R., “A 1-2 GHz pulsed and continuous wave electron paramagnetic resonance spectrometer,” Rev. Sci. Instrum. 67, 2514–2527 (1996). 10.1063/1.1147206 [DOI] [Google Scholar]

[c15] 15.Quine R. W., Eaton S. S., and Eaton G. R., “Pulsed saturation recovery 250 MHz electron paramagnetic resonance spectrometer,” Concepts Magn. Reson., Part B 26B, 23–27 (2005). 10.1002/cmr.b.20043 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c16] 16.Byrom B., personal communication from Tektronix representative (2017).

[c17] 17.Rinard G. A., Quine R. W., Song R., Eaton G. R., and Eaton S. S., “Absolute EPR spin echo and noise intensities,” J. Magn. Reson. 140, 69–83 (1999). 10.1006/jmre.1999.1823 [DOI] [PubMed] [Google Scholar]

[c18] 18.Rinard G. A., Eaton S. S., Eaton G. R., C. P. Poole, Jr., and Farach H. A., “Sensitivity in ESR measurements,” in Handbook of Electron Spin Resonance (Springer-Verlag, N.Y., 1999), Vol. 2, pp. 1–23. [Google Scholar]

[c19] 19.Rinard G. A., Quine R. W., Eaton S. S., Eaton G. R., and Froncisz W., “Relative benefits of overcoupled resonators vs. inherently low-Q resonators for pulsed magnetic resonance,” J. Magn. Reson., Ser. A 108, 71–81 (1994). 10.1006/jmra.1994.1090 [DOI] [Google Scholar]

[c20] 20.Rinard G. A., Quine R. W., McPeak J., Buchanan L., Eaton S. S., and Eaton G. R., “An X-band crossed-loop EPR resonator,” Appl. Magn. Reson. 48, 1219–1226 (2017). 10.1007/s00723-017-0945-2 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c21] 21.Hyde J. S., Froncisz W., and Kusumi A., “Dispersion electron spin resonance with the loop gap resonator,” Rev. Sci. Instrum. 53, 1934–1937 (1982). 10.1063/1.1136918 [DOI] [Google Scholar]

[c22] 22.Owenius R., Eaton G. R., and Eaton S. S., “Frequency (250 MHz to 9.2 GHz) and viscosity dependence of electron spin relaxation of triarylmethyl radicals at room temperature,” J. Magn. Reson. 172, 168–175 (2005). 10.1016/j.jmr.2004.10.007 [DOI] [PubMed] [Google Scholar]

[c23] 23.Harbridge J. R., Eaton G. R., and Eaton S. S., “Impact of spectral diffusion on apparent relaxation times for the stable radical in irradiated glycylglycine,” in Modern Applications of EPR/ESR: From Biophysics to Materials Science, Proceedings of the Asia-Pacific EPR/ESR Symposium, 1st, Kowloon, Hong Kong, January 20–24, 1997 (Springer, 1998), pp. 220–225. [Google Scholar]

[c24] 24.Harbridge J. R., Eaton S. S., and Eaton G. R., “Electron spin-lattice relaxation processes of radicals in irradiated crystalline organic compounds,” J. Phys. Chem. A 107, 598–610 (2003). 10.1021/jp021504h [DOI] [Google Scholar]

[c25] 25.Eaton S. S. and Eaton G. R., “Irradiated fused-quartz standard sample for time-domain EPR,” J. Magn. Reson. 102, 354–356 (1993). 10.1006/jmra.1993.1116 [DOI] [Google Scholar]

[c26] 26.Ghim B. T., Eaton S. S., Eaton G. R., Quine R. W., Rinard G. A., and Pfenninger S., “Magnetic field and frequency dependence of electron spin relaxation times of the E′ center in irradiated vitreous silica,” J. Magn. Reson., Ser. A 115, 230–235 (1995). 10.1006/jmra.1995.1171 [DOI] [Google Scholar]

[c27] 27.Rajca A., Kathirvelu V., Roy S. K., Pink M., Rajca S., Sarkar S., Eaton S. S., and Eaton G. R., “A spirocyclohexyl nitroxide amino acid spin label for pulsed EPR spectroscopy distance measurements,” Chem.: Eur. J. 16, 5778–5782 (2010). 10.1002/chem.200903102 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c28] 28.Biller J. R., McPeak J. E., Eaton S. S., and Eaton G. R., “Measurement of T_1e, T_1N, T_1HE, T_2e, and T_2HE by pulse EPR at X-band for nitroxides at concentrations relevant to solution DNP,” Appl. Magn. Reson. 49, 1235–1251 (2018). 10.1007/s00723-018-1049-3 [DOI] [Google Scholar]

[c29] 29.Du J.-L., Eaton G. R., and Eaton S. S., “Temperature, orientation, and solvent dependence of electron spin-lattice relaxation rates for nitroxyl radicals in glassy solvents and doped solids,” J. Magn. Reson., Ser. A 115, 213–221 (1995). 10.1006/jmra.1995.1169 [DOI] [Google Scholar]

[c30] 30.Harbridge J. R., Ph.D. dissertation, University of Denver, 2002. [Google Scholar]

[c31] 31.Fessenden R. W., Hornak J. P., and Venkataram B., “Electron spin-lattice relaxation times of transient free radicals,” J. Chem. Phys. 74, 3694–3704 (1981). 10.1063/1.441597 [DOI] [Google Scholar]

[c32] 32.Kundu K. and Das R., “Saturation recovery relaxation studies of benzene anion radical and its derivatives: Application of Kivelson-Orbach mechanism of electron spin relaxation,” Mol. Phys. 112, 1577–1588 (2014). 10.1080/00268976.2013.845701 [DOI] [Google Scholar]

[c33] 33.Haas D. A., Sugano T., Mailer C., and Robinson B. H., “Motion in nitroxide spin labels: Direct measurement of rotational correlation times by pulsed electron double resonance,” J. Phys. Chem. 97, 2914–2921 (1993). 10.1021/j100114a014 [DOI] [Google Scholar]

[c34] 34.Bridges M. D., Hideg K., and Hubbell W. L., “Resolving conformational and rotomeric exchange in spin-labeled proteins using saturation recovery EPR,” Appl. Magn. Reson. 37, 363–390 (2010). 10.1007/s00723-009-0079-2 [DOI] [PMC free article] [PubMed] [Google Scholar]

[c35] 35.See literature.cdn.keysight.com/litweb/pdf/5990-5800EN.pdf for Keysight Application Note 5990-5800EN, High Accuracy Noise Figure Measurements Using the PNA-X Series Network Analyzer; accessed 2014.

PERMALINK

An x-band continuous wave saturation recovery electron paramagnetic resonance spectrometer based on an arbitrary waveform generator

Joseph E McPeak

Richard W Quine

Sandra S Eaton

Gareth R Eaton

Abstract

INTRODUCTION