Pulse EPR Practice

Modern pulse EPR spectrometers perform an amazing feat. They detect tiny (< 1 nW) signals tens of nanoseconds after a powerful (> 1 kW) microwave pulse and can repeat this feat every 1 μs. This section describes how the Bruker E580 spectrometer accomplishes this feat. Figure 5.1 shows a photograph of an E580 spectrometer. The components are identified in the block diagram.

The microwave bridge creates the microwave pulses and detects the FIDs and echoes. Because of this two-fold duty for the pulse bridge it is a good idea to separate the two functions in our discussions. A few of the parts are actually required for both excitation and detection.

In order to excite or produce an FID or echo, we need to create a short high power microwave pulse. Typical pulse lengths are 12-16 ns for a π /2 pulse with up to 1 kW of microwave power. This is achieved by supplying low power microwave pulses to the TWT where they are amplified to very high power. (See Figure 5.3)

The MPFU (Microwave Pulse Forming Unit) produces the low power microwave pulses. Each unit consists of two “arms” with individual attenuators and phase shifters to adjust the relative amplitudes and phases in the two arms. To create a +x pulse, the +x PIN (P-type Intrinsic N-type) diode switch passes microwaves through for the specified pulse length. For a -x pulse, the -x PIN diode switch is used instead. If additional phases or amplitudes are needed, more MPFU are installed in parallel with the first MPFU.

The FIDs and echoes are very low level signals so we need a preamplifier to lift them up out of the noise. This is a bit tricky however, because we are using high power microwave pulses and the reflected pulses as well as the resonator ringdown (one of the causes of the so-called deadtime) can easily burn out our preamp. To avoid destroying it, we use a PIN diode switch (known as the defense diode) to block the high power microwave pulses from reaching the preamp. We cannot measure the signals until the high power microwaves are dissipated and we can turn the defense diode on again. (See Figure 5.5)

The amplified signal then proceeds to the quadrature detector. Quadrature detection is simply an electronic means for measuring both transverse magnetization components in the rotating frame. This gives us the required amplitude and phase information to transform the signals into a frequency representation. (See Figure 5.6 and Figure 4.19)

The outputs from the quadrature detector correspond to the real and imaginary components of the magnetization and are commonly labeled Channel a and Channel b. There is a phase shifter to adjust the reference phase for the quadrature detection. This phase rotates the detection axes and therefore changes the appearance of the signal. In Figure 5.7, we start with an on-resonance FID and the reference phase adjusted so that we only have a signal in Channel a. If we were to change the reference phase, some of the signal in Channel a appears in Channel b and vice versa.

The quadrature detection is followed by one more stage of amplification and filtering by the VAMP (Video Amplifier). Both the gain and bandwidth of the VAMP are adjustable. Six dB steps are required to change the signal amplitude by a factor of two.

The bandwidth is normally kept at the maximum value, 200 MHz. Narrower bandwidth reduces the noise, but also distorts higher frequency signals. There are a few cases where the bandwidth must be reduced. Figure 5.8 shows the effect of bandwidth reduction on the FT-EPR spectrum. Note that there is both a time shift and an attenuation of higher frequency components of the spectrum at narrower bandwidth.

In order to excite and detect FIDs and echoes, many events must be orchestrated. First, because the TWT is a pulse amplifier, it must be turned on a little before the microwave pulse. The microwave pulse must be supplied to the TWT at a precise time after the TWT is turned on. This pulse is produced by turning the +x and pulse gate PIN diodes on and off at precisely the same time. While the high power microwaves are on, the defense diode must protect the preamp. Lastly we must trigger the digitizer to acquire the signal.

Once we obtain a signal from the detection portion of the bridge, we need to digitize it somehow to process the signal with a computer. There are three different classes of digitizer required for pulse EPR spectroscopy; point digitizer, integrator, and transient recorder. (See Figure 5.10) The SpecJet digitizer performs these three classes of experiments as well as signal averaging to improve the signal to noise ratio of the signal.

In the point digitizer mode of the SpecJet, the digitizer only samples one point (< 2 ns) in the FID or echo at a time, thereby requiring multiple acquisitions for measuring signals. (See Figure 5.11) The most common measurements requiring this mode are ESEEM and relaxation measurements experiments where only the height of the echo needs to be measured. For example, in a two pulse experiment, we generate the signal by measuring the echo height for the initial τ value; then step out τ, digitize the second point of our signal; and so on until we have acquired the entire echo decay.

The point digitizer method is often called non-selective detection, whereas the integration method is called selective detection. We shall see why this is so.

Because of the limited excitation bandwidth in pulse EPR, we cannot always Fourier transform an FID or echo to obtain a broad EPR spectrum. (See Figure 4.13) We could, however, measure the echo height as we sweep the magnetic field to generate a broad EPR spectrum. There is a slight problem which is called power broadening. (This effect is different from power broadening in CW EPR.) We can easily achieve a B₁ of 10 Gauss in the rotating frame. If we have features narrower than 10 G, in an analogous fashion to field overmodulation, the power broadening will decrease our resolution. In CW EPR, we turn down the field modulation. In pulse EPR, we can use softer pulses to achieve the need for better resolution. (See Figure 5.12)

What we have essentially done is limit the bandwidth of excitation. By using an integrator, we can also limit the bandwidth of detection. It is the off-resonance high frequencies that contribute to the power broadening. If we are able to filter the high frequency components out, we can regain our resolution even with hard pulses. By integrating the area under the echo, we can achieve this filtering. How this filtering is accomplished can be seen in Figure 5.13. On-resonance, the area under the echo is large and positive. If we go off-resonance, we obtain the high frequency components with negative going contributions. These negative signals cancel out the positive signals when we integrate the echo, effectively achieving the desired filtering effect. The longer period of integration time, the more effective and selective the bandwidth limitation becomes. (See Figure 5.14 and notice the similarity with Figure 5.12)

The transient recorder is extremely efficient at recording and signal averaging FIDs and echoes because it captures a complete signal in one acquisition. In this mode, the SpecJet is functioning like a digital oscilloscope.

To use a digitizer effectively, we need to be careful about the rate at which we sample the signals. We must make sure that we fulfill the Nyquist criterion:

ν_max < ν_N

equation 5.1

where ν_max is the highest frequency in our signal and the Nyquist frequency is:

ν_N = 1/(2Δt)

equation 5.2

where Δt is the time between the points in the digitized signals. If we do not comply with this condition, we get fold-over or aliasing when we Fourier transform the signal. (See Figure 5.16) A lower frequency component equally fits the digitized points and the signal will appear as a lower frequency.

This foldover effect or aliasing is one of the reasons for limiting the detection bandwidth in the video amplifier. By using a narrower bandwidth, the high frequency signals that could cause problems are filtered out before they can be digitized.

In the digitization process, the signal is converted into a stream of integers. How well this data represents our signal depends on the amplitude resolution of the conversion. The SpecJet has a dynamic range of ± 0.5 Volts and separates this range into 256 (8 bits) equally spaced steps. The digitizer determines which of these 256 steps best matches the voltage of the signal. If we wish to distinguish between two signals that are very close in voltage, the voltage difference must be larger than the separation of adjacent steps of our digitizer. If we do not supply a large enough signal, we obtain noisy data exhibiting jagged step-like or digitization noise. (See Figure 5.17) It is important to use a video amplifier gain that is sufficient to supply approximately a ±0.5 Volt signal to use the digitizer fully.

A commonly used technique to increase the signal to noise ratio of a signal is to repeat the experiment and average the results of the repeated experiments. The signal will grow linearly whereas the noise will grow with the square root of the number of averages. Over all, the sensitivity increases with the square root of the number of averages.

Signal averaging not only increases the signal to noise ratio, but its also increases the effective dynamic range. If we need to resolve two signals that have almost the same voltage, the noise actually helps when we signal average. The noise randomly perturbs the signal up and down, so as we average the signals, we fill the space between the 256 equally spaced steps described in the previous section. If the signal is closer to one step than the other, statistically the upper step will be measured more often than the lower step.

As we average more, we obtain better amplitude resolution.

Resonators are perhaps the most critical element of a pulse EPR spectrometer. They convert the microwave power into B₁ and also convert the transverse magnetization into a FID or echo. In CW EPR, we typically use high Q cavities because they are efficient at converting spin magnetization into a detectable signal. This is not an option for pulse EPR because high Qs contribute to long deadtimes. The Q is the ratio of the energy stored and the power dissipated in the resonator. We need to dissipate the high power microwave pulses very quickly (the so called ring-down time) so that it does not interfere with the detection of the very weak FID and echo signals. Another requirement of the resonator is bandwidth so that we do not distort broad EPR signals. We therefore have two very good reasons to keep the Q as low as possible.

We still need to convert the microwave power into B₁ and the transverse magnetization into signals efficiently. The efficiency is proportional to sqrt(Q). We cannot increase Q, so we must increase the proportionality constant. It is optimized (for a given sample diameter) in small resonators such as dielectric and split-ring resonators.

In CW EPR, we normally critically couple the resonator. The two pulse resonators still have too high a Q when matched, so we need to further decrease the Q by overcoupling the resonator. This does mean some of the microwave power is reflected back, thereby decreasing the power to the sample, but we need to compromise and minimize the deadtime.

Imbalances in the quadrature detector can distort the Fourier transformed signal. We assume that both detectors in Figure 5.6 have exactly the same gains, the reference phases are π/2 phase-shifted from each other, and there are no DC offsets. This is very difficult to realize in practice. The imbalance in phase and amplitude causes aliasing in which positive frequency signals start appearing at negative frequencies and vice versa. The DC offsets appear as large features at zero frequency.

The four step phase cycle (See Figure 5.23) suppresses all of these quadrature artefacts. In the first step of the phase cycle, we apply a +x pulse and store the channel a signal as the real data and the channel b signal as the imaginary data. Next we apply a -x pulse, causing our signals to changes sign. Therefore, we subtract the second set of signals in order that our FID does not cancel but instead becomes twice as large. This step of the phase cycle eliminates the zero frequency artefact because the DC offsets are unaffected by the phase of the microwaves, therefore subtraction cancels it out.

The next two steps require application of a +y or -y pulse. This then exchanges the signal that originally was in channel a with the channel b signal. We now add and subtract the channel b signals with our previous real results and the channel a signals with the imaginary results. These two steps suppress the aliasing artefacts because we have sent identical signals through both channels a and b now, thus averaging the gain and reference phase imbalances to approximately zero. After Fourier transforming the FID, we now obtain a nice spectrum with no artefacts. (See Figure 5.24)

We saw in Figure 4.40 that three microwave pulses create five echoes. In a three pulse ESEEM experiment, we are only interested in the stimulated echo. The other echoes only give us artefacts as they run through our stimulated echo. There is a phase cycle that leaves the stimulated echo intact but subtracts the other echoes away. (See Figure 5.25) Almost all pulse EPR experiments are performed with some type of phase cycling in order to focus on the one echo or FID in which we are interested.