COMPARISON OF CW AND PULSED EPR SIGNAL INTENSITIES

MATCHING NETWORK

5. COMPARISON OF CW AND PULSED EPR SIGNAL INTENSITIES

For most pulsed EPR measurements the detected SIN is lower than the optimal CW EPR signal for the same sample. In this section we briefly outline the nature of the CW and pulsed EPR signals, and discuss the different impact on their relative SIN due to the fact that the noise in actual spectrometers is not entirely "white" thermal noise. As discussed in the next section, magnetic field modulation is used in CW ' EPR to suppress low-frequency noise, whereas rapid signal acquisition and averaging techniques (such as analog boxcar or digital summation) are used in pulsed EPR to suppress noise. Because of the differences in time response, pulsed EPR uses a much larger detector bandwidth, which, by Eq. (24) in section 6, decreases the SIN. If averaging techniques are performed long enough to make the effective time constants the same, pulsed EPR can have larger SIN than a CW spectrum when the modulation amplitude is small enough to avoid distortion of the derivative line width. Relaxation times are also important to

the comparison. If the relaxation time is long relative to the reciprocal of the modulation frequency, it is not possible to obtain an undistorted field-modulated CW EPR spectrum. If the spectrum is narrow enough that it can be fully excited in pulsed EPR, then in the same total time better SIN can be achieved in pulsed than in CW EPR. Most examples of this advantage for pulsed EPR occur for defect centers in solids (such as the irradiated fused Si02 standard sample available from Wilmad Glass, Buena, NJ, USA). It will also be true for some very narrow EPR signals, such as for the Nycomed radical discussed below , which are becoming useful in biological EPR.

5.1 Magnetic Field Modulation in CW EPR

Magnetic field modulation (often at 100 KHz) is used in CW EPR to encode the EPR signal at the modulation frequency so that subsequent phase-sensitive detection discards most of the noise except that in a narrow band near the modulation frequency. It is inherent in the properties of the phase-sensitive detector that the first-harmonic output signal is the first derivative of the magnetic resonance absorption. The principles are sketched in Figure D.6 on page 482 in Weil et al., 1994. In order to obtain a faithful representation of the first derivative of the absorption signal, it is necessary that the magnetic field modulation amplitude be small relative to the absorption line width so that the portion of the line traversed by the modulation approximates the tangent-to the absorption curve. As a practical compromise between fidelity and SIN, it is common to use a modulation amplitude approximately 1/10 of the line width. For detection of weak signals, modulation amplitude approximately equal to the line width is used , resulting in some distortion of the line shape. If a very large modulation amplitude is used, the EPR signal splits into two peaks of opposite polarity, each with an amplitude equal to the total absorption signal amplitude (see Figure E.6 on page 505 in Weil et al., 1994). When the modulation amplitude is chosen to minimize distortion of the derivative line shape, the EPR derivative signal amplitude is less than the maximum possible, and is proportional to the modulation amplitude. (There are further complications when the reciprocal of the modulation frequency is of the order of spin relaxation times, but these passage effects are beyond the scope of this chapter.) The principal advantage of magnetic field modulation is that it suppresses noise at frequencies substantially lower than the modulation frequency. There are many contributions to the spectrometer response at low frequencies, including building vibrations, power supply ripple , power line frequencies, temperature variations, cooling fan noise, and even microphonics caused by the magnetic field modulation itself. Magnetic field

3. FREQUENCY DEPENDENCEOFEPRSENSITIVITY 127 modulation and phase-sensitive detection yields a smaller than maximal signal, but very much smaller noise than direct detection.

5.2 Pulsed EPR

Precessing electron spin magnetization induces a current in the walls of the resonator. The task of calculating the resultant signal level encompasses four major steps. First, the relation between magnetization and signal in the resonator is calculated from first principles, using the inductance and resistance of the resonator. The relation between EPR line shape and microwave BI. as described by Bloom (1955) and Mims (1965, 1972), is used to calculate the echo amplitude. Then the signal in the resonator is transformed to the other side of the resonator coupling device. Gains and losses from this point to the detector are used in the calculation of the predicted echo.

The electron spin echo voltage induced in the resonator, as in Eq. (13), is given by

v

^{=N d4»o}

E dt (17)

where N is the number of turns in the resonator and~o is the magnetic flux produced by the spin magnetization,

Mo.

Since the flux density produced by

Mo

is

!-toMo,

<Po is given by

(18)

where

A

is the cross sectional area of the resonator sample loop, 11 is the filling factor, and

!-to =

41t1O·^7•

Mo

varies sinusoidally at the resonant frequency 00, and if the magnetization is fully turned to the xy plane by the microwave pulse, the peak voltage for a single-turn coil (N=1 for a LGR) is

(19)

in agreement with Bloembergen and Pound (1954). Then, from Eq. (22) of Rinard et al., (1994), the output voltage of the resonator coupling structure, V^Ell. is given by

(20)

where R is the resistance of the resonator and

Zo

is the impedance of the transmission line (usually 50Q). The coupling parameter J3 can be calculated from the overcoupledQ and the critically-coupledQ, QH,by

p

= 2QH -I Q

Combining Eqs. (19) and (20), V_EPcan be written as

5.3 Ratio of CW to Pulsed EPR Signal Intensities

(21)

(22)

The ratio of CW EPR signal intensity to electron spin echo intensity for the same sample is the ratio of Eq. (16) to Eq. (22). For clarity, set J3 :::: 1, which is always experimentally possible if the relaxation time is long enough. The algebra simplifies if it is noted that one can use the substitutions

B ^{BXo coL " co AR}

B=J.1oH , OO = y ,Mo =--, QL ::::-, X =Xo- , L=J.1o-, where

J.1o 2R _~co z

z is the length of the loop-gap resonator, and

Jt:..!..

^=H), with which it can vR Z

be shown that

CW rB) B)

: : : : =

-Echo ~co ~ (23)

For convenience, we have written the ratio in both frequency and field units. This ratio implies that if the echo is formed by all of the spins in the sample, the unsaturated CW spectral intensity is equal to the CW microwave HI divided by the EPR line width times the echo intensity. Most commercial EPR spectrometers have an output microwave power of 200 mW. For a standard rectangular resonator (loaded Q - 3600), this corresponds to aHIat the sample of ca. 0.5 G. If the EPR line is about 2.5 G wide, which could be fully excited by a microwave pulse, then the unsaturated CW EPR intensity at 200 mW would be ca. 0.2 times the intensity of the echo . In practice, most CW spectra are obtained with magnetic field modulation. If the magnetic field modulation were approximately equal to line width, this ratio would still hold . Such a large magnetic field modulation would distort the signal, so in practice a smaller modulation amplitude is usually used, resulting in proportionately smaller CW signal relative to echo signal.

3. FREQUENCY DEPENDENCEOFEPRSENSITIVITY