Info

I+

90y -

1 I+ 2 I

- 21-

-Iz

I+

90-x -

1 I+ 2 I

+ 21-

-iIz

I+

90-y -

1 I+ 2 I

- 21-

+ Iz

(these can all be calculated using the definitions I+ = Ix + i Iy, I- = Ix - i Iy and the relations Ix = 1/21+ + 1/21-, i Iy = 1/21+ - 1/21-) Note that as we increment the phase of the pulse by 90° (x, y, -x, -y), the phase factor multiplying the resulting I+ component (Ap = 0, no change in coherence order from the original I+ spin state) does not change, whereas the phase of the I- component (Ap = -2) is shifted by 180° each time. The Iz (sometimes written as Io) component (Ap = -1) is shifted in phase by 90° each time if we use the complex plane (x' = real, y' = imaginary) to represent the phase (i, -1, -i, 1 correspond to the /, -x', -y and x axes, respectively, in the rotating frame). In general, the effect of a change in pulse phase A$p on the phase of the resulting coherence depends on the change in coherence order Ap caused by the pulse

In the above example, A$p = 90° and A$c = 0°, 180°, and 90° for Ap = 0, -2, and -1, respectively.

We could select the I+ coherence if the experiment was repeated four times, with the signal added to the sum-to-memory each time at the receiver. The I- coherence (and any coherence derived from it in a longer, more complex pulse sequence) would cancel out because we would have 1/2 I- -1/2 I- + 1/2 I- - 1/2 I- for the four scans. The Iz part would not be observable, but even if it were converted to an observable coherence later in the pulse sequence, this coherence would carry along the phase factors i, -1, -i, and 1, which add together to give a zero signal after four scans. If instead we alternately add and subtract the FID signals from successive scans in the sum-to-memory, the I+ signal would cancel (1/2 I+ - 1/2 I+ + 1/2 I+ - 1/2 I+), the I- signal would accumulate (+ 1/2 I- - (-1/2 I-) + 1/2 I- - (-1/2 I-)), and the Iz component would cancel (+iI2 - (-Iz) - i Iz - (+Iz)). The net result is that we would select the I- component and destroy all other components in a four-scan phase cycle. To select the Iz component (or some observable coherence derived from it), we would advance the receiver phase by 90° with each successive scan. This is accomplished by adding the "real" (x' axis) signal from the ADC to the "imaginary" sum in the sum-to-memory and subtracting the "imaginary" (y' axis) signal coming from the ADC from the "real" sum in the sum-to-memory. In effect, we have rotated our reference frame by 90° because the x' axis is being detected as the y' axis and the y' axis has been moved to the -x' axis. For a four-scan phase cycle with A$r (receiver phase change) of 90°, the signal would be routed as follows:

Scan

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