Ernst angle

The initial pulse can be selected to conform to the Ernst angle to improve S/N, rather than being restricted to 90°. In that case a second 180° pulse is needed to... 

FIGURE 12.1 Pulse sequence for attached proton test (APT).The initial pulse width can be set to conform to the Ernst angle in order to optimize sensitivity. 

Richard Ernst, who won the 1991 Nobel Prize in Chemistry, conclusively demonstrated that the second method of using less-than-90° pulses with no delay times is superior (Ernst and Anderson, 1966). He calculated the ratio 7/7] (max) and related it to the optimum angle of rotation, (the Ernst angle). In this expression, T is the total time between pulses, which... 

While the Ernst angle relationship has worked very well for many years, problems can arise if 7/7] (max) moves, for a variety of reasons, off scale (to the left) or if the resulting... 

Figure 2-4 Plot used to identify optimum flip angle (Ernst angle).

For Jr/ T] =3 the Ernst angle is close to 90°. In a repetitive pulse experiment in which tR is chosen much shorter than this and a is set to q e an S/N advantage of about 2 is obtained. 

Under conditions where there is complete decay of transverse magnetisation between scans (i.e. the FID decays to zero) the optimum tip angle for a pulse repetition time h, known as the Ernst angle, Oe, is given by [1,2] ... 

Figure 4.2. The Ernst angle for optimum sensitivity when signal averaging. The pulse tip angle is dictated by the pulse repetition time, t relative to the longitudinal relaxation time, Ti.

Figure 4.28. Signal enhancement of the N spectrum of ammonium nitrate with INEPT. Direct observation using (a) the Ernst angle optimised for the nitrogen Ti and (b) INEPT optimised for the proton Ti. Both spectra were collected in the same total accumulation time.

Ernst angle as a function of the longitudinal relaxation time... 

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