This sinc function represents the B1 field as a function of frequency being sent into the sample. Only magnetization vectors in the sample with resonant frequencies that are also found in the sinc function will experience a rotation. The NMR signal is related to the amount of Z magnetization (MZ) rotated into the XY plane (MXY). For a rotation angle q, the signal is
For MXY to be greater than or equal to 0.9, θ must be between 64.15 and 115.85 degrees. The rotation angle is proportional to B1 through the rotation equation
B1 is proportional to the magnitude (sqrt(RE2 + IM2)) of the sinc function. Adopting a normalized B1 (B1=1 for a 116 degree rotation), B1=0.553 for a 64.15 degree rotation. Define ν as the frequency in the laboratory frame of reference. The RE and IM parts of the function are:
Solving this equation numerically we get the range of frequencies, Δν = 22.6 kHz, or 359 ppm.
This result is significant because it tells us that an 359 ppm wide spectrum would easily be rotated by approximately 64 to 116 degrees (giving 90% of the possible signal) with a 50 microsecond wide pulse.