Pulse Sequence Tools
Phase Cycling

Phase Cycling in 1D NMR

PAPS
CYCLOPS
EXORCYCLE
Difference Spectroscopy


Phase Cycling in 2D NMR

Phase Cycling in 1D NMR

An important concept in NMR is the concept of Phase Cycling. Phase Cycling is a method by which unwanted signals in an NMR experiment are eliminated on the basis of their phase property. Those signals can come for example from:

Those unwanted signals might have a different phase behavior from the signal we want to sample. For more information on the signal response to a change of pulse phase you can consult in the tools section: Pulse Phase and Pulse Power and the associated animation. In this animation we can see:

PAPS (Phase Alternating Pulse Sequence)

PAPS is one of the first example of phase cycling. It consists of two transients for which the pulse is applied on opposite axis (X and -X). As the magnetization appear also on opposite axis (+Y and -Y respectively), in order to produce signal averaging, the second signal must be subtracted from the first. The subtraction insures that the NMR signal CO-add while the artefacts that have not modified their phase between the two experiments will cancel.

In the literature this phase cycling is represented by the table below.

Scan Pulse Receiver

1

X

X

2

-X

-X

In the figure below we can see, using the vector model, the relationship between the pulse phase, the receiver phase and the lineshape in the corresponding spectra. If the Phase of the pulse is changed sequentially as shown below and the receiver phase is not moved, the sum of the four spectra will be zero! (the signal would cancel!!)

CYCLOPS (CYClically Ordered Phase Sequence)

CYCLOPS is the quadrature detection phase cycling method. During Quadrature detection, two signals, 90 degree out of phase, are sampled. If there is any imbalance between the two channels, image signals would appear. To remove those artefacts, the two channels need to be switched. The simplest way to do that is to acquire 4 transients where the phase of the pulse is varied in 90 degree increments every transients. The pulse phase cycling can be written as X, Y, -X, -Y which tilt the magnetization along the +Y, -X, -Y, -X respectively. The data from the two channels are then routed to the computer that produce CO-addition of the data by proper use of addition/subtraction and switching of the two channels.

This phase cycling is represented by the table below. The two last columns represents what is happening at the A and B channels in the computer (These channels are acquiring in a constructive fashion the Cosine (Real) and the Sine (Imaginary) wave signals from the Quadrature detection.)

Scan Pulse Receiver
Computer A: COS
Computer B: Sin

1

X

X
+Y
+X

2

Y

Y
-X
+Y

3

-X

-X
-Y
-X

4

-Y

-Y
+X
-Y

In terms of vector model, the two first steps of the CYCLOPS phase cycling are represented below.

Simpler representation of the CYCLOPS is given below. As we can see, with the pulse phase change, the magnetization appear along different axes. The receiver phase (indicated with a green circle in the drawing below) is also advance so that it is always in the same position relative to the magnetization. In this way, the data (real and imaginary) CO-add. Any artefact that do not follow this phase cycling will simply be canceled.

For encoding the phase cycling in the spectrometer, the phases are referred to as 0 1 2 3, representing the X, Y, -X and -Y axis (or the 0`, 90`, 180` and 270' respectively). Using that notation, the pulse and the receiver phase would be 0 1 2 3

Another phase cycling called EXORCYCLE is used in conjunction with refocusing pulse in spin echo

As we have seen above, it is perfectly possible to cancel an NMR signal just by adjusting the phase cycle. One of the usage of phase cycling in NMR spectroscopy is to cancel certain signals while keeping others. This is the case in Difference Spectroscopy where in two experiments, the signal of interest changes sign while the unwanted signal keeps the same sign between two experiment. If the two experiment are subtracted, the unwanted signal can be canceled.

Examples of that can be found in the

To examine 1D-phase cycling in more details you can consult the following animation