## Wednesday, August 27, 2008

### What is Quadrature Detection?

In order to distinguish between negative and positive frequencies relative to the carrier frequency (i.e. the frequency at the center of the spectrum), quadrature detection must be employed. Quadrature detection involves the collection of time domain NMR data on both the x and y axes of the rotating frame of reference. One of these FIDs is called "real" and the other one is called "imaginary". The assignment of the labels "real" and "imaginary" stems from the mathematics of a Fourier transform, which requires a complex input. The Fourier transform in turn produces a "real" spectrum and an "imaginary" spectrum". Having these two signals allows us to phase one of the NMR spectra (eg. the "real" one) entirely in absorption mode after the data have been collected. In an ideal world, it would be nice to have the two FID's collected via separate receiver coils. In this case, with a bit of manipulation, we could improve our signal-to-noise ratio by a factor of the square root of 2 by adding the real and imaginary spectra together. A very nice discussion of this has been presented by Carlos Cobas. In the real world we do not have two receiver coils in quadrature and we must rely on electronic "tricks" to achieve quadrature detection. These "tricks" do not allow us to gain a signal-to-noise advantage by combining the real and imaginary spectra. A simple block diagram of how a spectrometer collects data in quadrature is shown in the figure below. The yellow signal is the intermediate frequency (IF) of the spectrometer. The purple signal is the intermediate frequency of the spectrometer modulated with the NMR spectrum information (IF plus or minus delta nu). Two phase sensitive detectors (PSDs) are used. These devices produce a difference signal between two inputs. The inputs to the first PSD are the IF and the IF plus or minus delta nu. The output is therefore plus or minus delta nu (i.e. the information content of the NMR spectrum). The inputs of the second PSD are identical to the first except the phase of the IF is shifted by 90 degrees. The output is therefore similar to the first PSD except that it has a 90 degree phase difference. The two outputs are the "real" and "imaginary" FID's which provide the input for the Fourier transform.

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## 7 comments:

This was very insightful information. I was wondering if you could answer a question for me. Why does the rf coil in the probe have to be perpendicular to the external magnetic field?

Dear Alisha,

Thank you for your comment. In order to rotate an equilibrium magnetization vector from the z axis into the transverse plane, one must provide a pulse with an oscillating magnetic field transverse the the static field, Bo, at the Larmor frequency of the nucleus being observed. See this post from June 17, 2008 for further discussion:

http://u-of-o-nmr-facility.blogspot.com/2008/06/available-rf-field-for-mas-nmr-probes.html

Glenn

Dear Glenn!

I have a question-how to select quadrature mode when we process our data in NMR Pipe?

Is this parameter selected during aquisition of the spectrum or we can "play" with mode when we processing already obtained FID?

Beforehand thank you!

Zina

Dear Zina.

Thank you for your question. Unfortunately I have absolutely no experience with NMR Pipe so I am unable to answer your question. I have found a manual here:

http://www.nmrscience.com/ref/index.html

Perhaps some other readers can reply.

Glenn

It is interesting that you say 'in the real world we do not have two coils', because when I worked on MRI imaging (1979) we did use two coils. The Wikipedia article on 'quadrature detection' also seems to ignore that you can (and we did) use two physical coils.

Dear Glenn,

Thanks very much for the beautiful blog, your blog is the first place for me to consult if I have a question.

My question is: I am curious why we use quadrature detection. More explicitly, why don't we collect the frequencies as they are in MHz? I have read somewhere that the receiver electronics cannot handle large frequencies in NMR and that's why we use quad detection to distinguish between positive and negative frequency shifts wrt Larmor frequency. But even in that case, when the electronics can handle finding the Larmor frequency, why can't they handle a bit larger or smaller frequencies?

Thanks for your time,

Reza

Hi Reza,

"I am curious why we use quadrature detection".

One needs both a real and an imaginary input for a Fourier transform in order to distinguish positive from negative frequencies. These inputs are those from the x and Y axes of the rotating frame of reference.

"Why don't we collect the frequencies as they are in MHz?"

The true frequencies in MHz are sent to the receiver. These frequencies are mixed down to an intermediate frequency modulated with the offset frequencies. This frequency is chosen by the instrument manufacturer and is one conveniently handled by the spectrometer electronics. This process allows the NMR resonance frequencies of all isotopes to be handled in the same way by the spectrometer. The intermediate frequency is subtracted out later leaving only the offset frequencies which are present in the FID you see on the display. We don't collect and display the frequencies in MHz because this would not allow the comparison of data from one instrument to another. No two magnets are identical. This is why we use a ppm scale.

"I have read somewhere that the receiver electronics cannot handle large frequencies in NMR and that's why we use quad detection to distinguish between positive and negative frequency shifts wrt Larmor frequency"

I don't think this is true.

"when the electronics can handle finding the Larmor frequency, why can't they handle a bit larger or smaller frequencies?"

This is not the issue. It is the fact that the Fourier transform requires inputs from to axes that are 90 degrees apart in order to distinguish frequencies greater than aor less than the carrier frequency.

Glenn

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