NMR Part II, Quadrature Detection

Transcription

1 Nmr 6.mcd 5/3/97 NMR Part II, Quadrature Detecton Quadrature detecton uses two detector channels separated by 9 degrees. Ths dstngushes the drecton of rotaton (clockwse or counterclockwse) n the rotatng frame of the spectrometer. Ths document shows how the quadrature sgnal s transformed to produce the real and magnary spectra. Sgnals Generated: Ths secton defnes the sgnals that are observed. You can change the ampltude, frequency, phase, and relaxaton constants for each nucleus. The system wll accept two dfferent nucle so that you can compare the effect of dfferent settngs. Wave a Wave b Ampltude of Wave A a A b Frequency of Wave ν a. Hz ν b. Hz Phase of Wave θ a. rad θ b. rad Relaxaton Constant T a. 5 sec T b. 5 sec Samplng Parameters: Ths secton defnes the samplng parameters of the spectrometer. You can change the number of data ponts and the dwell tme. These settngs effect the resoluton, spectral wndow, and acquston tme. Number of Data Ponts Sampled N (must be a bnary number) Dwell Tme DW..8 sec Non-Ideal Problems: These parameters reflect non-deal condtons that occur n a real spectrometer. You can set these to non zero values to see how they effect the spectrum. Error n Quad Phase Shft φ. π Imbalance of Imagnary Amplfer Gan Gan rel_error. % DC n Real Channel (% of Total Ampltude) DC Real. % DC n Imagnary Channel (% of Total Ampltude) DC Imag. %

2 Nmr 6.mcd 5/3/97 Calculated Parameters: The followng are calculated from the above parameters. Acquston Tme AT DW. N AT = 8.9 sec Spectral Wndow SW. DW SW = 6.5 Hz Resoluton Resoluton AT Resoluton =. Hz Phase shft error φ = deg DC offset, Real channel DC. R DC Real A a A b DC R = DC offset, Imagnary channel DC. I DC Imag A a A b DC I = Amplfer Gan msmatch G I Gan rel_error G I = Angular Frequency Wave a Wave b ω.. a π ν a ω a = 6.83 rad. sec ω.. b π ν b ω b =.566 rad. sec Number of data ponts N =.4 3 Index: These ndexes are used for varous calculatons Index Counters,.. ( N ) j,.. Tme Index. DW Frequency Index j. N DW N Frequency Index for Quadrature spectra frequency quad. N DW N. N. DW

3 Nmr 6.mcd 5/3/97 Real Channel: For quadrature detecton, two sgnal channels are used. One s the called the real channel. The real channel produces a cosne wave. Below are the calculatons used to generate the sgnal for ths channel. Calculate FID: FID for the real channel based upon the above nformaton. Wave a W.. R_a A a cos t. ω a θ a e T a DC R Wave b W.. R_b A b cos t. ω b θ b e T b DC R Sum of Waves a and b W R W R_a W R_b Wave a, Real Channel W R_a Wave b, Real Channel W R_b FID, Real Channel W R

4 Nmr 6.mcd 5/3/97 Fourer Transform Sgnal From Real Channel: The Fourer transform of the sgnal from the real channel produces a real and an magnary spectrum. The real spectrum corresponds to the absorpton mode spectrum or the cosne component. The magnary spectrum corresponds to the dsperson mode spectrum or the sne component. These are labeled the real spectrum of the real channel (real of the real) and the magnary spectrum of the real channel (magnary of the real). FFT of Real FID a F R_a fft W R_a FFT of Real FID b F R_b fft W R_b FFT of Real FID (Sum) F R fft W R Wave a, Real Channel, Real & Imag Spec Re F R_aj Im F R_aj Wave b, Real Channel, Real & Imag Spec Re F R_bj Im F R_bj Real Channel, Real and Imagnary Spectra Re F Rj Im F Rj

5 Nmr 6.mcd 5/3/97 Generatng Imagnary Channel. The second quadrature channel s called the magnary channel. Is orented 9 degrees from the real channel. Ths produces a sgnal that corresponds to a sne wave. Generatng FID: W... I_a G I A a sn t. ω a θ a φ e T a DC I W... I_b G I A b sn t. ω b θ b φ e T b DC I W I W I_a W I_b Wave A, Imagnary Channel W I_a Wave b, Imagnary Channel W I_b FID, Imagnary Channel W I

6 Nmr 6.mcd 5/3/97 Fourer Transforms of Imagnary Channel FID: The FT of the magnary channel also produces a real and magnary spectrum. These are labeled the real spectrum of the magnary channel, and the magnary spectrum of the magnary channel. FFT of Imagnary FID a F I_a fft W I_a FFT of Imagnary FID b F I_b fft W I_b FFT of Imagnary Channel FID (Sum) F I fft W I Wave a, Imag Channel, Real & Imag Spec Re F I_aj Im F I_aj Wave b, Imag Channel, Real & Imag Spec Re F I_bj Im F I_bj Imagnary Channel, Real and Imag Spectra.5 Re F Ij Im F Ij

7 Nmr 6.mcd 5/3/97 Quadrature Manpulaton. The spectra from the Real and Imagnary channel are combned to produce a sngle set of quadrature detected real and magnary spectra. Generatng the Real Spectrum: The real spectrum s generated from the real spectrum of the real channel and the magnary spectrum of the magnary channel. The left sde of the real spectrum (frequences less than the spectrometer frequency) s generated by subtractng the real of the real and the magnary of the magnary. The resultng matrx s nverted to follow conventon for the dsplay of spectra. The rght sde of the spectrum (frequences greater than the spectrometer frequency) s generated by addng the magnary of the magnary and the real of the real. The fnal spectrum s dsplayed by placng the two spectra sde by sde. Hz s n the center. To the rghs ncreasng frequency, to the lefs reduced frequency (relatve to the spectrometer frequency). Ths conforms wth standard NMR data presentaton. To understand how ths spectrum s produced, examne the real spectrum from the real channel and the magnary spectrum of the magnary channel. Pay close attenton to the phase dfferences between sgnals wth postve and negatve frequences. REAL left Re F R Im F I REAL rght Re F R Im F I REAL j REAL left N j REAL N j REAL rghtj Quadrature Phase Detected Real Spectrum.5 Sgnal REAL frequency quad

8 Nmr 6.mcd 5/3/97 Generatng the Imagnary Spectrum: The quadrature detected magnary spectrum s produced n a smlar manner usng the magnary spectrum from the real channel and the real channel of the magnary spectrum. To understand what happens here, examne the magnary spectrum from the real channel and the real spectrum from the magnary channel. Imagnary left Re F I Im F R Imagnary rght Re F I Im F R Imagnary j Imagnary left N j Imagnary N j Imagnary rghtj Quad Phase Detected Imagnary Spectrum.5 Sngal Imagnary frequency quad Frequency

9 Nmr 6.mcd 5/3/97 Questons. Change the sgnal frequency and observe how ths changes the FID and the spectra. Pay close attenton to the phase of the ntermedate spectra, and thnk about how they are manpulated to produce the quadrature spectra. a. Change the frequency so thas greater than the spectral wndow. b. Enter a negatve frequency and see what happens.. Make changes to the non-deal settngs and observe how they effects the ntermedate spectra and the fnal spectrum. 3. What advantages does quadrature phase detecton have? Ths document was developed by: Scott E. Van Bramer Department of Chemstry Wdener Unversty Chester, PA 93 svanbram@scence.wdener.edu