1 Nuclear Magnetic Resonance ANIMATED ILLUSTRATIONS MS Powerpoint Presentation Files Uses Animation Schemes as available in MS XP or MS 2003 versions A class room educational material “Pulsed FT NMR” FID generation and acquisition Slide # 2-3 FID digitization and FFT computation Slide #4 FFT Computer Program Slide # 5 Obtained Spectrum Elaboration Slide # 6-8

2 For a π/2 pulse the value of ‘ω 1 t ‘=90º; ω 1 =γH 1 The impulse on … x,y-axes Rotating about Lab Z-axis; frequency same as the precession frequency Z X Y X Y X Y Rotating system viewed from within that system: STATIONARY X Y Z A rotating RF magnetic field results on application of RF at resonance frequency Viewed from within the rotating frame the RF field appears stationary Z = unit vector along z-axis Rotation about z-axis= e -iφ Z Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed. Rotation about z-axis= e -i ω t Z An equation representing this rotation would be displayed In terms of Angular momenta, I z replaces ‘z’; for rotation about z-axis = e -iφ I z Represents rotation by angle φ about z-axis; Φ can be replaced by frequency of rotation in radians ‘ω’ multiplied by ‘t’ the time lapsed. Rotation about z-axis= e -i ω t I z RF source/ transmitter Connected to coil. Linearly oscillating field along the coil axis (X-axis) The linearly oscillating field can be resolved into two counter rotating components Only one of the rotating component is effective in causing resonance 2 H 1 I -x cos(ωt) = H 1 e -iI -x ωt H 1 e +iI -x ωt A Pulse lasts only for a few μ Secs. For proton NMR a H 1 of ~25Gauss along ‘-x’, pulse widths are approximately 10-15μs + The impulse off… RF field is along –X in the XY plane, the effect caused would be rotation about X- axis, unlike the precession about z-axis To repeat the animated RF depictions “right click” and choose option: ‘previous’ Click to end this slide CLICK ! Repeat pulsing?.....Right Click and choose menu option ‘previous’ and CLICK!

3 Apply the 90º, -X pulse now, P -X π/2 X Y Z Viewed from within the rotating frame the RF field appears stationary Tilted Magnetization in xy plane viewed from Lab Frame. Precessing at resonance frequency. X Y After the pulse: at t>0 Induced NMR signal at receiver (RF 300 MHz ) Rotating x,y axes :rotation about Lab z-axis A BLUE line for z-Axis indicates the view from within the rotating coordinate system. Z Y Magnetization in XY plane appears stationary when viewed in Rotating Frame from within the rotating frame X Y Z When the XY magnetization decays with transverse relaxation time T 2, immediately after the pulse…… When PSD reference is in phase off set from Resonance frequency; NMR signal at receiver (RF 300 MHz ) If No T 2 …….. Free Induction Decay Signal No More Clicks ! This show has automatic timings The F.I.D. When PSD reference is in phase at Resonance frequency; NMR signal at receiver (RF 300 MHz ) Tilting of magnetization Described in rotating frame: Rotation about the X-axis I(t p ) = e -iI -x φ I z e +iI -x φ with φ=90º & t p is pulse duration At the end of pulse, time for F.I.D. begins with t=0 tptp t=0 Acquisition time ~5T 2 FID CLICK to Transit

4 PULSED NMRAcquire F.I.D. Free Induction Decay NMR detection soon after a strong pulse: precessing nuclear magnetization induces a signal in coil when it is free of the perturbing EM radiation F.I.D. DIGITIZE Analogue to Digital Converter A.D.C. AddressContents Computer memory Time domain FFT from FID Computer input Frequency Domain Spectrum Computer output This one- dimensional FT NMR spectrum is the same information as the C.W. NMR spectrum Acquisition is automatically in the digitized form Next Slide

5 dimension A(50),B(50),Y(50),X(50) K=32 open (unit=1, file="output") Print 10,K DO 11 N=1,K X(N)=(N-1)*3.5/K X(N)=EXP(-1.0*X(N)) Y(N)=X(N)*(COS(2*3.14*(N-1)*10.0/K)+ 1 COS(2*3.14*(N-1)*4.0/K)) 11 write (1,20) N,Y(N) DO 12 M=1,K A(M)=0 B(M)=0 DO 13 N=1,K-1 A(M)=A(M)+Y(N)*COS(2*3.14*(M-1)*(N-1)/K) 13 B(M)=B(M)+Y(N)*SIN(2*3.14*(M-1)*(N-1)/K) A(M)=A(M)/K B(M)=B(M)/K M2=M/2 12 write (1,30) M2,A(M2),B(M2) 10 FORMAT(1x,I2) 20 FORMAT(1x,I2,2x,F10.5) 30 FORMAT(1x,I2,2x,F10.5,2x,F10.5) close (unit=1) STOP END A program in Fortran for “Fast Fourier Transform” Digitized FID Signal Digital Computer FFT Program run OUTPUT

6 Time domain FID data: 32 points Real Imaginary 16 data 16data points points Frequency domain spectrum

7 COS Real Imaginary F.T Real Imaginary F.T SIN RealImaginary F.T Arbitrary Phase Provision is made in the data processing system, for routinely applying phase corrections t= Value between +1 & 0 f c cos(2πνt) + f s sin (2πνt) with f c 2 +f s 2 =1

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