1. 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 http://ugc-inno-nehu.com/links_from_web.html “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. 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 http://www.geocities.com/sankarampadi/eulexp.html 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. 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. 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 1 0000 15 1111 2 0001 14 1110 3 0010 13 1101 4 0011 11 1011 5 0100 8 1000 6 0101 4 0100 7 0110 1 0001 8 0111 0 0000 --------- Computer memory Time domain 15 0 11 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. 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. 6 Time domain FID data: 32 points Real Imaginary 16 data 16data points points Frequency domain spectrum

7. 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=0 +1 0 Value between +1 & 0 f c cos(2πνt) + f s sin (2πνt) with f c 2 +f s 2 =1

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