Instrumentation Primer for NMR

Transcription

1 Instrumentation Primer for NMR P. J. Grandinetti L Ohio State Univ. Jan. 10, Check out Terry Gullion s ENC tutorial video link: ***Basic Useful Circuits for NMR Spectroscopy*** 2 Check out Kurt Zilm s ENC tutorial link: Design, Care and Feeding of NMR Probes: A Tutorial P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

2 Precessing tops Precessing top Magnetic top in zero gravity precessing in a magnetic field Spin Angular Momentum Precession Direction N S How do we measure precession frequency of a magnetic top? P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

3 SirMr. Michael Faraday ( ) During his lifetime, he was offered a knighthood in recognition for his services to science, which he turned down on religious grounds, believing that it was against the word of the Bible to accumulate riches and pursue worldly reward, and stating that he preferred to remain plain Mr Faraday to the end. Wikipedia, 2018 P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

4 How to measure precession frequency of a magnetic top? One approach is to exploit Faraday s law of induction, discovered in 1831, which tells us that a changing magnetic flux will induce a current in a surrounding loop of wire. Faraday s law of induction: = dφ dt is the EMF and Φ is the magnetic flux. Electromotive Force (EMF, i.e., voltage) induced in coil is related to change in magnetic flux through the loop of wire with time. Φ(t) = B(t) d a is surface attached to loop of wire. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

5 N S How to measure precession frequency of a magnetic top? Place a coil of wire of radius R coil around our spinning magnetic top to detect the precession frequency. Magnetic dipole vector of top changes with time according to μ(t) = μ [ sin ψ cos(ωt + ξ 0 ) e x + sin ψ sin(ωt + ξ 0 ) e y + cos ψ e z ] μ is length of precessing vector, ψ is angle between precessing vector and z-axis, ξ 0 is initial phase of precessing vector, and ω is angular precession frequency. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

6 Advanced Exercise 1. Show that the EMF induced in a loop of wire surrounding a precessing magnetic dipole, μ(t) = μ [ sin ψ cos(ωt + ξ 0 ) e x + sin ψ sin(ωt + ξ 0 ) e y + cos ψ e z ] is given by x (t) = dφ x(t) dt = ω μ 0 2R coil μ sin ψ sin(ωt + ξ 0 ) Hint: Start with definition of magnetic flux and use Stoke s Theorem, Φ(t) = B dip (t) d a = ( A dip (t)) d a = A dip (t) d l represents circumference of wire loop; A dip (t) is magnetic vector potential for point dipole (see Griffiths 3rd Ed. E&M text, p. 244) A dip ( r) = μ 0 μ e r 4π r 2. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

7 Faraday Detector of precessing magnetic dipole x (t) = dφ x (t) dt = ω μ 0 2R coil μ sin ψ sin(ωt + ξ 0 ) From this signal we measure precession frequency. Amplitude is directly proportional to magnetic dipole moment strength, μ. Signal scaled by sin ψ. The closer the magnetic dipole precesses to z-axis, the smaller the EMF signal. Signal scaled by inverse of coil radius. EMF amplitude decreases with increasing coil radius. EMF amplitude increases with increasing precession frequency. When magnetic top precesses in higher static magnetic flux densities we get higher precessing frequencies and hence larger signal amplitudes. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

8 Exercises 2. Based on x (t) = dφ x(t) dt = ω μ 0 2R coil μ sin ψ sin(ωt + ξ 0 ) calculate the increase in signal from doubling the external magnetic field strength. 3. Explain why no NMR signal is usually detected when the long axis of the NMR receiver coil is parallel to the external magnetic field direction. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

9 In 1820 Hans Christian Ørsted discovered that electric current produces a magnetic field that deflects compass needle from magnetic north, establishing first direct connection between fields of electricity and magnetism. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

10 Biot-Savart Law Jean-Baptiste Biot and Félix Savart worked out that magnetic flux density produced at distance r away from section of wire of length dl carrying steady current is d l r r 3 Biot-Savart law Direction of magnetic field vector is given by right-hand rule: if you point thumb of your right hand along direction of current then your fingers will curl in direction of magnetic field. d B = μ 0 4π current P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

11 Calculate magnetic field produced by current in wire loop Magnetic field along z axis away from current loop B(z) = e z μ 0 4π = e z μ 0 4π cos θ R 2 coil + z2 d l R 2 coil (R 2 coil + z2 ) 3 2 Magnetic field at center of current loop B(0) = e z μ 0 4π 1 R coil Magnetic field strength at center scaled by inverse of coil radius. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

12 Let s build an NMR Spectrometer! Radio Frequency Source Output of Freq. Source is Continuous Transmitter Switch N S Sample Receiver Switch Receiver 6 essential components in our primitive NMR spectrometer: 1 a radio frequency (rf) source tuned to resonance frequency of nuclei 2 a switch (or gate) for turning rf irradiation on and off 3 a magnet to polarize and split nuclear spin energy levels 4 a transmitter and detector coil containing sample 5 a switch (or gate) in front of receiver for protection 6 receiver, which could simply be oscilloscope in this design P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

13 Let s build an NMR Spectrometer! Radio Frequency Source Output of Freq. Source is Continuous Transmitter Switch N S Sample Receiver Switch Receiver Construction of such an instrument is straightforward. Because time scale of NMR experiment is on order of microseconds, switching times for gates need to be on the order of nanoseconds for precise time resolved measurements. Computer controlled low power radio frequency gates having such switching speeds are readily available commercially. Check out link: In primitive spectrometer computer controls timing for opening and closing of transmitter and receiver gates. Check out link: Arduino boards P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

14 A Primitive NMR Spectrometer Radio Frequency Source Output of Freq. Source is Continuous Transmitter Switch N S Sample Receiver Switch Receiver Simplest experiment pulse and detect signal consist of 3 steps: Step Transmitter switch state Receiver switch state Duration 1 OFF OFF 30 seconds 2 ON OFF 4 microseconds 3 OFF ON 100 milliseconds Elementary version of Pulse Sequence or Pulse Program Important part of pulse sequence is duration of each step, or event. NMR spectrometers have many more computer controlled switches than receiver and transmitter switches. NMR spectrometers have pulse sequence languages to write sequences containing loops, if statements, and other possibilities. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

15 The NMR Probe In spectrometer coil wrapped around sample is called transceiver coil. 1 Used to produce oscillating B 1 field that rotates magnetization 2 Used as Faraday detector of precessing magnetization after pulse Let s examine what is needed to enhance efficiency of this coil in producing B 1 fields. These same changes, in turn, will also enhance efficiency of this coil as a detector. We start by reviewing the basics about voltages and currents in electronic components like resistors, capacitors, and inductors. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

16 The Resistor Apply oscillating voltage (t) = 0 cos ωt to a resistor in the circuit below Oscillating current across resistor is given by (t) = (t) R = 0 R cos ωt = 0 cos ωt Maximum current through resistor, 0, related to 0 by Ohm s law: 0 = 0 R P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

17 The Inductor Apply same oscillating voltage to inductor (like our transceiver coil) Oscillating current across inductor is given by (t) = t t 0 (t) L ds = 0 ωl sin ωt = 0 sin ωt Current oscillation is 90 out of phase with voltage oscillation. (t) = 0 cos ωt and (t) = 0 ωl cos(ωt π 2) = 0 cos(ωt π 2) Ignoring phase difference, 0 is related to 0 according to 0 = 0 ωl P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

18 The Inductor 0 = 0 ωl Inductor behaves like frequency dependent resistance of ωl, with current oscillation 90 out of phase with voltage oscillation. Because it is 90 out of phase it is called reactance (not resistance). Low frequency currents pass through inductors and high frequencies are blocked. in out XL = ωl in out ω Here you see problem of using inductor alone as transceiver coil. As receiver coil, oscillating current from EMF, (t), due to precessing magnetization decreases rapidly as precession frequency increases. As a transmitter of oscillating B 1 field, need to push higher currents through coil to get same B 1 field at higher frequencies. For fixed oscillating voltage source (i.e., fixed power), current decreases with increasing frequency, and so does B 1 field strength. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

19 The Inductor - Practical Note Estimate inductance of coil from its dimensions. Inductance, L, in μh is L = r2 n 2 9r + 10l r is radius of coil in inches, n is number of turns, l is coil length in inches. Quality factor or Q factor of inductor at operating frequency ω is defined as ratio of reactance of coil to its resistance Q = ωl R Optimum Q is attained when the length of the coil (l) is equal to its diameter (2R) P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

20 The Capacitor Apply oscillating voltage to capacitor Oscillating current across inductor is given by (t) = C d (t) dt = Cω 0 sin ωt = 0 sin ωt 1 Current oscillation is 90 out of phase with the Voltage oscillation (t) = 0 cos ωt and (t) = Cω 0 cos(ωt + π 2) = 0 cos(ωt + π 2) 2 Ignoring phase difference, 0 is related to 0 according to 0 = 0 1 (ωc) P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

21 The Capacitor Capacitor behaves like a frequency dependent reactance of 1 (ωc) with current oscillation 90 out of phase with voltage oscillation. Capacitor blocks (reacts against) low frequency currents, but allows high frequencies to pass the opposite behavior of inductor. Xc = 1/(ωC) in in out out ω P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

22 Complex Voltage and Current Relationships between maximum current and maximum voltage across a resistor, capacitor, and inductor 0 = 0 R (resistor), 0 = 0 1 (ωc) (capacitor), and 0 = 0 ωl (inductor) Need relationship for current and voltage at all times, not just for maximum values; and includes the phase information. Defining complex voltage c (t) = 0 e iωt, where actual voltage is real part, (t) = R{ 0 e iωt } = 0 cos ωt Similarly, define complex current c (t) = 0 e iωt, where actual current is real part (t) = R{ 0 e iωt } = 0 cos ωt To phase shift (t) by 90 multiply complex voltage c (t) by e iπ 2, (t) = R{ 0 e iωt e iπ 2 } = 0 cos(ωt + π 2) P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

23 Capacitor Impedance Applying this approach to current-voltage relationship for capacitors we write { (t) = 0 c (t)e iπ 2 } cos(ωt + π 2) = R 1 (ωc) 1 (ωc) Since e iπ 2 = i we can simplify to { } { } c (t) c (t) (t) = R = R i (ωc) where Z C = i (ωc) is the impedance of the capacitor. In terms of complex current across capacitor we write c (t) = c(t) Z C Obtain familiar Ohm s law, describing relationship between current and voltage at all times, but now it includes phase information. Z C P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

24 Inductor Impedance Applying this approach to current-voltage relationship for inductors we find { } c (t) (t) = R iωl In terms of complex current across inductor we write c (t) = c(t) Z L where Z L = iωl is the impedance of the inductor. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

25 Impedance, Z Z = R + ix R is Resistance: impedes current flow from collisional processes and dissipates energy as heat. Analogous to friction. X is Reactance: impedes current from changing electric and magnetic fields associated with alternating currents. It is not associated with power dissipation. Analogous to inertia. Z R = R for resistors, Z C = i (ωc) for capacitors, and Z L = iωl for inductors Ohm s law can be generalized to include inductors and capacitors. For components in series we have For components in parallel we have Z T = Z 1 + Z 2 + Z Z T = 1 Z Z Z 3 + P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

26 A Tuned Circuit Ready to solve our problem with transceiver coil. To make problem more realistic include wire resistance, R t, as in circuit below transceiver coil Ζ Τ Total impedance is Z T = Z R + Z L = R t + iωl ω/2π Magnitude of impedance is Z T = Z T Z T = R 2 t + ω 2 L 2 Only at ω = 0 do we have lowest impedance and highest current. NMR signal oscillates at megahertz frequencies so this is not optimal. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

27 A Tuned Circuit We can solve this problem by adding a capacitor in series as shown below. transceiver coil Total impedance is ( Z T = Z R +Z L +Z C = R+i ωl 1 ) ωc Set Z L = Z C, so ω 0 = 1 LC and then Z T = R Highest current amplitude at ω 0. Ζ Τ ω/2π P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

28 A Tuned and Matched Circuit Power in the coil is rf xmitter NMR Probe P(ω 0 ) = 2 (ω 0 )R t = 2 (ω 0 )R t (R s + R t ) 2 Want maximum power transfer from transmitter to coil. ( Z T = R s + R t + i ωl 1 ) ωc at resonant frequency ω 0 = 1 LC Current is Z T = R s + R t (ω 0 ) = (ω 0) R s + R t dp(ω 0 ) dr t = (ω 0 )2 (R m + R t ) 2 2 (ω 0 )2 R m (R m + R t ) 3 = 0 Solving this expression gives the condition R t = R s for the maximum power transfer. When R t = R s we say that the impedance of the tuned circuit is matched to the transmitter s impedance. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

29 A Tuned and Matched Circuit Transmitter s impedance (resistance) is usually fixed at R s = 50 Ω. R t is generally less than 1 Ω. How do we match impedances? Add another capacitor to circuit. rf xmitter NMR Probe In this series tuned, parallel matched circuit probe impedance is 1 Z T = iωc m + 1 ( R t + i ωl 1 ωc t If C t and C m are adjusted so impedance is completely real (no imaginary part) and equal to Z T = 50 Ω at frequency ω 0 then we have maximum power transfer between transmitter and sample, or also between sample and receiver. ) P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

30 Another Tuned and Matched Circuit rf xmitter To learn more... 1 Check out Terry Gullion s ENC tutorial video link: Basic Useful Circuits for NMR Spectroscopy 2 Check out Kurt Zilm s ENC tutorial link: Design, Care and Feeding of NMR Probes: A Tutorial NMR Probe P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

31 Jupiter: self-assembled P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

32 The Duplexor Our spectrometer needs to switch probe between transmitter and receiver to protect receiver from high power rf pulse of transmitter called the duplexor. N S Radio Frequency Source Transmitter Switch db High Power Amplifier Duplexor Switch Receiver Switch Receiver Because duplexer is switching between high power rf from transmitter and low power rf from probe there is an inexpensive and simple passive circuit that can be used to rapidly perform this switching. To understand how this works need to review 2 important devices: (1) the cross diodes, and (2) quarter-wave transmission lines. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

33 Diode Plot of current flow versus applied voltage for diode 20 ma 10 ma Diode symbol: Diodes is one-way valve for current (i.e. direction of arrow) v -50 v -1 μa 1 v 2 v Applied Voltage Current Flow -2 μa Current Flow No Current Flow Note axes ranges. For diode current flows forward after voltage of greater half a volt is applied. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

34 Cross-Diodes Cross-diodes have property that current flows in either direction as long as voltage is greater than half a volt in magnitude. Two diodes connected antiparallel 20 ma = 10 ma Symbol for Cross diodes -2 v -1 v -10 ma 1 v 2 v Applied Voltage -20 ma Current Flow P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

35 Cross-Diodes in NMR Use cross-diode to protect receiver from high power rf pulse from probe Receiver 50 Ω Use cross-diode to block low power noise from transmitter from entering probe. Transmitter 50 Ω to probe High voltage pulse would turn diodes on and go to ground instead of going into receiver with its 50 Ω impedance. Broadband noise from transmitter can easily saturate NMR signal and needs to be eliminated. As long as noise voltage doesn t exceed threshold voltage of diode it will be blocked from going to probe. When signal-to-noise ratio unexplainably drops it is often a blown cross-diode that is problem. Solid-state NMR experiments which use long high power pulses such as cross-polarization are often responsible for blown out diodes. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

36 Transmission lines Impedance of all devices (i.e. probes, transmitter, receiver) need to be matched for maximum power transfer. Connect all these devices together making sure impedance is 50 Ω everywhere. Transmitter 50 Ω If transmitter impedance is 50 Ω then current and voltage oscillations will be in-phase transmission line (usually a coaxial cable) Load (Probe) 50 Ω Will load (Probe) see 50 Ω impedance? Will the load see current and voltage oscillations in phase? To match impedance of source, Z s, and load, Z l, the characteristic impedance of transmission line, Z 0, must be Z 0 = Z s Z l = = 50 Ω If transmission line is terminated by load that doesn t match its characteristic impedance then voltage and current waves are partially reflected and standing waves are set up in transmission line. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

37 Quarter-Lambda lines - Shorted End Terminate transmission line with short to ground, that is, connect inner conductor to outer conductor Outer Conductor End shorted so that Z l = 0 Ω All voltage and current oscillation will reflect and set up a standing wave. Transmitter 50 Ω λ/4 Inner Conductor Voltage is zero and current is maximum I(x) at shorted-to-ground end. Current is zero and voltage is maximum at λ 4 away from shorted-to-ground end where source is connected. Cable impedance at point where source is connected looks like V(x) x x Z = (0) (0) = 0 0 amps = Ω Transmitter can t tell difference between nothing and λ 4 with shorted end connected. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

38 Quarter-Lambda lines - Open End What if we didn t short the end, but left the two conductors unconnected? Transmitter 50 Ω λ/4 V(x) x I(x) x Voltage is maximum, and current is zero at open end. Current is maximum and voltage is zero at λ 4 away from open end where source is connected. Cable impedance at point where source looks like Z = (0) (0) = 0 volts = 0 Ω 0 All transmitter power is being sent to ground when λ 4 with an open end is attached. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

39 Quarter-Lambda lines Summary λ 4 length cables with shorted ends look like an infinite impedance at the source. λ 4 length cables with open ends look like a zero impedance (short to ground!) at the source. Counter intuitive if you ve only ever thought about DC circuits. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

40 Duplexor Circuit Duplexer switches probe between transmitter and receiver. Consider circuit below: Probe 50 Ohms Transmitter 50 Ohms λ/4 Receiver 50 Ohms High voltage pulse from transmitter turns on all cross-diodes and transmitter sees Probe 50 Ohms Transmitter 50 Ohms Pulse On λ/4 Receiver 50 Ohms At tee (marked with dot) transmitter sees 50 Ω load of probe, and infinite load in front of receiver. No rf pulse goes into receiver. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

41 Duplexor Circuit When transmitter is off, then weak NMR signal from probe cannot turn on diodes: Probe 50 Ohms Transmitter 50 Ohms λ/4 Receiver 50 Ohms All cross-diodes are off so probe signal goes only to receiver. Cross diode also blocks noise from transmitter from reaching probe. Since λ 4 length depends on frequency (i.e. λ = c ν) then any time you change NMR frequency (i.e. when changing to different nucleus), duplexer has to be changed (different λ 4 cable). With wrong λ 4 length, then part of transmitter power will go to ground and not to probe. If cross-diodes are blown (current flows in both directions with no resistance in blown diodes), then transmitter noise will saturate magnetization and signal from probe will not go only to receiver and sensitivity will suffer. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

42 Specifying Power Levels Power is energy transfer per unit time. P = 2 rms R and rms = pp 2 2 rms is rms voltage and pp is peak to peak voltage. Example Calculate power from 50 Ω rf source with output of pp = V rms = pp 2 2 = V 2 2 = V P = ( V)2 50Ω = W or 1 mw. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

43 Amplifier Gain Amplifier gain given in decibels (db). Logarithmic scale calculated according to db = 20 log 10 ( pp )out ( pp ) in If amplifier input is pp = V then after 50 db gain we get ( pp ) out = ( pp ) in 10 db 20 = (0.632 volts) = 200 V After 50 db amplifier, 1 mw would be amplified to P = (200 V (2 2)) 2 50 Ω = 100 W. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

44 Checking Power Levels RF levels are also specified in units of dbm, given by dbm = 10 log P(mW) 1 mw dbm is gain in terms of db s with respect to 1 mw. If rf source outputs 1 mw, then power in dbm is zero. A 50 db amplifier turns 0 dbm into 50 dbm which is 100 W. Amplifiers have a maximum input level. Anything higher will overdrive amplifier and lead to distorted output (higher harmonics added). Important to check rf power levels going into probe and make sure they are within specifications. Never connect the output of a high power amplifier directly to the oscilloscope. Oscilloscope may not handle that much power and can be damaged. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

45 Checking Power Levels Place high power attenuator (check power rating) between amplifier and oscilloscope. 50 db 30 db Attemuator (high power rating) high power rf attenuator With setup above 1 measure voltage peak-to-peak on oscilloscope, 2 convert this to dbm, 3 add 30 db to get output power level of amplifier. P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

46 Make Calibration Plot for Probe Measure NMR signal as a function of pulse length Power/watts Measure power going into probe P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

47 Let s build an NMR Spectrometer! N S Probe Others, e.g. gradients, temperature control, etc... Transmitter Duplexor Receiver Computer P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48

48 Further Reading Also... Transient Techniques in NMR of Solids: An Introduction to Theory and Practice, by Gerstein and Dybowski Experimental Pulse NMR: A Nuts and Bolts Approach, by Fukushima and Roeder The ARRL Handbook for Radio Communication Radio-Frequency Electronics, Circuits and Applications, by Hagen 1 Check out Terry Gullion s ENC tutorial video link: ***Basic Useful Circuits for NMR Spectroscopy*** 2 Check out Kurt Zilm s ENC tutorial link: Design, Care and Feeding of NMR Probes: A Tutorial P. J. Grandinetti (L Ohio State Univ.) Electronics Primer for NMR Jan. 10, / 48