Design, Care and Feeding of NMR Probes: A Tutorial 2011 Experimental NMR Conference, Asilomar CA

sources of inspiration.... Don Alderman Mark Conradi David Hoult Bob McKay Eichii Fukuskima David Doty Toby Zens Frank Engelke Allen Palmer John Stringer. and many, many, many others too numerous to mention.... Don Alderman Mark Conradi David Hoult Bob McKay Eichii Fukushima David Doty Toby Zens

Design, Care and Feeding of NMR Probes: A Tutorial Part I What is a tank circuit? Impedance matching transmission lines the Smith chart experimental techniques Circuit resonance Q and voltage rise arcing and avoiding arcing Part II Signal to noise Rf efficiency comparing specifications Circuit balancing and multiple resonance circuits Finite element field simulations Tuning tube and transmission line probes

Disclaimer: semi-professional driver on a closed track. Do not attempt at home. The "management" of ENC is not responsible for damages as a result. Opinions of the speaker do not reflect those of the ENC unless you happen to like them, and in that instance ENC takes full credit.. "it is easier to repent than it is to get permission" - D. M. Grant

NMR probe basics An NMR probe is a tank circuit used to excite NMR signals and detect them by Faraday induction resonator RF input impedance matching network signal emf = -

Solenoidal coil B 1 (t) BoBo Saddle coil slotted tube scroll coil Zens resonator bird cage all resonators are inductive elements Resonators...type usually dictated by sample geometry and frequency N S

transmission line RF input resonator primitive probe very inefficient because of impedance mismatch RF signals have wave character and require phase matching

index of refraction n 1 index of refraction n 2 for p-polarized light the transmission coefficient depends on n 1, n 2 and the incident angle θ. Impedance matching of light waves R = 0 and T = 1 when n1n1 n2n2

DC electronics basics – Ohm's Law V V = I R V RF electronics – Ohm's law works using Impedance V(t) = V o cos(ωt + φ) or V(t) = R e (e j(ωt +φ) ) VRCL

RF electronics basics – Impedance and Reactance V V = I Z R V from V(t) = e j(ωt +φ) V = I Z C V = I Z L Z R = R Z = R + jX Define a complex impedance Z Z C = 1/jωC Z L = jωL X = Reactance VRCL

Transmission lines and characteristic impedance ρ = | Γ | The voltage standing wave ratio is then equal to: Can't just connect a load to a source with a wire – it will radiate the power Dipole antenna radiates power from transmitter into space To transmit RF to a load need a structure to contain the EM waves

Transmission lines and characteristic impedance twin-line coaxial line characteristic impedance Z o is the equivalent of a refractive index length l for dielectric b d Minimum attenuation cable: if ε R = 1.0, Z o = 75Ω; ε R = 2.0, Z o = 51Ω

Z L = 50 Ω reflection coefficient V inc V ref V ref out of phase 180 o for short V ref in phase for open Z L = 25 Ω if Z S = Z o = 50 Ω VSWR = V max /V min = (1 + |Γ L |)/(1 |Γ L |) VSWR = 1 VSWR = VSWR = 2

Impedance matching the coil R set X = 0 to find allowed ω there will be 2 ! Then choose C T /C M to render R' = Z o resonant frequency ω ~

easier to use a Smith chart VSWR = 0 50Ω 200Ω L C load 200Ω Example: match a 200Ω load

Measuring Spectrum analyzer + tracking generator RF output RF receiver directional coupler Forward wave DUT reflected wave 50Ω frequency matched 0 1

Resonator inductance for solenoid length, diameter d, n turns usually more practical to measure L dimensions in inches

Resonant RLC circuits when ω 2 = 1/LC the circuit is "resonant" RF energy at ω is stored alternately in C and L Circuit can be excited by an antenna or other source

ZoZo ZoZo ZoZo Using resonance to span a break in a transmission line circuit

ZoZo ZoZo ZoZo Using resonance to span a break in a circuit C L

Impedance matching the coil R set X = 0 to find allowed ω there will be 2 ! Then choose C T /C M to render R' = Z o resonant frequency ω ~

Measuring Spectrum analyzer + tracking generator RF output RF receiver directional coupler Forward wave DUT reflected wave 50Ω frequency

Voltage at circuit resonance when ω 2 = 1/LC Z in = R and |X C | = |X L | I = V in /Z in = V in /R What is the voltage V H – V in across C?

Coil quality factor Q =ωL/R = E stored/E dissipated per cycle = ω/3dB bandwidth typical Q ~ 100 or more Input pulse power V ptp Peak V across C ~ 10,000 V !!!

Conditions for arcing through air

Non-magnetic fixed and variable capacitors 20 kV 10 kV 500V 2.5 kV Vacuum variable Teflon variable Sapphire trimmer RF transmitting ceramic chips

Probe testing under power Power amplifier Directional coupler output forward reflected

Probe testing under power Power amplifier Directional coupler output forward arcing reflected

Arc testing tune and match at low power increase drive 1 dB at a time while watching reflected power operate 2 dB lower than initial arc avoid hard sustained arcing – carbonized capacitors do not heal don't try and rematch to compensate for arcing

Always make sure you have air flow into the probe

Dewar's frequently provide sources of arcing If the probe only arcs in the magnet suspect the dewar

Optimizing RF efficiency and S/N signal emf = - = B 1 from unit current "principle of reciprocity" Excitation and detection are equally efficient Part II maybe for next year

Acknowledgements For inspiration and graphics A.Abragam D. VanderHart M. Conradi T. and H. Barbara T. Zens D. Alderman B. Mckay A.Palmer J. Stringer F. Engelke G. Facey J. Daniels E. Fukushima D. Doty L. Page S. Brin S. Wolfram J. Wales J. Hornak R. Schurko For support NSF ExxonMobil Agilent Yale University all of my present and former students

Disclaimer: semi-professional driver on a closed track. Do not attempt at home. The "management" of ENC is not responsible for damages as a result. Opinions of the speaker do not reflect those of the ENC unless you happen to like them, and in that instance ENC takes full credit.. "your students only learn your worst habits" - C. P. Slichter