Design, Care and Feeding of NMR Probes: A Tutorial

2011 Experimental NMR Conference, Asilomar CA

sources of inspiration....

Don AldermanMark ConradiDavid HoultBob McKayEichii FukuskimaDavid DotyToby ZensFrank EngelkeAllen PalmerJohn Stringer....

and many, many, many others too numerous to mention ....

Don Alderman

Mark ConradiDavid Hoult

Bob McKayEichii Fukushima

David Doty

Toby Zens

Design, Care and Feeding of NMR Probes: A Tutorial

Part I

What is a tank circuit?

Impedance matchingtransmission linesthe Smith chartexperimental techniques

Circuit resonanceQ and voltage risearcing and avoiding arcing

Part II

Signal to noiseRf efficiencycomparing 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

CT L

CM

Z O

resonator

RF input

impedance matching network

+-

v ( t )

L

signal emf = -

s

1V

d(B M(t))dV

dt

Solenoidal coil

B1(t)

Bo

Saddle coil

slotted tube

scrollcoil

Zensresonator

birdcage

all resonators are inductive

elements

Resonators...type usually dictated by sample geometry and frequency

N

S

transmission lineRF

inputresonator

primitive probe

very inefficient because of impedance mismatch

RF signals have wave character and require phase matching

index of refraction n1

index of refraction n2

for p-polarized light the transmission coefficient depends on n1, n2 and the incident angle θ.

Impedance matching of light waves

R = 0 and T = 1 when

1 1

B2

nn

-θ tan

n1 n2

DC electronics basics – Ohm's Law

V

V = IR

V

dVI =C

dt dIV =L

dt

RF electronics – Ohm's law works using Impedance

V(t) = Vocos(ωt + φ) or V(t) = Re(ej(ωt +φ))

VR C L

RF electronics basics – Impedance and Reactance

V

V = IZR

V

from V(t) = ej(ωt +φ)

V = IZC

V = IZL

ZR = R

Z = R + jX

Define a complex

impedance Z

ZC = 1/jωC

ZL = jωL

X = Reactance

VR C L

j = 1

Transmission lines and characteristic impedance

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 Zo is the equivalent of a refractive index

L o

in oo L

Z jZ tan(βl)Z (l) Z

Z jZ tan(βl)

length l

2πβ

λ

μη

ε for dielectric

o

ηZ ln(b/ a)

2π

b

do

ηZ ln(d/ a)

2π

Minimum attenuation cable: if εR = 1.0, Zo = 75Ω; εR = 2.0, Zo = 51Ω

ZL = 50 Ω

refl ected L s

L sincident

V Z ZΓ

V Z Zreflection coefficient

VincVinc

Vinc Vinc

VrefVref

Vref out of phase

180o for short

Vref in phase

for open

ZL = 25 Ω

if ZS = Zo = 50 Ω

VSWR = Vmax/Vmin

= (1 + |ΓL|)/(1 − |ΓL|)

VSWR = 1

VSWR = ∞ VSWR = ∞

VSWR = 2

Impedance matching the coil

in o m

T

1Z Z jωC R' jX

1jωL R

jωC

CT L

CM

Z O

R

set X = 0 to findallowed ω

there will be 2 !

Then choose CT/CM

to render R' = Zo

resonant frequency ω ~ T1/ LC

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 outputRF receiver

directional coupler

Forward wave

DUT

reflected wave

50Ω

frequency

matched

Γ

Γ

0

1

Resonator inductance

for solenoid length , diameter d, n turns

22 d

L 250n (nH)4.5d 10

usually more practical to measure L

dimensions in inches

Resonant RLC circuits

when ω2 = 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

C

L

R

Zo

Zo

Zo

Using resonance to span a break in a transmission line circuit

Zo

Zo

Zo

Using resonance to span a break in a circuit

C

L

2

1plot vs. C

ω

Impedance matching the coil

in o m

T

1Z Z jωC R' jX

1iωL R

jωC

CT L

CM

Z O

R

set X = 0 to findallowed ω

there will be 2 !

Then choose CT/CM

to render R' = Zo

resonant frequency ω ~ 1/ LC

Measuring

Spectrum analyzer + tracking generator

RF outputRF receiver

directional coupler

Forward wave

DUT

reflected wave

50Ω

frequency

Γ

Voltage at circuit resonance

C LV in

V H R

in

1Z = +jωL+R

jωC

j = - +jωL+R

ωC

when ω2 = 1/LC Zin = R and |XC| = |XL| I = Vin/Zin = Vin/R

What is the voltage VH – Vin across C?

L inc in inH in c in

| Z | V| Z | V ωLVV V | Z | I QV

R R R

Coil quality factor Q =ωL/R = E stored/E dissipated per cycle = ω/3dB bandwidth

typical Q ~ 100 or more

Input pulse power

2 2 22

ptp ptpRMSptp

o o

(V / 2 2) VV100 Watts V 200V

Z Z 400

Vptp

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

2.5 kV

Vacuum variable

Teflon variable

Sapphire trimmer

RF transmittingceramic 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 = -

s

1V

d(B M(t))dV

dt

1B= B1 from unit current

"principle of reciprocity"

Excitation and detection are equally efficient

o 1xy o s oemf ωB M V (cosω t)

2 2o o sM Nγ I (I 1)B / 3kT

2o

1

1

emf B

emf B / unit current

B / power

Part II.......maybe for next year

Acknowledgements

For inspiration and graphics

A. AbragamD. VanderHartM. ConradiT. and H. BarbaraT. ZensD. AldermanB. MckayA. PalmerJ. StringerF. EngelkeG. FaceyJ. DanielsE. FukushimaD. Doty

L. PageS. BrinS. WolframJ. WalesJ. HornakR. Schurko

For support

NSFExxonMobilAgilentYale 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