lecture 2: instrumentation - spin dynamics

CHEM-6154 Lecture 2: Instrumentation |

Lecture 2: InstrumentationCHEM 6154 – Nuclear Magnetic Resonance

Marcel Utz

January 26, 2020

CHEM-6154 Lecture 2: Instrumentation |

2 | Learning Goals for Today

In this lecture, we will:

É Examine the hardware necessary for NMR Spectroscopy

At the end, you will

É Understand how RF signals are generated, transmitted, and processed;

É Appreciate the technical requirements for NMR magnets;

CHEM-6154 Lecture 2: Instrumentation |

2 | Learning Goals for Today

In this lecture, we will:É Examine the hardware necessary for NMR Spectroscopy

At the end, you will

É Understand how RF signals are generated, transmitted, and processed;

É Appreciate the technical requirements for NMR magnets;

CHEM-6154 Lecture 2: Instrumentation |

2 | Learning Goals for Today

In this lecture, we will:É Examine the hardware necessary for NMR Spectroscopy

At the end, you will

É Understand how RF signals are generated, transmitted, and processed;

É Appreciate the technical requirements for NMR magnets;

CHEM-6154 Lecture 2: Instrumentation |

2 | Learning Goals for Today

In this lecture, we will:É Examine the hardware necessary for NMR Spectroscopy

At the end, you willÉ Understand how RF signals are generated, transmitted, and processed;

É Appreciate the technical requirements for NMR magnets;

CHEM-6154 Lecture 2: Instrumentation |

2 | Learning Goals for Today

In this lecture, we will:É Examine the hardware necessary for NMR Spectroscopy

At the end, you willÉ Understand how RF signals are generated, transmitted, and processed;

É Appreciate the technical requirements for NMR magnets;

CHEM-6154 Lecture 2: Instrumentation | Outline

3 | Outline

Overview

Magnets

Probes and Detectors

RF Signals

Detection and Data Processing

Recapitulation

CHEM-6154 Lecture 2: Instrumentation | Overview

4 | Block Diagram

Synth 1 Modulator 1 T1

PReceiverADC

B1

CHEM-6154 Lecture 2: Instrumentation | Magnets

5 | NMR Magnets

Coil

Bore

He Dewar

He fill port

LN2 fill port

Vacuum portVacuum port

NMR Cryomagnets

contain a superconducting coil which carries a persistent current. The magnetic fieldsgenerated vary between 5 T and 25 T. The stored field energy is of the order of 50 . . . 100 MJ,similar to that stored in the fully charged battery of an electric car.

CHEM-6154 Lecture 2: Instrumentation | Magnets

6 | Superconducting Wire

T

R

R ∼ T 3

R = 0

Tc

T

B

Tc

Bc 2

Bc 1

NMR Magnet

CHEM-6154 Lecture 2: Instrumentation | Magnets

6 | Superconducting Wire

T

R

R ∼ T 3

R = 0

Tc

T

B

Tc

Bc 2

Bc 1

NMR Magnet

CHEM-6154 Lecture 2: Instrumentation | Magnets

6 | Superconducting Wire

T

R

R ∼ T 3

R = 0

Tc

T

B

Tc

Bc 2

Bc 1

NMR Magnet

CHEM-6154 Lecture 2: Instrumentation | Magnets

6 | Superconducting Wire

T

R

R ∼ T 3

R = 0

Tc

T

B

Tc

Bc 2

Bc 1

NMR Magnet

CHEM-6154 Lecture 2: Instrumentation | Magnets

6 | Superconducting Wire

T

R

R ∼ T 3

R = 0

Tc

T

B

Tc

Bc 2

Bc 1

NMR Magnet

CHEM-6154 Lecture 2: Instrumentation | Magnets

7 | Superconductor Metallurgy

Nb3SnTc = 18 K, Bc 2 = 30 T, Bc 1 = 19 mTA15 crystal structureExtremely brittle

CHEM-6154 Lecture 2: Instrumentation | Magnets

8 | Cryostat

QuenchNMR magnets can contain several 100L of liquid He. Loss of Dewar vacuum or exposure toferromagnetic objects can lead to a runaway loss of superconductivity. Beware: Asphyxiationhazard!

CHEM-6154 Lecture 2: Instrumentation | Magnets

8 | Cryostat

QuenchNMR magnets can contain several 100L of liquid He. Loss of Dewar vacuum or exposure toferromagnetic objects can lead to a runaway loss of superconductivity. Beware: Asphyxiationhazard!

CHEM-6154 Lecture 2: Instrumentation | Probes and Detectors

9 | NMR Probe

13C Coil1H Coil

Tuning Cap

CHEM-6154 Lecture 2: Instrumentation | Probes and Detectors

10 | B1 Homogeneity

Probe Quality

É Efficiency (B1/p

P ) (Determines sensitivity)

É B0 homogeneity (resolution!)

É B1 homogeneity (enables complex pulse sequencees)

É Channel separation (enables high-power decoupling)

Nutation Experiment:

Exc. Pulse [µs]0 10 20 30 40 50 60 70 80 90

CHEM-6154 Lecture 2: Instrumentation | Probes and Detectors

10 | B1 Homogeneity

Probe Quality

É Efficiency (B1/p

P ) (Determines sensitivity)

É B0 homogeneity (resolution!)

É B1 homogeneity (enables complex pulse sequencees)

É Channel separation (enables high-power decoupling)

Nutation Experiment:

Exc. Pulse [µs]0 10 20 30 40 50 60 70 80 90

A90/A810 = 30%: Poor homogeneity

CHEM-6154 Lecture 2: Instrumentation | Probes and Detectors

10 | B1 Homogeneity

Probe Quality

É Efficiency (B1/p

P ) (Determines sensitivity)

É B0 homogeneity (resolution!)

É B1 homogeneity (enables complex pulse sequencees)

É Channel separation (enables high-power decoupling)

Nutation Experiment:

Exc. Pulse [µs]0 10 20 30 40 50 60 70 80 90

A90/A810 = 85%: Good homogeneity

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric field

Magnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

11 | Transmission Lines

Electric fieldMagnetic field

x

U , I

x

U , I

I0

U0

λ

Z = |U0||I0|

λ= cν ≈

200 MHz·mν

CHEM-6154 Lecture 2: Instrumentation | RF Signals

12 | RF Pulses

Reference signal (“Carrier”)

x -pulse

duration

amplitude

y -pulse

phase

−x -pulse

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

13 | Block Diagram

Synth 1 Modulator 1 T1

PReceiverADC

B1

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

14 | Detection and Demodulation

2 cosαt cosβ t = cos(αt +β t ) + cos(αt −β t )

Mixing

Before digitisation, RF signals are demodulated by mixing with the carrier at frequencyω0.This produces a signal that contains sum and difference components.

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

Original signal

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After mixing

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After low-pass filter

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

14 | Detection and Demodulation

2 cosαt cosβ t = cos(αt +β t ) + cos(αt −β t )

Mixing

Before digitisation, RF signals are demodulated by mixing with the carrier at frequencyω0.This produces a signal that contains sum and difference components.

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

Original signal

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After mixing

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After low-pass filter

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

14 | Detection and Demodulation

2 cosαt cosβ t = cos(αt +β t ) + cos(αt −β t )

Mixing

Before digitisation, RF signals are demodulated by mixing with the carrier at frequencyω0.This produces a signal that contains sum and difference components.

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

Original signal

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After mixing

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After low-pass filter

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

14 | Detection and Demodulation

2 cosαt cosβ t = cos(αt +β t ) + cos(αt −β t )

Mixing

Before digitisation, RF signals are demodulated by mixing with the carrier at frequencyω0.This produces a signal that contains sum and difference components.

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

Original signal

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After mixing

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After low-pass filter

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

14 | Detection and Demodulation

2 cosαt cosβ t = cos(αt +β t ) + cos(αt −β t )

Mixing

Before digitisation, RF signals are demodulated by mixing with the carrier at frequencyω0.This produces a signal that contains sum and difference components.

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

Original signal

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After mixing

5 10 15 20t

-1

-0.75

-0.5

-0.25

0.25

0.5

0.75

1SHtL

After low-pass filter

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Detection and Data Processing

15 | Quadrature Detection

NMR Signal

Carrier (sin)

M

Carrier (cos)M

ω

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:

É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.

CHEM-6154 Lecture 2: Instrumentation | Recapitulation

16 | Recapitulation

Take-home messages from today:É NMR magnets are based on low-Tc superconductors, and require cooling with liquid He;

É The quality of the NMR probe is crucial for sensitivity and resolution;

É Coaxial cables are conduits for electromagnetic radiation. They are characterised by theirwave impedance Z (typically 50 Ω);

É RF pulses are characterised by their duration, amplitude, and phase;

É NMR signals are demodulated to audio frequencies (kHz) before digitisation;

É Quadrature detection allows distinction of positive and negative frequency offsets.