Efficient, balanced, transmission line RF circuits by back propagation of common impedance nodes

doi:10.1016/j.jmr.2013.02.017

Journal of Magnetic Resonance

Volume 231, June 2013, Pages 32-38

https://doi.org/10.1016/j.jmr.2013.02.017 Get rights and content

Highlights

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Balanced transmission line probe.
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Back propagation of common impedance nodes.
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Low RF powers, high γB₁.

Abstract

We present a new, efficient strategy for designing fully balanced transmission line RF circuits for solid state NMR probes based on back propagation of common impedance nodes (BPCIN). In this approach, the impedance node phenomenon is the sole means of achieving mutual RF isolation and balance in all RF channels. BPCIN is illustrated using a custom double resonance 3.2 mm MAS probe operating at 500 MHz (¹H) and 125 MHz (¹³C). When fully optimized, the probe is capable of producing high homogeneity (810°/90° ratios of 86% and 89% for ¹H and ¹³C, respectively) and high efficiency (γB₁ = 100 kHz for ¹H and ¹³C at 70 W and 180 W of RF input, respectively; up to 360 kHz for ¹H). The probe’s performance is illustrated by 2D MAS correlation spectra of microcrystals of the tripeptide N-f-MLF-OH and hydrated amyloid fibrils of the protein PI3-SH3.

Graphical abstract

Introduction

Due to multiple advances in magic angle spinning (MAS) NMR in the last two decades, it is rapidly becoming accepted as a powerful and versatile tool for many fields and particularly structural biology [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15]. These advances are the result of progress in both MAS methodology [1], [7], [16], [17] and instrumentation [18], [19], [20], [21].

Contemporary biological MAS applications set stringent, often contradictory, requirements for NMR probes, with the most important subsystem being the radio-frequency (RF) circuit. Critical features include RF efficiency, RF field homogeneity, and RF heating at high (¹H) and low (¹³C and ¹⁵N) frequencies, as well as the robustness and stability. In addition, advanced applications, such cryogenic MAS and dynamic nuclear polarization (DNP) enhanced NMR, require that the probe RF circuit function over a wide range of temperatures [22], [23], [24], [25], [26], [27], [28], [29], [30], [31].

An NMR probe circuit comprises a resonator, which houses the sample, and a tuning/matching network. Different types of commonly used NMR resonators, each having certain strengths and weaknesses, are reviewed elsewhere [18]. A suitable tuning/matching network not only tunes the resonator, but can also compensate for certain weaknesses.

Tuning/matching circuits may provide common mode (Fig. 1a) or balanced (Fig. 1b) input, with a balanced design providing a number of advantages over common mode design [32], [33], [34], [35]. These include improved RF field homogeneity [32] and power efficiency [36]. While the former is generally important for multiple pulse and recoupling experiments [32], the latter is particularly crucial for experiments on biological samples, which are often sensitive to RF heating caused by ¹H decoupling. We have recently introduced a novel balanced transmission line RF circuit design [33], [34], [37]. Here we present results from a fully balanced ¹³C/¹H transmission line probe and discuss the underlying theory of the circuit design.

Section snippets

Circuit overview

The schematic in Fig. 2a illustrates a double resonance, balanced RF circuit design, and Fig. 2b shows a block diagram of the same circuit. The circuit can be divided into two parts connected to opposite ends of the solenoid resonator. The combination of the left “tuning/matching” side and the right “balun” side results in a completely balanced output to the sample coil (Fig. 2b). On each side, individual RF channels are connected at common impedance nodes (black dots in Fig. 2), which assure

Experimental verification

The experimental implementation of the procedures outlined above was divided into several stages. The first stage was the fabrication of a double resonance ¹H and ¹³C static NMR probe, with careful optimization of its circuit and static performance tests. The second stage was conversion of the static probe into a MAS probe with tests under MAS conditions. At this point we did not perform a full circuit optimization, since additional modifications of the probe will be necessary for future

Conclusions and outlook

We presented an efficient new strategy for designing fully balanced transmission line RF circuits for MAS probes based on back propagation of common impedance nodes. This strategy was illustrated using a custom double resonance (¹H, ¹³C) 3.2 mm NMR probe. With high quality implementation, BPCIN yielded a RF circuit that demonstrated outstanding RF field characteristics (810°/90° ratios of 86% for ¹H and 89% for ¹³C; γB₁ = 100 kHz for ¹H and ¹³C at 70 W and 180 W of RF input, respectively, and up to

Disclosure statement

Brandeis University holds a patent for the circuit design described in this paper [37].

Acknowledgments

This research was supported by the National Institutes of Health through Grants EB003151, EB002026, EB001960, and EB001035. We thank Michael Mullins and Ajay Thakkar, for crucial assistance with construction of the probe.

References (53)

A.B. Barnes et al.
High-resolution solid-state NMR structure of alanyl-prolyl-glycine
J. Magn. Reson.
(2009)
A.B. Barnes et al.
Dynamic nuclear polarization at 700 MHz/460 GHz
J. Magn. Reson.
(2012)
A.B. Barnes et al.
Cryogenic sample exchange NMR probe for magic angle spinning dynamic nuclear polarization
J. Magn. Reson.
(2009)
E.K. Paulson et al.
Cross polarization, radio frequency field homogeneity, and circuit balancing in high field solid state NMR probes
J. Magn. Reson.
(2004)
M. Renault et al.
Solid-state NMR spectroscopy on complex biomolecules
Angew. Chem., Int. Ed.
(2010)
A. Lesage
Recent advances in solid-state NMR spectroscopy of spin I = 1/2 nuclei
Phys. Chem. Chem. Phys.
(2009)
O.C. Andronesi et al.
Characterization of Alzheimer’s-like paired helical filaments from the core domain of tau protein using solid-state NMR spectroscopy
J. Am. Chem. Soc.
(2008)
M. Etzkorn et al.
Probing molecular interfaces using 2D magic-angle-spinning NMR on protein mixtures with different uniform labeling
J. Am. Chem. Soc.
(2004)
A. Lange et al.
A concept for rapid protein-structure determination by solid-state NMR spectroscopy
Angew. Chem., Int. Ed.
(2005)
S.D. Cady et al.
Structure of the amantadine binding site of influenza M2 proton channels in lipid bilayers
Nature (London, UK)
(2010)

R.G. Griffin

Dipolar recoupling in MAS spectra of biological solids

Nat. Struct. Biol.

(1998)

M.L. Mak-Jurkauskas et al.

Energy transformations early in the bacteriorhodopsin photocycle revealed by DNP-enhanced solid-state NMR

Proc. Natl. Acad. Sci. USA

(2008)

F. Castellani et al.

Determination of solid-state NMR structures of proteins by means of three-dimensional 15N–13C–13C dipolar correlation spectroscopy and chemical shift analysis

Biochemistry (NY)

(2003)

M. Hong et al.

Structure and dynamics of cationic membrane peptides and proteins: insights from solid-state NMR

Protein Sci.

(2011)

S.P. Brown et al.

Advanced solid-state NMR methods for the elucidation of structure and dynamics of molecular, macromolecular, and supramolecular systems

Chem. Rev. (Washington, DC)

(2001)

V. Ladizhansky

Dipolar-Based Torsion Angle Measurements for Protein Structure Determination, Encyclopedia of Magnetic Resonance

(2007)

G. De Paepe et al.

Proton assisted recoupling and protein structure determination

J. Chem. Phys.

(2008)

P.C.A. Van der Wel et al.

Solid-state NMR study of amyloid nanocrystals and fibrils formed by the peptide GNNQQNY from yeast prion protein Sup35p

J. Am. Chem. Soc.

(2007)

R. Tycko

Biomolecular solid state NMR: advances in structural methodology and applications to peptide and protein fibrils

Annu. Rev. Phys. Chem.

(2001)

L. Frydman

Spin-1/2 and beyond. A perspective in solid state NMR spectroscopy

Annu. Rev. Phys. Chem.

(2001)

V. Grant Christopher et al.

Probes for high field solid-state NMR of lossy biological samples

J. Magn. Reson.

(2010)

R.A. McKay

Probes for Special Purposes, Encyclopedia of Magnetic Resonance

(2007)

J. Schaefer, R.A. Mckay, Multi-tuned Single Coil Transmission Line Probe for Nuclear Magnetic Resonance Spectrometer,...

P.L. Gor’kov et al.

Probe Development for Biosolids NMR Spectroscopy, Encyclopedia of Magnetic Resonance

(2007)

A.B. Barnes et al.

Instrumentation for Cryogenic MAS and High-Field Dynamic Nuclear Polarization, Magnetic Resonance Gordon Research Conference

(2009)

A.B. Barnes et al.

High-field dynamic nuclear polarization for solid and solution biological NMR

Appl. Magn. Reson.

(2008)

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View full text

Efficient, balanced, transmission line RF circuits by back propagation of common impedance nodes

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Circuit overview

Experimental verification

Conclusions and outlook

Disclosure statement

Acknowledgments

J. Magn. Reson.

J. Magn. Reson.

J. Magn. Reson.

J. Magn. Reson.

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Angew. Chem., Int. Ed.

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Phys. Chem. Chem. Phys.

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J. Am. Chem. Soc.

Probing molecular interfaces using 2D magic-angle-spinning NMR on protein mixtures with different uniform labeling

J. Am. Chem. Soc.

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Nature (London, UK)

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