Generalized electrical analysis of low-pass and high-pass birdcage resonators

The radio-frequency 'birdcage resonator' has found wide use in MRI/MRS for its field homogeneity and signal-noise characteristics. This paper presents a general analysis, derived from lumped element transmission line theory, of the electrical behavior of unloaded, N-column birdcage resonators applicable to several versions of the basic design including low-pass and high-pass coils. Analytic expressions and computer results are presented for both types of coil describing resonant frequencies, input and characteristic impedances, dispersion relations, pass-bands, resonant peak bandwidth and Q. Theoretical expressions for normalized resonant frequency difference ratios independent of element values and resonator geometry have been developed for generic low- and high-pass coils. Experimental measurements of resonant frequencies were made for six coils, and the average agreement with theoretical predictions was approximately 4%.     

Ultra-broadband NMR probe: numerical and experimental study of transmission line NMR probe

We have reinvestigated a transmission line NMR probe first published by Lowe and co-workers in 1970s [Rev. Sci. Instrum. 45 (1974) 631; 48 (1977) 268] numerically and experimentally. The probe is expected to be ultra-broadband, thus might enable new types of solid-state NMR experiments. The NMR probe consists of a coil and capacitors which are connected to the coil at regular intervals. The circuit is the same as a cascaded LC low-pass filter, except there are nonzero mutual inductances between different coil sections. We evaluated the mutual inductances by Neumann's formula and calculated the electrical characteristics of the probe as a function of a carrier frequency. We found that they were almost the same as those of a cascaded LC low-pass filter, when the inductance L of a section was estimated from the inductance of the whole coil divided by the number of the sections, and if C was set to the capacitance in a section. For example, the characteristic impedance of a transmission line coil is given by Z=(L/C)(1/2). We also calculated the magnitude and the distribution of RF magnetic field inside the probe. The magnitude of RF field decreases when the carrier frequency is increased because the phase delay between neighboring sections is proportional to the carrier frequency. For cylindrical coils, the RF field is proportional to (pinu/2nu(d))(1/2)exp(-nu/nu(d)), where the decay frequency nu(d) is determined by the dimensions of the coil. The observed carrier frequency thus must be much smaller than the decay frequency. This condition restricts the size of transmission line coils. We made a cylindrical coil for a 1H NMR probe operating below 400 MHz. It had a diameter 2.3mm and a pitch 1.2mm. Five capacitors of 6pF were connected at every three turns. The RF field strength was 40 and 60 kHz at the input RF power 100 W by a calculation and by experiments, respectively. The calculations showed that the RF field inhomogeneity along the coil axis was caused by a standing wave of current, which arose from the reflections at the coil ends. The calculation showed that the homogeneity could be improved by decreasing the pitch near the both ends and making their impedance close to that at the center.     

Estimation and measurement of flat or solenoidal coil inductance for radiofrequency NMR coil design

The inductance of a radiofrequency coil determines its compatibility with a given NMR probe circuit. However, calculation (or estimation) of inductance for radiofrequency coils of dimensions suitable for use in an NMR probe is not trivial, particularly for flat-coils. A comparison of a number of formulae for calculation of inductance is presented through the use of a straightforward inductance measurement circuit. This technique relies upon instrumentation available in many NMR laboratories rather than upon more expensive and specialized instrumentation often utilized in the literature. Inductance estimation methods are suggested and validated for both flat-coils and solenoids. These have proven very useful for fabrication of a number of new coils in our laboratory for use in static solid-state NMR probes operating at (1)H frequencies of 300 and 600MHz. Solenoidal coils with very similar measured and estimated inductances having inner diameters from 1 to 5mm are directly compared as an example of the practical application of inductance estimation for interchange of coils within an existing solid-state NMR probe.     

Three-dimensional high-inductance birdcage coil for NQR applications

A birdcage coil capable of operating simultaneously and independently in three orthogonal dimensions has been developed. A co-rotational end-ring mode producing an RF field in the longitudinal direction was utilized in addition to the two common transverse orthogonal modes. Two conductor turns were used for each of the coil's windows, increasing its inductance by a factor of four, thereby, making the coil suitable for low-frequency applications. Two or three-frequency detection can be easily carried out with this device. Orthogonality of the coil's channels allows arbitrarily close frequency positioning of each resonant mode, potentially useful in wide-line NQR studies, in which simultaneous excitation/detection of signals from three adjacent regions of a single wide line can be performed. The coil's performance was evaluated using a three-dimensional scheme, in which a circularly polarized experiment was combined with a linearly polarized measurement at another frequency, resulting in SNR improvement by 55%.     

Investigation of tunnel-diode oscillators activated on the internal capacitance of their coils

Comparison of two tunnel-diode oscillators is performed, one of them having a solenoid pick-up coil, while another one has a single-layer flat-geometry coil. Oscillators operate in the frequency ranges, respectively, 6–25 MHz and 8–24 MHz and the coils had approximately equal inductances. These oscillators have been activated both without and with an external capacitance C ₀ in their resonant circuit, i.e., the studied oscillators could be activated also with their internal (own) capacitances C _c . It was succeeded to obtain more stable oscillations in case of flat coils. The analysis of data indicates that this fact is a consequence of a relatively high value of the own capacitance C _c of the flat coils as compared to their parasitic capacitance C _par with respect to the environment. This causes the advantages of flat-coil based oscillators. Also the inductance and the quantity C _c + C _par have been determined for both coils from the data of measurements.     

Comparison of 12 Quadrature Birdcage Coils with Different Leg Shapes at 9.4 T

The purpose of this study was to analyse the relationship between the radio frequency (RF) coil performance and conductor surface shape for ultra-high field (UHF) magnetic resonance imaging. Twelve different leg-shaped quadrature birdcage coils were modeled and built, e.g., 4 mm-width-leg conventional birdcage coil, 7 mm-width-leg conventional birdcage, 10 mm-width-leg conventional birdcage coil, 13 mm-width-leg conventional birdcage coil, inside arc-shape-leg birdcage coil, outward arc-shape-leg birdcage coil, inside right angle-shape-leg birdcage coil, outward right angle-shape-leg birdcage coil, vertical 4 mm-width-leg vertical birdcage, 6 mm-width-leg vertical birdcage, 8 mm-width-leg vertical birdcage and 10 mm-width-leg vertical birdcage. Studies were carried out in both electromagnetic simulations with finite element method as well as in vitro saline phantom experiments at 9.4 T. Both the results of simulation and experiment showed that conventional birdcage coil produces the highest signal-to-noise ratio (SNR) while the vertical birdcage coil produces the most homogeneous RF magnetic (B ₁) field at UHF. For conventional birdcage coils, as well as the vertical birdcage coils, only the proper width of legs results in the best performance (e.g., B ₁ homogeneous and SNR). For vertical birdcage coils, the wider the leg size, the higher RF magnetic (B ₁) field intensity distribution.     

L-C耦合电路对散粒噪声探测器电子学噪声的影响

通过分析基于L-C耦合跨阻运放电路的散粒噪声探测器噪声来源,提出了电感的寄生电容对电子学噪声影响的分析模型,并进行了实验验证.研究表明,电感的寄生电容会增大跨阻运放的输入电压噪声增益,从而增加探测器的电子学噪声.当总电感值为1mH时,选用两个0.5mH的电感串联结构相比选用单个1mH的电感,探测器电子学噪声明显降低.由于电感的自共振频率越低,寄生电容越大,选用高自共振频率的电感有助于进一步降低电子学噪声.实验测量得到,在2.5 MHz分析频率处,选用两个0.5mH、自共振频率为6 MHz的电感串联相比选用单个1mH、自共振频率为1.6 MHz的电感,电子学噪声的降低了3dB.在相同入射激光条件下,该改进模型可以有效提高探测器的信噪比.     

Low-pass and high-pass filters using coaxial-type dielectric resonators

This paper proposes new low-pass and high-pass filters using coaxial-type dielectric resonators. The low-pass filter has a LC-type circuit structure and is composed of three inductances and two resonance circuits. The resonance circuits are the open-ended coaxial-type dielectric resonators whose length is g/4. The high-pass filter has a CL-type circuit structure. Two high-pass filters are described, one of them is composed of three capacitances andtwo resonance circuits, the other is composed of five capacitances and four resonance circuits. The operating frequency range of the low-pass filter is 0.13–0.9 GHz and the cutoffency is 900 MHz, and the insertion loss is 0.3 dB. The corresponding quantities of the high-pass filter are 0.9–2.5 GHz, 900 MHz, and 0.3 dB, respectively.     

一种多层螺线管电感计算拟合公式（英）

提出了一种多层螺线管线圈电感的精确计算方法,其思想是叠加螺线管单层线圈的自感和不同线圈层之间的互感。建立了用于计算单层线圈自感的显示表达理论模型,给出了两层线圈之间互感的数值计算方法。使用提出的精确算法,计算出一个实验中使用的螺线管线圈的电感为4.30 mH,与实验测量的电感值4.33 mH的偏差小于1%。     

Numerical and Experimental Analysis of Modular-Toroidal-Coil Inductance Applicable to Tokamak Reactors

In this paper, equations for the calculation of the self- and mutual inductances of the modular toroidal coil (MTC) applicable to Tokamak reactors are presented. The MTC is composed of several solenoidal coils (SCs) connected in series and distributed in the toroidal and symmetrical forms. These equations are based on Biot–Savart's and Neumann's equations, respectively. The numerical analysis of the integrations resulting from these equations is solved using the extended three-point Gaussian algorithm. Comparing the results obtained from the numerical simulation with the experimental and the empirical results confirms the presented equations. Furthermore, the comparison of the behavior of these inductances, when the geometrical parameters of the MTC are changed, with the experimental results shows an error of less than 0.5%. The behavior of the inductance of the coil indicates that the optimum structure of this coil, with the stored magnetic energy as the optimization function, is obtained when the SCs are located on the toroidal planes.      

Design and performance of a double-tuned bird-cage coil

The “high-pass” and “low-pass” designations commonly given to bird-cage coils derive in each case from the relationship of the individual sections of the bird cage to simple filters. By extension of the concept of constructing a bird-cage coil from elementary filter sections, it is possible to create coils which support “bird-cage mode” resonances at more than one frequency. Designs based on both simple bandpass and band-stop filters, for example, provide means to realize bird-cage coils which may be tuned simultaneously to two frequencies. Construction and performance of a band-stop bird cage operating at both 200 and 81 MHz are described.     

Two Configurations of the Four-Ring Birdcage Coil for 1H Imaging and 1H-Decoupled 31P Spectroscopy of the Human Head

The four-ring birdcage resonator, a new class of dual-tuned birdeage resonators, is described. We report two configurations of the coil: the low-pass, high-pass (LP-HP) and the low-pass, low-pass (LP-LP), both of which can be operated in dual quadrature mode at 1.5 T. As head coils, both configurations exhibit greatly reduced tuning interactions between frequencies, permitting rapid, noniterative tuning. Compared with single-tuned, two-ring birdcage resonators of similar volume, the sensitivity and transmitter efficiencies of the resonators are better than 85% for the proton frequency and the same to within 5% for the phosphorus frequency. Circuit models have been developed to refine coil tuning and aid the calculation of B₁ field contour plots. Both configurations have been used for integrated examinations involving acquisition of high-quality ¹H images and ¹H-decoupled ³¹P CSI spectra of the human head. A scaled-down version of the LP-LP configuration has been demonstrated for use with the human calf.     

Multiple Parallel Round Leg Design for Quadrature Birdcage Coil in Ultrahigh-Field MRI

Copper foil has been widely employed in conventional radio frequency (RF) birdcage coils for magnetic resonance imaging (MRI). However, for ultrahigh-field (UHF) MRI, current density distribution on the copper foil is concentrated on the surface and the edge due to proximity effect. This increases the effective resistance and distorts the circumferential sinusoidal current distribution on the birdcage coils, resulting in low signal-to-noise ratio (SNR) and inhomogeneous distribution of RF magnetic (B₁) field. In this context, multiple parallel round wires were proposed as legs of a birdcage coil to optimize current density distribution and to improve the SNR and the B₁ field homogeneity. The design was compared with three conventional birdcage coils with different width flat strip surface legs for a 9.4 T (T) MRI system, e.g., narrow-leg birdcage coil (NL), medium-leg birdcage coil (ML), broad-leg birdcage coil (BL) and the multiple parallel round wire-leg birdcage coil (WL). Studies were carried out in in vitro saline phantom as well as in vivo mouse brain. WL showed higher coil quality factor Q and more homogeneous B₁ field distribution compared to the other three conventional birdcage coils. Furthermore, WL showed 12, 10 and 13% SNR increase, respectively, compared to NL, ML and BL. It was proposed that conductor’s shape optimization could be an effective approach to improve RF coil performance for UHF MRI.     

高通鸟笼线圈激发螺旋波等离子体特性研究

研制了高通鸟笼线圈,使用氩气作为工质气体对射频天线的工作性能进行了初步评估。利用COMSOL5.4模拟出了鸟笼天线在13.56MHz的工作频率下,电场和磁场呈线性极化分布。对鸟笼线圈进行了电路结构解剖,推导出了其谐振频率计算公式。利用热耦合红外测温仪测试了正常工作状态下的鸟笼线圈外表温度明显低于传统射频天线,电容器最高温度仅65.8°。使用光谱仪对螺旋波等离子体放电光谱特性进行诊断。通过朗缪尔探针诊断了不同压强和磁场强度下螺旋波等离子体密度,在1.0Pa、600Gs、射频功率700W条件下等离子体密度达到1.62×10¹⁸m^-3。诊断了正向功率和反向功率对应的等离子体密度,其与磁滞现象变化趋势雷同。测试了螺旋波等离子体的径向密度分布,其在轴心处密度达到最高。探究了无磁场条件下等离子体特性,其密度值不会发生大幅度跃迁,纵向磁场是引发螺旋波等离子体放电的关键因素,低压条件下有利于得到更低的电子温度,最低达到2.67eV。表明鸟笼线圈低热耗、高馈入的特性使其在激发大体积的高密度螺旋波等离子体方面具有明显优势,可以投入到下一阶段氢气螺旋波等离子体的激...     

Design of a capacitively decoupled transmit/receive NMR phased array for high field microscopy at 14.1T

A design is presented for a "phased array" of four transmit/receive saddle-geometry volume coils for microimaging at 600 MHz within a 45 mm clear-bore vertical magnet. The small size of the coils, approximately 10 mm in length, and high frequency of operation both present considerable challenges for the design of a phased array. The particular design consists of four saddle coils, stacked vertically, in order to produce an array suitable for imaging samples, typical of many microimaging studies, with a large length:diameter ratio. Optimal coil overlap is used to reduce the mutual inductance between adjacent coils, and capacitive networks are used to maximize the isolation between all of the coils. Standard 50 Omega input impedance preamplifiers are used so that the preamplifiers do not have to be integrated directly into the probe. Isolation between coils was better than 20 dB for all coil pairs. An increase in signal-to-noise of 70 +/- 3% was achieved, averaged over the whole array, compared to a single coil of the same dimensions. High resolution phased array images are shown for ex vivo tissue samples.     

Design and Analysis of Microstrip-Based RF Birdcage Coil for 1.5 T Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) technique is widely used to capture the images of the liquid items inside the human body. The radio-frequency (RF) coil is one of the important modules present inside an MRI system, which plays a major role in image quality. In this work, a microstrip-based high-pass RF birdcage coil is proposed for 1.5 T MRI. The cylindrical-shaped birdcage coil consists of 12 microstrip radiating elements and tuning capacitors to achieve a resonance at 63.85 MHz. The coil is made up of 10 mm polytetrafluoroethylene substrate coated by a conducting transmission line of desired length and width. A finite difference time domain simulation is carried out to analyze the return loss (S₁₁), magnetic field homogeneity and Specific Absorption Rate (SAR) parameters of the RF coil. The SAR values of the proposed microstrip-based 1.5 T birdcage coil was compared with 3 T RF birdcage coil. The simulation results indicate the proposed birdcage coil structure gives optimal values of S₁₁, magnetic field homogeneity and SAR.     

Mutual inductance bridge for magnetic relaxation measurements at low temperatures

An apparatus using a mutual inductance bridge has been designed to measure real and imaginary parts of the magnetic ac susceptibility simultaneously in the frequency range from 1 Hz to 230 kHz at helium temperatures. From 230 kHz up to 3 MHz the real part can be determined. The susceptibility as a function of temperature or external magnetic field at constant frequency may be measured. In addition, frequency sweeps can be performed with temperature and magnetic field held constant. The experiment is controlled by an on-line computer.     

Design of an inductively decoupled microstrip array at 9.4 T

By independent control of the phases and amplitudes of its elements, the microstrip transmission-line array can mitigate sample-induced RF non-uniformities, and has been widely used as the transceiver in parallel imaging applications. One major challenge in implementing the microstrip array is the reduction of mutual coupling among individual elements. The low-input impedance preamplifier is commonly used for the decoupling purpose. However, it is impractical in the transceiver array design. Although interconnecting capacitors can be utilized to reduce the mutual coupling, they only efficiently work for the neighbor elements. In addition, this approach is impractical at fields higher than 300 MHz, in which the required decoupling capacitance is commonly less than 0.5 pF. We propose a novel decoupling approach by using decoupling inductors in this study. Due to the fact that the decoupling inductance is independent of the resonant frequency, the microstrip arrays can be well decoupled at ultra-high fields. To verify the proposed approach, an eight-channel microstrip array is fabricated and tested at 9.4 T. For this prototype, couplings between elements are significantly reduced by using the interconnecting inductors. The phantom experiment shows that the inductively decoupled microstrip array has good parallel imaging performance.     

HIRFL新B1聚束器耦合环的设计与计算

 通过将聚束器腔体等效为RLC并联回路,求得了功率馈入耦合环与腔体的互感及自感的公式,根据对腔体的计算结果求出了在聚束器的工作频段内达到阻抗匹配所要求的互感变化范围,并在该互感变化范围设计了可移动的耦合电感环,计算了它的自感及整个腔体的剩余电感。     

A fully analytic treatment of resonant inductive coupling in the far field

For the application of resonant inductive coupling for wireless power transfer, fabrication of flat spiral coils using ribbon wire allows for analytic expressions of the capacitance and inductance of the coils and therefore the resonant frequency. The expressions can also be used in an approximate way for the analysis of coils constructed from cylindrical wire. Ribbon wire constructed from both standard metals as well as high temperature superconducting material is commercially available, so using these derived expressions as a basis, a fully analytic treatment is presented that allows for design trades to be made for hybrid designs incorporating either technology. The model is then extended to analyze the performance of the technology as applied to inductively coupled communications, which has been demonstrated as having an advantage in circumstances where radiated signals would suffer unacceptable levels of attenuation.