To increase longitudinal homogeneity of the magnetic field in transmission line resonators. The described approach to control magnetic field distribution would be useful in the design of coils with large in terms of wavelength field of view.In order to boost the sensitivity of transmission line coils they are usually operated as resonators. Hence, the loading of transmission lines is either open-circuit, short-circuit, or purely reactive. Such a loading results in infinite standing wave ratio, SWR, (assuming lossless case), where the distance between the consecutive minima or maxima is one-half a wavelength. To avoid dark regions on MR image and achieve reasonable homogeneity, current minima should be avoided. For that reason, coils based on transmission line resonators are typically shorter than half a wavelength and proper capacitive loading is used to achieve symmetric current distribution along the line¹. The current magnitude reduces at the ends of the line due to destructive interference of the incident and reflected electromagnetic waves. It is, however, preferable to have a uniform current distribution. That would result in a more homogeneous magnetic field.

A more uniform current distribution is achieved by inserting series capacitors C_s into the transmission line (Fig. 1). These capacitors can compensate for self-inductance of the transmission line by introducing opposite phase shift ^2,3. Such arrangement results in a smaller SWR than in the conventional resonator case. The optimal in terms of SWR value of the series capacitor C_s is expressed as follows:

$$ C_{s}=\frac{sin(\frac{\beta l}{N})}{4 \pi f_{0}Z_{0}(1-cos(\frac{\beta l}{N}))} ,$$

where l is the total length of the segmented transmission line coil; N is the number of segments after inserting series capacitors (for example, using two series capacitors will result in N = 3); β is the phase constant; Z₀ is the characteristic impedance of the implemented transmission line; f₀ = 298 MHz is the operating frequency. The value of the loading capacitor is 2C_s, which provides symmetric current distribution.

An example of a transmission line coil using suspended microstrip technology is shown in Fig.2. Series capacitors are formed by overlapping adjacent transmission line sections. The magnetic field profiles for the regular transmission line resonator and coil in Fig. 2 in free-space are illustrated by full-wave simulations in Fig. 3. The field profiles are presented for different r, which is the perpendicular distance from the coil to the point of observation. As can be seen, segmentation improves homogeneity of the field. For example, at r = 3 cm homogeneity, which is defined as a ratio min {|B(z)|} / max {|B(z)|}, increases from 33.6 % for regular line resonator to 56.2 % for segmented resonator with two series capacitors. Since the field strength reduces at the ends of the line, even a higher degree of homogeneity can be achieved by reducing the field of view. To evaluate efficiency of the designed coil in the presence of lossy tissue, phantom studies were conducted using a 7T system. Photographs of the implemented prototype resonators are shown in Fig. 4. The measurement results using a saline phantom are shown in Fig.5.

As can be seen in Fig.5, there is an improvement in the homogeneity along the transmission line. Though the intensity of the field closer to the coil is higher for traditional resonator, the segmented resonator exhibits deeper penetration depth.

It is demonstrated, that the magnetic field homogeneity for the transmission line resonators can be improved by segmenting them with series capacitors. The higher the number of capacitors, the more uniform field can be generated. Virtually, any degree of homogeneity is possible. The only limitation is the finite length of the coil (which can be overcome by reducing the field of view) and, potentially, losses in the capacitors. Another benefit of using series capacitors is the capability to provide in a simple manner the required uniform field over a very long length, and construct transmission line coils, which can be even longer than one-half of a wavelength.

Evenly distributed capacitors were considered in this work (equal value capacitors inserted between equal length line sections). It is expected, that higher homogeneity over a wider field of view could be achieved using unevenly distributed capacitors with variable values.