Power Scaling Methods for RF Excitation Fields in MRI Systems

Article information

J. Electromagn. Eng. Sci. 2025;25(2):175-183

Publication date (electronic) : 2025 March 31

doi : https://doi.org/10.26866/jees.2025.2.r.289

Seon-Eui Hong ¹

, Giuseppe Carluccio ²

, Christopher M. Collins ³

, Hyung-Do Choi ¹

, Sukhoon Oh ⁴^,

¹Terrestrial & Non-terrestrial Integrated Telecommunications Research Lab., Electronics and Telecommunications Research Institute, Daejeon, Korea

²Department of Electrical and Information Technology of the Universita’ Federico II di Napoli, Napoli, Italy

³Department of Radiology of New York University, New York, NY, USA

⁴MRI Imaging and Translational Research Group, Korea Basic Science Institute, Cheongju, Korea

^*Corresponding Author: Sukhoon Oh (e-mail: sukhoonoh@kbsi.re.kr)

Received 2024 March 8; Revised 2024 July 7; Accepted 2024 August 4.

Abstract

In this paper, we analyze the homogeneity of the transmitted radiofrequency (RF) field by applying different power scaling methods ranging from low-field (12.8 MHz, 0.3 T) to high-field (298 MHz, 7.0 T) magnetic resonance imaging (MRI) systems. Homogeneity strongly depends on RF power scaling, especially in higher-field MRI. While no notable homogeneity problem is usually observed in lower-field MRI, strong center brightening occurs at a higher field, owing to shortened wavelength. In particular, the dependence of homogeneity on RF power scaling appears during the initial MRI system calibration. In this study, we evaluate the 10-g averaged specific absorption rate (SAR) to evaluate RF safety. This rate may suffer from severe phase interferences, especially in the case of higher-field MRI, due to the increased strength of the static magnetic field and the complex distribution of electrical properties in structures, such as the human head. In particular, the 10-g averaged SAR level is up to six times higher in higher-field MRI with entire-area RF power scaling than with center scaling. Overall, this study establishes the importance of accounting for MRI scan homogeneity and RF safety during MRI examinations.

Keywords: Magnetic Resonance Imaging; Power Scaling; Homogeneity; Radiofrequency Signal; Specific Absorption Rate

I. Introduction

Radiofrequency (RF) power calibration is an essential step performed at the beginning of a series of magnetic resonance imaging (MRI) scans. An MRI system automatically calibrates the RF power under changing loading conditions, such as when examining a new patient or when changing the scanned body part, to create a 90° flip angle (FA) of the magnetization vector. Once the RF power is calibrated, all subsequent MRI scans refer to this calibration for each FA. The correct FA setting improves image contrast, thereby aiding physicians in diagnosing diseases based on MRI scans. Therefore, an initial RF power calibration must be conducted for every patient or body part. In this regard, RF safety is an even more important aspect because the RF power setting determines the specific absorption rate (SAR) of biological tissues during MRI. Miscalibration may lead to adverse thermal events, such as tissue burns [1]. Along these lines, in [2], the signal-to-noise ratio and the total absorbed power in terms of the SAR were analyzed according to the static magnetic field strength by defining a 90° FA. The analysis was performed by maintaining a 90° FA at the center of the RF coil. The maximum amplitude of the free induction decay signal was generated from the imaging subject, and the total signal amplitude of the reconstructed MRI scan was maximized. The study summarized the signal-to-noise ratio and SAR characteristics based on an increase in the strength of the static magnetic field.

Larmor frequency (ω₀ in hertz) is an important parameter pertaining to an MRI system. It determines the system resonance frequency and is proportional to the static magnetic field strength. It can be expressed as follows:

(1) ω0=γ×B0,

where γ indicates the gyromagnetic ratio (42.57 MHz/T for protons) and B₀ refers to the static magnetic field strength (in teslas). In addition, the obtained FA (in degrees) is directly proportional to the strength of the magnetic field generated by an RF coil, which is driven in transmit mode ( B1+) during MRI. This can be formulated as follows:

(2) FA=2π×γ×τ×B1+,

where τ is the RF pulse width (in seconds) and B1+ is the amplitude of the transmitted RF pulse or field (in teslas). In this regard, applying a homogeneous B1+ RF field to an imaging subject is necessary to ensure adequate signal intensity based on anatomical or disease information. B1+ homogeneity strongly depends on the wavelength in the tissue. Therefore, it also depends on electrical properties, such as the electrical conductivity (σ) and relative permittivity (ɛ_r) of a subject, owing to the standing wave effect [3]. The wavelength can be expressed as follows:

(3) λ=2πω00.5ɛrɛ0μrμ0(1+1σ-2ɛr2ɛ02ω02+1)

where λ is the wavelength (in meters), ɛ_r refers to the relative permittivity of the subject, ɛ₀ indicates the permittivity of free space (in farads per meter, F/m), μ_r is the relative permeability, μ₀ signifies the permeability of free space (in henry per meter, H/m), and σ refers to the electrical conductivity of the subject (in Siemens per meter, S/m). For example, according to (3), the wavelength of muscle tissue is 102.9 cm at 12.8 MHz (0.3 T MRI) and 12.4 cm at 298 MHz (7.0 T MRI). Furthermore, the conductivity (relative permittivity) of muscle tissue at 12.8 MHz and 298 MHz is 0.626 S/m (143.71) and 0.77 S/m (58.23), respectively [4, 5].

In particular, the wavelength affects the field of view of MRI scans. Substantial image shading (excessively dark or bright areas) is observed in MRI scans if the field of view is larger than the wavelength [6, 7]. As a result, to achieve the best image quality, the field of view is typically set to be no larger than half the wavelength. Overall, B1+ homogeneity should be considered when an MRI system initially calibrates the RF power for a 90° FA. Homogeneity can be assessed by analyzing the mean and standard deviation of a signal or image, with a higher mean (above 0) and/or lower standard deviation indicating better homogeneity [8].

In this study, we investigate the B1+ homogeneity at different static magnetic field strengths, ranging from 0.3 T to 7.0 T, available in commercial MRI systems. For homogeneity analysis, electromagnetic field simulations were performed. The means and standard deviations of the FA within cylindrical brain tissue and human head phantoms were obtained using different RF power scaling methods. In addition, we also analyzed the 10-g averaged SAR for different RF power scaling methods.

II. Materials and Methods

1. RF Coil and Phantom Configuration

A head-sized birdcage (BC) RF coil, as shown in Fig. 1(a), was employed for all electromagnetic field simulations [9]. Since this study is only concerned with B1+ homogeneity, and not with unwanted tuning or matching parameters, an ideal BC RF coil was modeled. The diameter and length of the BC RF coil were 268 mm and 256 mm, respectively. Notably, an ideal BC RF coil can be modeled using constant current sources instead of tuning and matching circuits. Twelve rungs were evenly spaced and connected between two end rings, with the width of every rung and the end rings being 10 mm. A gap of 2 mm was maintained between every pair of rungs on the end ring to install a constant current source.

Fig. 1

(a) Head-sized birdcage RF coil for MRI systems, consisting of rungs, end rings, and signal (constant current) sources and (b) cylindrical brain tissue phantom.

Usually, lumped elements are used in BC RF coils, but the constant current sources were substituted with the phase setting in this study to generate the circularly polarized mode. One ampere of electrical current flowed circularly along one end ring. On the other end ring, the current flowed in the opposite direction but with the same amplitude, thus generating a circularly polarized electromagnetic field within the BC RF coil. The frequency of each current source was assigned according to the Larmor frequencies of 0.3 T, 1.5 T, 3.0 T, and 7.0 T MRI systems, which were 12.8 MHz, 64 MHz, 128 MHz, and 298 MHz, respectively.

A cylindrical phantom was employed to mimic brain tissue (gray and white matter), as shown in Fig. 1(b). The electrical properties of the cylindrical phantom, such as conductivity and relative permittivity, were averaged in terms of the gray and white matter to facilitate calculation, as listed in Table 1 [4,5]. The material density (ρ) of the cylindrical phantom was 1,042.8 kg/m³ for all Larmor frequencies, but its conductivity and relative permittivity were assigned according to the Larmor frequency. Table 1 lists the half-wavelengths in the cylindrical phantom, estimated using (3) per Larmor frequency. The diameter and length of the cylindrical phantom were 176 mm and 240 mm, respectively.

Table 1

Electrical properties of a cylindrical brain tissue phantom and its half-wavelength

As depicted in Fig. 2, a numerical human head phantom was also simulated within the BC RF coil. The head (head-toshoulder length of 364 mm) was separated from the whole-body numerical model (Duke male model, IT’IS Foundation, Zurich, Switzerland [10]) to reduce the overall simulation time. The human head phantom consisted of 49 different biological tissues, including internal air. Its eyebrow position was aligned with the central slice of the RF coil (z = 0 mm), and its electrical properties were assigned according to each Larmor frequency from 12.8 MHz to 298 MHz [4, 5].

Fig. 2

Birdcage RF coil loaded with numerical human head phantom separated from Duke whole-body model.

Electromagnetic field simulations were performed using commercial XFdtd software (Remcom, State College, PA, USA), which runs a finite-difference time-domain algorithm. The mesh sizes of the cylindrical and human head phantoms were 214 mm × 216 mm × 208 mm and 325 mm × 216 mm × 288 mm, respectively. A total of 40 meshes were added along each direction for boundary padding, and seven perfectly matching layers were added to the meshes. The cell size was 2 mm × 2 mm × 2 mm, and the sizes of the total analysis regions were 428 mm × 428 mm × 416 mm (cylindrical phantom) and 650 mm × 432 mm × 576 mm (human head phantom). Numerical calculations were performed using a high-performance computing system equipped with an AMD Ryzen Threadripper processor (3970X, 32 cores), 256 GB of system memory, and an NVIDIA RTX A6000 graphics processor (48 GB of memory). The calculation time ranged from 31 to 727 seconds for the cylindrical phantom, and from 47 to 1,108 seconds for the human head phantom. Notably, a lower frequency increased the calculation time.

2. RF Power Scaling for 90° FA

The square root of the RF power used to drive the BC RF coil should be proportional to the magnitude of the excitation magnetic field ( B1+). Since a homogeneous B1+ field contributes to accurate disease diagnosis using MRI scans, the homogeneity of the B1+ field was evaluated when a 90° FA was achieved using different RF scaling methods. For instance, if the RF pulse width is 3 ms, approximately 2 μT of a B1+ amplitude is required to achieve 90° FA [2]. In this study, the mean and standard deviation of the resulting B1+ field were analyzed for three different RF scaling methods: (i) The RF power was scaled to simply set the center of the phantom to 2 μT; (ii) The half-wavelength at each Larmor frequency was determined, following which the equal area of the circle was set when the diameter was equal to the half-wavelength. Subsequently, the RF power was scaled to produce an average of 2 μT on the area; (iii) The RF power was scaled according to the second method, but within the entire phantom area. The three RF scaling methods at 128 MHz are illustrated in Fig. 3. Notably, all homogeneity analyses (mean and standard deviation) of the transmitted magnetic field ( B1+) were performed on the central slice of the BC RF coil (z = 0 mm).

Fig. 3

Setup of RF power scaling methods during the initial RF calibration of an MRI system. The scaling is based on the mean and/or standard deviation of the transmitted RF magnetic field ( B1+) at the (a) center, (b) area of the circle when the diameter is equal to the half-wavelength (134 mm for 128 MHz, in Table 1), and (c) entire head area.

III. Results and Discussion

1. Transmit RF Field ( B1+) Homogeneity

Two-dimensional B1+ maps for the central slice of the cylindrical brain tissue phantom under different Larmor frequencies and RF power scaling methods were simulated using XFdtd software, as shown in Fig. 4. Regardless of scaling, no significant inhomogeneous B1+ field distributions were observed below 64 MHz. However, inhomogeneous B1+ patterns emerged at frequencies above 128 MHz, particularly in the central region, owing to the shortened wavelength at higher Larmor frequencies relative to the subject size.

Fig. 4

Results of the RF power scaling methods during the initial RF calibration of the MRI system. Scaling is based on the mean and/or standard deviation of the transmitted RF magnetic field ( B1+) at the (a–d) center, (e–h) area of the circle when the diameter is equal to the half-wavelength (134 mm for 128 MHz, see Table 1), and (i–l) entire cylindrical phantom area.

As illustrated in Fig. 3(b) and Table 1, the half-wavelength of the human head phantom at 128 MHz was 134 mm, which was shorter than the left/right lengths of the human head phantom. The maximum B1+ strength was clearly observed at the center of the field of view (Fig. 4(c), 4(g), and 4(k)). This was expected because the scaling factor for the target 90° FA was calculated for the entire area. However, the standard deviation was also the largest of all scaling methods for this case (9.00°). For the half-wavelength (Fig. 4(g)), the FA mean and standard deviation were 85.1° and 8.51°, respectively—approximately 95% of the target FA—while the standard deviation remained below 9.00°. Notably, the smallest standard deviation (7.18°) was obtained when scaling was performed at the center (Fig. 4(c)). However, the achieved FA was only 80% of the target value. Furthermore, the results were similar even at 298 MHz (7.0 T MRI).

The relationship between the mean and standard deviation of the FA in terms of achieving the target FA was also evaluated (Table 2). The trend of the results for the human head phantom was observed to be the same as that for the cylindrical phantom, as shown in Fig. 5. The only difference was the aspect ratio between the lengths of the left/right and anterior/posterior sides, which worsened the shading patterns around the cerebral ventricles and front/back of the head. Overall, the RF power scaling method using half-wavelength exhibited the best homogeneity.

Table 2

Homogeneity results according to RF power scaling methods at different frequencies

Fig. 5

Transmitted RF magnetic fields ( B1+) for RF scaling methods at (a–d) the center, (e–h) the area of the circle when the diameter is equal to half-wavelength, and (i–l) the entire area of the human head phantom.

At 128 MHz, the mean and standard deviation of the FA for the human head phantom were 84.2° and 8.8°, respectively. However, the absolute means and standard deviations were worse than those for the cylindrical phantom. This finding can mainly be attributed to the dielectric resonance effect of geometric shapes and the constructive and/or destructive phase interference of complex distributions of electrical properties in the tissues of the human head phantom [11]. Less shading could be expected if the aspect ratio of the phantom was approximately 1:1 (circular). However, the aspect ratio of the human head phantom used in this study was approximately 1:0.77 (206 mm:158 mm, that is, elliptical).

Fig. 6 shows the results of the homogeneity analysis. The lowest homogeneity was observed for RF scaling at the center, especially at 128 MHz and 298 MHz (that is, high-field MRI). As the scaling area increased, the mean FA approached the target value of 90°. Notably, the best mean FA was achieved when RF power scaling was performed over the entire phantom area (Fig. 6(c) and 6(f)). As mentioned earlier, this is a natural phenomenon. However, the maximum standard deviation was observed at 298 MHz (7.0 T). Given the overemphasis on B1+ in the central region, its image might have appeared brighter than the real image intensity. In addition, the RF power might be localized in a specific region within the human head phantom or brain tissue phantom possibly causing thermal burns due to the focused RF energy in a worst-case scenario [12–14]. In the one-dimensional profile observations of the cylindrical brain tissue phantom (Fig. 7), no excessive FA was observed when the scaling point was located at the phantom center in the high-field MRI (Fig. 7(a)). However, for 128 MHz and 298 MHz, FAs considerably higher than 90° (solid black arrows in Fig. 7) appeared in the case of RF power scaling with half-wavelength (Fig. 7(b)) and the entire phantom area (Fig. 7(c)), which exhibited brighter image intensity.

Fig. 6

Homogeneity analysis considering each RF power scaling method for (a–c) the brain tissue (cylindrical) phantom and (d–f) the human head phantom. Black dashed lines indicate the target FA (90°), blue lines (with open circles) indicate the mean FA, and orange lines (with open squares) indicate the standard deviations of the FA.

Fig. 7

One-dimensional profiles at the middle of the (cylindrical) brain tissue phantoms at various frequencies for RF power scaled at (a) the center, (b) the half-wavelength, and (c) the entire phantom area (solid black arrows: regions with FA above 90°; open black arrows: heavily shaded regions).

Brighter regions in an MRI scan do not always represent increased SAR. A shortened wavelength may increase the strength of unwanted electric fields in local regions by inducing phase interference within the subject. In addition, heavily shaded regions (open black arrows in Fig. 7), mainly arising from the shortened wavelength in high-field MRI, are also problematic for disease diagnosis. Notably, this is also a major drawback of quantitative MRI techniques, including magnetization transfer imaging, electrical properties mapping, and T1 mapping [15–18].

2. SAR

The local hotspot in a high-field MRI system (of 128 MHz and/or 298 MHz) for the brain tissue phantom is demonstrated in Fig. 8, and that for the human head phantom is depicted in Fig. 9. For the brain tissue phantom, the highest 10-g averaged SAR was distributed along the edge of the phantom, owing to the single tissue property (for the averaged brain tissue) without any phase interference. The maximum 10-g averaged SAR was observed at 298 MHz (7.0 T MRI), with the SAR increasing with a square increase in the static magnetic field (or Larmor frequency) [19]. The same scale was applied to all 10-g averaged SAR values, since the values for 12.8 MHz were difficult to observe. The 10-g averaged SAR values are listed in Table 3.

Fig. 8

A 10-g averaged SAR for the brain tissue (cylindrical) phantom under different RF scaling methods (rows) and Larmor frequencies (columns). The highest 10-g averaged SAR values for each RF scaling method were reached at 298 MHz (7.0 T MRI).

Fig. 9

A 10-g averaged SAR for the human head phantom under different RF scaling methods (rows) and Larmor frequencies (columns). A local hotspot resulting from phase interference is clearly visible at the highest Larmor frequency.

Table 3

A 10-g averaged SAR of the brain tissue (cylindrical) and human head phantom for each Larmor frequency and RF scaling method

As for the human head phantom, regardless of the RF scaling method, severe phase interference was observed, especially at 298 MHz, as shown in Fig. 9. Overall, 49 electrical properties were observed within the human head phantom, implying that highly complex phase interferences affected the electric field strength and distribution. Since the RF power scaling factor was the largest when considering the entire area, the maximum 10-g averaged SAR was observed when scaling over the entire area. Notably, the SAR values under different conditions were compared using the square of the average FA.

Fig. 10 traces the differences in 10-g averaged SAR among the RF scaling methods relative to the center-based scaling in percentiles. Regardless of the kind of phantom and Larmor frequency, RF power scaling for the entire phantom area achieved the worst (highest) 10-g averaged SAR increment, which was more than six times higher than that of the center-based method.

Fig. 10

Relative 10-g averaged SAR in percentiles with respect to RF power scaling at the center for (a) the brain tissue (cylindrical) and (b) human head phantoms according to Larmor frequency.

IV. Conclusion

In this study, we analyzed the homogeneity of the transmitted RF field ( B1+) by applying different RF power scaling methods ranging from low-field (12.8 MHz, 0.3 T) to high-field (298 MHz, 7.0 T) MRI systems. No homogeneity issue was found at lower field strengths, such as 12.8 MHz and 64 MHz. However, at 128 MHz and 298 MHz, strong center brightening was observed, mainly due to the shortened wavelength within the phantoms.

The 10-g averaged SAR showed severe phase interference, especially in the human head phantom in higher-field MRI, owing to the strong static magnetic field and complex distribution of electrical properties within the human head. Furthermore, the RF power scaling method was found to affect the overall SAR. Notably, the 10-g averaged SAR increased up to six times depending on the RF power scaling method chosen for higher-field MRI.

Overall, this study found that RF power-scaling methods affect the homogeneity and RF safety performance of MRIs. Therefore, appropriate RF power scaling methods should be selected for different static magnetic field strengths during initial RF power calibration in an MRI system.

Notes

This work was supported by the Institute for Information and Communications Technology Promotion (IITP) grant funded by the Korean government (MSIP) (No. 2021-0-00490, Development of precision analysis and imaging technology for biological radio waves) and the ICT R&D program of MSIT/IITP (No. 2019-0-00102, A study on public health and safety in a complex EMF environment).

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Biography

Seon-Eui Hong, https://orcid.org/0000-0003-4037-1853 received her M.S. and Ph.D. degrees in Radio Science and Engineering from Chungnam National University, Daejeon, Rep. of Korea in 1999 and 2017, respectively. Since 1999, she has been working at the Electronics and Telecommunications Research Institute, Daejeon, Rep. of Korea, and is currently a principal member of the Radio Environment & Monitoring Research Section. Her current research interests include numerical dosimetry and methods for assessment of electromagnetic sources.

Giuseppe Carluccio, https://orcid.org/0000-0001-5376-3843 received the Laurea degree in Electronics Engineering (summa) and the Laurea Specialistica degree in Electronics Engineering (summa cum laude) from the Politecnico di Milano, Milan, Italy, in 2005 and 2010, respectively, and the M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of Illinois at Chicago, (UIC), in 2011. He is currently working in the Department of Electrical and Information Technology Engineering, Universita’ Federico II di Napoli, Italy, as a researcher. His research interests are in applied electromagnetic, specifically in waves propagation in biological tissues, RF shimming in magnetic resonance imaging, safety in magnetic resonance imaging, temperature increase in biological tissues. Dr. Carluccio is the recipient of the 2011 Provost and Deiss Award at University of Illinois at Chicago.

Christopher M. Collins, https://orcid.org/0000-0002-4928-7503 is a professor of Radiology at New York University. He earned his B.S. in Engineering Science from The Pennsylvania State University in 1993 and his Ph.D. in Bioengineering from The University of Pennsylvania in 1999. He then joined the Faculty of Radiology at The Pennsylvania State University, where he worked until he joined the faculty at New York University in 2012. His interest is in engineering and safety of RF electromagnetic fields for MRI. He has published more than 100 peer-reviewed papers. He is a Senior Member of the Institute for Electrical and Electronics Engineers (IEEE) and a Fellow of the International Society for Magnetic Resonance in Medicine (ISMRM).

Hyung-Do Choi, https://orcid.org/0000-0003-2652-7524 received his M.S. and Ph.D. degrees in materials science from Korea University in 1989 and 1996, respectively. Since 1997, he has been working at the Electronics and Telecommunications Research Institute, Daejeon, Rep. of Korea, where he is currently a principal member of the Radio Research Division. He has conducted research on the biological effects of RF radiation and developed standards for RF radiation protection.

Sukhoon Oh, https://orcid.org/0000-0002-9625-240X received the B.S. degree in biomedical engineering from Konkuk University, South Korea, in 1998, and the M.S. and Ph.D. degrees in biomedical engineering from Kyung Hee University, Rep. of Korea, in 2002 and 2006, respectively. In 2006, he joined the Center for NMR Research, Pennsylvania State University, PA, USA, as a post-doctoral fellow. From 2008 to 2012, he was a research associate (full-time faculty) at Department of Radiology, Pennsylvania State University, PA, USA. In 2012, he continued his research at New York University, NY, USA as a research scientist until he moved to Samsung Electronics, South Korea in 2013. In Samsung Electronics, he participated in development projects of 3 T MRI system. From 2016, he has been working at Korea Basic Science Institute, South Korea, as a senior researcher. Dr. Oh’s research of interest is about the RF safety assessments at high field MRI system. For that, he has been conducting various EM field simulations, electric properties mapping, and MR thermometry experiments for the RF coils in the phantoms and in-vivo.

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Scaling area	Phantom	Homogeneity (°)

		12.8 MHz	64 MHz	128 MHz	298 MHz
Center	Brain tissue (cylinder)	93.1±1.65	86.2±1.70	71.8±7.18	56.8±16.77
Center	Head	93.7±2.73	87.1±2.62	75.0±7.84	55.5±12.58
Half-wavelength	Brain tissue (cylinder)	90.0±1.59	90.0±1.77	85.1±8.51	82.8±24.43
Half-wavelength	Head	90.0±2.63	90.0±2.71	84.2±8.80	63.7±14.43
Entire phantom	Brain tissue (cylinder)	90.0±1.59	90.0±1.77	90.0±9.00	90.0±26.56
Entire phantom	Head	90.0±2.63	90.0±2.71	90.0±9.41	90.0±20.39

Scaling area	Phantom	10-g averaged SAR (W/kg)

		12.8 MHz	64 MHz	128 MHz	298 MHz
Center	Brain tissue	0.0323	0.7256	1.9352	2.8365
Center	Head	0.0263	0.6006	1.9668	3.7075
Half-wavelength	Brain tissue	0.0302	0.7909	2.7200	6.0193
Half-wavelength	Head	0.0243	0.6410	2.4771	4.8782
Entire phantom	Brain tissue	0.0302	0.7909	3.0450	7.1126
Entire phantom	Head	0.0243	0.6410	2.8305	9.7464

	12.8 MHz	64 MHz	128 MHz	298 MHz
σ (S/m)	0.2477	0.4012	0.4644	0.5521
ɛ_r	213.5	82.6	63.0	52.0
ρ (kg/m³)	1,042.8	1,042.8	1,042.8	1,042.8
0.5 λ (mm)	657	222	134	67