Fig.1A shows the ratio-adjustable power splitter (RAPS) comprising a Wilkinson splitter and a hybrid coupler connected by two transmission lines of different lengths, which induce phase shifts of Φ1 and Φ2. The amplitude relationship between the two output ports is derived in Fig.1B as: $$|V_1 |⁄|V_2 |=|co t((Φ_1-Φ_2)⁄2-45)| [1]$$ $$ V_1^2+V_2^2=V_{in}^2 [2]$$
Eq.1 indicates that the output ratio has a $$$cot$$$ dependence on the difference between the transmission line lengths, and can thus be tuned by adjusting those lengths. Eq.2 indicates that it is a lossless network where the sum of output power always equals the input power.
Fig. 2 shows a fabricated RAPS made on PCB with dimensions 3x7 cm2. Two cables (one fixed and one variable) are used to change the relative phase shifts of the split signals and consequently the ratio between the output voltage amplitudes. A library of cable lengths was populated to achieve output ratios from 0 dB to 7 dB in steps of 1 dB. Bench measurements were performed with a network analyzer, and MR experiments were performed on a 7T whole-body scanner (Philips Healthcare, Best, Netherlands). In the MR experiments, a RAPS was inserted between the RF amplifier and a birdcage head coil (Nova Medical, Wilmington, MA). Axial B1+ maps were then acquired in a 15 cm phantom using the DREAM method9, across the range of output ratios.
Fig. 3 shows S-parameter results from the bench tests with target ratios from 0 dB (equal splitting) to 7 dB. The RF signal was input to port 1, and output from ports 2 and 3. The deviations between measured and desired ratios between outputs (S12-S13) are less than 0.05 dB (Fig. 3A). The total power loss is approximately 10% (~0.5 dB) at each ratio (Fig. 3B). Fig. 3C shows the matching performance of each port and Fig. 4D shows the isolation between the two output ports, in which acceptable matching (<-16 dB) and excellent isolation (<-22 dB) was achieved across ratios.
Fig. 4A shows normalized B1+ maps measured using splitters of different ratios. Fig. 4B plots predicted (using S-parameter measurements) and measured average B1+ at each ratio. The measured and predicted ratios match well, with errors less than 4%. Fig. 4C shows calculated power loss based on the measured average B1+. As expected from the bench measurements, the power loss was low (<12%), which means that >94% of the B1+ magnitude was maintained.
Fig. 5 compares array compression network topologies for the accelerated spiral parallel pulse design of Ref. 2. The networks implement the same relative coil weightings, but the RAPS-based network is lossless, while the topology from Ref. 2 dissipates 61% of the input power (neglecting insertion loss in both cases).
1. Cao, Z., Yan, X. and Grissom, W. A. (2016), Array-compressed parallel transmit pulse design. Magn Reson Med, 76: 1158–1169. doi: 10.1002/mrm.26020
2. Yan, X., Cao, Z. and Grissom, W. A. (2016), Experimental implementation of array-compressed parallel transmission at 7 Tesla. Magn Reson Med, 75: 2545–2552. doi: 10.1002/mrm.26239
3. Mao, W., Smith, M. B. and Collins, C. M. (2006), Exploring the limits of RF shimming for high-field MRI of the human head. Magn Reson Med, 56: 918–922. doi: 10.1002/mrm.21013
4. Van den Bergen, B., van den Berg, C. A.T., Klomp, D. W.J. and Lagendijk, J. J.W. (2009), SAR and power implications of different RF shimming strategies in the pelvis for 7T MRI. J. Magn. Reson. Imaging, 30: 194–202. doi: 10.1002/jmri.21806
5. Deniz, C. M., Brown, R., Lattanzi, R., Alon, L., Sodickson, D. K. and Zhu, Y. (2013), Maximum efficiency radiofrequency shimming: Theory and initial application for hip imaging at 7 tesla. Magn Reson Med, 69: 1379–1388. doi: 10.1002/mrm.24377
6. Adriany G, Van de Moortele PF, Wiesinger F, Moeller S, Strupp JP, Andersen P, Snyder C, Zhang X, Chen W, Pruessmann KP, Boesiger P, Vaughan T, Ugurbil K: Transmit and receive transmission line arrays for 7 Tesla parallel imaging. Magn Reson Med. 2005; 53(2):434-45. PubMed PMID: 15678527
7. Shajan, G., Hoffmann, J., Budde, J., Adriany, G., Ugurbil, K. and Pohmann, R. (2011), Design and evaluation of an RF front-end for 9.4 T human MRI. Magn Reson Med, 66: 594–602. doi: 10.1002/mrm.22808
8. Hoffmann, J., Shajan, G., Scheffler, K. et al. Numerical and experimental evaluation of RF shimming in the human brain at 9.4 T using a dual-row transmit array. Magn Reson Mater Phy (2014) 27: 373. doi:10.1007/s10334-013-0419-y
9. Nehrke, K. and Börnert, P. (2012), DREAM—a novel approach for robust, ultrafast, multislice B1 mapping. Magn Reson Med, 68: 1517–1526. doi: 10.1002/mrm.24158