A novel technique of modulating both the amplitude and frequency of the desired MR Radiofrequency pulse in a class-E amplifier topology, without utilizing supply-modulation, is presented. Amplifier’s MATLAB model is developed and the carrier frequency bitstream is intelligently controlled to achieve both the amplitude and phase modulation of the output waveform. Benchtop experiments are performed showing
Under the assumption of an ideal switch, the amplifier operation is broken down into two modes: switch-on and switch-off [Fig.1(b-c)]. State-space matrix representations for both these modes are written, from which the waveform equations are derived, and implemented in MATLAB.
The amplitude and phase of the output waveform are now modulated by digitally controlling the duty cycle and phase of the carrier frequency applied to the gate of the transistor. Working at f = 64 MHz, we associate each cycle (T = 15.625 ns) of the carrier frequency with k bits, where in our case, k = 4. An RF pulse of duration w = 2 ms would require a carrier signal of the same duration, consisting of $$$\frac{w}{T}$$$ cycles and consequently $$$n=\frac{k\times w}{T}$$$ bits. In order to achieve the desired pulse shape at the output, 2n combinations for the carrier frequency exist to choose from, requiring infeasible computational power.
At this point, the carrier bitstream is divided into multiple subsections. In each subsection, $$$k\times m$$$ number of bits (where m is an integer ranging from 1 to 16 and equals the number of cycles being controlled per each subsection) are controlled and repeated over the entire subsection (for m = 16, sampling rate equals $$$T\times m=0.25\ \mu s$$$ at 64 MHz, providing a bandwidth of 4 MHz), and the amplifier model is run for that subsection. A set of only three bitstream patterns {0000=0%, 0001=25%, 0011=50%} is used for controlling each cycle. The resulting output waveform for each subsection is compared in amplitude with the desired pulse for that subsection. Once the amplitude match is obtained, the bitstream elements are shifted left or right to achieve the phase match. This process is repeated for all subsections until a customized carrier bitstream, with least error between the desired and predicted waveforms, is generated.
To test the validity of the technique, the generated carrier bitstream was tested on hardware setup similar to Ref-1 [Fig.2(a-b)]. MR experiments were conducted in 1.5 T (Scimedix Inc., Incheon, South Korea) MR Scanner to test the slice selective capability of the generated RF pulse (Fig.3).
1. Poni, R., Silemek, B., Gundogdu, U., Demir, T., Ertan, N.K. and Atalar, E., Modified Class E Amplifiers Used For Two Channel Digital RF Transmit Array System With Integrated Coil, ISMRM, Singapore, 2016.
2. Zahra, F.T., Silemek, B., Poni, R., Ashfaq, B.N. and Atalar, E., A Highly Efficient 250 W Digitally Controlled Supply-Modulated Modified Class-E Amplifier for on-Coil Implementation in 1.5T MRI, ESMRMB, Barcelona, Spain, 2017.
3. Poni, R., MS.Thesis: A Digitally Controlled Class E Amplifier for MRI, Bilkent University, 2016.
4. Poni, R., Demir, T. and Atalar, E., A Digital Power Amplifier for 1.5 T, ISMRM, Toronto, Canada, 2015.
5. Sokal, N. O. and Sokal, A. D., "Class E-A New Class of High-Efficiency Tuned Single-Ended Switching Power Amplifiers," in IEEE Journal of Solid-State Circuits, vol. 10, no. 3, pp. 168-176, Jun 1975.
6. Sokal, N.O., Class-E High-Efficiency Power Amplifiers, from HF to Microwave, Proceedings of the IEEE International Microwave Symposium, Baltimore, June 1998.
7. Sokal, N.O., Class- E Switching-Mode High-Efficiency Tuned RF Microwave Power Amplifier: Improved Design Equations, Proceedings of the IEEE International Microwave Symposium, Boston, June 2000.
8. Gudino N, Heilman JA, Riffe MJ, Heid O, Vester M, Griswold MA. On-coil multiple channel transmit system based on class-D amplification and pre-amplification with current amplitude feedback. Magn Reson Med 2013;70:276–289.
9. Gudino N, Duan Q, de Zwart JA, Murphy-Boesch J, Dodd SJ, Merkle H, van Gelderen P, Duyn JH. Optically controlled switch-mode current-source amplifiers for on-coil implementation in high-field parallel transmission. Magn Reson Med 2016;76:340–349.