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RF Current Element Design for Independent Control of Current Amplitude and Phase in Transmit Phased Arrays KRISHNA N. KURPAD,1 STEVEN M. WRIGHT,1 EDDY B. BOSKAMP2 1 Department of Electrical Engineering, Magnetic Resonance Systems Laboratory, Texas A&M University, College Station, TX 77843 2 Applied Science Laboratory, GE Healthcare Technologies, 3200 N. Grandview Boulevard, Waukesha, WI 53188 ABSTRACT: Both the optimization of B1 field homogeneity in high-field MRI and the implementation of the exciting new theory of transmit SENSE can be accomplished by individual and independent control of the amplitude and phase of current on the elements or rungs of a radio frequency (RF) transmit coil array. One way of achieving this is by using the concept of the active rung, which consists of one rung of a volume coil connected across the output terminals of an RF power MOSFET. The RF power MOSFET is used as a voltage-controlled current source and drives RF current through the rung. The amplitude and phase of the RF current are controlled by the amplitude and phase of the RF control voltage. In this article, we demonstrate that the active rung may be used as a current element by tuning the rung to series resonance. We then demonstrate, using field measurements, that the current induced by adjacent rungs is suppressed by greater than 15 dB in a current element relative to a resonant loop representing a single element of the well known TEM coil. Thus, the active rung configuration enables significantly greater isolation and independence between rungs than in conventional designs where each rung is fed by a voltage source. Measurements and theory demonstrate a dynamic range of independent control of the rung current amplitude of 17 dB. We conclude that the degree of suppression is dependent on the size of the MOSFET output parasitic capacitance. The active rung should find application as a building block in the construction of parallel transmit coils. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 29B: 75– 83, 2006 KEY WORDS: high-field MRI; RF current source; active rung; MOSFET; phased array transmit coil INTRODUCTION by the RF currents on the coil elements or rungs. The amplitude and phase of the B1 field contribution of each rung are governed, respectively, by the amplitude and phase of the rung current. Volume coils, such as birdcage coils (1) and TEM coils (2), are designed to support a sinusoidal amplitude distribution of rung currents, which results in the generation of a resultant B1 field that is homogeneous in the unloaded case. However, the introduction of a dielectric load such as a human body or head is known to perturb B1 field homogeneity at high-static magnetic (B0) fields. At high B0 fields (3T and higher), the wavelength of the B1 field in a dielectric medium, such as human In volume transmit coils used in MRI, the radio frequency (RF) transverse magnetic (B1) field is created Received 20 April 2005; revised 1 November 2005; accepted 6 November 2005 Correspondence to: Krishna N. Kurpad; E-mail: [email protected] Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering), Vol. 29B(2) 75– 83 (2006) Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/cmr.b.20059 © 2006 Wiley Periodicals, Inc. 75 76 KURPAD, WRIGHT, AND BOSKAMP tissue, is comparable to the cross-sectional dimension of the human body. The superposition of the B1 fields from multiple sources results in the formation of interference patterns, with the characteristic bright spot in the center. There is therefore considerable interest in the development of radio frequency volume coils that are capable of generating uniform B1 field at high frequency. This requires a parallel transmit system with independent control of the amplitude and phase of the rung currents to enable optimization of B1 field homogeneity (3–5). The recent development of the theory of transmit SENSE (5, 6) and the consequent renewal of interest in multidimensional RF pulses (7), which allows selective excitation of specific regions of interest and optimization of B1 field homogeneity (4), has further contributed to the increased interest in parallel transmit coils (5). A parallel transmit coil with independent control of the rung current amplitude and phase may be achieved by ensuring that the rungs are well decoupled from each other. Decoupling between the elements of a receive coil is accomplished using a combination of preamplifier and capacitive or inductive decoupling mechanisms. Preamplifier decoupling works on the principle of suppression of element currents induced by the spins, thus preventing cross-talk, and is well suited for parallel receive coil design because the measured parameter is the spin-induced emf and not the induced current. However, in parallel transmit arrays, large current amplitudes are required to generate the desired B1 field. A decoupling mechanism for transmit arrays would therefore be required to suppress current induced by neighboring rungs, while simultaneously allowing large currents to be driven through the rungs. Recently, Zhu et al. (5) have suggested a transmit phase array design. Inductive or capacitive decoupling mechanisms have been used to decouple the nearest neighbor elements. Though inductive decoupling is effective for nearest neighbor elements, it is not effective for distant neighbor elements. The above design relies on the loading to improve isolation between the distant neighbor elements and may not be reliable. An alternative decoupling mechanism that involves the use of an active device such as a transistor integrated with the rung is the topic of discussion of this article. We refer to such an arrangement as an “active rung” (8, 9). The active rung is based on the principle of the antennafier element (10). The use of active devices such as BJTs and MOSFETs to drive integrated antenna elements has been investigated before (11–13). Studies have shown that such an arrangement makes the feed network of antenna arrays less sensitive to the effects of mutual impedance than Figure 1 Large signal equivalent circuit of an n-channel enhancement mode RF power MOSFET (a). The three terminals of the MOSFET are the gate (G), the drain (D), and the source (S). The MOSFET is represented as a voltage controlled current source. The rung is represented by a series RL circuit (b). The rung impedance is determined by the variable capacitor, CT, in series with the rung (c). passive arrays because of the unidirectional nature of the active devices (11). In this work, we develop further the concept of the active rung as an element of a volume coil. We demonstrate the key concept of independent control of the rung current amplitude and phase enabled by suppression of induced currents in an active rung. THEORY The RF power MOSFET is a transistor that behaves as a voltage-controlled current source, when placed in the saturation region of its DC characteristics (14). The large signal equivalent circuit of the N-channel MOSFET is shown in Fig. 1 (15, 16). In the common source configuration, the gate (G) is the input terminal, the drain (D) is the output terminal, and the source (S) is the ground terminal. In this configuration, the drain-source current, ID, is proportional to the applied gate-source voltage, VGS. The constant of proportionality is called the transconductance and is denoted by gfs. Cis, Cos, and Crs are, respectively, the input, output, and feedback parasitic capacitances of the MOSFET. The transistorized array element or active rung may be implemented by connecting one end of the rung to the drain of the MOSFET and the other end to the common source. This arrangement is illustrated by the schematic in Fig. 1. The parasitic output capacitance, Cos, of the MOSFET forms a parallel path to ground for RF current. For maximum current to be driven through the rung, the rung impedance to ground should be small compared with the reactance offered by Cos. This may be achieved by tuning out the rung inductance with series capacitors. Such an arrangement where RF current is driven directly Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b DESIGN FOR CURRENT AMPLITUDE AND PHASE 77 quency as the current on the adjacent rung to simulate the situation in resonant volume coils such as TEM coils (2), the loop impedance, Zp, is then a real quantity and is equal to Rloop. Rloop will, in general, be larger than Rrung by a few ohms as it includes the MOSFET resistances, not shown in the equivalent circuit of Fig. 1. The emf induced in the current element due to the adjacent rung is governed by Faraday’s law of electromagnetic induction and remains unchanged for a given current on the adjacent rung. The amplitude of the induced current in the resonant loop is therefore given by Figure 2 Equivalent output circuit of a MOSFET with the rung tuned to series resonance (a). In this case, the rung forms a low impedance path to ground for the driven current. The loop formed by the rung and the output capacitance (Cos) is substantially off resonance and contributes to suppression of induced current. The equivalent output circuit of a MOSFET with the rung tuned as a TEM element (b) shows that the loop formed by the rung and Cos is low impedance for both the driven and induced currents. 兩I p兩 ⫽ 兩E ind兩 R loop [3] The ratio of the induced currents in the two cases is then I ratio ⫽ 兩I s兩 R loop ⫽ 兩I p兩 兩Z s兩 [4] Expressed in decibels, through the active rung by the RF power MOSFET may be referred to as a current element. The schematic in Fig. 1 shows that the current element consists of two loops. One loop is formed by the RF current source and the rung, and the other is formed by the rung and Cos. When a current element is placed adjacent to a rung carrying current at the Larmour frequency, the rung induces an emf in the current element, as shown in Fig. 2(a). The emf induced in the current element by the adjacent rung may then be represented as a voltage source, Eind, which drives a current through the loop formed by Cos and the rung. Because the current source has high internal resistance, it is an open circuit to induced current. The complex impedance of the loop formed by the series tuned loop and Cos is given by Z s ⫽ R rung ⫺ jX Cos [1] where Rrung is the series resistance of the rung. The rung impedance is a pure resistance because of the series tuning of the rung. The amplitude of the induced current in the loop is given by 兩I s兩 ⫽ 兩E ind兩 兩Z s兩 [2] 2 where 兩Zs兩 ⫽ 冑Rrung ⫹ X2Cos. If the current element is replaced by a loop (see Fig. 2b) that is tuned to resonance at the same fre- I ratio兩 dB ⫽ 20关log 10 共Rloop 兲 ⫺ log10 共兩Zs 兩兲兴 [5] The amplitude of current induced in a current element depends on the magnitude of impedance presented to the induced emf. The impedance magnitude is, in turn, governed by the magnitude of Cos as Rrung is, ideally, a constant and small compared to XCos. Therefore, from Eqs. [4] and [5], the current induced in a current element is small compared with that induced in a resonant loop, and the extent of suppression is determined by the value of the parasitic output capacitance of the MOSFET. METHODS Design and Construction The active rung design is similar to the concept of active integrated antennas, where the radiating element is a part of the output circuit of the amplifier. The circuit schematic of the active rung design is shown in Fig. 3. The BLF245 (Philips Semiconductors, Eindhoven, Netherlands), a RF power MOSFET with rated maximum output power of 30 watts and 11 dB gain, was used to drive RF current through the rung. The rung was connected between the drain and source terminals of the MOSFET. Because the MOSFET was used in a common source configuration, the source terminal was tied to ground. The amplitude Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b 78 KURPAD, WRIGHT, AND BOSKAMP Figure 3 Circuit schematic of the RF current source. The array element or rung is connected across the output terminals of the MOSFET. The MOSFET drives current directly through the rung. AA⬘ is the plane at which the rung impedance is measured with and without the MOSFET in the circuit. CB is the DC block capacitance. and phase of the RF rung current was determined by the amplitude and phase of the RF voltage that appeared across the gate-source terminals of the MOSFET. This was achieved by providing the MOSFET drain with a DC supply voltage of 28V, which placed the MOSFET in the saturation region of its DC characteristic, where it behaves as a voltage-controlled current source. The gate was also provided with a DC bias voltage of 3.6V, thus setting up the MOSFET for class AB operation. An explanation of the DC characteristics and classes of operation of the RF power transistor may be found in literature (14, 17). The rung was broken up into five segments by four chip capacitors, each of 47 pF capacitance. This was done to increase the uniformity of current amplitude along the z direction and also to raise the self-resonance frequency of the rung higher. The other end of the rung was connected to ground by a trimmer capacitor (Johanson, Boonton, NJ). The range of the trimmer was chosen such that the rung impedance, as measured from the drain terminal of the MOSFET, varied from capacitive to inductive through a series resonance point. An input matching network was implemented to match the input impedance of the MOSFET to the source impedance of 50⍀ to ensure maximum power transfer into the MOSFET and also to prevent reflections back into the cable, which would result in formation of standing waves, leading to cable coupling problems. The active rung design was implemented on a printed circuit board (PCB). The PCB layout was fabricated using a PCB prototyping machine (Protomat C60, LPKF Laser and Electronics, Wilsonville, OR). A picture of a completed PCB showing the MOSFET, the DC bias circuits, the input circuit, and the output circuit, which is a part of the rung, is displayed in Fig. 4. The PCB was mounted on a cylindrical acrylic former (292 mm inner diameter, Figure 4 Picture of the PCB implementation of the active rung showing the output circuit (1), the drain bias circuit (2), the MOSFET (3), the input matching network (4 ), and the gate bias circuit (5 ). Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b DESIGN FOR CURRENT AMPLITUDE AND PHASE 79 and mounted on the spring loaded fixture. The current induced in the probe was transferred to the measurement apparatus by a RG316 coaxial cable through a lattice balun that was mounted on the plastic rod at the mouth of the cylindrical cavity. The balun was used to prevent currents induced on the cable shields from entering the measurement apparatus. Experiments Figure 5 A drawing of the side view of the active rung construction, showing the placement of the magnetic field probe (a) and a frontal view showing the manner in which the PCB containing the RF current source is mounted on the cylindrical acrylic former. 305 mm length) whose outer surface was wrapped in a thin copper foil. The copper foil was used not only as a RF shield but also as the ground plane. The rung consisted of a length of copper tape that spanned the length of the former and was placed directly under the PCB. The rung was supported by a rectangular acrylic strip that was 19 mm wide and 305 mm long. One end of the rung was connected to the output trace on the PCB through openings created in the former, the RF shield, and the PCB. The other end of the rung was connected to the RF shield by the trimmer capacitor described above. The drawing in Fig. 5(a) illustrates the active rung arrangement. Figure 5(b) shows the front view of the active rung arrangement mounted on the cylindrical former. The RF rung current measurement apparatus consisted of a magnetic field probe mounted on a mechanism that would allow the probe to be moved in both the axial and azimuthal directions. This enabled the probe to be placed directly under the current element of interest at any position along its length. The probe placement is illustrated in Fig. 5(a). The mechanism consisted of a plastic rod that was placed coincidental to the axis of the cylindrical former. A spring-loaded fixture, which pressed against the inner cylinder, was mounted on the rod and fastened firmly to it. The magnetic field probe was fabricated on a small copper-clad PC board as a 10 ⫻ 10-mm trace of copper In conventional amplifier design, the parasitic output capacitance (Cos) of the MOSFET is compensated by the output matching network. However, in the active rung design, there is no output matching network. To determine the effect of rung tuning using the series trimmer capacitor on the rung impedance as seen by the MOSFET, the rung impedance was measured for various settings of the trimmer capacitor, CT, both with and without the MOSFET in the circuit at the plane AA⬘ shown in the schematic of Fig. 3. The impedance measurements were made at the 3 T Larmour frequency of 128 MHz. A unique property of the active rung design is the ability to suppress current induced by an adjacent current-carrying conductor, thereby allowing a large dynamic range of independent control of the amplitude and phase of the current on the active rung. To demonstrate this key property, two sets of three experiments were performed to obtain the desired coupling data. The first set of experiments was performed with the test rung tuned to series resonance at 128 MHz, when the active rung behaves as a voltagecontrolled current element. The second set of corresponding experiments was performed with the test rung tuned so as to simulate a resonant loop of a TEM coil. The TEM elements are essentially transmission line elements that form resonant loops with the RF shield. The TEM elements are strongly coupled to each other. When the active rung is tuned such that the rung forms a resonant loop with Cos, the arrangement is similar to a TEM element excited by a voltage source. The experiments are described below. Experiment A. The test rung was tuned to series resonance at 128 MHz, the drive port to the active rung was terminated in 50⍀, and the DC supply to the MOSFET was turned on. The frequency of the RF current on the adjacent conductor was set to 128 MHz and its amplitude was set at several incremental values by ramping up the input voltage amplitude. The magnetic field probe was placed under the test element, and the spectrum analyzer readings of the field sensed by the probe were recorded. The purpose of Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b 80 KURPAD, WRIGHT, AND BOSKAMP Figure 6 Plots of measured rung impedance with the MOSFET in the circuit and biased (i) and without the MOSFET in the circuit (ii). The coincident dip in the two plots is the area in which the MOSFET behaves as a true current source with respect to the rung. this experiment was to measure the current induced in the test element. It was expected that the current induced in a current element would be significantly less than that induced in a TEM element. Experiment B. With the adjacent conductor carrying no current, the current on the test rung was ramped up. The magnetic field probe was again placed under the test rung. The purpose of this experiment was to determine the magnitude of current driven in element A under no influence from the adjacent conductor. The result expected from this experiment was a curve that represented the ideal response of the B1 field to the amplitude of the input RF control voltage. Experiment C. The amplitude of RF current on the test rung was ramped up with the current on the adjacent conductor set to its maximum amplitude of 1.6 A. The magnetic field probe was placed under the test element. The purpose of this experiment was to determine the dynamic range of independent control of current amplitude on the test rung for the worst case scenario of the adjacent conductor carrying current at maximum amplitude. The result expected from this experiment was a significantly larger dynamic range of independent control of the B1 contribution of a current element compared with the TEM element. RESULTS AND DISCUSSION The plots of the rung impedance magnitude for various settings of the trimmer capacitor, both with (curve [i]) and without (curve [ii]) the MOSFET in the circuit, are shown in Fig. 6. The region where the two curves coincide and exhibit a dip in the impedance magnitude, as indicated in Fig. 6, represents the region of series resonance tuning of the rung. In this region, Cos has no effect on the magnitude of rung current. Curve (ii) displays an impedance peak at a rung impedance measurement of (2.7 ⫹ j15.8)⍀. This peak may be attributed to the resonant loop formed by the rung inductance and Cos. These results validate the output circuit model discussed in section 2. Two important inferences may be made from these results. First, maximum current is driven through the rung when the rung impedance is small compared with the reactance presented by Cos. This occurs when the rung is tuned to series resonance and the Cos path appears as an open circuit to the driven current. Second, Cos forms a closed loop with the rung, which is resonant at 128 MHz for a different setting of the rung impedance. This can be viewed as a single loop of a TEM coil that is excited by a voltage source. Equivalently, the loop formed by Cos and the series resonant rung (at 128 MHz) is resonant at a frequency that is significantly shifted from the Larmour frequency. As shown in Fig. 7, the current induced in the test rung that is tuned to series resonance by an adjacent current-carrying conductor is, on average, less than that induced in the test rung that is tuned as a TEM element by the same adjacent conductor carrying the same current amplitude by 15.52 dB. From the impedance measurements, the resistance of the series resonant test rung is measured to be 0.4⍀. The impedance of the test rung tuned as a TEM element is measured to be (2.7 ⫹ j15.8)⍀. Therefore, the impedance of the loop formed by the series resonant test rung and Cos at a frequency of 128 MHz is (0.4 ⫺ j15.8)⍀, and the impedance of the TEM element at the same frequency is 2.7⍀. Substituting these values in Eqs. [4] and [5], the current in the TEM element is Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b DESIGN FOR CURRENT AMPLITUDE AND PHASE 81 Figure 7 Plots of B1 field measurements made using the magnetic field probe placed directly under test rung. The series tuned and parallel tuned measurements were made with the test rung tuned as a current element and TEM element, respectively. The average difference in dB between the measurements is shown. found to be greater than that in the series resonant test rung by 15.34 dB. The calculated and measured values are in good agreement. Two important inferences can be made from the above results. First, the active rung design with the rung tuned to series resonance suppresses induced current by a significant amount when compared to the TEM element. This may be attributed to the significant shift in the resonance frequency of the induced current loop from that of the driven current path. Second, the magnitude of suppression depends entirely on the value of Cos. The smaller the value of Cos, the greater the suppression of induced current. The plots shown in Fig. 8 are measured values of the magnetic field sensed by the magnetic field probe generated by the current on the test rung that is tuned to series resonance at 128 MHz in the presence of an adjacent conductor carrying varying current amplitudes at the same frequency. Plot (a) is the magnetic field sensed by the probe due to the current induced on the test rung. Plot (b) represents the magnetic field sensed by the probe due to current driven in the test rung in the absence of the adjacent conductor, and plot (c) represents the resultant magnetic field sensed by the probe due to the current driven into the test rung with the adjacent conductor carrying maximum current. This represents the worst-case scenario for coupling between neighboring current elements. Plot (c) can be divided into three regions as shown in Fig. 8. In region 1, the field sensed by the probe is Figure 8 Curves showing dynamic range of independent control of RF current on the current element. (a) The sensed field due to induced current on the test rung tuned to series resonance; (b) the sensed field due to driven current on the test rung with the adjacent conductor removed from the circuit; and (c) the sensed field due to driven current on the test rung with the adjacent conductor carrying maximum current. Region 1 of curve (c) is induced-current dominated, and region 3 is driven-current dominated. The current probe senses the resultant current due to driven and induced currents on the test rung in region 2. Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b 82 KURPAD, WRIGHT, AND BOSKAMP Figure 9 Curves show the effect of induced currents on the dynamic range of independent control of current amplitude and phase on the test rung tuned as a TEM element. (a) The sensed field due to induced current on the test rung; (b) the sensed field due to driven current on the test rung; and (c) the sensed field due to driven current on the test rung under worst-case conditions of maximum current on the adjacent conductor. This set of curves shows that there is no region dominated by the driven current on the test rung. predominantly due to the current induced on the test rung by current on the adjacent conductor. Region 2 is where the magnitude of current driven in the test rung is comparable to that induced by the adjacent conductor. Hence, the field sensed by the probe is the resultant field due to the resultant of the driven and induced currents on the test rung. Region 3 is where the driven current in the test rung dominates the induced current due to the adjacent conductor, and the magnetic field probe senses the field predominantly due to current driven on the test rung. The dynamic range of independent control of the current amplitude, as seen in Fig. 8, is represented by region 3 and is 17dB. The curves in Fig. 9 correspond to those in Fig. 8 and are due to the test rung, tuned as a TEM element. Comparison of plots (a) and (b) in this case shows that the induced current is, on average, only 5.2 dB down from the driven current. This is only a factor of 1.8 less than the driven current. For the worst-case scenario of maximum current on the adjacent conductor, the driven current on the test rung never completely dominates the induced current. This is borne out by the fact that plot (c) can be divided into only two regions, whereas region 1 is induced current dominated and region 2 represents the resultant field due to the driven and induced currents. It is evident from the above results that the degree of suppression of induced currents determines the dynamic range of independent control of the amplitude and phase of the rung current. A TEM element is strongly coupled to similar adjacent elements and therefore does not exhibit independent control. The active rung with the rung tuned to series resonance, on the other hand, exhibits a large range of independent control of the rung current amplitude and phase as a result of the key property of suppression of induced current from similar adjacent rungs. Further, the degree of suppression of induced current is limited by the parasitic output capacitance of the MOSFET. The results presented above show that with the RF current source implementation, the induced currents on neighboring elements may be suppressed, though the mutual impedances and the induced emfs remain the same. This serves to reduce the influence of neighboring array elements on the amplitude and phase of the current on any given element or rung. This result has significant implications for the design of transmit coils for high-field MRI. CONCLUSION In this article, we described the development of an RF current source integrated with an array element or rung, which we refer to as the active rung. Series resonance tuning of the rung makes the effects of parasitic MOSFET capacitance negligible. The amplitude and phase of the current on the rung may be controlled accurately by the amplitude and phase of the input RF control voltage. The existence of separate paths for the driven and induced currents within the MOSFET results in suppression of induced current. The degree of suppression is largely dependent on the size of the MOSFET parasitic output capaci- Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b DESIGN FOR CURRENT AMPLITUDE AND PHASE tance. Induced current suppression is an important feature that is necessary for the design of parallel transmit arrays. ACKNOWLEDGMENTS The authors gratefully acknowledge the support from the National Science Foundation (BES0101059). The authors would also like to thank Mr. John Lorbiecki for building the acrylic former and Mr. LeRoy Blawat for stimulating conversations on RF circuit design. REFERENCES 1. Hayes CE, Edelstein WA, Schenck JF, Mueller OM, Eash M. 1985. An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T. J Magn Reson 63:622– 628. 2. Vaughan JT, Hetherington HP, Otu JO, Pan JW, Pohost GM. 1994. High frequency volume coils for clinical NMR imaging and spectroscopy. Magn Reson Med 32:206 –218. 3. Ibrahim TS, Abduljalil AM, Baertlein BA, Lee R, Robitaill PM. 2001. Analysis of B1 field profiles and SAR values for multi-strut transverse electromagnetic RF coils in high field MRI applications. Phys Med Biol 46:2545–2555. 4. Stenger VA, Saekho S, Zhang Z, Yu S, Boada FE. 2004. B1 inhomogeneity reduction with transmit SENSE. Proc 2nd International Workshop on Parallel MRI, Zurich, 2004 p 94. 5. Zhu Y. 2004. Parallel excitation with an array of transmit coils. Magn Reson Med 51:775–784. 6. Katscher U, Bornert P, Leussler C, van den Brink JS. 2003. Transmit SENSE. Magn Reson Med 49:144 – 150. 83 7. Pauly J, Nishimura D, Macovski A. 1989. A k-space analysis of small-tip-angle excitation. J Magn Reson 81:43–56. 8. Kurpad KN, Boskamp EB, Wright SM. 2004. Implementation of coil integrated RF power MOSFET as voltage controlled current source in a transmit phased array coil. 12th Scientific Meeting of the International Society of Magnetic Resonance in Medicine, Kyoto, Japan. p 1585. 9. Kurpad KN. 2004. Transmit field pattern control for high field magnetic resonance imaging with integrated RF current sources. Ph.D. dissertation. College Station, TX: A&M University. 10. Copeland J, Robertson W, Verstraete R. Antennafier arrays. 1964. Antennas and Propagation, IEEE Trans 12:227–233. 11. Anderson A, Davies W, Dawoud M, Galanakis D. 1971. Note on transistor-fed active-array antennas. Antennas and Propagation, IEEE Trans 19:537–539. 12. Anderson A, Dawoud M. 1973. The performance of transistor fed monopoles in active antennas. IEEE Trans Antennas and Propagation 21:371–374. 13. Chang K, York RA, Hall PS, Itoh T. 2002. Active integrated antennas. IEEE Trans Microwave Theory and Techniques 50:937–944. 14. Krauss HL, Bostian CW, Raab FH. Solid state radio engineering. New York: Wiley; 1980. 15. Caviglia A, Iliadis AA. 1995. A large-signal model for SOI MOSFETs including dynamic self-heating effects. Proceedings, 1995 IEEE International SOI Conference, Tucson, AZ. p 16 –17. 16. Grebennikov AV, Lin F. 2000. An efficient CADoriented large-signal MOSFET model. IEEE Trans Microwave Theory and Techniques 48:1732–1742. 17. Sokal NO. 1997. RF power amplifiers, classes A through S— how they operate, and when to use each. Electronics Industry Forum of New England, 1997. Professional Program Proceedings, Boston, MA. p 179 –252. Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering) DOI 10.1002/cmr.b