LEGO-MIMO Architecture: A Universal Multi-Input Multi-Output (MIMO .

Fig. 6. Equivalent circuits of series bricks and parallel bricks in one port.Fig. 4. Principles of the group control strategy for the LEGO-MIMOarchitecture. Modular bricks can be plugged in without changing the overallcontrol strategy. The system is “linearly extendable” with voltage balancingand current sharing.current in an n-winding transformer can be described as ann n impedance matrix: VW 1L11 · · · M1nIW 1 . . . ,.(3) . jω . . VW nFig. 5. LEGO bricks and the cantilever model of a multi-winding transformer.dc blocking capacitors are neglected in this model due to theirsmall impedance. Following the principles of multi-activebridge (MAB) converter [5], the average power delivered toBrick i from the transformer is:Pi Ni Vi X Nj Vj (Φi Φj ) (π Φi Φj ).2π 2 fs(Ni2 Nj2 Lij Nj2 Li Ni2 Lj )Mn1···LnnIW nwhere VW i is the winding voltage, IW i is the winding current,Lii is the self-inductance of Winding i, Mij Mji arethe mutual-inductance between Winding i and Winding j.The self-inductance and mutual-inductance can be exactedby analytical model, experimental measurements, or FEAsimulations. The winding resistance is neglected.Fig. 6 shows the equivalent circuit model of the stackedbricks in Port X and parallel bricks in Port Y . The equivalentwinding voltage of Port X is the summation of windingvoltage of each stacked brick:VP X VW h VW i VW j · · · .(4)Since Brick h to Brick j are modulated in phase with the samegroup of gate drive signals, we can assume that the windingcurrent in every brick of Port X are equal:(1)IP X IW h IW i IW j · · · .j6 i(5)The equivalent external branch inductance LP X is the summation of the series inductance of all brick branch inductors:Here Φi and Φj are the phase-shift angles of Brick i and Brickj; Li and Lj are the external branch inductors (LH and LLin Fig. 3); Ni , Nj are the turns number; Vi , Vj are the dc busvoltage of LEGO bricks; fs is the switching frequency.The small signal model for the dc bus voltage of the totaln LEGO bricks in the LEGO-MIMO converter is [5], [11]:For Port Y with parallel LEGO bricks, the equivalent windingvoltage equals the winding voltage of every brick:v̂ Gv v̂ Gφ φ̂.VP Y VW k VW l VW m · · · .LP X LW h LW i LW j · · · .(2)Here Gv is the the small signal transfer matrix from the busvoltage perturbations of other bricks. Gφ is the small signaltransfer matrix from phase-shift perturbations to the dc busvoltage of LEGO brick. Both Gv and Gφ require the loadimpedance of each LEGO brick.However, this small signal model is not suitable for theLEGO-MIMO architecture. As mentioned in Section II, ifmany LEGO bricks are connected in series or parallel, the loadimpedance of each LEGO brick can not be directly obtainedin a port with multiple parallel or stacked bricks. The smallsignal matrix becomes over complicated when the LEGOMIMO converter has a large number of bricks.A matrix reduction method is developed to analyze the smallsignal model of the LEGO-MIMO architecture with sophisticated series-parallel configurations. The winding voltage and(6)(7)The equivalent winding current is the summation of all theindividual brick winding currents:IP Y IW k IW l IW m · · · .(8)The equivalent branch inductance equals to the parallel inductance of all brick branch inductors:LP Y LW k LW l LW m · · · .(9)Suppose the total n LEGO bricks are divided into mports (m n), the voltage conversion matrix QV convertsthe voltage of each brick winding into the voltage of eachequivalent port winding: VP 1QV 11 . . . .VP mQV m1···.··· VW 1QV 1n . . . . QV mn m n VW n(10)

Fig. 7. LEGO bricks and a simplified cantilever model with m windingswhich can be used to model the large-signal and small-signal dynamicbehaviors of the system.Fig. 8. A 500W LEGO-MIMO converter with 12 LEGO bricks, including 4HV bricks (green) and 8 LV bricks (red) with interleaved winding structure.Each element of QV can be found by: if Port i consists series-connected bricks, and Brick jbelongs to Port i, then QV ij 1; Otherwise, QV ij 0. if Port i consists parallel-connected bricks, and Brickj, k, l belong to Port i, then set any one of QV ij , QV ikor QV il be 1, and all other QV i? on the same row as 0.The equivalent port winding current can be extracted bycurrent conversion matrix QC with the similar rules: IW 1QC11 . . . .IW mQCn1···.··· QC1mIP 1 . . . . QCnm n m IP n(11)Each element of QC can be found by: if Brick i belongs to a series-connected Port j, thenQCij 1; Otherwise QCij 0. if Brick i, k, l belong to a parallel-connected Port j, thenset QV ij QV kj QV lj 1.The m m “port-to-port” impedance matrix MP 2P is:MP 2P QV MW 2W QC .(12)where MW 2W is the n n impedance matrix in (3).If one port has both series-connected bricks and parallelconnected bricks. The matrix conversion can be performedin two steps: firstly converting the port to several sub-portswith series-connected bricks; then converting these parallelconnected sub-ports to one port.With the m m impedance matrix, the n-winding transformer can be simplified to a cantilever model with mequivalent windings as shown in Fig. 7. NP i is the equivalentturns number, which equals to the total turns number of seriesconnected bricks and the identical turns number of parallelconnected bricks. Based on the simplified cantilever model,the equivalent winding voltages and winding currents can belinked by the equivalent inductance linking different ports:IP MV 2C VP .(13)Here IP and VP are the equivalent winding current matrixand voltage matrix. MV 2C is the admittance matrix linkingwinding voltage with winding current: Y11 · · · Y1m1 . ,.MV 2C (14) . jωYm1 · · · YmmYii 1LP Gi 1 X 1 1, Yij .2NP iLP ijNP i NP j LP ij(15)j6 iThis admittance matrix is the inverse of the “port-to-port”impedance matrix:MV 2C MP 12P .(16)All parameters in the simplified cantilever model can beobtained from (16). Substituting them into (1) and replacingthe brick voltage with port voltage gives the average powerdelivered to Port i from the other ports. For example, inthe MIMO converter with 12 LEGO bricks, the small signaltransfer matrices of the brick bus voltage Gv and Gφ areboth 12 12 matrices. With the matrix conversion, the smallsignal transfer matrices are simplified to 4 4 matrices (with4 input and output ports), which significantly mitigates thecontrol complexity. The phase-shift feedback control and timesharing control introduced in [11] can be similarly applied tothe LEGO-MIMO converter.IV. M ULTI - WINDING T RANSFORMER D ESIGNFig. 8 shows the prototype MIMO converter including 8modular PCB boards, one UU type magnetic core, one motherboard and one controller board. One modular PCB board hasone HV LEGO brick or two LV LEGO bricks. There are 4HV bricks and 8 LV bricks in total in this prototype. TheUU core is installed through the central cutout holes of thePCB windings, which couples all the HV bricks and LV brickstogether. The mother board connects the LEGO bricks in seriesor in parallel as group operated ports. The key parameters ofthe LEGO-MIMO converter are listed in Table I.There are many ways of placing the HV and LV bricksaround the magnetic core. Two winding structures are investigated and compared in this paper. Fig. 9 shows the crosssection view of the two winding structures - one interleaved,and the other non-interleaved. The HV bricks are labeled ingreen and the LV bricks are labeled in red. Since the modularPCB board is manufactured with 4-layer copper foils, the 1turn winding of the LV brick is divided into two parallelconnected copper layers. Suppose all the HV bricks are onthe primary side and all the LV bricks are on the secondaryside, the primary current Ip and secondary current Is in the

TABLE IPARAMETERS OF THE LEGO-MIMO P ROTOTYPESpecifications & SymbolDescriptionHV Bus Voltage VHHV Winding Turns NHHV Branch Inductor LHHV Blocking Capacitor CHHV SwitchLV BUS Voltage VLLV Winding Turns NLLV Branch Inductor LLLV Blocking Capacitor CLLV DrMOSSwitching Frequency fsTransformer Core72V8Coilcraft XEL6060 – 2.7µH200µFGS61004B 100V9V1Coilcraft SLC7530S – 64nH440µFSIC632 24V200kHz0P4413UC, µr 2500Fig. 9. Winding cross-section view and MMF distribution in an ideal multiwinding transformer with infinite permeability and high coupling coefficient.multiple windings of this multi-winding transformer with anungapped infinite permeability core satisfy:1 Is .(17)2Fig. 9 also shows the magnetomotive force (MMF) inthis multi-winding transformer with interleaved and noninterleaved winding structures. In the non-interleaved structure, the horizontal flux Φh is canceled by the same windingcurrent of two adjacent HV or LV windings and the MMFat the same position of the window area is zero, which canrelief the proximity effect on the top and bottom surface of thePCB coppers. However, the opposite currents of one HV brickon the left side and one LV brick on the right side enhancethe vertical flux Φv and the maximum MMF is 32Ip at thecentral vertical axis of the window area, which will induceeddy current at the side surface of PCB coppers.In the interleaved structure, the flux and MMF distributionare very different from those in the non-interleaved structure.The horizontal flux in the window area is enhanced while thevertical flux is canceled. The maximum MMF is 8Ip at thegap between one HV brick and one LV brick. The proximityeffect on the side surface of the PCB windings is reducedwhile eddy current will be induced on the top surface of PCBboard on the 2nd and 4th row (HV1, HV4, LV3, LV7), and thebottom surface of PCB board on the 1st and 3rd row (LV2,LV6, HV2, HV3).For a practical magnetic core with a permeability of µr , theMMF on the left pillar with non-interleaved winding structureis 32Ip , while it is 16Ip 4Is with interleaved windingstructure. Both the magnetic field strength and the core lossare reduced with interleaved winding structure.The copper thickness is 70µm, which is much smaller thanthe skin depth (170µm) at the switching frequency (200kHz)and much smaller than the width of PCB trace (2.75mm forHV winding and 6mm for LV winding). As a result, it ismore important to equally distribute current along the radiusof PCB winding to reduced the ac resistance. Considering ofthe ac winding resistance, the interleaved winding structure isthe better than the non-interleaved option with smaller MMF,proper flux distribution and lower ac resistance.32 Ip 16 Fig. 10. 3D FEM simulation of the magnetic field strength and core fluxdensity in the interleaved and non-interleaved winding structures.Fig. 11. 3D FEM simulation of the current density in the PCB windings ofthe interleaved and non-interleaved winding structures.We use FEM to verify the magnetic analysis. The relativepermeability of the core is 2500. The excitation current is4A on the primary side and 16A on the secondary side. Theexcitation frequency is 200kHz. The magnetic field strengthH in the window area and core flux density B are shownin Fig. 10. The magnetic field strength with non-interleavedstructure is much stronger than the field strength in theinterleaved structure. The distribution of H also matches theflux distribution analysis. The flux density in the core of thenon-interleaved structure is significantly higher than that inthe interleaved structure, especially on the two vertical sides.Fig. 11 shows the current density in the PCB windings. Theouter edge of the PCB winding in the non-interleaved structurehas higher current density due to the eddy current induced bythe vertical flux, which matches the theoretical analysis andthe FEM simulation in Fig. 10. The simulated winding loss inthe interleaved structure is only 56% of the winding loss inthe non-interleaved structure.

TABLE IIE QUIVALENT I NDUCTANCE LINKING T WO W INDINGS IN THEC ANTILEVER M 11µH13.6µH12.52nH23.2µHAnother challenge in the multi-winding transformer designis to maintain voltage balancing and current sharing amongthe series or parallel connected LEGO bricks. Since allthe parallel-connected and series-connected LEGO bricks arecontrolled by the same group of gate drive signals, activebalancing control of each brick is not applicable. The voltagebalancing and current sharing among the LEGO bricks aredetermined by the symmetry of the impedance matrix. Asymmetric impedance matrix would enable passive voltagebalancing and current sharing. As a result, the geometry andthe winding structure of the magnetic structure should becarefully designed to achieve the highest level of symmetryamong the LEGO bricks.Table II listed the equivalent linkage inductance linking twowindings in the interleaved magnetic structure as shown inFig. 9. The data labeled in yellow is the grounding inductance.The equivalent linkage inductance is related to the “magneticdistance” between two brick windings. Take LV1 as theexample, the linkage inductance between LV1 and LV2 is lowand the inductance between LV1 and LV7 is high. Power tendsto flow between windings that are physically closer to eachother (due to the smaller linkage inductance). Suppose all theHV bricks and all the LV bricks are respectively controlledby two group of gate drive signals. The power processed bythe ith brick is determinedP by the linkage inductance that thisbrick is connected to: j6 i 1/(Lij Li /Ni2 Lj /Nj2 ). Fig. 12illustrates the power distribution in the HV and LV bricks.All HV bricks are connected in series, and all LV bricks areconnected in parallel.The power processed by the HV bricks in the interleavedwinding structure is well balanced due to the symmetricwinding structure of HV1 to HV4 (and a highly uniformimpedance matrix, e.g., the inductance between HV1 and LV5equals to the inductance between HV2 and LV8). The powerdistribution in the HV bricks with the non-interleaved windingstructure is highly unbalanced due to the asymmetric windingstructure. The total power that a non-interleaved structure cantransfer from one port to another with the same phase-shift issignificantly lower than that in an interleaved structure. Thenon-interleaved structure has higher equivalent linkage inductance among windings, which enhances the control resolutionbut limits the maximum power that can be transferred fromport to port.The power processed by the LV bricks is non-uniformin both cases due to the asymmetric LV winding structures(e.g., for the interleaved structure, LV1 and LV2 are stillasymmetric and have different inductance matrix parameters).Fig. 12. Power distribution among the HV bricks and LV bricks. All the HVbricks work as one group with the same phase-shift angle. All the LV brickswork as another group with the same phase-shift angle.Fig. 13. Configurations of the HV/LV bricks in the LEGO-MIMO prototype.Furthermore, the LV PCB boards in the interleaved structureare symmetric and the power of the two LV bricks placed onthe same PCB in the interleaved structure is equal to eachother (PLV 1 PLV 2 PLV 3 PLV 4 · · · ). Note this powerdistribution analysis is based on the assumption that the samephase-shift is applied to all HV bricks and all LV bricks. Theparasitic components and the impedance of PCB traces andvias are neglected, which may offset the power imbalance. Ifsignificant external inductance are included in the system, thestructural asymmetry caused by the multi-winding magneticscan be eliminated.V. E XPERIMENTAL V ERIFICATIONFig. 13 shows a few different ways of configuring the LEGObricks with four HV bricks and eight LV bricks. Each HV brickcan block 72V and carry 2 A (dc). Each LV brick can block9V and carry 7 A (dc). Four HV bricks are connected in seriesto interface with a 288V/2A dc bus. Two LV bricks (LV1 andLV2) are connected in parallel to support a 9V bus with 14A of current. LV3 and LV4 are series-connected as a 18V/7Aport and LV5–LV8 are connected in series as a 36V/7A port.

Fig. 14. Measured inductor currents in the four HV bricks at output powerof 300W with interleaved and non-interleaved winding structures. The HVGroup is the input port and the LV Group 1 (Fig. 13) are the output ports.Fig. 16. Measured efficiency of the LEGO-MIMO prototype with two windingstructures. The output ports are configured into 9V, 18V and 36V (Fig. 13).Fig. 15. Thermal images of the core with the interleaved and non-interleavedstructures. The output power is 80W. The ambient temperature is 20 C.They can also be reconfigured into a high power 9V/56A portand a high power 36V/14A port.Fig. 14 shows the branch inductor current of four HVbricks with 288V input and 9V-18V-36V output. The currentwaveforms are all in phase because all the HV bricks arecontrolled by synchronized gate drive signals. The current ofthe HV bricks in the interleaved winding structure are morelike an ideal trapezoidal waveform than the current in noninterleaved structure.Fig. 15 shows the thermal images of the magnetic corewith the interleaved and non-interleaved winding structures.The thermal images are captured by a thermography camera(FLIR E6) after the converter running for 8 minutes withoutput power of 80W. The ambient temperature is 20 C withno air cooling. The interleaved winding structure has lowercore temperature due to the lower magnetic field strength. Thehottest spot is 51.7 C in the non-interleaved structure and is45.1 C in the interleaved structure.Fig. 16 shows the measured efficiency of the LEGO-MIMOconverter with the interleaved and non-interleaved windingstructures. The interleaved winding structure offers highersystem efficiency and higher power rating. The peak systemefficiency is 96%. The maximum power that the system candeliver is 500W. All the LV bricks are controlled by thesame phase-shift angle. The interleaved structure has higherefficiency due to the balanced power distribution and lowercurrent amplitude. Since the 36V port has 4 LV bricksand both 9V port and 18V port have 2 LV bricks, thepower processed by the 9V port, 18V port and 36V portare proportional to the brick number of each port: P36V Pi 5,6,7,8 PLV i P9V P18V . In the interleaved windingstructure, P9V PLV 1 PLV 2 P18V PLV 3 PLV 4 .Fig. 17 shows the measured port power in the two cases.In the non-interleaved structure, the power processed by theFig. 17. The measured power of the 9V, 18V and 36V ports. Unbalancedpower exists in the non-interleaved structure. Power is well distributed in theinterleaved structure.9V port (PLV 1 PLV 2 ) is higher than the power processedby the 18V port (PLV 3 PLV 4 ), which matches with thetheoretical analysis presented in Fig. 12. With interleavedwinding structure, the power of all the three ports are wellbalanced and evenly divided. The experiment results of portpower also show that the two winding structures have different“power resolution” with the same phase-shift angle.The experimental results verified that the LEGO-MIMOarchitecture is linearly extendable if the magnetic windingstructure is symmetric enough. The number of HV and LVbricks can be further extended to cover wider input/outputvoltage and current ratings.Fig. 18 shows the measured inductor current waveforms offour LV LEGO bricks with the three output groups configuredas in Fig. 13. In LV Group 1, the bus voltages of LV Brick 1and 2 are clamped to the port voltage and regulated to 9V. Thevoltage of the 18V port and the 36V port are regulated, but thevoltage of each individual brick is not regulated. The voltage ofLV Brick 3–8 is still unbalanced, causing unbalanced currentslopes and higher inductor current magnitudes in iL4 , iL5 , iL7 .In the case of LV Group 2, all the LV bricks are parallelconnected and all their bus voltages are regulated. The inductorcurrent waveform shows better current sharing. The currentwaveform is highly trapezoidal with low amplitude. In LVGroup 3, voltage unbalancing still exists among the LV brickssince none of them are individually regulated.Fig. 19 compares the efficiency of the three output portconfigurations. LV Group 2 achieves the highest efficiencyespecially with higher output power. The reasons are the

Fig. 18. Me

of a universal Multi-Input Multi-Output (MIMO) power con-verter with many Linear Extendable Group Operated (LEGO) building blocks, namely LEGO-MIMO architecture. The LEGO-MIMO architecture can be used to synthesize a wide range of power converters with universal input and output range. In a LEGO-MIMO design, multiple dc-ac units are coupled