Analysis and Design of an Integrated Magnetics Planar Transformer for High Power Density LLC Resonant Converter

Recent studies on compact and lightweight electronic devices have demonstrated that the LLC resonant converter (LRC) can facilitate achieving high efficiency and high power density. Moreover, employing a planar transformer can further improve the overall system power density. Although the planar transformer can assist in reducing the size of the converter, its high magnetic coupling makes the leakage inductance too small for a resonant inductor in the LRC. Therefore, an extra inductor must be employed separately, leading a considerable decrease in the power density. From this reason, significant research on integrated magnetics has been conducted to combine a transformer and external inductor into a single core. However, they require additional wires or magnetic sheets, and their structures are complex and costly. To overcome these limitations, the integrated magnetics planar transformer (IMPT) for a high power density LRC is proposed in this paper. In the proposed approach, since the primary wire is split into each side leg of the EE-type magnetic core and each operates as a transformer and a resonant inductor alternatively, an external inductor or additional wires are unnecessary. In addition, since the magnetic flux density of the IMPT is approximately equivalent to that of conventional transformer, the core size and the number of turns are almost the same. Therefore, the proposed IMPT features higher efficiency and power density without additional size and costs. To confirm the validity of the proposed IMPT, the operational principles, theoretical analysis, design considerations, and experimental results from a 350 W prototype are presented.


Ao
: Cross-sectional area of the side leg Ac : Cross-sectional area of the center leg Today, most electronic devices and systems are not only becoming compact and lightweight but their power consumptions are also continuously increased. Therefore, high-efficiency and high-power density converters have received significant attention. For example, recent trends in the TV market require thinner and lighter TV sets, despite the demand for more power due to the increased number of pixels up to tens of millions. In order to keep up with this trend, higher-power density converters with higher efficiency are essential. Among various power converter topologies, the LLC resonant converter (LRC) is an excellent candidate to satisfy high efficiency and high power density due to its favorable merits, such as the zero voltage switching (ZVS) of all power switches, zero current switching (ZCS) of all output rectifiers, good electromagnetic interference, and other aspects [5][6][7][8][9][10]. As a result, many approaches aimed at further increasing power density of the LRC have been the scope of many studies, considering these advantages.
Generally, magnetic components, such as a transformer and an inductor, are critical because they occupy a large amount of space in electronic systems. Therefore, many researches have tried to reduce the size of magnetic components, which are essential in achieving a high power density converter. Among them, increasing the switching frequency can be a good approach [1]. However, the switching losses of power semiconductors are increased in proportion to switching frequency. Although power switches with excellent performance (i.e., small parasitic capacitors, high on and off speed, small turn on resistance) have been steadily released, a limitation is still existed in reducing the size of a magnetic device by increasing only the switching frequency [2][3][4].
Meanwhile, to further reduce the size of converter, employing a planar transformer can be a good approach. In a planar transformer, the wires and bobbins can be replaced by a printed circuit board (PCB); thus, the size and thickness of a converter can be considerably reduced. However, the number of PCB layers must be increased in proportion to the number of turns. Therefore, for a large number of turns, the volume and cost may be significantly increased. To reduce the number of PCB layers, conventional studies have proposed an integrated dual transformer (IDT) [10]. Namely, the primary wire is split in half, and each wire is placed on each side leg of the EE-or UU-type magnetic core.
Thus, the separated primary turns reduce the thickness as well as the number of PCB layers [11]. However, since the high magnetic coupling of a planar transformer makes leakage inductance too small to be used as a resonant inductor in the LRC, an extra inductor must be employed and it considerably decreases the power density. To overcome this problem, several types of integrated magnetics transformers have been proposed to integrate an external inductor into a transformer [12][13][14][15][16][17]. In [12], the resonant inductor is integrated with the transformer in a single magnetic core using the decoupling integration method. However, this method requires additional windings for the resonant inductor except for the main transformer, which may significantly increase the size and volume of the integrated magnetics. Moreover, since the copper wire must be wound around all legs of the magnetic core, the large number of turns can be required to achieve sufficient resonant inductance. Therefore, implementing this method with the planar transformer can significantly increase the number of PCB layers, the size of the PCB, and the magnetic core. In [13], primary wires are constructed at a spatial distance from secondary wires to obtain sufficient leakage inductance required to function as a resonant inductor. However, the spatial distance between the primary and secondary wires increases the height of the transformer. Moreover, its complex structure may not be suitable for a planar transformer. In [14], a resonant inductor and transformer are physically integrated into a single magnetic core (i.e., each one is placed on each side leg of the EE-type magnetic core, respectively). Although this approach has the advantage of a single magnetic core, it has the disadvantages of a magnetic flux imbalance in each leg and the large number of PCB layers. Namely, the primary and secondary wires of the transformer must be wound on only one of the three legs. As a result, the many PCB layers are required to implement the planar transformer. Moreover, since the flux density (B) of the resonant inductor generated by the resonant current is high, the cross-sectional area and core loss may be significantly increased. In [15], resonant inductor and transformer wires are placed together on the center leg and magnetically divided by the I-core inserted between the upper and lower E-cores of the EE-type magnetic core. Since the magnetic fluxes in the I-core generated by the transformer and resonant inductor are cancelled with each other, the flux density and subsequent core loss of the additional I-core can be reduced. However, the large number of PCB layers are still required, and additional loss and larger size from the inductor are inevitable. Especially, due to the existence of the I-core between EE-core, at least two PCBs are required to implement a planar transformer. In [16,17], a magnetic sheet is inserted between the primary and secondary wires to increase the leakage inductance as a resonant inductor. Therefore, additional wire for an inductor is unnecessary, and it is easy to secure sufficient inductance for a resonant inductor. However, it is not only difficult to insert the magnetic sheet into the PCB, but there also exists a concern of high manufacturing costs.
To overcome these limitations of prior approaches, the integrated magnetic planar transformer (IMPT) is proposed in this paper. As shown in Fig. 1(a), the split primary wire is placed on each side leg of the EE-type magnetic core, and two secondary center-tap wires are also placed on each side leg one by one. Thus, Np1 and Ns1 are coupled and work as a transformer during positive half switching cycle. Further, Np2 functions as an inductor, because no current flows through Ns2 due to the output rectifier. During the negative half switching cycle, the operation is inverted. Therefore, since each primary wire alternatively operates as a transformer and a resonant inductor, an external inductor or additional wires for the resonant inductor are unnecessary. Specifically, as a large resonant current flows directly through the external inductor in conventional approaches, the core loss and maximum flux density (Bm) of the inductor are high. Nevertheless, the IMPT requires no external inductor. As a result, the abovementioned problem can be overcome. Moreover, because the flux density of the IMPT is similar to that of a conventional transformer, the core size of the transformer and its number of turns are also almost the same. Therefore, the proposed IMPT features higher efficiency and power density without additional size, cost, and power loss. Fig. 1(a) illustrates the magnetic structure of the proposed IMPT, and the structure is symmetric with the air gap go1 = go2 = go, primary number of turns Np1 = Np2 = Np, and secondary number of turns Ns1 = Ns2 = Ns. For the circuitry analysis, the physical magnetic structure can be converted into an equivalent inductance model through a reluctance model. As depicted in Fig. 1(b), there are three magnetic paths and each path can be represented to the reluctance [18][19]. Here, the reluctances of the side leg (ℜ  ) and center leg (ℜ  ) can be determined as follows:

A. EQUIVALENT INDUCTANCE MODEL OF THE PROPOSED IMPT
Generally, since μr is much larger than μ0, the reluctance is mainly determined by the air gap. Then, according to the duality theory, an equivalent inductance model of the IMPT can be finally obtained and applied to the LRC as shown in Fig. 2. Each parameter of the equivalent inductance model can be determined as follows: where all the inductances can be adjusted by the number of primary turns and air gap. ㆍAll operations are considered in the steady state. ㆍThe switching frequency fsw is almost equal to the resonant frequency fr. ㆍAll parasitic components except those specified in Fig. 2 are neglected. ㆍThe output capacitor Co is large enough to be considered as a constant voltage source. ㆍThe dead time between M1 and M2 is very short compared to one switching period. ㆍLo1 = Lo2 = Lo, Np1 = Np2 = Np, and Ns1 = Ns2 = Ns.  In the simplified circuit, Np1 and Ns1 work as a transformer, whereas Lo2||Lc acts as a resonant inductor. At this point, iLo1 is increased linearly with the slope of (Np1/Ns1)Vo/Lo1, and Lo2||Lc resonates with Cr.
Here, the currents and voltages are determined as follows: where  = 2π  = 1  Assuming that fsw is equal to fr, the following relationship is satisfied according to Kirchhoff's voltage law (KVL):

Mode 2 (t1 -t2):
When ipri equals iLo1, Do1 is blocked, and M1 is turned off. Therefore, Lo1 and Lo2 are connected in series and resonate with Cr, as shown in Fig. 4(b). However, since t1 -t2 is very short from the assumption, ipri = iLo1 = iLo2 can be considered as a constant current source during this mode. Therefore, ipri starts to charge Cds1 from 0 V to Vin and discharges Cds2 from Vin to 0 V. When vds2 equals 0 V at t2, M2 can be turned on, with ZVS in the next mode.

Mode 3 (t2 -t3):
When M2 is turned on, ipri flows to the nondot terminal of the transformer, as shown in Fig. 4(c). Therefore, Do1 is blocked and the input power is transferred to the output through Do2. Unlike the mode 1, the reflected voltage (Np2/Ns2)Vo is applied to the winding Np2 of the second ideal transformer; thus, the series-connected Lc and (Np2/Ns2)Vo are connected in parallel to Lo1 through the first ideal transformer with the turn ratio of Np1:Np1. Then, the circuit inside the dashed box on the left side in Fig. 5(b) can be simplified to Thevenin's equivalent circuit, comprising a voltage source (Np2/Ns2)VoLo1/(Lo1+Lc) and inductor Lo1||Lc, as shown on the right side in Fig. 5(b). In the equivalent circuit, Np2 and Ns2 work as a transformer, whereas Lo1||Lc acts as a resonant inductor. Therefore, iLo2 is increased linearly with the slope of (Np2/Ns2)Vo/Lo2, and Lo1||Lc resonates with Cr. Here, the currents and voltages are determined as follows: where Meanwhile, considering the same assumption at mode 1, the following relationship is also satisfied according to KVL: When ipri equals iLo2 after resonance, this mode ends.

Mode 4 (t3 -t4):
When ipri equals iLo2, Do2 is blocked and M2 is turned off. Therefore, Lo1 and Lo2 are connected in series and resonate with Cr, as shown in Fig. 4(d). However, since t3 -t4 is very short, from the earlier assumption, ipri = iLo1 = iLo2 can be considered as a constant current source during this mode. Therefore, ipri starts to charge Cds2 from 0 V to Vin and discharges Cds1 from Vin to 0 V. When vds1 equals 0 V at t4, M1 can be turned on, with ZVS in following mode. From the abovementioned operations, whereas Lo1 works as a magnetizing inductor and Lo2||Lc acts as a resonant inductor at mode 1, Lo1||Lc operates as a resonant inductor, and Lo2 functions as a magnetizing inductor at mode 3. As a result, since the separated primary wire alternately operates as a transformer and an inductor, any external inductor or additional wires are unnecessary. In the IDT, the number of primary turns is split into half in each side leg; thus, the height of the transformer can be decreased, and the power density can be improved [10]. As shown in Fig. 6, each winding on the side leg is decoupled by the center leg of the core, and its wire connection is configured with series-input and parallel-output. Thus, the equivalent magnetizing inductance and turn ratio become Lm = 2Lo_IDT and neq = 2Np_IDT:Ns_IDT, respectively. However, if the IDT is implemented using a planar transformer to achieve a lower profile, its leakage inductance is too small to be used as a resonant inductor. Thus, an additional external inductor must be employed. However, the IMPT requires no additional inductor because Lo||Lc of the IMPT acts as a resonant inductor (Lr = Lo||Lc).
Meanwhile, while the equivalent turn ratio of the IDT is determined as neq = 2Np_IDT/Ns_IDT, and that of the IMPT is neq = (Np/Ns) {1 + Lo/(Lo + Lc)}. Namely, the turn ratio of the IMPT can be roughly set to Np/Ns and finely tuned by Lo/(Lo + Lc). For example, assuming that Vin(max) = 390 V and Vo = 20.5 V, the required turn ratio of the IDT should be 0.5 Vin(max)/Vo:1 = 9.5:1 to ensure operation at fsw = fr. Thus, since the number of turns must be an integer, the IDT should have Consequently, the number of turns and core size of the IDT may become larger, regardless of the handled power.

FIGURE 7. LRC configured with the equivalent inductance model of the IDT and external inductor
However, in the proposed IMPT, various turn ratios can be implemented using Lo and Lc. Namely, when Ns = k [turns] (k = 1, 2, 3 …), the turn ratio can be set precisely to 9.5:1 by setting Np = m [turns] (m = an integer greater than or equal to 9.5 k/2) and adjusting Lo and Lc to (Np/Ns){1 + Lo/(Lo + Lc)} =9.5. Therefore, the proposed IMPT can have as many turns as required, and its size can be optimally designed in any input/output (I/O) specifications.
Meanwhile, the following relationship from (14) should be satisfied to make the same voltage conversion ratios of the traditional single transformer (TST) and the proposed IMPT equal to each other: Moreover, since the current slope of the magnetizing inductor also should be the same as the TST, following relationship should also be satisfied.
Therefore, the equivalent magnetizing inductor of the proposed IMPT is represented by Lo{1 + Lo/(Lo + Lc)}. As a result, the equivalent parameters of the TST, conventional IDT, and proposed IMPT can be summarized in Table 1.

A. TURN RATIO OF THE IMPT
In the mode analysis, the turn ratio of the IMPT was determined as (8) and (14). By defining the ratio of Lo and Lr as Ln (= Lo/Lr = Lo/(Lo||Lc)), the turn ratio can be expressed again as follows: where the turn ratio is determined by Ln.
As Lo and Lc are always greater than 0, Lo/(Lo + Lc) in (17) has a value between 0 and 1. Thus, the range of the turn ratio is considered to be 0.5Vin(max)/Vo to 0.25Vin(max)/Vo.

B. VOLTAGE GAIN OF THE PORPOSED IMPT LRC
Using the equivalent parameters described in Table 1, the IMPT LRC can be converted into the equivalent TST LRC. Therefore, the voltage gain of the IMPT LRC can be derived by performing the same process as the TST LRC. Assuming that the fundamental components of all alternating voltages and currents in the LRC are dominant, the I/O voltage gain H(s) can be easily obtained using the fundamental harmonic approximation (FHA) as follows [20]: where   =   /  = 2  − 1 , Based on (18), the H(s) is a function of the normalized switching frequency, and Qe is shown in Fig. 8. The Fig. 8 indicates that as Qe increases, the minimum switching frequency fmin for peak voltage gain approaches the asymptotic frequency fasym, which is determined by Lm + Lr and Cr [5,20]. Since the voltage gain at fasym is not only always lower than at fmin but also similar to each other, the fmin that guarantees the required peak voltage gain can be assumed to be equal to fasym as follows: To ensure the required peak H(s) at the minimum input voltage Vin(min), the converter is operated in fmin and Fmin = fmin/fr. Thus, the range of Lo can be determined from (16) and (17) as follows: (20) In addition, Lr and Cr can be determined from the relationship among Lo, Ln, and fr as follows:  From (20), (21), and (23), the range of Cr that ensures the required peak voltage gain can be determined as follows:

C. RESONANT CAPACITOR FOR ENSURING NORMAL OPERATION
As described in Section II-B, Do2 is turned off and the input power is transferred to the output through Do1 during mode 1 because ipri flows to the dot terminal of the transformer. At the same time, vcr increases while vLo2 decreases according to vcr. However, if vcr exceeds Vin at tA in Fig. 10, vLo1 and vLo2 become nVo and -nVo, respectively. Then, vcr is clamped on Vin. Thus, as shown in Figs. 9 and 10, ipri becomes 0 A during tA -tB, and iDo1 and iDo2 flow through Do1 and Do2 as follows: The fact that ipri equals 0 A indicates that the I/O voltage gain is reduced because the input power is not transferred to the output. To overcome this problem and guarantee normal operation for the IMPT, vcr should be kept lower than Vin until the resonance is over.
Meanwhile, the peak value of vcr occurs when Vin = Vin(min) and fsw = fmin. Considering the FHA mentioned in Section III-B, the peak value of vcr can be easily obtained from (4). Therefore, the Cr that guarantees the normal operation can be obtained as follows:  Fig. 11. It can be observed that overlapping areas represent the available values for Cr which satisfy both the required peak voltage gain and the normal operation.

FIGURE 10. Key waveforms at vcr = Vin in mode 1 (t0 -t1)
Meanwhile, the larger turn ratio requires smaller Lo and Lc from (17); thus, the circulating current and current stress may be increased. Furthermore, the number of turns and layers in the planar transformer are also increased. Therefore, these points should be considered when designing circuit parameters. Finally, the appropriate resonant frequency should be selected to achieve the highest efficiency through loss analysis, which is considered later.

A. LOSS ANALYSIS FOR THE OPTIMAL PARAMETERS
The overall efficiency of the converter is mainly determined by critical components, such as the main switches, magnetic devices, and output rectifiers. Since the main switch is turned on under the ZVS condition, its turn-on switching loss can be ignored. In the output rectifier, the synchronous rectifier FET is generally used instead of a diode to reduce the conduction loss in high-current applications. In magnetic devices, power losses are divided into core and copper loss. The core loss is greatly affected by magnetic materials at high frequency as high as 800 kHz. Thus, the core loss densities at 800 kHz of four different magnetic materials as a function of the flux density are shown in Fig. 12. Here, the ML90S exhibits the lowest core loss.
Meanwhile, in the copper loss, it is also greatly affected by the AC resistance of the conductor at high frequency. Therefore, the thickness of the layer in the planar transformer should be optimally designed to minimize the copper loss caused by the effective resistance. From [21], the effective resistance is given by: Based on the abovementioned points, the loss analysis equations are summarized in Table 2. In this table, tf and Rds(on) are the FET turn-off time and turn-on resistance, and Ve is the volume of the magnetic core. Additionally, the core loss coefficients of ML90S and the key currents equations are given in Tables 3 and 4, respectively. Meanwhile, performance and efficiency of the LRC are greatly affected by resonant parameters. Thus, it is desirable to design the circuit parameters to have the highest efficiency within the range, ensuring a sufficient voltage gain and normal operation of the LRC.
For these reasons, based on the efficiency analysis according to the turn ratio and fr, the design process of optimal circuit parameters is presented as follows. The efficiency analysis is performed under the I/O specifications in Section III-C (Vin(max) = 390 V, Vo = 19.5 V, Po = 350 W) as an example. Moreover, fsw is set equal to fr to minimize circulating current and variation of fsw according to load.
First, from the I/O voltage specifications, the range of turn ratio can be derived as 5 < Np/Ns < 10 by (17). Assuming that fsw is high enough to ensure that the magnetic core is not saturated, the available number of turns to minimize the transformer size can be determined as follows. Considering the fact that the number of turns in the transformer should be an integer, the number of primary and secondary turns can be implemented as Np = 6T, 7T, 8T, 9T, and Ns = 1. And, Ln in each case can also be determined from (17).
Next, the fmin according to the given fr can be determined from (19), and the range of Lo to satisfy the enough voltage gain can also be derived from (20). At this point, it is desirable

Parameter Equation
Transformer to select Lo as the maximum value within the range satisfying the voltage gain because lower Lo can cause the larger switching and conduction losses, listed in Table 2 to Table 4. Finally, Lr, Lc, and Cr can be determined from (21) -(23), respectively. At this point, it must be checked whether Cr satisfies the conditions (24) and (27) to ensure the voltage gain and normal operation. If both conditions above are not met due to the small Cr, Lr, and Lc, then Cr should be reselected by reducing Lo.
Through the abovementioned process, Fig. 13 shows the power conversion efficiency according to the fr and turn ratio. It can be observed that the highest efficiency can be achieved in Np/Ns = 6, fr = 800 kHz, which is originated from the fact that rms currents in the circuit and total losses become small at the low turn ratio because lower turn ratio requires larger Lo. Therefore, the optimal parameters of the proposed IMPT LRC can be finally designed as Np:Ns = 6:1, Lo = 18 uH, Lr = 5.9 uH, Lc = 8.9 uH, and Cr = 6.6 nF at fr =800 kHz. Additionally, the optimal thickness of the PCB layer can be determined to minimize copper losses. In Table 2, the copper loss of the planar transformer is affected by the rms currents and Reff of the PCB. From (28) and (29), it can be observed that Reff is mainly affected by the copper thickness, number of layers and switching frequency. Based on the determined parameters, the conduction losses of primary, secondary, and overall wires according to the copper thickness are calculated under full load conditions, as shown in Fig. 14. From these results, it can be observed that the 2 oz layer can minimize the total copper losses and it can be the optimum thickness of the layer at fsw = 800kHz.

B. COMPARISON BETWEEN IDT AND IMPT IN TERMS OF MAXIMUM FLUX DENSITY AND CORE LOSS
A comparison of the magnetic flux density between the IDT and IMPT is shown in Fig. 15. From the above determined parameters of IMPT, equivalent parameters of the IDT and IMPT can be derived from Table 1 as follows: Lm = 30 uH, Lr = 5.9 uH, Cr = 6.6 nF, neq = 10, and fr = 800 kHz. In addition, EE3112-ML90S (Ac = Ao = 128 mm 2 ) and EE1604-ML90S (Ac = 40.5 mm 2 , Ao = 18 mm 2 ) are used as a transformer and external inductor core, respectively. As shown in Fig. 15(a), the IDT exhibits a flux density (B) of -0.05 T < BL = BR < 0.05 T in the side legs and a zero flux density in the center leg with the aid of flux cancellation. Consequently, the core loss is as low as 1.94 W.
Nevertheless, since the large resonant current flows directly through the external inductor Lr, where B is -0.13 T < Bext < 0.13 T; thus, its core loss is as high as 3.08 W. Although the larger number of turns or a larger core are capable of reducing the core loss of the external inductor, more PCB layers are required, causing higher manufacturing costs or a significant reduction in the power density.
However, in the IMPT, the magnetic flux generated from the magnetizing current flows through one of the side legs, whereas the magnetic flux generated from the resonant current is divided into the side and center legs. From the reluctance model in Fig. 16, each magnetic flux can be determined as follows [22 -25]: From (30) -(32), the IMPT exhibits a flux density of -0.05 T < BL = BR < 0.05 T in the side leg and 0 < BC < 0.021 T in the center leg, as shown in Fig. 15 (b). Accordingly, since the flux density (B) in the side legs of the IMPT and IDT are almost identical; thus, their core losses are also the same. However, as B in the center leg of the IDT is zero, its core loss also becomes zero. Whereas in the IMPT, since the magnetic flux flows through the center leg, B is not zero and the resultant core loss exists. Nevertheless, the maximum magnetic flux density (Bm) in the center leg is not only low but the center leg also occupies a small fraction of the total core volume. Thus, the core loss of the IMPT is slightly larger than that of the IDT. However, both are approximately the same, as shown in Fig. 17. Meanwhile, as described in Table 1, the IDT and IMPT have different turn ratios, but their equivalent turn ratios neq can be exactly the same. Therefore, the copper loss of the IMPT is slightly higher than that of the IDT as shown in Fig.  17, because the IMPT has two more turns than the IDT. Nevertheless, since the additional losses caused by the external inductor can further degrade the efficiency of the IDT LRC, as shown in Fig. 17; therefore, the IMPT is more advantageous in terms of overall system efficiency and size. As a result, the IMPT can be an excellent solution for high power density and high efficiency in the LRC.

C. INDUCTANCE MEASUREMENT METHOD OF THE IMPT
In order to ensure the input-to-output voltage conversion ratio and stable resonant operation in the TST LRC, the magnetizing inductor Lm and resonant inductor Lr should be appropriately designed. Likewise, to implement the equivalent Lm and Lr in the IMPT LRC, Lo and Lc should be appropriately designed according to equivalent parameters presented in Table 1. Therefore, the inductance measurement method of the IMPT is presented, as shown in Fig. 18.
First, the primary inductance Lac is measured between nodes a and c with the secondary side open. If it is assumed that Np1 = Np2 = Np and Lo1 = Lo2 = Lo, the voltage across Lc always becomes zero due to the same voltage and opposite polarity of Np1 and Np2. Therefore, Lc can be neglected and the equivalent inductance between nodes a and c is equal to the series-connected Lo1 and Lo2, as shown in Fig. 18(b). Namely, Lac is equal to Lo1 + Lo2 = 2Lo; thus, Lo can be expressed as follow: Second, the half primary inductance Lab is measured between nodes a and b with the other half primary side (between nodes b and c) and secondary side open. In Fig.  18(a), Lo2 is connected in series with Lc through the second ideal transformer with a turn ratio of Np2:Np2. At the same time, series-connected Lo2 and Lc are again connected in parallel to Lo1 through the first ideal transformer with the turn ratio of Np1:Np1 as shown in Fig. 18(c). Therefore, Lac is equal to Lo1//(Lo2+Lc)=Lo//(Lo+Lc); thus, Lc can be expressed as follow: In summary, the equivalent inductances Lo and Lc can be obtained by measuring the inductances Lac and Lab among nodes a, b and c.

V. EXPERIMENTAL RESULTS BASED ON OPTIMAL DESIGN
The 350W -LRC prototypes equipped with the IDT and IMPT are shown in Fig. 19. The IMPT allows the LRC to operate without an external inductor. Therefore, the power density of the IMPT LRC can be improved by approximately 7.15% compared to the IDT LRC and by up to 137.16 W/in 3 . The I/O specifications and parameters used in the experiment are listed in Table 5. To achieve the high efficiency and low heat generation of the high switching frequency and high power density converter, 600 V GaN-FETs and 80 V Si-FETs with low turn-on resistance are used as primary side power switches and secondary side Synchronous Rectifiers respectively.    Figs. 20 (a) -(c) present the experimental key waveforms of the IMPT LRC according to the load conditions. These prove that the IMPT LRC operates in exactly the same way as the conventional LRC. In addition, M2 is turned on after vds2 becomes 0 V (i.e. the ZVS of M2 is achieved for the entire load range).
Since M1 operates exactly symmetrically with M2, the ZVS of M1 can also be achieved (corresponding waveforms are not presented here). The voltage gain for the input voltage range is verified by the key experimental waveforms in Fig. 20 (d) at Vin = 320 V and a full load, proving that the converter can regulate the output voltage at 19.5V under minimum input voltage condition with sufficient voltage gain. Fig. 21 shows the experimental key waveforms of the IDT LRC at full load condition. As shown in this figure, it can be observed that the IDT LRC and IMPT LRC work almost identically and have almost the same switching frequency because they have the same equivalent resonant parameters, as shown in Table 5 Fig. 22 shows the experimental key waveforms in dynamic load transients of the IMPT LRC, where the load is changed from a typical (200 W) load to no-load with a 6-msec period and 50% duty cycle. As shown in Fig. 22, the output voltage is well regulated within 5% while the load is changed, and the switching frequency is changed narrowly from 775kHz to 794kHz. These results prove that the IMPT has good output voltage regulation and load transient performance without an external inductor. The theoretical and measured efficiency of the IMPT LRC is presented in Fig. 23. The measured efficiency of the IDT LRC is also presented for comparison. These results prove that the theoretical efficiency of the IMPT LRC is almost equivalent to the measured efficiency, confirming the validity of the theoretical analysis. The measured efficiency of the IMPT LRC is more than 91.88% under conditions of 40% or more load, and the maximum efficiency is measured up to 95.26% at a full load condition. Mea   However, the efficiency is somewhat low at a light load because the operating frequency is as high as about 800 kHz. Meanwhile, the IMPT has a higher efficiency than that of the IDT through the entire load range. This difference in efficiency is originated from the fact that the IMPT does not require a separate external inductor, unlike the IDT.

VI. CONCLUSION
In this paper, an IMPT for a high efficiency and high power density LRC is proposed. In the proposed methodology, the primary wire is split into each side leg of the EE-type magnetic core, and each operates as a transformer and inductor alternatively in every switching period. Therefore, a lowprofile single planar transformer can be implemented without the need of an external inductor or additional wires. Moreover, since the magnetic flux density of the proposed IMPT is similar to that of a conventional transformer; thus, the same size core can be implemented. As a result, further losses from the external inductor are saved. Therefore, with a single planar transformer, the IMPT can achieve higher efficiency and power density than with a conventional transformer. The operation of the LRC configured with the IMPT was verified by an equivalent inductance model, providing detailed design considerations. Based on the loss analysis comparison with that of a conventional transformer, improved performance of the IMPT was verified by the experimental results of the 350 W prototypes. These results confirm that the IMPT can operate exactly the same as the LRC without an extra inductor or additional wires. In addition, the comparisons of the measured and theoretical efficiency indicate the reliability of the design considerations and magnetic analysis. From these results, the IMPT is suitable for various LRC applications that require high power density and high efficiency.