# Bidirectional Single-Input Multiple-Output Power Converters: Model and Performance Analysis

Diego Bernal Cobaleda, Hans Wouters, Fanghao Tian, Yu Zuo, Wilmar Martinez

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## To cite this version:

Diego Bernal Cobaleda, Hans Wouters, Fanghao Tian, Yu Zuo, Wilmar Martinez. Bidirectional Single-Input Multiple-Output Power Converters: Model and Performance Analysis. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0325. hal-05073882

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Submitted on 19 May 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Bidirectional Single-Input Multiple-Output Power Converters: Model and Performance Analysis

Diego Bernal Cobaleda, Hans Wouters, Fanghao Tian, Yu Zuo, Wilmar Martinez,

Department of Electrical Engineering (ESAT)

KU Leuven - EnergyVille

Diepenbeek-Genk, Belgium

diego.bernal, hans.wouters, fanghao.tian, yu.zuo, wilmar.martinez@kuleuven.be

**Abstract**—This paper introduces a small-signal transformation model based on the cantilever approximation for transformers commonly used in LLC converters. The proposed transformation is evaluated towards extending resonant converters in multiport applications. The transformation is compared in a traditional LLC multi-active bridge against a cascade multilevel inverter configuration on the secondary side. The objective is to analyze the differences and similarities in their implementation and assess their impact on system efficiency based on topology, with a focus on comprehensively describing losses in resonant multi-output converters. Two low-power prototypes were developed to validate the proposed model and approximation. The case study examines the efficiency and cross-regulation trade-offs between the configurations. Simulation and experimental results verify the accuracy of the analytical approach, offering valuable insights for designing and implementing high-frequency transformers in multiport applications.

**Index Terms**—DC-DC converter, Multi-Port Converter, Resonant Converter, wide load, planner transformer.

## I. INTRODUCTION

The demand for higher performance [1]–[5] and the increasing number of electrical loads has stimulated research efforts towards multiport converters able to interface all inputs and outputs in a single system. This opportunity has been clearly exploited, as seen in the growing number of publications in the past decade, cf. Fig. 1. These converters intend to integrate multiple inputs and outputs into a single package [6]–[10]. For example, onboard chargers for electric vehicles deliver power to the high-voltage 400 V or 800 V battery, but an additional charger is needed to charge the low-voltage 12 V or 48 V battery. Increasingly, these two converters are combined in a single-input multiple-output converter [11], [12]. While such systems promise centralized control, it remains unclear whether they can truly improve efficiency and reliability.

Various converter topologies have been proposed, making it difficult to determine the most suitable configuration for a specific application. In this context, [13] introduced a resonant cascade multilevel converter (CMI-AB) with a multiport configuration by using a cascade secondary converter that competes with architectures constituted by multiple windings such as the traditional Multi-Active Bridge (MAB) [14], [15]. However, the efficiency and practicality of the CMI-AB still miss comparison against its competitors.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Publication trends for "Multiport Converter" from the IEEEXPlore database, highlighting IEEE Transactions on Power Electronics (TPEL), IEEE Transactions on Industrial Electronics (TIE), and IEEE Journal of Emerging and Selected Topics in Power Electronics (JESTPE)</figcaption></figure>

The contribution of this paper can be resumed by implementing two transformers for different topologies, aiming to fairly compare the trade-offs of having a cascade configuration and a multi-secondary in a resonant LLC structure. Furthermore, this paper also proposed a small signal transformation analysis that reduces the converters to be compared into a general model. The model aims to simplify the design and compare the systems fairly. A complete analysis is presented in the following sections.

This paper is divided as follows. Section II describes the topologies and nomenclature used during the study, and Section III presents the small signal transformation between the three topologies. In section IV, the results are presented, both in simulation and experimental work. Finally, conclusions and future work are presented.

## II. TOPOLOGIES DESCRIPTION

This paper proposes a small-signal analysis that compares the performance of different converters, including the design of the magnetic components. The schematics of the compared topologies are presented in Fig. 2. Furthermore, Table I lists the acronyms used to describe the converter's components. The converters are formed with active bridges interfaced by a transformer; the first topology in Fig. 2a has one active
bridge on the primary side, a transformer with one secondary winding, and two active bridges in series on the secondary side. The topology in Fig. 2b differs from its competitor by having a transformer with two secondary windings and one active bridge connected to each winding of the transformer.

<figure><img src="image_4.png" /><figcaption>Fig. 2: a) Resonant cascade multi-level converter b) Multi-active bridge</figcaption></figure>

<table><caption>TABLE I: CONVERTERS ACRONYMS</caption><thead><tr><th>Primary</th><th>S<sub>pj</sub><br>V<sub>H</sub><br>v<sub>AB</sub></th><th>Primary Inverter switches<br>High Voltage DC input source<br>Primary Inverters voltage</th></tr></thead><tbody><tr><td rowspan="5">Secondary</td><td>S<sub>Aj</sub></td><td>Cell A switches</td></tr><tr><td>S<sub>Bj</sub></td><td>Cell B switches</td></tr><tr><td>v<sub>CD A</sub></td><td>Cell A voltage</td></tr><tr><td>v<sub>CD B</sub></td><td>Cell B voltage</td></tr><tr><td>v<sub>CD</sub></td><td>CMI-AB voltage</td></tr><tr><td rowspan="4">LLC-Tank</td><td>L<sub>r</sub></td><td>Leakage Inductance</td></tr><tr><td>L<sub>m</sub></td><td>Magnetizing Inductance</td></tr><tr><td>C<sub>r</sub></td><td>Resonant Capacitor</td></tr><tr><td>n</td><td>Transformer ratio</td></tr></tbody><tfoot><tr><td colspan="3">j = {1, 2, 3, 4}</td></tr></tfoot></table>

The premise is that achieving the same power using the two proposed topologies results in different resonant tank characteristics yet a similar modulation strategy. Variations in the practical magnetic components' size, losses, and parasitic components, e.g., a bigger transformer size due to a higher number of turns, will result in a different external resonant inductor. Furthermore, variations in the parasitic capacitance affect the resonant tank characteristics. The topologies under investigation are 3-port structures but are expandable to n-port topologies.

### III. ANALYTICAL MODEL

To analyze the systems, a reduction in small signal level is proposed. After the reduction, the objective is to derive a

Cantilever model of the converters. This is done to deal with the high number of loads. It should be noted that this method can be extrapolated for several loads and that for a simpler implementation, only three port converters are addressed in this paper.

#### A. Resonant Cascade Multilevel Inverter

The simplest of the three analyses can be done with the CMI-AB of Fig. 2. When all the low voltage small signal sources are sum together ($v_{CD_A} + v_{CD_B}$) and referred to the secondary ($v'_{CD}$), the result is the traditional representation of an LLC Dual Active Bridge (LLC-DAB) converter. Fig. 3

<figure><img src="image_5.png" /><figcaption>Fig. 3: LLC-DAB traditional representation</figcaption></figure>

#### B. Multi Active Bridge

For the MAB converter, the procedure must consider the leakage of each winding of the transformer. This leakage helps to ease the analysis in small signal as follows. When the sources are referred to the primary winding, the circuit follows the next representation, see Fig. 4.

<figure><img src="image_6.png" /><figcaption>Fig. 4: MAB small signal representation</figcaption></figure>

The final step is to change the circuit to a Norton equivalent by changing the voltage sources to current sources, as shown in Fig. 5.

<figure><img src="image_7.png" /><figcaption>Fig. 5: MAB Norton representation</figcaption></figure>

The sources can be summed algebraically and turned back to a single voltage source, whose value results from the following transformation, cf. Fig. 6.

The transformer in this representation follows the model of a two-leakage transformer. This can be changed into a simpler Cantilever representation, as shown in a further subsection. The expressions for this transformation can be generalized by Equations (1)-(4), as depicted in Fig. 7.
<figure><img src="image_8.png" /><figcaption>Fig. 6: T equivalent representation</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7: Generalized representation of a two leakage transformer</figcaption></figure>

$$V_{eq_{MAB}} = Z_{L_{eq_{MAB}}} \sum_{i=2,3...}^{n} \frac{V'_{CD_i}}{j\omega L_{lk_i}} \quad (1)$$

$$Z_{L_{eq_{MAB}}} = \frac{(j\omega)^n \prod_{i=2,3...}^{n} L_{lk_i}}{j\omega \sum_{i=2,3...}^{n} L_{lk_i}} \quad (2)$$

$$V_{eq_{CMI}} = \sum_{i=2,3...}^{n} V'_{CD_i} \quad (3)$$

$$Z_{L_{eq_{CMI}}} = j\omega L_{lk} \quad (4)$$

In these equations, the voltages $V'$ are the voltage of the sources referred to the primary winding, and the inductances $L_{lk}$ are the leakage inductances referred to as the primary, both values considering the number of turns of each equivalent model.

### C. LLC Parameter Design

The resonant tank is designed following the first harmonic approximation, assuming that the maximum power of the converter is achieved when the inverters are driven with maximum duty cycles, shaping square waveforms in the transformer. For this approximation, a gain of 1 is decided on the number of turns, a frequency of 100 kHz, and a quality factor of 0.4. The input DC voltages are chosen $V_H = 100V$ for the primary side and $V_A = V_B = 50V$ for the secondary and load voltages. The values are determined as follows.

$$R_{ac} = R_L(\Omega) \frac{8(2)^2}{\pi^2} \quad (5)$$

$$C_r = \frac{1}{2\pi Q f_r R_{ac}} \quad (6)$$

$$L_r = \frac{1}{(2\pi f_r)^2 C_r} \quad (7)$$

Based on the equations, a dead time of 470 ns is chosen, and a ratio between the leakage inductance and the magnetizing

inductance of 5, cf. Equation 8. The theoretical values results are $L_m = 25\mu H$, $L_r = 5\mu H$, and $C_r = 79nF$.

$$\frac{0.99 \cdot 100}{2L_m f_r} > \frac{C_{oss} 100}{t_{dead}} \quad (8)$$

### D. Two-Leakage Model to Cantilever

The design of the LLC tank for a traditional LLC-DAB converter results in a resonant inductor and capacitor, a magnetizing inductance, and a turns ratio, assuming the resonant inductor is the leakage of the transformer. This parameter, alongside the turns ratio and the magnetizing inductance, can be utilized to fill up the Cantilever model in Fig. 8. This means the leakage inductance is equal to the resonant inductance $L_r = L_{lk}$, while the magnetizing inductance of the transformer is equal to the magnetizing inductance of the model $L_m = L_{mag}$, and the turns ratio calculated is also equal to the Cantilever turns ratio $n = n_{Cantilever}$ from Fig. 3.

<figure><img src="image_10.png" /><figcaption>Fig. 8: Cantilever model</figcaption></figure>

From this point, changing the Cantilever model to a two-leakage transformer model is straightforward. Following the common equivalent circuit of a two-winding transformer. Equations (9)-(11) show the parameters $L_{lk}$, $L_p$, $L_m$, and Equations (12)-(13) the parameters $k$, $L_{p_{ss}}$ and $\frac{N_2}{N_1}$. The schematic of the two-leakage transformer is shown next in Fig. 9.

$$L_{lk} = L_p(1 - k^2) \quad (9)$$

$$L_{mag} = k^2 L_p \quad (10)$$

$$L_{lk} = L_p - L_{mag} \quad (11)$$

$$k^2 = 1 - \frac{L_{p(ss)}}{L_p} \quad (12)$$

$$\frac{N_2}{N_1} = \frac{n_{Cantilever} k^2 L_p}{L_{mp}} \quad (13)$$

With $L_{lp} \approx \frac{L_{p(ss)}}{2}$ and $L_{mp} \approx L_p - L_{lp}$ and $L_{ls} \approx \frac{L_{p(ss)} n^2}{2}$

<figure><img src="image_11.png" /><figcaption>Fig. 9: Two leakage transformer model</figcaption></figure>
<table><caption>TABLE II: LLC TANK DESIGN PARAMETERS</caption><tr><td>L<sub>r</sub></td><td>5.16 μH</td></tr><tr><td>L<sub>m</sub></td><td>25.801 μH</td></tr><tr><td>C<sub>r</sub></td><td>78.54 nF</td></tr><tr><td>Q</td><td>0.4</td></tr><tr><td>L<sub>n</sub></td><td>5</td></tr><tr><td>V<sub>H</sub></td><td>20 V</td></tr><tr><td>V<sub>A</sub> = V<sub>B</sub> = V</td><td>10 V</td></tr><tr><td>n</td><td>1</td></tr></table>

## IV. RESULTS

### A. Design parameters

The parameters selected for the implementation are shown next in Table II.

As mentioned before, for the CMI-AB, the Cantilever follows the approximation, meaning the parameters of Table II comply with the devices to be built. However, for the MAB, assuming symmetry in the windings and knowing the voltage sources are all the same for all the circuits, the MAB converter can be inversely solved from (1) to (2). The result of the transformation is shown next in Table III

<table><caption>TABLE III: TWO LEAKAGE TRANSFORMER PARAMETERS</caption><tr><td>N<sub>1</sub></td><td>1</td></tr><tr><td>N<sub>2</sub></td><td>0.991</td></tr><tr><td>k<sup>2</sup></td><td>0.909</td></tr><tr><td>L<sub>mp</sub></td><td>28.381 μH</td></tr><tr><td>L<sub>ls</sub></td><td>2.5375 μH</td></tr><tr><td>L<sub>lp</sub></td><td>2.5801 μH</td></tr></table>

### B. Modulation Strategy

The full degrees of freedom for controlling the system are as follows. Fig. 10 shows the switching events and the definition of the parameters.

Table IV summarizes the terminology used.

<table><caption>TABLE IV: SWITCHING EVENTS ACRONYMS</caption><tr><td rowspan="3">Primary</td><td>β<sub>p</sub></td><td>Primary Phase</td></tr><tr><td>d<sub>p</sub></td><td>Primary Duty Cycle</td></tr><tr><td>T</td><td>Period (1/f)</td></tr><tr><td rowspan="2">Secondary</td><td>β<sub>j</sub></td><td>Cells Phase</td></tr><tr><td>d<sub>j</sub></td><td>Cells Duty Cycle</td></tr><tr><td colspan="3">j = {A, B}</td></tr></table>

To ease the implementation, a phase shift modulation is applied, meaning the phases of the cells are fixed to be the same among them, as well as their duty cycles $d_A = d_B = d$, $\beta_A = \beta_B = \beta$, $d_p = 1$, and $\beta_p = 0$. Following this, the power is solely controlled by $\beta$

### C. Simulations

Two cases are simulated in this paper when the duty cycle of the cells is $d_A = d_B = d = 1$. The results are shown next. Fig. 11 shows the current variations in the low voltage sources $V_A$ and $V_B$ when the duties are maximum, changing the load

using $\beta$. The simulation is pursued with the software PSIM alongside Hyperstudy, a tool that allows parallel simulations of PSIM. Furthermore, alongside the two circuits proposed for the comparison, a two-transformer circuit is implemented in a multi-transformer (MT) configuration of the LLC. As the voltages used in the simulation are constant voltage sources, the fluctuations in the output current are proportional to the power variations.

Due to the addition of static losses in the simulation models, a difference in implementation can already be seen. For example, the power is symmetrical from $\beta = 0$, meaning the three converters achieve similar bidirectionality. Adding stray elements on the switches keeps the model of the transformer idealistic. The behavior of the converter's load mismatches in absolute values, but the power fluctuations keep the same trend.

The same behavior can be seen when the duty cycle of the cells is changed to $d = 0.5$. Fig. 12 shows these variations.

It can be appreciated that the approximation proposed can design two different converters that behave similarly; it is not straightforward to determine if one converter can give less or more power than the others or its differences. However, for most of the combination of parameters, the MAB gives slightly less power than its competitor.

### D. Transformer Design

Efforts are made to create a fair comparison of the transformer implementation for the varying converter implementations. Since the total required current through the transformer windows of each evaluated topology is equal, these can be constructed using the same core. For example, the conventional transformer uses $N$ primary and $N$ secondary turns, each carrying the rated current. Conversely, the MAB implements two secondary windings, each using $N/2$ turns, resulting in the same total current carrying capability within the window area. Thus, the same core is selected; all transformers comprise an EE-structure of commercial planar E64/10/50 core using Ferroxcube 3F36 ferrite material. For windings carrying the rated current, a 180x0.1mm litz wire is selected based on the operating frequency, whereas windings carrying half the rated current implement the 90x0.1 mm counterpart.

A transformer design method is implemented based on the converter parameters to minimize the magnetic losses [16]. Accordingly, winding losses are modeled by the Dowell equation [17] while core loss is estimated by the improved generalized Steinmetz equation [18]. The resulting losses for varying numbers of turns are presented in Fig.13. An optimum is found as the winding losses increase with the number of turns, and core losses decrease thanks to the reduced flux density. As such, 10 turns are selected for these specific converter parameters.

Since a low resonant inductance of 5.2 μH is desired in the evaluated converter, the leakage inductance of a conventional transformer would already exceed this target value by a factor of two to three. Hence, the primary and secondary windings are interleaved, i.e., the applied turns are alternating between
<figure><img src="image_12.png" /><figcaption>Fig. 10: Switching events</figcaption></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11: Current variations $d = 1$ a) Cell A current ($I_A$) vs $\beta$ b) Magnification in light load</figcaption></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 12: Current variations $d = 0.5$ a) Cell A current ($I_A$) vs $\beta$ b) Magnification in light load</figcaption></figure>

the primary and secondary winding, cf. Fig. 14. For each design, an air gap is applied to achieve the specified magnetizing inductance of 25.8±0.1 µH. To match the values of all resonant tanks, the total leakage inductance of the transformer referred

to the primary side is experimentally measured. Subsequently, the external leakage inductance is added to reach the desired primary resonant inductance of 5.2±0.1 µH.
<figure><img src="image_17.png" /><figcaption>Fig. 13: Transformer design optimisation of the number of turns *N* in primary and secondary winding</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 14: a) Cross-section of the planar transformer with interleaved litz-wire primary (P) and secondary (S) windings; b) Reference 1:1 transformer prototype with E64 core and 180x0.1mm litz wire</figcaption></figure>

### E. Experimental results

As previously stated, the selected cores are the E64/10/50 and the PLT64/50/5, both made from Ferroxcube's 3F36 material. This material was chosen for its low magnetic core losses at high frequencies, minimizing discrepancies in implementation caused by stray core elements. Furthermore, the selection of semiconductor components targets the most efficient devices at the operational points. Fig. 15 shows the implemented low-power prototype. Cells A and B can be interconnected as an MAB or a CMI-AB as desired; the transformer is designed for the topology to implement.

Fig. 16 shows the experimental result of driving the CMI-AB converter, having a phase shift between the primary and the two secondaries: $\beta = -1$ and a fixed duty cycle $d = 1$. The output currents have a high ripple, with an average value of 0.6 A.

<figure><img src="image_19.png" /><figcaption>Fig. 15: Experimental converter setup</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 16: Experimental results frequency modulation $\beta = -0.05$ and $d = 1$ CMI-AB</figcaption></figure>

Next, Fig. 17 shows the experimental result of driving the MAB converter using the same parameters as the previous oscillogram ($\beta = -1$ and $d = 1$). For this implementation, the output currents have considerably less ripple. However, the DC component of the currents is not symmetric in the cells. Despite this effect, the resonant current $I_r$ behaves in analogy as the CMI-AB

<figure><img src="image_21.png" /><figcaption>Fig. 17: Experimental results frequency modulation $\beta = -0.05$ and $d = 1$ MAB</figcaption></figure>

The implementation demonstrates that the primary side of both converters exhibits similar behavior, with nearly identical resonant and DC input currents in both cases. However, despite these similarities, the CMI-AB converter achieves better output
current regulation and superior cross-regulation performance compared to the MAB. On the other hand, the MAB exhibits a lower current ripple than the CMI-AB, which in turn involves a tradeoff related to power sharing among the loads.

Another significant aspect is the influence of parasitic switch capacitances, combined with interwinding capacitances, on circuit performance during dead time. This effect is particularly evident in the dead time behavior of the implementations, where a resonant phenomenon can be observed in the MAB but not in the CMI-AB converter. The equivalent circuit representations of both implementations during the dead time are illustrated in Fig. 18 and Fig. 19. In this equivalent circuit,

<figure><img src="image_22.png" /><figcaption>Fig. 18: Equivalent circuit during DT CMI-AB</figcaption></figure>

the capacitance $C_{eqDT}$ is defined by (14). The effects of the DC link capacitors in parallel with $V_A$ and $V_B$ are neglected, as their values are significantly larger than the parasitic capacitance of the switches, $C_{oss}$. The equivalent capacitance for each bridge is determined by summing, in parallel, two capacitances that are in series with the parallel combination of the other two capacitances from the opposite leg of the full bridge. Consequently, the equivalent capacitance for each cell is equal to $C_{oss}$. Since these bridges are connected in series, the equivalent capacitance in the secondary winding is given by $\frac{C_{oss}}{2}$. In the following expressions, + denotes the series equivalent, while // represents the parallel equivalent.

$$C_{eqDT_{CMI}} = \frac{[C_{oss} // C_{oss}] + [C_{oss} // C_{oss}] + [C_{oss} // C_{oss}] + [C_{oss} // C_{oss}]}{2} \quad (14)$$

Based on that, the number of turns for the application presented in this paper is $n = 1$ for the CMI, and the referred capacitance is equivalent to the sum between the transformer stray capacitance plus $C_{eqDT}$ (15)

$$C'_{eqDT_{CMI}} = C_{eqDT_{CMI}} + C_{stray_{CMI}} \quad (15)$$

In the case of the MAB cf. Fig. 16, the equivalent circuit capacitance $C_{eqDT}$ follows (16), as in the previous case, the effects of the DC link capacitors in parallel to $V_A$ and $V_B$ are neglected due to being much larger than the parallel of $C_{oss}$. The equivalent capacitance for each bridge follows the same value as before because both circuits have been

driven with the same modulation. However, as the bridges are not in series, two equivalent capacitances are drawn in each secondary winding.

<figure><img src="image_23.png" /><figcaption>Fig. 19: Equivalent circuit during DT MAB</figcaption></figure>

$$C_{eqDT_{MAB1,2}} = C_{oss} \quad (16)$$

As mentioned before, for constructing the MAB transformer, using the same levels of voltage in the loads ($V_A$ and $V_B$) required a bigger number of turns; this means the result $C_{eqDT}$ is the result of referring the capacitances to the primary and summing them together with the stray capacitance of the transformer. (17)

$$C'_{eqDT_{MAB}} = \frac{C_{eqDT_{MAB1}}}{0.5^2} + \frac{C_{eqDT_{MAB1}}}{0.5^2} + C_{stray_{CMI}} \quad (17)$$

Suppose the capacitance of the transformer is neglected; in that case, it can be seen that the capacitance on the MAB is larger than the capacitance on the CMI-AB, explaining the resonance during dead time. Moreover, manufacturing multi-winding transformers increases stray elements due to the interwinding capacitances.

$$C'_{eqDT_{MAB}} = \frac{C_{oss}}{0.5^2} + C_{stray_{MAB}} > C'_{eqDT_{CMI}} = \frac{C_{oss}}{2} + C_{stray_{CMI}} \quad (18)$$

The resume characteristics are shown next in Table V.

<table><caption>TABLE V: CONVERTERS TRADE-OFFS</caption><thead><tr><th></th><th>Advantages</th><th>Disadvantages</th></tr></thead><tbody><tr><td>CMI-AB</td><td>Reduce number of turns<br>Equilibrated load</td><td>High current ripple<br>Bigger DC link filter required</td></tr><tr><td>MAB</td><td>Lower C'<sub>eqDT</sub><br>Less current ripple in the load<br>High isolation among the loads</td><td>Miss-matched currents<br>Larger C'<sub>eqDT</sub></td></tr></tbody></table>

## V. CONCLUSIONS AND FUTURE WORK

This paper presented a small signal transformation between multiport topologies; it makes it easy to compare a resonant Cascade Multilevel Inverter (CMI-AB) with traditional topologies such as the resonant Multi-Active Bridge (MAB). The
converter's power fluctuates similarly in all the topologies by applying conventional modulation strategies, like phase shift of the cells. However, non-ideal elements play a significant role in the implementation. In the analysis of the simulation results, it was easily seen that without considering the transformer implementation or DC-line stray elements, the power fluctuations do not match strictly for all the topologies. Furthermore, the implementation reveals that variations in power exist, as expected. The CMI-AB converter presented a better symmetrical response, as the currents $I_A$ and $I_B$ do not miss matches notably among them, in line with the simulation results. This effect helps cross-regulation issues, avoiding challenging control strategies. Power density-wise, the CMI-AB also presented the lightest implementation, as it only needed half of the number of turns. Another important aspect revealed in this paper is that the series configuration of the bridges reduces the capacitance referred to the primary side of the converter, reducing oscillations during the dead time of the converter; regarding the MAB, the larger capacitance causes visible overshoots when the switches are off, this together with the interwinding capacitance affects the functioning of the circuit. Yet, as the MAB has galvanic isolation between the loads regarding the fault tolerance of the converter, it is an easier option to implement in terms of reliability. Finally, the MAB has a lower current ripple in the loads; this is important as for single-phase inverters, the DC link capacitances also play a great role power density-wise.

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