# Analysis of a high gain step-up converter 48V/1kV for piezoelectric driving application

Nassim Rayane Bennacer, Christian Martin, Loris Pace

► To cite this version:

Nassim Rayane Bennacer, Christian Martin, Loris Pace. Analysis of a high gain step-up converter 48V/1kV for piezoelectric driving application. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0129. hal-05097860

HAL Id: hal-05097860

https://utc.hal.science/hal-05097860v1

Submitted on 4 Jun 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Analysis of a high gain step-up converter 48V/1kV for piezoelectric driving application

Nassim Rayane BENNACER, Christian MARTIN, Loris PACE

Universite Claude Bernard Lyon 1, Ampère, UMR5005, INSA Lyon, Ecole Centrale de Lyon, CNRS, Villeurbanne, F-69100, France

Tel.: +33 / (0) - 751.81.44.84

E-Mail: nassim.bennacer@univ-lyon1.fr

christian.martin@univ-lyon1.fr ; loris.pace@ec-lyon.fr

URL: http://www.ampere-lab.fr/

*Index Terms*—Piezo actuators, step-up converter, high-gain, DC-DC converter, boost, device characterisation

*Abstract*—Piezoelectric actuators have been widely used in low-power applications to improve size and performance. However, a high-voltage is required to drive these actuators. This paper considers a three-switching-state step-up DC-DC topology able to drive multiple actuators at 1kV, used for hydraulic application. The topology analysis, design and experimental results are shown in this paper. The prototype shows off an efficiency higher than 94.5% on the whole power range (20 – 200W).

## I. INTRODUCTION

Several studies have looked into replacing traditional actuators and electrical transformers with piezoelectric materials to provide better performance and compactness [1], especially for low-power applications such as microrobotics, machining tools, and step motors [2].

In our case, high-speed piezoelectric actuators are introduced in a hydraulic transmission, for the sake of improving the transmission's efficiency, control capabilities, and reducing undesired vibrations.

Compared to conventional actuators, they are voltage-controlled devices and therefore require less power. However, in our case, a single battery cannot supply the necessary voltage (1kV) for the actuators, and a DC-DC step-up converter is needed. To obtain a voltage of 1kV from a 48V battery, the selected topology requires a high-voltage gain while considering size, current ripple, and efficiency criteria in a wide power range.

The most well-known step-up topology is the conventional boost. In theory, the voltage gain value is

limitless. However, it is hardly true when a gain higher than 10 is needed. The converter study presented in [3] demonstrates the saturation of the gain at an extreme duty cycle due to components parasitic elements of components and cabling. Two categories of DC-DC topologies are found in high gain applications:

* Isolated converters, such as Flyback, push-pull, and half-bridge/full-bridge converters [4], where a high gain is satisfied using HF transformer.

* Non-isolated converters, such as cascaded boost, hybrid switched capacitor, and coupled inductor boost [5], are improved versions of conventional boost converter.

In this paper, a non-isolated step-up topology was considered, known as a "three-state-switching" converter [6]. It combines both push-pull and coupled-inductor topologies to achieve a high-voltage gain/power density, low current ripple and low voltage stress on switches.

The proposed converter has to provide a voltage of 1kV under a power range between 0 and 200W, corresponding to the operations of several piezoelectric actuators (see Fig. 1). The sections of this paper will be presented as follows:

* Section II focuses on the presentation of the power supply architecture used for our application.

* Section III concerns on the choice of the appropriate DC-DC topology.

* Section IV describes the study of the chosen DC-DC converter and the design of passive components.

* Section V is focused on the results and waveforms obtained for the DC-DC converter, considering the HF models of each component.
## II. CONVERSION ARCHITECTURE

The hydraulic transmission is satisfied by driving in-dividually each piezoelectric actuator with a trapezoidal waveform 0/1kV voltage signal. The transition time is fixed at 1ms at a maximum frequency of 100Hz. The system is powered by a 48V battery and a suitable con-version architecture is needed. The proposed conversion architecture shown in Fig. 1, consists of:

* A single DC-DC step-up converter to supply 1kV for the DC-AC converters.

* A bus capacitor for each DC-AC converter is added to store the energy recovered from each actuator and avoid the need of a bidirectional DC-DC topology. The inrush current caused by the piezoelectric ac-tuators can also be limited by the bus capacitors, lowering it's impact on the DC-DC converter design.

* A DC-AC unipolar converter to drive each piezo-electric actuator. Due to the capacitive behaviour of the actuators, a bidirectional DC-AC topology is needed in order to recover energy stored and improve the efficiency of the supply chain. The DC-AC converter has been presented in [7] and it is not considered in this work.

In this architecture, the DC-DC converter is used to charge the bus capacitors until 1kV, then to maintain the DC bus voltage for each operation of the piezoelectric actuators. The maximal power needed for the DC-DC converter is obtained by calculating the average power consumption of the piezoelectric actuators working to-gether at a maximal frequency of 100Hz. The power consumption of one piezoelectric actuator is calculated by the energy difference when the actuator is driven high

and low respectively. As a result, the output power of the DC-DC converter covers a range between 0 and 200W.

In brief, the choice of the DC-DC topology must consider the following criteria:

* Low input current ripple, to avoid over-consumption that could affect the battery life-time [8].

* Guarantee a high efficiency throughout a wide power range.

* Size requirements to permit the integration of the converters with the hydraulic transmission.

* A high dynamic response to maintain the output voltage at 1kV when the actuators are driven.

## III. HIGH VOLTAGE GAIN DC/DC TOPOLOGY SELECTION

As stated earlier, the conventional boost converter requires a duty cycle near 100% to obtain the required voltage gain, leading to three main difficulties:

* The output voltage would be very sensitive to the duty cycle variation.

* The diode conduction phase is quite brief, which requires specific transistors and a more complex control as shown in [9].

* The gain voltage saturation [3].

<table><caption>TABLE I
MAIN STEP-UP TOPOLOGIES COMPARISON [4], [5]</caption><thead><tr><th></th><th>Topologies</th><th>Advantages</th><th>Disadvantages</th></tr></thead><tbody><tr><td rowspan="3">Isolated topologies</td><td>Flyback</td><td>-High gain.<br/>-Simplicity.</td><td>-High current ripple.<br/>-Poor transformer utilization.<br/>-Overvoltage.</td></tr><tr><td>Full-bridge</td><td>-High efficiency.<br/>-High power density.</td><td>-Complex structure.<br/>-large transformer ratio.<br/>-High current ripple.</td></tr><tr><td>Push-pull current-fed</td><td>-High gain.<br/>-Low input current.<br/>-High power density.</td><td>-Overvoltage.<br/>-Limited range of duty cycle.</td></tr><tr><td rowspan="5">Non-isolated topologies</td><td>Cascaded boost</td><td>-Simplicity.<br/>-Extendable gain.</td><td>-Complex design.<br/>-High EMI noise</td></tr><tr><td>Hybrid switched capacitor</td><td>-Extendable gain.<br/>-Low voltage stress.</td><td>-Low dynamic response.<br/>-Complex structure.<br/>-unbalanced diodes losses.</td></tr><tr><td>Coupled inductor boost</td><td>-High gain.<br/>-Low voltage stress</td><td>-Overvoltage.<br/>-Poor transformer utilization.</td></tr><tr><td>Three-switching state converter</td><td>-High gain.<br/>-High power density.<br/>-Low input current.</td><td>-Limited range of duty cycle.</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>Fig. 1. Proposed conversion architecture to drive the piezoelectric actuators (power flow directions in blue).</figcaption></figure>
Other topologies are taken into consideration for a higher gain, avoiding an extreme duty cycle. The most common step-up topologies are shown in the Table I.

Isolated topologies have the benefit of using an HF transformer to easily achieve a high gain voltage and also allow to use MOSFET with lower $R_{ds(ON)}$ since the voltage stress are reduced. The push-pull current-fed topology is the most interesting for this category. It has the benefit of high power density, low current ripple, and a higher gain compared to other isolated topologies. On the other hand, the limited range of duty cycle ($D > 50\%$) leads to difficulties during start-up. Furthermore, the presence of leakage inductance may result in over-voltages, and a clamp circuit is required, which adds complexity to the topology [10].

In non-isolated topologies such the cascaded boost and the hybrid switched capacitor, it is possible to prevent the use of HF transformers and avoid their drawbacks. However, a voltage gain greater than 20 involves a large number of components, which makes the design more challenging. Another non-isolated topology also exists, based on a coupled-inductor used in the conventional boost, which offers a better gain than most of the topologies (including the isolated topologies). However, using a coupled-inductor would include the same drawbacks as isolated topologies, such as the need for a clamp circuit. Additionally, the use of a coupled-inductor leads to poor utilization of the magnetic circuit, which increases the size of the converter.

In our work, a "three-state switching step-up" converter [6] topology was considered to benefit from both the push-pull and the coupled-inductor advantages, including a clamp circuit to evacuate the leakage energy to the output. This topology consists of (see Fig. 2):

* Two main switches $S_1$ and $S_2$ with a phase difference of $T_s/2$ to supply the primary windings with a low current ripple using interleaving technique.

* A voltage doubler topology ($D_3, D_4, C_2, C_3$) to further increase the voltage gain and to decrease the voltage across the secondary winding.

* A clamp circuit ($D_1, D_2, C_1$) connected to the output, to improve the voltage gain.

## IV. DC/DC CONVERTER ANALYSIS

In previous section, a DC-DC step-up topology has been chosen for the conversion architecture. This topology operates only at a duty cycle $D > 50\%$. Assuming that the converter works under continuous conduction mode (CCM), the operational phases of this topology are

<figure><img src="image_3.png" /><figcaption>Fig. 2. Selected DC-DC step-up topology</figcaption></figure>

given by Fig. 3. The relationship between the primary and secondary windings voltages and currents are given by: $V_s = 2mV_p$; $i_{p1} - i_{p2} = 2m i_s$; $m = \frac{N_s}{N_p}$

* **Mode I:** Switches $S_1$ and $S_2$ are turned on. The primary windings are short circuited ($V_p = 0$). All the diodes are reversed bias. The inductor $L$ is charged, while all capacitors are discharged to the output. The inductor voltage and the capacitors currents are given by:

$$i_{c1} = i_{c2} = i_{c3} = -i_{out} ; V_L = V_{in}$$

* **Mode II:** Switch $S_2$ is turned off, and $S_1$ remains on. The primary leakage inductance forces the conduction of diode $D_2$. The inductor $L$ is discharged to the capacitors $C_1$ and $C_2$, by passing through the diode $D_4$ ($V_s = V_{c2}$). The inductor voltage and the capacitors currents are given by:

$$i_{c1} = i_{p2} - i_{out} ; i_{c2} = i_s - i_{out} ; i_{c3} = -i_{out} \\ V_L = V_{in} - \frac{V_{c1}}{2} = V_{in} - \frac{V_{c2}}{2m}$$

* **Mode III:** Switch $S_2$ is turned on, and $S_1$ remains on. This mode is the same as Mode I.

* **Mode IV:** Switch $S_1$ is turned off, and $S_2$ remains on.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Operating phases of three-state switching step-up converter</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Currents and voltages waveforms of the proposed converter</figcaption></figure>

on. The primary leakage inductance forces the conduction of diode D₂. The inductor L is discharged to the capacitors C₁ and C₃, by passing through the diode D₃ (Vₛ = -Vc₃). The inductor voltage and the capacitors currents are given by:

$$ 
\begin{aligned}
i_{c1} &= i_{p1} - i_{out} ; i_{c2} = -i_{out} ; i_{c3} = -i_{s} - i_{out} \\
V_{L} &= V_{in} - \frac{V_{c1}}{2} = V_{in} - \frac{V_{c3}}{2m}
\end{aligned}
$$

The Fig. 4 illustrates the different currents and voltages waveforms in one switching period. The output voltage V<sub>out</sub> is obtained using the voltage balance condition (V&#773;<sub>L</sub> = 0):

$$ V_{out} = \frac{(2m + 1)V_{in}}{1 - D} \quad (1) $$

Using the values of inductor voltage, the expression of current ripples is provided by:

$$ \Delta I_L = \frac{V_{in}}{Lf_s} \left(D - \frac{1}{2}\right) \quad (2) $$

## V. PASSIVE COMPONENTS DESIGN

### A. Inductor design

The current ripple ΔI<sub>L</sub> is given by the equation (2), which depends on the duty cycle D, and therefore the value of transformer ratio m. Using the expressions (1) and (2), it is possible to find the relative current ripple (ΔI<sub>L</sub>)<sub>r</sub>[%], given by:

$$ (\Delta I_L)_r [\%] = \frac{V_{in}^2}{P_{out}Lf_s} \left(D - \frac{1}{2}\right) \quad (3) $$

To understand the influence of the ratio m on the current ripple, the Table II shows the minimal-maximal values (corresponding to the battery voltage variation)

<table><caption>TABLE II
DUTY CYCLE AND RELATIVE RIPPLE WHEN V<sub>in</sub> = 42 – 54V</caption><thead><tr><th>Turns ratio m</th><th>Duty cycle D [%]</th><th>relative current ripple Δi<sub>L</sub> / i<sub>L</sub> [%]</th></tr></thead><tbody><tr><td>2</td><td>73.0–79.0</td><td>19.4–25.4</td></tr><tr><td>2.5</td><td>67.6–74.8</td><td>16.5–19.5</td></tr><tr><td>3</td><td>62.2–70.6</td><td>13.5–14.3</td></tr><tr><td>3.5</td><td>56.8–66.4</td><td>7.5–11</td></tr><tr><td>4</td><td>51.4–62.2</td><td>1.5–8.2</td></tr></tbody></table>

of the duty cycle and the relative current ripple at an output power of 200W. The transformer ratio m has been limited to 4, in order to stay at a duty cycle D superior to 50%. The inductor value L and the switching frequency fs are fixed (L = 330µH; fs = 40kHz). The value of the ripple tends to decrease when the duty cycle D approaches 50%. A value of the transformer ratio m > 3.5 permits to obtain a relative current ripple (Δi<sub>L</sub>)<sub>r</sub> less than 11%, which would satisfy the current ripple requirement for the converter.

### B. Transformer design

The topology is similar to the push-pull current-fed, hence the same transformer design can be applied [10].

1) The core section S<sub>C</sub> is determined through the expression of the maximal flux Φ<sub>m</sub> obtained in Mode 2 or Mode 4, in order to keep low both maximal flux density and magnetic losses:

$$ \Phi_m = \frac{V_{bat}}{2N_p f_s} \rightarrow S_C = \frac{V_{bat}}{2N_p f_s B_{max}} \quad (4) $$

B<sub>max</sub> is the maximal flux density fixed at 0.2T.

2) To calculate the copper sections, it is necessary to find the RMS currents in primary and secondary sides. Using the waveforms obtained in fig. 4, the expressions of RMS currents are given by:

$$ i_{p1,rms} = i_{p2,rms} = \sqrt{k_1 \cdot \left(\bar{i}_L^2 + \frac{\Delta i_L^2}{12}\right)} \quad (5) $$

$$ i_{s,rms} = \sqrt{k_2 \cdot \left(\bar{i}_L^2 + \frac{\Delta i_L^2}{12}\right)} \quad (6) $$

$$ k_1 = \frac{2D-1}{4} + \frac{(1-D)[(4m+1)^2+1]}{(4m+2)^2} ; k_2 = \frac{2(1-D)}{(2m+1)^2} $$
The primary and secondary copper sections are fixed by the current density J = 5A/mm²:
$S_{p,copper} = i_{p,rms}/J$ ; $S_{s,copper} = i_{s,rms}/J$

3) The core's window surface area S<sub>W</sub> is given by:

$$ K_W S_W = N_p S_{p,copper} + N_s S_{s,copper} \quad (7) $$
$K_W$ is the window utilization factor fixed at 0.7.

Using the equations (4) and (7), the expression of the area product is given by:

$$S_W \cdot S_C = \frac{V_{in} \cdot (i_{p,rms} + m \cdot i_{s,rms})}{2 f_s B_{max} K_W J} \quad (8)$$

Using equation (8), an ETD34 ferrite core was chosen. Lastly, the primary transformer turns $N_p$ can be calculated using (4), and the secondary transformer turns $N_s$ is deduced from the transformer ratio $m$ ($m = N_s/N_p$).

## VI. HF TRANSFORMER CHARACTERISATION

In order to acquire correct results of the conversion architecture through simulation, HF models of each component has to be introduced. SPICE models of MOSFET and diodes are available, and simple circuit models can be used for inductor and capacitors. Transformer on the other hand consists of three windings and requires a more complex model.

The designed transformer is presented in Fig. 5, alongside the windings disposition (see Fig. 6). The primary/secondary windings are interleaved, in order to minimize the AC copper losses and the leakage inductances using Dowell approximation [11].

In [12], an HF circuit model was presented for a three windings transformer as shown in Fig. 7.

This method is based on small signal impedance measurements to obtain both magnetic and dielectric parts separately by using impedancemeter Agilent 4294A. At first, the dielectric part is neglected and the magnetic parameters are obtained by considering the different cases when windings are in open/short circuit configurations. Then, the capacitances are obtained either from the resonances frequencies of previous measurements or by measuring the inter windings impedances. Further details are given in [12].

The results obtained by the given model are presented in Table III. The value obtained for the coupled

<figure><img src="image_6.png" /><figcaption>Fig. 7. HF circuit model of a three windings transformer.</figcaption></figure>

<table><caption>TABLE III
TRANSFORMER PARAMETERS VALUES</caption><tr><td>Primary P1</td><td>r<sub>p1</sub> = 21.7mΩ<br>Z̄<sub>p1</sub> : L<sub>p1</sub> + ΔL<sub>p1</sub> // R<sub>L1</sub><br>(L<sub>p1</sub> = 1.2064μH; ΔL<sub>p1</sub> = 0.75μH; R<sub>L1</sub> = 0.8Ω)</td></tr><tr><td>Primary P2</td><td>r<sub>p2</sub> = 21.7mΩ<br>Z̄<sub>p2</sub> : L<sub>p2</sub> + ΔL<sub>p2</sub> // R<sub>L2</sub><br>(L<sub>p2</sub> = 1.2694μH; ΔL<sub>p2</sub> = 0.62μH; R<sub>L2</sub> = 0.575Ω)</td></tr><tr><td>Secondary</td><td>r<sub>s</sub> = 1.0519Ω<br>Z̄<sub>s</sub> : L<sub>s</sub> // R<sub>f</sub> (R<sub>f</sub> = 930.178kΩ; L<sub>s</sub> = 10.2mH)</td></tr><tr><td>Turns ratio</td><td>m̄<sub>p1,s</sub> = 7.2622 ; m̄<sub>p2,s</sub> = 7.2150</td></tr><tr><td>Capacitances</td><td>C<sub>1</sub> = 9.32pF; C<sub>2</sub> = 59.01pF; C<sub>3</sub> = 10.68pF<br>C<sub>4</sub> = 68.22pF; C<sub>5</sub> = 73.59pF; C<sub>6</sub> = -12.39pF</td></tr></table>

transformer ratio is low (< 0.4), therefore it can be neglected according to [12]. The transformer ratio $m$ defined earlier, is approximately equal to 3.62 ($2m \approx m_{p1,s} \approx m_{p2,s}$).

## VII. COMPLETE TOPOLOGY AND SIMULATION WAVEFORMS

The DC-DC converter is used to charge the bus capacitor at 1kV and maintain its voltage when the actuators operate. The chosen DC-DC topology can only operate at a duty cycle $D$ higher than 50% [6]. Hence,

<figure><img src="image_7.png" /><figcaption>Fig. 5. Picture of the realized HF transformer.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Windings disposition.</figcaption></figure>

<table><caption>TABLE IV
SIMULATION DATA AND REFERENCES</caption><tr><td>Simulation data</td><td>V<sub>in</sub> = 48V; V<sub>out</sub> = 1kV; P<sub>out</sub> = 200W<br>f<sub>s</sub> = 40kHz; m = 3.62; D = 60.45%</td></tr><tr><td>Mosfet S<sub>1</sub>, S<sub>2</sub></td><td>BSC600N25NS3 250V 25A</td></tr><tr><td>Diode D<sub>1</sub>, D<sub>2</sub></td><td>RSX088LAP2STR 200V 5A</td></tr><tr><td>Diode D<sub>3</sub>, D<sub>4</sub></td><td>GD05MPS17H 1.7kV 5A</td></tr><tr><td>Inductor L</td><td>AGP4233-334ME 330uH 5.6A</td></tr><tr><td>Capacitor C<sub>1</sub></td><td>885342214003 250V 2.2uF</td></tr><tr><td>Capacitors C<sub>2</sub>, C<sub>3</sub></td><td>885342214001 630V 1uF</td></tr></table>
<figure><img src="image_9.png" /><figcaption>Fig. 8. Complete schematic of the DC-DC converter.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Simulation results waveforms.</figcaption></figure>

the inductor current $i_L$ during start-up is relatively high due to the high bus capacitor value (60μF).

A solution is to gradually increase the input voltage $V_{in}$ by adding a buck converter ($S_0, D_0$) to control the inductor current $i_L$, as presented in Fig. 8. The buck converter shifts in bypass when the bus capacitor is sufficiently charged by measuring the output voltage.

Furthermore, the DC-DC step-up converter can oper-

ate in DCM conditions regarding the output power range from 0 – 40W, which results in an excessive increase in the output voltage $V_{out}$. In that case, the switch $S_0$ is open to fully discharge the inductance $L$ and stop the output voltage from increasing. The buck part would return to bypass mode once the output voltage fell to a minimum threshold value.

A simulation has been carried out using LTSPICE to visualize the different currents and voltages waveforms by taking into account all the components HF models. The Table IV shows the simulation parameters, alongside the components references. The different waveforms are illustrated by Fig. 9 for two switching periods.

First, it is worth noticing that the MOSFET voltages $V_{s1}$ and $V_{s2}$ contain no overshoot when turned off due to the clamp circuit ($D_1, D_2$ and $C_1$), which enables the leakage energy evacuation.

However, when $S1$ and $S2$ are turned on, it is possible to notice that the secondary winding voltage $V_s$ is not exactly in short circuit as the ideal case. Instead, the voltage oscillates between –432V and 432V because of the resonance between the diodes $D_3, D_4$ capacitances and leakage inductances, which also has an impact on the primary currents ($i_{p1}, i_{p2}$) and diode voltages ($V_{D3}, V_{D4}$). Nevertheless, these oscillations have a slight effects on the inductor current $i_L$ and the output voltage $V_{out}$. The obtained output voltage $V_{out}$ is equal to 986V compared to 1kV in (1), while the average inductor current $\bar{i}_L$ is equal to 4.189A vs 4.166A in theory. The primary currents can reach up to 6A, which is higher than the inductor current $i_L$, but it is harmless to the primary wire since it can sustains a much higher current.
<figure><img src="image_11.png" /><figcaption>Fig. 10. Picture of the realized DC-DC converter.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 11. Efficiency curve of the DC-DC converter at $V_{out} = 1kV$.</figcaption></figure>

## VIII. EXPERIMENTAL RESULTS

A prototype has been developed (shown in Fig. 10) to measure the efficiency of the selected topology. The output power range depends on the various actuation events of the piezo-actuators driven each by a DC-AC converter (see section II), with an estimated total value between 20W and 200W. A resistive load has been used to obtain the efficiency curve in this power range. The switch $S_0$ is in bypass mode, with the output voltage $V_{out}$ maintained at 1kV, while the input voltage is set at 48V for continuous conduction mode (CCM) operating points and below 48V for discontinuous conduction mode (DCM) operating points ($P_{out} \le 40W$). The efficiency is calculated by measuring the input and output voltages/currents for each operating point. The results are shown in Fig. 11, indicating a value ranging from 94.5% to 96%. The efficiency reaches its peak at $P_{out} = 40W$, due to the alteration in the operating mode (DCM for $P_{out} = 20W, 40W$), which cancels the turn-on switching losses.

An efficiency estimation was conducted using LT-SPICE to perform a comparison with measurements. The estimated efficiency is presented alongside the measurements in Fig. 11. The two curves are almost identical when $P_{out} = 20W – 100W$ with a maximum absolute error of 0.1%. However, as $P_{out}$ exceeds 100W, the error increases until it reaches a value of 0.9% when $P_{out} = 200W$. The inaccuracy in modelling the AC winding losses of the HF transformer and the inductance accounts for this divergence. The AC resistances were modelled by an R//L circuit to include the impact of the frequency on the AC losses [12]. However, this approach

is insufficient because the parameters were obtained based on a small signal measurement (impedancemeter), which doesn't take into consideration large signal non linear behavior of the DC-DC converter operation.

Figure 12 illustrates the breakdown losses (LT-SPICE) at an output power of 200W. The winding losses of inductors and the high-frequency transformer are the most significant due to the AC resistances. Moreover, the winding losses are expected to be higher if we consider the difference with the measured efficiency.

<figure><img src="image_13.png" /><figcaption>Fig. 12. Losses distribution for $P_{out} = 200W$.</figcaption></figure>
## IX. CONCLUSION

In this work, a conversion architecture was introduced to drive multiple piezo actuators at 1kV, considering an input 48V battery supply. This architecture contains a DC-DC step-up converter with a voltage gain above 20 to achieve an output voltage of 1kV, while taking into account constraints such as size, dynamics, and performance.

A brief presentation was carried out for high gain step-up topologies found in the literature. A "three switching state step-up" converter was chosen for our application, due to its high power density, low current ripple, and low voltage stress on switches. The analysis of the chosen topology has been presented, as well as the design procedure for the HF transformer, while considering an input voltage $V_{in}$ fluctuation between 42V and 54V.

A simulation in LTSPICE has been performed for the DC-DC converter, including the HF models of all components (passive components, MOSFET, diodes), in order to evaluate the behaviour of the DC-DC converter and the values obtained for the output voltage $V_{out}$ and the input current $i_L$. The obtained values are coherent with the analytical expressions, despite the presence of oscillations between the leakage inductance and diodes capacitances.

A prototype of the DC-DC converter has been developed to measure the efficiency between 20W and 200W at $V_{out} = 1kV$. The obtained efficiency is higher than 94.5% on the whole power range. The results were subsequently compared with an efficiency estimation derived using LTSPICE to identify the most significant losses. The winding losses, particularly in the transformer, account for 43% of the total losses at full power. To enhance the efficiency of the DC-DC topology, a more precise design of the high-frequency transformer is required, incorporating several winding layers and employing interleaving techniques to reduce magnetic forces. Therefore, AC resistances with low values can be obtained.

Finally, the DC-DC converter will be tested in the conversion architecture with a prototype of the DC-AC converter presented in [7].

[2] X. Gao, J. Yang, J. Wu, X. Xin, Z. Li, X. Yuan, X. Shen, and S. Dong, "Piezoelectric actuators and motors: materials, designs, and applications," *Advanced Materials Technologies*, vol. 5, no. 1, p. 1900716, 2020. Publisher: Wiley Online Library.

[3] V. Michal, D. Cottin, and P. Arno, "Boost DC/DC converter nonlinearity and RHP-zero: Survey of the control-to-output transfer function linearization methods," in *2016 International Conference on Applied Electronics (AE)*, pp. 1–10, IEEE, 2016.

[4] M. Hossain and N. Rahim, "Recent progress and development on power DC-DC converter topology, control, design and applications: A review," *Renewable and Sustainable Energy Reviews*, vol. 81, pp. 205–230, 2018. Publisher: Elsevier.

[5] A. Amir, A. Amir, H. S. Che, A. Elkhateb, and N. Abd Rahim, "Comparative analysis of high voltage gain DC-DC converter topologies for photovoltaic systems," *Renewable energy*, vol. 136, pp. 1147–1163, 2019. Publisher: Elsevier.

[6] G. V. Torrico-Bascopé, S. A. Vasconcelos, R. P. Torrico-bascope, F. L. Antunes, D. S. De Oliveira, and C. G. Branco, "A high step-up dc-dc converter based on three-state switching cell," in *2006 IEEE International Symposium on Industrial Electronics*, vol. 2, pp. 998–1003, IEEE, 2006.

[7] N. R. Bennacer, C. Martin, and L. Pace, "A high voltage dc/ac unipolar converter to drive a piezoelectric actuator with controlled response times," in *CIPS 2024; 13th International Conference on Integrated Power Electronics Systems*, pp. 190–195, VDE, 2024.

[8] M. J. Brand, M. H. Hofmann, S. S. Schuster, P. Keil, and A. Jossen, "The influence of current ripples on the lifetime of lithium-ion batteries," *IEEE Transactions on Vehicular Technology*, vol. 67, no. 11, pp. 10438–10445, 2018. Publisher: IEEE.

[9] A. Leon-Masich, H. Valderrama-Blavi, J. M. Bosque-Moncusí, J. Maixe-Altes, and L. Martínez-Salamero, "Sliding-mode-control-based boost converter for high-voltage-low-power applications," *IEEE Transactions on Industrial Electronics*, vol. 62, no. 1, pp. 229–237, 2014. Publisher: IEEE.

[10] D. Maiti, N. Mondal, and S. Biswas, "Design procedure of a push Pull Current-Fed DC-DC Converter.," *NPEC-2010*, 2010. Publisher: Indian Institute of Technology Roorkee.

[11] P. Dowell, "Effects of eddy currents in transformer windings," in *Proceedings of the Institution of electrical Engineers*, vol. 113, pp. 1387–1394, IET, 1966.

[12] X. Margueron and J.-P. Keradec, "Identifying the magnetic part of the equivalent circuit of n-winding transformer," in *2005 IEEE Instrumentation and Measurement Technology Conference Proceedings*, vol. 2, pp. 1064–1069, IEEE, 2005.

## REFERENCES

[1] M. Karpelson, G.-Y. Wei, and R. J. Wood, "Driving high voltage piezoelectric actuators in microrobotic applications," *Sensors and actuators A: Physical*, vol. 176, pp. 78–89, 2012. Publisher: Elsevier.