# A New Combined Boost Converter with Improved Voltage Gain as a Battery-Powered Front-End Interface for Automotive Audio Amplifiers

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## Abstract

**:**

## 1. Introduction

## 2. Converter Topology and Operation Principles

_{1}, capacitor C

_{1}, active switch S

_{1}and diode D

_{1}. The other is the inverted boost circuit, which contains inductor L

_{2}, capacitor C

_{2}, active switch S

_{2}, and diode D

_{2}. The inductors L

_{1}and L

_{2}are amount to L, and the capacitors C

_{1}and C

_{2}are amount to C. C

_{o}is the common output capacitor, V

_{i}is the supply voltage, V

_{o}is the output voltage, and R

_{o}is the output load resistance.

_{s}; (4) The converter works in continuous conduction mode (CCM). In the combined boost converter, all working modes and their equivalent circuits corresponding to the ON/OFF status of the active switches have been illustrated in Figure 3. The steady-state waveforms of the combined boost converter are demonstrated in Figure 4. The working modes can be described clearly as follows.

- (1)
- Mode 1 [t
_{0}–t_{1}] and Mode 3 [t_{2}–t_{3}]: In these two modes, the active switches S_{1}and S_{2}are switched on while the diodes, D_{1}and D_{2}are reverse-bias. The current in the inductors, i_{L}_{1}and i_{L}_{2}, increase to store energy in L_{1}and L_{2}, respectively. The output power for the back-end amplifier is provided by capacitor C_{o}. The total current i_{Lt}and inductor currents of L_{1}and L_{2}are expressed below.$${i}_{Lt}={i}_{L1}+{i}_{L2}$$$$\frac{d{i}_{L1}}{dt}=\frac{{V}_{i}}{{L}_{1}}$$$$\frac{d{i}_{L2}}{dt}=\frac{{V}_{i}}{{L}_{2}}$$ - (2)
- Mode 2 [t
_{1}–t_{2}]: The active switch S_{1}remains conducting and S_{2}is switched off. D_{1}is reverse-bias and D_{2}is forward-bias. While the current i_{L}_{1}increase to store energy in L_{1}, the energy stored in inductor L_{2}is now released through D_{2}, C_{2}, C_{1}, and C_{o}to the output. The total current i_{Lt}and inductor currents of L_{1}and L_{2}can be expressed as follows:$${i}_{Lt}={i}_{L1}+\frac{{i}_{L2}}{2}$$$$\frac{d{i}_{L1}}{dt}=\frac{{V}_{i}}{{L}_{1}}$$$$\frac{d{i}_{L2}}{dt}=\frac{{V}_{i}-{V}_{C2}}{{L}_{2}}=\frac{{V}_{C1}-{V}_{o}}{{L}_{2}}$$ - (3)
- Mode 4 [t
_{3}–t_{4}]: S_{2}is switched on and S_{1}is switched off. D_{2}is reverse-bias and D_{1}is forward-bias. The energy stored in L_{1}is released through D_{1}to charge capacitor C_{1}and C_{o}. The total current i_{Lt}and inductor currents of L_{1}and L_{2}can be expressed as follows:$${i}_{Lt}={i}_{L2}+\frac{{i}_{L1}}{2}$$$$\frac{d{i}_{L1}}{dt}=\frac{{V}_{i}-{V}_{C1}}{{L}_{1}}=\frac{{V}_{C2}-{V}_{o}}{{L}_{1}}$$$$\frac{d{i}_{L2}}{dt}=\frac{{V}_{i}}{{L}_{2}}$$

## 3. Analysis of Steady-State

#### 3.1. Voltage Gain

_{1}and L

_{2}as follows:

_{1}and C

_{2}capacitors are connected in series with the supply voltage, and the equation of output voltage of the converter is expressed as:

#### 3.2. Voltage Stress of the Switches

_{1}and S

_{2}can be obtained by the aforementioned analyses of operations. The relevant expression is written as (15).

#### 3.3. Inductor Current Ripples

_{1}and L

_{2}, in the proposed combined boost converter can thus be expressed as:

#### 3.4. The Mode for Boundary Conduction

_{L,B}is expressed as:

_{sw}is the switching frequency.

_{L}is planned to be higher than the boundary curve of τ

_{L,B}, the converter operates in continuous conduction mode (CCM). Conversely, the proposed converter works in discontinuous conduction mode (DCM) when τ

_{Lb}is chosen to be smaller than the boundary curve of τ

_{Lb,B}.

#### 3.5. Component Stress and Loss

## 4. Converter Control Strategy

_{1}and S

_{2}. By appropriately adjusting duty ratio, the output voltage can be flexible. The circuit model is established by PSIM© simulation software (Powersim Inc., Rockville, MD, USA) under the later suppositions to devise the closed-loop controller and reduce the mathematics for the converter. The suppositions includes (1) power switches and diodes are ideal; (2) equivalent series resistances (ESRs) of all the inductors and capacitors of the converter are thought to acquire a comparatively precise dynamic model; (3) the converter works in under CCM. The taken circuit parameters are L

_{1}= L

_{2}= 250 μH, C

_{1}= C

_{2}= 10 μF, C

_{o}= 1000 μF, output resistance R = 30 Ω, and ESRs r

_{L}

_{1}= r

_{L}

_{2}= r

_{C}

_{1}= r

_{C}

_{2}= 100 mΩ.

_{o}) is sensed and compared with the reference (V

_{o,ref}). The output voltage controller produces those two inductor current reference (i

_{L}

_{1,ref}, i

_{L}

_{2,}

_{ref}) for the entire system, and the equal current sharing between the two interleaved phases can be also acquired. Furthermore, during the system startup, using a soft start system (V

_{conss}) is used to avoid the capacitor charge surge current causing damage to the converter components.

_{M}is the constant gain of the PWM generator; G

_{i}

_{1d}and G

_{i}

_{2d}is the transfer function from the duty ratio to the two different inductor current; C

_{i}

_{1}and C

_{i}

_{2}indicates the transfer function of current controllers; and H

_{i}

_{1}and H

_{i}

_{2}are the sensing gains of the current sensor. In the outer voltage control loop, G

_{vd}is the transfer function from the duty ratio to the output voltage; C

_{v}indicates the transfer function of output voltage controller; and H

_{v}indicates the sensing gain of the voltage sensor.

_{M}= 1/100, H

_{i}

_{1}= H

_{i}

_{2}= H

_{v}= 1.

_{i}

_{1d}and G

_{i}

_{2d}and the duty ratio to output voltage G

_{vd}can be shown below.

## 5. Simulated and Experimented Results

_{1}and C

_{2}are calculated using (10) and (11). The values across both C

_{1}and C

_{2}are calculated to be about 36 V (i.e., V

_{C}

_{1}= V

_{C}

_{2}= 36 V).

_{GS}

_{1}and V

_{GS}

_{2}and two-phase inductor currents i

_{L}

_{1}and i

_{L}

_{2}, respectively.

_{1}and S

_{2}, respectively.

_{1}and D

_{2}, respectively.

_{1}and C

_{2}capacitors. The results verify the feasibility of the converter.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 3.**Working modes and equivalent circuits of the combined boost converter. (

**a**) Mode 1 and Mode 3, (

**b**) Mode 2, and (

**c**) Mode 4.

**Figure 5.**The comparison of the voltage gains produced by the proposed combined boost converter, the conventional boost converter, and the interleaved boost converter with two-phases.

**Figure 6.**The ratio between the total current ripple and the inductor current ripple versus the duty cycle.

**Figure 10.**Frequency responses of the loop gain. (

**a**) compensated current loop and (

**b**) compensated voltage loop.

**Figure 12.**Realized combined boost converter prototype. (

**a**) Top view; (

**b**) Front view; (

**c**) Side view.

**Figure 13.**Realized test bench system (the oscilloscope, power source, electronics load, pulse-width modulation (PWM) generator, and the proposed combined boost converter prototype are labeled).

**Figure 14.**Waveforms of the combined boost converter for gate driving signals V

_{gs1}and V

_{gs2}and two-phase inductor current i

_{L}

_{1}. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 15.**Waveforms of the combined boost converter for gate driving signals V

_{GS}

_{1}and V

_{GS}

_{2}and two-phase inductor current i

_{L}

_{2}. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 16.**Waveforms of the combined boost converter for the cross voltages across S

_{1}and S

_{2}. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 17.**Waveforms of the proposed combined boost converter for the cross voltages across D

_{1}and D

_{2}. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 18.**Waveforms of the combined boost converter for the cross voltages across C

_{1}and C

_{2}. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 19.**Waveforms of transient response in the load period steps from 120 W to 60 W and then back to 120 W. (

**a**) Simulated waveforms; (

**b**) Experimented waveforms.

**Figure 20.**The measured conversion efficiency for the proposed combined boost converter, the conventional boost converter, and the interleaved boost converter with two-phase.

Items | State |
---|---|

RMS current stress on S_{1} (i_{S}_{1}) | ${I}_{S1\left(\mathrm{RMS}\right)}={I}_{L2\left(\mathrm{RMS}\right)}\sqrt{D}$ |

RMS current stress on S_{2} (i_{S}_{2}) | ${I}_{S2\left(\mathrm{RMS}\right)}={I}_{L1\left(\mathrm{RMS}\right)}\sqrt{D}$ |

RMS current stress on L_{1} (i_{L}_{1}) | ${I}_{L1\left(\mathrm{RMS}\right)}=\sqrt{{({I}_{L1})}^{2}+{\left(\frac{\Delta {i}_{L1}}{2\sqrt{3}}\right)}^{2}}$ |

RMS current stress on L_{2} (i_{L}_{2}) | ${I}_{L2\left(\mathrm{RMS}\right)}=\sqrt{{({I}_{L2})}^{2}+{\left(\frac{\Delta {i}_{L2}}{2\sqrt{3}}\right)}^{2}}$ |

RMS current stress on L_{t} (i_{Lt}) | ${I}_{Lt\left(\mathrm{RMS}\right)}=\sqrt{{({I}_{L1}+{I}_{L2})}^{2}+{\left(\frac{\Delta {i}_{L2}}{4\sqrt{3}}\right)}^{2}}$ |

RMS current stress on D_{1} (i_{D}_{1}) | ${I}_{D1\left(\mathrm{RMS}\right)}={I}_{L2\left(\mathrm{RMS}\right)}\sqrt{1-D}$ |

RMS current stress of D_{2} (i_{D}_{2}) | ${I}_{D2\left(\mathrm{RMS}\right)}={I}_{L1\left(\mathrm{RMS}\right)}\sqrt{1-D}$ |

RMS current stress of C_{1} (i_{C}_{1}) | ${I}_{C1\left(\mathrm{RMS}\right)}={I}_{o}\sqrt{\frac{D+\frac{{r}^{2}}{12}}{1-D}},\text{\hspace{0.17em}}r=\frac{\Delta I}{{I}_{ft}},\text{\hspace{0.17em}}{I}_{ft}=\frac{{I}_{o}}{1-D}$ |

RMS current stress of C_{2} (i_{C}_{2}) | ${I}_{C2\left(\mathrm{RMS}\right)}=={I}_{o}\sqrt{\frac{D+\frac{{r}^{2}}{12}}{1-D}},\text{\hspace{0.17em}}r=\frac{\Delta I}{{I}_{ft}},\text{\hspace{0.17em}}{I}_{ft}=\frac{{I}_{o}}{1-D}$ |

RMS current stress of C_{o} (i_{Co}) | ${I}_{Co\left(\mathrm{RMS}\right)}={I}_{o}\sqrt{\frac{D}{1+D}}$ |

Items | State |
---|---|

Total loss of S_{1} | $\begin{array}{l}\frac{{V}_{S1(DS1)}\times {I}_{S1(D1)}\times {T}_{r1}\times {f}_{sw}}{2}+\frac{{V}_{S1(DS2)}\times {I}_{S1(D2)}\times {T}_{f1}\times {f}_{sw}}{2}+\\ {R}_{DS1(ON)}\times {\left[{I}_{S1(\mathrm{RMS})}\right]}^{2}+{Q}_{g1}\times {V}_{GS1}\times {f}_{sw}\end{array}$ |

Total loss of S_{2} | $\begin{array}{l}\frac{{V}_{S2(DS1)}\times {I}_{S2(D1)}\times {T}_{r2}\times {f}_{sw}}{2}+\frac{{V}_{S2(DS2)}\times {I}_{S2(D2)}\times {T}_{f2}\times {f}_{sw}}{2}+\\ {R}_{DS2(ON)}\times {I}_{S2(RMS)}{}^{2}+{Q}_{g2}\times {V}_{GS2}\times {f}_{sw}\end{array}$ |

Conduction loss of L_{1} | ${r}_{L1}\times {\left[{I}_{L1(\mathrm{RMS})}\right]}^{2}$ |

Conduction loss of L_{2} | ${r}_{L2}\times {\left[{I}_{L2(\mathrm{RMS})}\right]}^{2}$ |

Total loss of D_{1} | ${V}_{F1}\times {I}_{o}\times K+0.5\times {V}_{R1}\times {T}_{RR1}\times {f}_{sw}\times {I}_{RR1}$ |

Total loss of D_{2} | ${V}_{F2}\times {I}_{o}\times K+0.5\times {V}_{R2}\times {T}_{RR2}\times {f}_{sw}\times {I}_{RR2}$ |

Conduction loss of C_{1} | ${r}_{C1}\times {\left[{I}_{C1(\mathrm{RMS})}\right]}^{2}$ |

Conduction loss of C_{2} | ${r}_{C2}\times {\left[{I}_{C2(\mathrm{RMS})}\right]}^{2}$ |

Conduction loss of C_{o} | ${r}_{Co}\times {\left[{I}_{Co\left(\mathrm{RMS}\right)}\right]}^{2}$ |

_{g}represents the total charge on the gate of the metal-oxide-semiconductor field-effect transistor (MOSFET). The rise time T

_{r}is the time it takes to complete charging the gate of the MOSFET after the threshold voltage V

_{GS}

_{(th)}has been reached. The fall time, T

_{f}, is the time it takes to reach the threshold voltage following the MOSFET’s switch-off delay time [34]. V

_{F}represents the forward voltage drop of the diode. K is the time of the conduction period of the diode. V

_{R}represents the reverse voltage of the diode. I

_{R}is the reverse leakage current of the diode [35].

Specification | Value |
---|---|

Input Voltage, V_{i} | 12 V |

Output Voltage, V_{o} | 60 V |

Duty Cycle, D | 0.67 |

Switching Frequency, f_{sw} | 40 kHz |

Output power, P_{o} | 120 W |

Specification | Value |
---|---|

MOSFET | IPP080N06NG |

Diode | STPS8H100 |

Load Resistance, R | 30 Ω |

Inductors, L_{1} and L_{2} | 250 μH |

Filter Capacitors, C_{1} and C_{2} | 10 μF |

Output Capacitor, C_{o} | 1000 μF |

Items | Results (50% Load) | Results (100% Load) |
---|---|---|

Switching loss of S_{1} | 0.049 W | 0.059 W |

Switching loss of S_{2} | 0.049 W | 0.059 W |

Conduction loss of L_{1} and L_{2} | 0.64 W | 3.2 W |

Conduction loss of D_{1} and D_{2} | 0.0384 W | 0.23 W |

Conduction loss of C_{1} and C_{2} | 0.196 W | 1.02 W |

Conduction loss of C_{o} | 0.035 W | 0.075 W |

Total losses | 1.8828 W | 9.134 W |

Calculated Efficiency | 98.5% | 92.4% |

Measured Efficiency | 97.3% | 89.1% |

Items | Topology | |||
---|---|---|---|---|

This Converter | [11] | [19] | [24] | |

Switching control structure | two-phase | single-phase | three-Phase | single-phase |

Input current ripple | Low | High | Low | Medium |

Voltage gain | (1 + D)/(1 − D) | (1 + D)/(1 − D) | (3+ nD − D^{2} )/(1 − D) | 1/(1 − D)^{2} |

High-side voltage | 60 V | 60 V | 200 V | 62.5 V |

Low-side voltage | 12 V | 12 V | 24 V | 10 V |

Number of main power devices | 4 | 3 | 8 | 4 |

Number of storage components | 5 | 4 | 8 | 5 |

Maximum efficiency | 98.7% | 92.1% | 92.3% | 92.5% |

Realized prototype power rating | 120 W | 40 W | 100 W | 100 W |

BOM Cost | Low | Low | High | Medium |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lai, C.-M.; Cheng, Y.-H.; Teh, J.; Lin, Y.-C.
A New Combined Boost Converter with Improved Voltage Gain as a Battery-Powered Front-End Interface for Automotive Audio Amplifiers. *Energies* **2017**, *10*, 1128.
https://doi.org/10.3390/en10081128

**AMA Style**

Lai C-M, Cheng Y-H, Teh J, Lin Y-C.
A New Combined Boost Converter with Improved Voltage Gain as a Battery-Powered Front-End Interface for Automotive Audio Amplifiers. *Energies*. 2017; 10(8):1128.
https://doi.org/10.3390/en10081128

**Chicago/Turabian Style**

Lai, Ching-Ming, Yu-Huei Cheng, Jiashen Teh, and Yuan-Chih Lin.
2017. "A New Combined Boost Converter with Improved Voltage Gain as a Battery-Powered Front-End Interface for Automotive Audio Amplifiers" *Energies* 10, no. 8: 1128.
https://doi.org/10.3390/en10081128