A Novel Minimum-Phase Dual-Inductor Hybrid Boost Converter with PWM Voltage-Mode Controller

This paper presents a new dual-inductor hybrid boost converter (DI-HBOC) with two inductors located at the output. This structure allows continuous current delivered to the load, thus, reducing the output filtering capacitor size and the output voltage ripple. By relocating the inductor at the output, which is the lower current path, the conduction loss on the inductor can be significantly reduced. The right half plane zero (RHPZ) in the control-to-output transfer function can also be eliminated; therefore, a simple pulse-width modulation (PWM) voltage-mode controller can be used for the proposed DI-HBOC while still achieving high closed-loop bandwidth and fast transient response. The distinct features of the proposed converter are analytically demonstrated. A 12-to 24 V DI-HBOC and a conventional BOC (CBOC) using low-RON GaN switches with PWM voltage-mode controller are also implemented in PSIM for verification and comparison. The simulated peak power efficiency is 97.4 % that is 1.17 % higher than the CBOC. At 3 A load current, the power efficiency is improved by 9.7 % and the output ripple is only 17.5 mV, 6x lower than in CBOC. Keywords— Step-up DC-DC converter, boost converter, hybrid DC-DC boost converter, low EMI boost converter, minimum-phase boost converter, voltage-mode control, GaN.


INTRODUCTION
Step-up converters have been widely used in various applications such as uninterruptible power supplies, LED drivers, backlit TV LCDs, flash LEDs and audio amplifiers [1][2][3][4]. Among three categories of DC-DC step-up converters shown in Fig. 1, the SC and VM converters are simple and can be fully integrated on-chip. But their conversion efficiency is low (< 85%), and the output power is also limited (mW range). For moderate to high power applications, the conventional switched-inductor boost converter (CBOC) has dominated because of its higher power capability and power efficiency compared to SC and VM counterparts [5]. However, there remain four critical problems associated with the CBOC, which are graphically summarized in Fig. 2 and explained as below: First, the conduction loss is mainly contributed by I 2 R loss from direct current resistance (DCR) of the inductor, affecting the power efficiency and heat issue of CBOC. This is because (1) RON of new-generation power switches (e.g. GaN HEMT [6]) and the equivalent series resistance (ESR) of capacitors are generally much smaller than the DCR of the inductor, (2) inductor stays in the input, which is the high current path of the CBOC. Second, the output voltage ripple is high because the current supplied to the load is discontinuous, requiring a large filtering capacitance CO to achieve low output ripple. Third, output conducted electromagnetic interference (EMI) is high because of discontinuous critical current path, which results in the voltage spiking noise at the output as the converter output is directly tied to the switching node. Fourth, there exists a right half plane zero (RHPZ) in the control-to-output transfer function of the CBOC. This RHPZ is movable and can stay at low frequency at heavy load, limiting the bandwidth and transient response of the CBOC. As a result, complex currentmode control and sliding-mode control have been utilized to improve the converter's dynamic performance [7][8]. Several key works have been reported to improve CBOC performance, mainly focused on enhancing the converter efficiency [9][10][11][12]. A KY boost converter is reported in [9] with its inductor moved from the input (high current path) to the output (low current path). This reduces DCR loss, eliminates pulsating output current, thereby reducing the output voltage ripple and output EMI noise. However, the voltage gain of this boost converter is limited at 1+2D. The multi-phase boost converter reported in [10] can also reduce the conduction loss by splitting the current into many inductors, thereby reducing total DCR loss. Another solution is to use a multi-level boost converter (MBC) [11]. The idea is to reduce the voltage stress at the switching node of the inductor, thus, a smaller inductor with lower DCR can be used yielding higher efficiency and smaller converter size. In [12], a dual-path step-up converter (DPUC) was proposed. A capacitive path is added to share the delivered current to the output, thus reducing the inductor current and reducing the conduction loss of the inductor as well. In these boost converters, even the I 2 R loss of the inductor can be reduced; however, other losses increase. The hard-charging loss occurs in most reported hybrid DC-DC converter designs [9][10][11][12]. The high amount of power switches and capacitors in these boost topologies also contributes extra loss. With the exception of the boost topology in [9], complex controllers are needed as the RHPZ still exists in the control-tooutput small-signal transfer function of these boost converters.

S1
In light of these issues, this paper presents a novel dualinductor hybrid boost converter (DI-HBOC) that can improve concurrently four main problems that exist in the CBOC. The proposed DI-HBOC has: (1) high efficiency by reducing loss on the inductor without any hard-charging loss, (2) continuous input/output current which helps to reduce EMI and ripple at the output, (3) eliminate RHPZ in the small-signal transfer function that improves the converter's dynamic performance. Additionally, the voltage gain is similar to CBOC.
The paper is organized as follows: Section II analyses steady-state operation and loss of the DI-HBOC. Section III briefly presents small-signal analysis. Preliminary simulation results in PSIM are presented in Section IV. Section V ends the paper with some conclusions.

Steady-state operation
The structure of the proposed DI-HBOC consists of two switches S1, S2; two inductors L1, L2 and two capacitors CF, CO (Fig. 3). The DI-HBOC operates in 2 phases as shown in Fig. 4 with the key waveforms shown in Fig. 5.  Phase 1 (During DT): switch S1 is turned ON and S2 is turned OFF, the voltage across L1 is the input voltage vIN, the voltage across L2 is the input voltage plus the voltage vCF across CF minus the output voltage vO. Both L1 and L2 are magnetized. In this mode, CF is discharged.
Phase 2 (During (1-D)T): as soon as S1 is turned OFF and S2 is turned ON, the voltage across L2 is vIN -vO, the voltage across L1 is vIN -vCF. Both of L1 and L2 are demagnetized. In this mode, CF is charged.
Based on the volt-second balance of the two inductors and capacitor-charge balance of the flying capacitor CF, the following key equations can be derived: Clearly, the conversion gain of the proposed DI-HBOC is not limited as in [1,3] and is similar to the CBOC design. As shown in Fig. 5, the flying capacitor CF is charged/discharge by inductor currents iL1 and iL2. Soft switching can be achieved, reducing significantly the loss causes by the hard-charging effect that degrades power efficiency in various DC-DC hybrid converters [9][10][11][12][13][14]. Furthermore, since the output current is continuous, the conducted EMI is relaxed as compared to the CBOC design. The continuous output current also reduces the output filtering capacitor (CO) size.

Conduction loss analysis
The DI-HBOC improves the power efficiency as compared to CBOC as a consequence of moving the inductor from highcurrent to lower current path. Without loss of generality, assume that ΔiL1,2 can be ignored, the on-resistance of the two switches are equal (RON) and inductor L1 and L2 are similar (L1= L2, RL1=RL2). Also, it is assumed that the ESRs of CF and CO are small as compared to RON and the DCR of the power switches and inductors and can be neglected. With the support of Fig. 6, the conduction loss ratio between the proposed DI-HBOC and CBOC can be easily derived as follows: For a fair comparison, assuming that two L1/L2 are connected in series to construct an equivalent inductor for CBOC; therefore, L = 2×L1 = 2×L2 and RL = 2×RL1 = 2×RL2. Fig. 7 shows the conduction loss ratio between the CBOC and the proposed DI-HBOC at different RL/RON. Intuitively, the conduction loss is proportional to the resistance and the square of the current. Since the DI-HBOC has the inductor located at the low current path, its conduction loss can be less than that of the CBOC even though the DI-HBOC has same total DCR as shown in Fig. 7, leading to higher efficiency than the CBOC.
The best conduction loss reduction can be achieved at D = 0.5 and reduces when D moves toward the two extremes D = 0 and D = 1. When RL/RON increases (i.e. lower RON switches are utilized), the proposed DI-HBOC becomes more efficient as the conduction loss is mainly contributed by inductors.

III. SMALL-SIGNAL MODEL OF PROPOSED DUAL-INDUCTOR HYBRID BOOST CONVERTER
The small-signal model of the proposed DI-HBOC can be derived using the state space averaging (SSA) method [15]. A simple linear circuit can represent each of the two states where the switches in the circuit are replaced by their equivalent circuits during each state. Fig. 8(a) and (b) show the equivalent circuit corresponding to phase I and phase II operation, respectively. From these equivalent circuits, state equations for each phase can be derived. By applying the method presented in [13], the full control-to-output transfer function Gvd(s) of the DI-HBOC can be given by: where: (1 ) The transfer function of the power stage is a fourth-order system with two sets of complex-conjugate poles, a pair of complex-conjugate zeros and a zero produced by the ESR of the output capacitor. Close examination of the transfer function (3), along with (5) and (6) reveals all of its poles are located in the left half of the s-plane (LHP). However, its zeros can be either in the LHP or in the right half of the s-plane (RHP). The location of the zeros can be easily established by applying the Routh-Hurwitz criteria to the numerator polynomial of Gvd(s) [16]. Here, the coefficient of s 2 is always positive, hence the remaining coefficient 1 / z z Q ω defines the locations of the zeros. The necessary and sufficient condition to have all zeros in the LHP is 1 / z z Q ω > 0, i.e. according to (5), By satisfying the relation in (10), the proposed DI-HBOC performs minimum phase (MP) characteristics, i.e. there are no RHPZ in the transfer function (3). As explained in Section I, MP enables the design of a boost converter with a conventional voltage-mode controller while still achieving a high bandwidth, speeding up the converter's response. Fig. 9 shows the Bode plot of the transfer function Gvd(s) of the DI-HBOC using circuit models in PSIM and a derived model in MATLAB. The high matching between them demonstrates that the derived analytical model fully describes small-signal properties of the real circuit model.

IV. SIMULATION OF VOLTAGE-MODE CONTROL HYBRID BOOST CONVERTER
A 12 V-to-24 V DI-HBOC was simulated in PSIM to verify its performance. The selected components used in PSIM are shown in Table I. The maximum load current is set at IO,max = 3 A. Based on (10), the minimum value of flying capacitor is 22.94 μF. To ensure the zero stays in the LHP, CF = 40 μF is selected. This also increases the damping factor caused by a pair of complex-conjugate LHP zeros which might reduce the gain of the DI-HBOC as shown in Fig. 9    As there is no RHP zero in the control-to-output transfer function of the DI-HBOC, a type III (PID) controller can be used to design a wide bandwidth closed-loop voltage-mode controlled DI-HBOC. The PID compensation network and the associated values are shown in Fig. 10 help to achieve 200 kHz bandwidth at 1 MHz switching frequency. Fig. 11 shows the load transient response of the proposed DI-HBOC with an overshoot of 123 mV (5.1%) and a recovery times are within 30 µs when the load current steps down from 1 A to 0.5 A. Fig. 12 shows the output voltage ripple ΔVO of the CBOC and DI-HBOC. It should be noted that for a fair comparison, CO,CBOC = 50 μF while CF,DI-HBOC = 40 μF and CO,DI-HBOC = 10 μF (same total capacitance). A parasitic inductance LC = 50 pH of output capacitor CO,CBOC/CF,DI-HBOC was added to examine high-frequency noise at the output. For the worse case at Iload,max = 3 A, ΔVO,DI-HBOC is only 17.5 mV, compared to 105 mV for ΔVO,CBOC. Also, the spiking noise appears in the output of CBOC with a peak-peak value of up to 129 mV while it is absent for the case of DI-HBOC; thus, conducted EMI at the output of the DI-HBOC can be lower. Fig. 13 compares the simulated power efficiency of the CBOC and DI-HBOC with the setup L1/L2 = 20 μH, RL1/RL2 = 109 mΩ, L = 2×L1, RL = 2×RL1, in which the calculated switching losses are also included based on [17] using GaN parameters [18]. At light load Io = 0.15 A, the efficiency is slightly improved by 0.32 % while at heavy load Io= 3 A, the efficiency is significantly improved by 9.7 %. As the load increases, efficiency improvement is even more significant. The peak efficiency of the DI-HBOC (97.39 %) is 1.17% higher than of the CBOC (96.21 %). Furthermore, if L1 and L2 are coupled, effective L1 and L2 increase, current ripples ΔiL1,2 and ΔiSW on L1/L2 and S1/S2 decrease; thus, reducing the associated ac losses on L1/L2 and S1/S2. This scheme can further increase the power efficiency. Fig. 13 also shows the power efficiency of the uncoupled DI-HBOC (L1 and L2 are uncoupled, i.e. L1/L2 = 20 μH), and a coupled DI-HBOC (L1 and L2 are coupled with a coupling factor = 1, i.e. L1,eff/L2,eff = 40 μH). The power efficiency difference is very small, meaning that ac losses are low and can be excluded from the analysis as assumed in Section II.   V. CONCLUSIONS This paper has described a novel boost converter that provides the various attractive features to compete to existed step-up converters in terms of power efficiency, output ripple, EMI noise and dynamic response with a cost of using two separated inductors. The theoretical analysis and simulation results partially confirm the claimed merits of the proposed DI-HBOC. To demonstrate the superiority of the proposed DI-HBOC in terms of power efficiency, EMI, output ripple and dynamic response, measurement results will be implemented in our future work.