Modeling and Analysis of Adaptive-Conversion-Ratio-Basedbidirectional Switched-Capacitor

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Modeling and Analysis of Adaptive-Conversion-Ratio-BasedBidirectional Switched-Capacitor Converter

Yuen-Haw Changand Kun-WeiWu

Abstract—This research deals with the modeling and analysis of a new adaptive-conversion-ratio-basedbidirectionalswitched-capacitor converter (BSCC) for the bidirectional step-up/down DC-DC conversion and regulation. The power part consists of one -stage cell and one -stage cell in cascade between low-voltage (LV) and high-voltage (HV) sides to obtain a step-up gain of from LV to HV sides, or a step-down gain of from HV to LV at most. Here, the adaptive-conversion-ratio (ACR) control with adapting stage number is suggested to change the topological path for a proper step-up/down gain: or (,) so as to improve efficiency, especially for the lower desired voltage.Finally, the performance of this converter is verified experimentally on a BSCC prototype, and all results are illustrated to show the efficacy of this scheme.

I.INTRODUCTION

A bidirectional power-flow converter is important for the electricitysupply of multi-source systems, such as photo- voltaic systems, fuel-cell systems, and hybrid electric vehicles. The function is to transfer the stronger energy on one side into the weaker energy on the other side. This kind of converter has two ends: HV and LV sides, and both step-up and step-down conversions are essential to bidirectional converters.Recently, the switched-capacitor converter (SCC)is one of solutions to power conversion.Unlike traditional ones, inductor-less SCCs have light weight and small volumebecause they containsemiconductor switches and capacitors. Up to now, many types have been suggested [1], and some well-known topologies are: (i) Dickson, (ii)Ioinovici, (iii) Ueno, and (iv) Makowskicharge pump or SCC.In 1976, Dickson charge pump was proposed with a two-phase diode-capacitor chain [2-3], but it has the drawbacks of fixed gain and large device area. In the 1990s, Ioinoviciproposeda SCC with twosymmetrical capacitor cells[4-5]. In 1997, Zhu andIoinovici performed a comprehensive steady-state SCC analysis [6]. In 2003, Henryet al. proposed a generalized structure of bidirectional SCC [7]. In 2005, Axelrodet al. suggested some types of hybrid SC converter for the step-up applications [8-9].Following up, Lee et al. proposed a zero-current-switching bidirectional SCC with an extra resonant inductor [10-11].Chang proposed an integrated step-up/down unidirectional SCCin 2011 [12]. However, Ioinovici SCChasthe gain proportional to the capacitor count.In 1991, Ueno proposed a SC transformer for step-up ratio of Fibonacci series as well as low-ripple SCC [13-14]. However, these converters suffered from a limited line regulation. In 1997, Makowski suggested a two-phase canonical multiplier [15]. An n-stage Makowski charge pump has the gain limited by the (n+1)-th Fibonacci number [16-17]. Starzyk presented a multiphase voltage doubler (MPVD) in 2001, [18]. An n-stage MPVDhas the gain of2n at most [19], i.e. the capacitor count in Starzyk is fewerfor the same gain. Nevertheless, the improved spaces still exist. (i) Starzyk MPVD has the merits of fewer capacitor count and high gain, but it needs a complicated multiphase control circuit. Dickson or Ioinovici SCC has a simple two-phase control circuit, but the gain is proportional to capacitor count. In this paper, a new two-phase BSCC is proposed not only for a bidirectional DC-DC conversion, but also for the goals of large gain, few capacitor count, and simple control circuit. (ii) When the desired output is lower, the fixed gain often results in efficiency degradation. Here, the ACR control is suggested to change stage number for a proper gain to improve power efficiency. This idea by adapting stage number is not completely new. Recently, many researchers utilized this idea for realizing efficiency-enhanced [20-21]. In this paper, we take a lead in an attempt to present the ACR-control-based BSCC for the efficiency-enhancedbidirectional conversion.

II.Configuration of ACR-based BSCC

Fig. 1 shows a closed-loop scheme of ACR-based BSCC with power and control parts. As in the upper half of Fig. 1, the power part is composed of one -stage SC cell (A1) and one -stage SC cell (A2) in cascadebetween LV and HV sides. For more details, cell A1contains pumping capacitors() andCMOS gates, cell A2 hascapacitors() andCMOS gates, two side capacitors(,) and 4 MOSFETs () are included, where assume each pumping capacitor has the same capacitance with equivalent series resistance , and eachswitch has the same on-resistance .Thus, each capacitor voltage in cell A1/A2 can be identical and denoted by /. The LV/HV side contains a source voltage (/), relays (,/,), and a local load (/). As in the lower half of Fig. 1, the control part is composed of two pulse-width-modulation (PWM)blocks and ACR phase generator. The goal is to keep LV /HV side voltage (/)on followingLV/HV desired reference (/)under an efficiency-enhanced ACR control. Here,all discussions are based on circuitlevel aspect, not based on physicallevel. Thus, parasitic capacitances can be assumed small enough to be neglected here.

To deal with the different voltages (,,,), there are 4 modes to be considered as follows. (i) Individual

Figure 1.Configuration of ACR-based BSCC.

mode: If ,, then , are ON and , are OFF. In this case, no energy is transferred between LV and HV sides. The HV side separates from LVside because two sides haveenough source voltages to supply their own loading. (ii) Step-up mode: If ,,then ,, are ON and is OFF. In this case, the HV side has no enough source voltage to supply the HV loading. By using PWM-ON control of , the converter is transferring the energy from LV side to HV side. (iii) Step-down mode: If ,, then,, are ON and is OFF. In this case, the LV side has no enough source voltage to supply the LV loading. By using PWM-ON of , the converter is transferring the energy from HV side to LV side. (iv) Bidirectional mode: If , , then the converter is running in step-up mode or step-down mode, i.e. the energy is transferred from LV side to HV side through , or from HV side to LV side through .Our plan is to transfer the energy as more as possible from the stronger side to the weaker side, where the stronger side is the one with the source voltage closer to the desired reference. Obviously, both step-up and step-down modes are essential. The detailed operations are discussed as follows.

A.Step-Up Mode of BSCC

For the good of explanation, assume that the stage number is temporarily at ,and the “running“ stage number is no more than 3 ().First, let us consider step-up mode as . Fig. 2 shows thetheoretical waveforms within (, :switching frequency), where contains Phase I and II, and each phase has the same phase cycle . (i) Phase I: turn on , as in Fig. 3(a). are charged in parallel by , and are discharged in series to supply . (ii) Phase II: turn on as in Fig. 3(b). aredischarged in series to transfer thepower into in parallelvia PWM-ONof .Thus, , are toward the goal values of , respectively, and is boosted to at most. In fact, is regulated relative to how long is, where is the duty cycle of ().It stands to reason that the step-up gain can reach at most.

B.Step-Down Mode of BSCC

Fig. 4 shows the waveforms in step-down mode. (i) Phase I: turn on , as topology in Fig. 5(a). are charged in seriesby , and are discharged in parallel to supply . (ii) Phase II: turn on as in Fig. 5(b). are discharged in parallel to transfer the power into in series via PWM-ON of (: duty cycle of ). Based on the cyclical operation, and are toward the goal values of and respectively, and can be converted to at most.So, it stands to reason that the step-down gain can reach at most. Here, it is noticeable that the Phase I and II topologies in Fig. 3 (up) are identical to those in Fig. 5 (down), i.e. the operations of in the two modes are the sameexcept the direction of current flow. So, bidirectional switches are used here. It is helpful to integrate various topologies into one circuit structure.

C.ACR and PWM Control

The control part as in the lower half of Fig.1is composed of HV/LV PWMblocks and ACR phase generator.Whenthe BSCC is running in the step-up mode, isfedback into low-pass filter (LPF)for high-frequency noise rejection, and

Figure 2 Theoretical waveforms instep-up mode.

(a)

(b)

Figure 3. Step-up topology as running : (a) Phase I. (b) Phase II.

thenthe filtered is compared with to produce dutycycle of via HV PWM block. The goal is to keep followingwith duty-cycle regulation.When the BSCC is in the step-down mode, isfedback into the LPF, and then compared with to produce duty cycle of via LV PWM block so as to keep following. Of course, when ,, i.e. the BSCC is running in the bidirectional mode, the energy from LV to HV side can be controlled by PWM-ON of , or energy from HV to LV side is controlled by PWM-ON of .

In order to improve efficiency, the idea of ACR control is suggested with adapting stage number to change topological path for a proper conversion ratio.Here, the ACR phase generator is realized by logic circuit or programmable chip, and it includes two parts as follows. (i) ACR Decision: This

Figure 4Theoretical waveforms instep-down mode.

(a)

(b)

Figure 5. Step-down topology as running : (a) Phase I. (b) Phase II.

partdetermines which mode is appropriate based on the present values of HV/LV sources and desired references. Further, this part must choose a step-up gain of greater than and close to the value of most, or a step-down gain of greater than and near to . (ii) Phase Generator: Based on this chosen mode and stage number,it generatesthe driver signals of to manipulate topological path. For example (step-up mode), =, =.Because, , is selected (step-up gain), i.e.there are still 3 capacitors running in cell A1 (), but only 2 capacitors running in cell A2 (). Table Ishowthe ACR-based switch operations for different gains in the step-up/down modes.Because of the identical switch operations in both modes, it is helpful to the controller realization.

Table I. ACR-based switch operations (:ON, *:PWM-ON)

III.Modeling of ACR-based BSCC

A.Formulation of Step-Up BSCC

Firstly, the formulation of step-up BSCC is discussed. According to the Phase I-II circuits as in Fig.3, the dynamic equations can be derived as: ( means )

(i) Phase I: (Fig. 3(a))

, (1a)

, (1b)

, (1c)

, (1d)

, (1e)

(ii) Phase II: (Fig. 3(b))

, (2a)

, (2b)

, (2c)

, . (2d,e)

where ,,, and ,, are the parallel and series parasitic resistances.,areHVvoltage and LV supply-terminal current, respectively. By using state-space averaging,the stateequation of ACR-based BSCCin step-up mode can be derived as:

, (3a)

, (3b)

where

, (4a)

, (4b)

,, (4c,d)

, (4e)

. (4f)

B.Formulation of Step-Down BSCC

According to the Phase I-II circuits as in Fig.5, the relevant dynamic equations can be derived as:

(i) Phase I: (Fig. 5(a))

, (5a)

, (5b)

, (5c)

, (5d)

, (5e)

(ii) Phase II: (Fig. 5(b))

, (6a)

, (6b)

, (6c)

, . (6d,e)

where isLV side voltage and is HV supply- terminal current. By using SSA technique,the stateequation of ACR-based BSCCin step-down mode can be derived as:

, (7a)

, (7b)

where

, (8a)

, (8b)

,, (8c,d)

, (8e)

. (8f)

IV.Analysis of ACR-based BSCC

A.Steady-State Analysis and Conversion Ratio

By substituting /of (3)/(7), the steady-state HV/LV side voltage (/) and supply-terminal current (/)can be obtained as:

, (9a)

, (9b)

, (10a)

, (10b)

where , . From (9a)/(10a), it is obvious that / can be regulated by duty cycle/, and then the step-up/down voltage conversion ratio is suggested as

, (11a)

. (11b)

When /, /. When /, / is close to the value of /under ( is in -level, and is in -level). Thus, the step-up/down gain is / at most. For nominal conditions, the maximum attainable value of / is / minus voltage drops in the charging or discharging circuits.

B.Power Efficiency by using ACR Control

The input and output power can be computed as

, (12a)

, (12b)

, (13a)

. (13b)

According to (12)/(13) plus (9)-(10), the power efficiency of step-up/down BSCCis derived as

Figure 6. Hardware implementation of ACR-based BSCC.

, (14)

. (15)

Clearly, /is rising when is closer to / is closer to .Next, let's discuss the benefit toefficiency by usingthe ACR control. For example of step-up mode, assume is and is desired at . When ,, based on (14), the best efficiency is only 31.1%. When ,, the best is 46.67%. When ,, the best is 70.0%. But, if ,, the efficiency can be improved to 93.3%. The reason is that is the level closeto most. Really, the efficiency can be enhanced by adapting stage number, especially for the lower desired side voltage.

V.Example of ACR-based BSCC

A closed-loop ACR-based BSCCwith is simulated by OrCAD, and its hardware circuit is implemented and tested.First, based on Fig. 1, theBSCC is designed for simulation to realize bidirectional conversion with step-up and down gain of and at most. Further, the circuit parameters are listed as: ,,, , , , , , , , for the simulation cases. Besides, the BSCC hardware circuit is realized as photo shown in Fig. 6. There are two parts including: (i) BSCC (right:), (ii) ACR and PWM (left: ), mainly implemented in the circle-marked chip (I.C. no.: D35-99C- 70e, TSMC 0.35μm 2P4M, size: 150μm×193μm,3.5mW, maximum frequency: 50kHz) via full-custom fabrication of National Chip Implementation Center, Taiwan. Finally, this hardware circuit is tested practically for the experimental cases.

(i) Simulation cases: TheACR-based BSCCis simulated at respectively for (step-up)/ (step-down), and the wave- forms of ,/, are shown in Fig. 7/8. In Fig. 7(a),(c), (e)/8(a),(c),(e), it is found that theconverteris stable to keep / following / , and the settling time is really shorter than .In Fig. 7(b),(d),(f)/8(b),(d),(f),all the ripplesarelower than .The efficienciesare:

(a)

(b)

(c)

(d)

(e)

(f)

Figure 7. Step-up steady-state response:, for
(a)(b), (c)(d), (e)(f).

(a)

(b)

(c)

(d)

(e)

(f)

Figure 8. Step-down steady-state response:, for
(a)(b), (c)(d), (e)(f).

(a)

(b)

Figure 9. (a)(b)Step-up/downefficiency for various desired voltage.

(" ": ACR-based , " ": no-ACR )

/.Now, if the BSCC is operating at the “fixed” stage number (no ACR: ,), then the efficiencies are obtained as: /.Clearly, no-ACR efficiencies become worsewhen the lower voltages are desired. Here, a remark is given about efficiency using ACR. Fig. 9(a)/9(b) shows the step-up/down efficiencies for various desired voltages. The bold line representsthe ACR-based /, andit contains 6 divisions to correspond to (14)-(15). The dotted line representsno-ACR /, and it is a sloping line with /. Clearly, when / is lower, ACR-based / is much better than no-ACR /. (ii) Experimental cases: The experiment of BSCC is discussed. (,,, oscilloscope tool: Agilent Infiniium 54830B). The hardware is tested at for (step-up)/ (step-down) respectively, and the waveforms of /are obtained as in Fig. 10(a)-(c)/10(d)-(e).Obviously,/ is following /.The values of output ripples and efficiencies of ACR-based BSCC are measured as:/, and /.

VI.Conclusion

The modeling and analysis of the ACR-based BSCC is presented for the bidirectional step-up/down DC-DC conversion and regulation. In order to improve efficiency, the ACR idea is suggested with adapting stage number to obtain a suitable step-up/down gain of or ,where , . The advantages of the proposed scheme are listed as follows.(i) This SC-based bidirectional converter needs no magnetic element, so I.C. fabrication will be promising.But, the topology of charge pump has low efficiency as integrated circuit nowadays due to parasitic capacitances in fabrication process. Thus, the proposed scheme is suitable for discrete application more.

(a)

(b)

(c)

(d)

(Continue)

(e)

(f)

Figure 10. Step-up: for (a), (b), (c).
Step-down: for (d), (e), (f).

(ii) By using CMOS gate as a bi-directional switch,it is helpful to integrate various topologies into one structure.(iii) By using ACR control, the efficiency is improved much better than that just by thefixed running stage number, especially for the lower desired voltage.(iv)Since the BSCC hasthe large conversion ratio: (step-up) or (step-down) at most, the capacitor count is fewerfor the same gain. A relevant discussion is given here. Starzyk MPVDhas the merits of fewer capacitor count and high gain of , but itneeds a complicated multiphase control circuit. Dickson charge pump or Ioinovici SChas a simple two-phase control circuit, but its gain is just proportional to the capacitor count.In this paper, thisBSCC is presented for a compromise among voltage gain, capacitor count, and control circuit. For example, assume the maximum gain is 9.Starzyk MPVD needs 4 capacitors ()viamultiphase operation for uni-directional step-up conversion. Dickson or Ioinovici SC needs 8 ones ()with two-phase operation for uni- directional step-up conversion. This BSCC needs just 6 ones () with two-phase operation for bi-directional step- up/down conversion.

Acknowledgment

This research of converter circuit theory and application is financially supported by NationalScience Council of Taiwan, R.O.C., under Grant NSC 101-2221-E-324-016.

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