126

- SIMO Power Converters with Adaptive PCCM Operation
- References

*Yi Zhang and D. Brian Ma*

*Yi Zhang and D. Brian Ma*

Driven by modern very large scale integration (VLSI) systems and their fast-emerging applications, the demands on multiple on-chip power supplies have been ever increasing due to two main reasons. First, as complexity of electronic devices such as cell phones and laptops increases, multiple power supplies are essential to power key functional blocks, such as processors, liquid crystal display, and radio transceivers. Second, as power consumption in semiconductor chips rises, efficient system power management techniques are in high demand. This leads to the high popularity of the so-called dynamic voltage/frequency scaling (DVFS) techniques (Burd et al. 2000, Chang and Pedram 1997, Cheng and Baas 2008, Ma and Bondade 2010, Usami et al., 1998), where multiple-supply-based power management schemes are crucial. By powering distinct functional modules and subsystems with different supply voltages and by adaptively switching their supplies according to instantaneous power needs, power and energy savings achieved through DVFS techniques are significant (Burd et al. 2000, Luo et al. 2007, Ma and Bondade 2010).

Historically, multiple DC power supplies are implemented by transformer-based isolated DC–DC converters or several nonisolated DC–DC converters. However, due to the use of bulky off-chip inductive components and many power switches, system volume, printed circuit board (PCB) footprint, and electromagnetic interference noise are all considerably large. In the meantime, regulation accuracy can be compromised by commonly used “master–slave” regulation approaches (Ma et al. 2001a).

To mitigate these issues, single-inductor multiple-output (SIMO) power converters were proposed (Ki and Ma 2001, Ma et al. 2001a, 2003a,b). By time-sharing a single inductor and some power switches, a SIMO power converter offers multiple power outputs, which can be regulated independently. This leads to a significant reduction in cost, volume, and PCB footprint. Because of their cost-effective features, the application of SIMO power converters has been proliferating in recent years, spanning from hybrid power source units (Huang et al. 2010), energy-harvesting systems (Kim and Rincon-Mora 2009, Sze et al. 2008) to light-emitting diode backlighting (Chen et al. 2012), active matrix OLED display panels (Chae et al. 2009), and electronic paper displays (Lee et al. 2010).

As more SIMO converter-based IC products are being commercialized in the market, cross-regulation effect, as one of the most critical design challenges, has drawn extensive attention. In a SIMO switching converter, because the inductor is time-shared by several subconverters, a duty ratio change in one subconverter may affect the amount of energy transferred to other subconverters even if the operating conditions (load currents, duty ratios, etc.) in other subconverters remain constant. As a result, this may cause voltage variations on the affected outputs. This effect was named as cross-regulation in Ma et al. (2003b) because a local operating condition change in one subconverter has impacted the regulation performances across the others. In worst-case scenarios, a SIMO converter fails to operate due to severe cross-regulation.

In order to avoid the cross-regulation effect, the regulation time slot designated to each subconverter should be completely isolated. For this reason, SIMO converters in the early stage usually operate in discontinuous conduction mode (DCM) (Ki and Ma 2001, Ma et al. 2001a, 2003b). However, in heavy-load scenarios, peak inductor current may rise very high in DCM, causing substantial voltage and current ripples and switching noise. Alternatively, if continuous conduction mode (CCM) is applied to alleviate large peak current, cross-regulation occurs immediately. In order to reduce the heavy current stress while retaining low cross-regulation, a pseudo-continuous conduction mode (PCCM) operation was first proposed in Ma et al. (2002). Instead of returning to zero as in DCM, the inductor current stays constant at a predefined current level through freewheel switching actions. With the same load condition, the peak inductor current in PCCM can be much lower than that in DCM, while still avoiding cross-regulation effect since the regulation actions on any two outputs are isolated by one freewheel switching period. Unfortunately, the PCCM operation also has its own drawbacks. Especially, in the unbalanced load conditions, large conduction power loss is observed in subconverters handling light loads. Moreover, since the freewheel switch turns on/off multiple times in one switching cycle, the overall switching power loss also increases. To overcome these drawbacks, a new control technique is required to reduce both conduction and switching power loss in the freewheel switch.

Figure 3.1 Power stage architecture and discontinuous conduction mode inductor currents of (a) two conventional switching power converters and (b) one single-inductor multiple-output converter. (From Zhang, Y., Single-inductor multiple-output power converters: Architectures, control techniques and applications, PhD dissertation, The University of Texas at Dallas, Richardson, TX, 2013.)

To better understand the PCCM operation for SIMO converters, we first examine the development of SIMO power converter, as illustrated in Figure 3.1 (Ma et al. 2001a, 2003b). Consider two conventional switching boost converters in DCM operating at the same switching frequency. One possible operation scheme is illustrated in Figure 3.1a. At the beginning of each switching cycle *T*, the inductor *L*_{1} is charged at a rate of *V _{IN}*/

If the two inductor currents can be alternately assigned to occupy different parts of the switching cycle without overlapping, only one single inductor will suffice for their operation, as shown in Figure 3.1b. During the first half switching cycle from 0 to *T*/2, the inductor current is diverted to *V*_{O1} by properly controlling the power switches *S _{X}* and

Obviously, this operation scheme can be readily extended for SIMO power converters with more than two outputs. For SIMO power converters with *N* subconverters, one switching cycle is divided into *N* phases, with the inductor current being multiplexed into each output during the corresponding phase. Furthermore, the topology is not only limited to boost converter. It can be easily extended to many existing switching power converter topologies (Ki and Ma 2001), such as buck and noninverting buck–boost.

It should be noted that the time-multiplexing operation is critical for a SIMO power converter. The inductor current is assigned to each subconverter alternately. Each output only occupies its own phase in one switching cycle. These phases are expected to be isolated in order to prevent cross-regulation. When the inductor current is being diverted into one subconverter, the other one is separated from the control loop. In other words, only one switching subconverter is being regulated at a time instant.

Similar to the conventional single-output switching power converters, the SIMO power converters can also be categorized into different types based on the topologies. In this section, the three primary topologies for SIMO power converters—boost, buck, and noninverting buck–boost topologies—are introduced.

The power stage architecture and timing diagram of a SIMO boost switching converter with two outputs are illustrated in Figure 3.2. The two subconverters are regulated by a pair of complementary clocks Φ_{1} and Φ_{2}, with power delivered to each output from the supply *V _{IN}* in a time-multiplexed manner. The working principle can be described with reference to the timing diagram illustrated in Figure 3.2b. When the first subconverter is operating, Φ

3.1
$$\frac{d{i}_{L}}{dt}=\frac{{V}_{IN}}{L}.$$

Figure 3.2 (a) Power stage architecture and (b) timing diagram of single-inductor multiple-output boost converter.

During *D*_{21}*T*, the switch *S _{X}* is off and

3.2
$$\frac{d{i}_{L}}{dt}=\frac{{V}_{IN}-{V}_{O1}}{L}.$$

As the output voltage of a boost converter is greater than the supply voltage, the rate of the inductor current change is negative. As illustrated in Figure 3.2b, the inductor current decreases and delivers the required charge to the output. When it goes to zero, the converter enters *D*_{31}*T* and the switch *S*_{1} is turned off. The inductor current stays at zero until the phase Φ_{2} begins. Hence, the duty ratios *D*_{11}, *D*_{21}, and *D*_{31} satisfy the requirements shown as follows:

3.3
$${D}_{11}+{D}_{21}\le \frac{1}{2},$$

3.4
$${D}_{11}+{D}_{21}+{D}_{31}=1.$$

During Φ_{2} = 1, the inductor current is multiplexed into the output *V*_{O2} and similar switching actions repeat for the subconverter 2. With this method, the two outputs are regulated in a time-multiplexing manner by sharing the inductor *L* and the power switch *S _{X}*. Compared with two traditional switching boost converters, the number of off-chip magnetic component and power switches is both reduced. Obviously, with the increase of the number of subconverters, this cost reduction effect will become more significant.

Another primary type of SIMO power converters are constructed with buck topology. Figure 3.3a shows the power stage architecture of a SIMO buck power converter with two outputs. The power stage consists of one inductor *L*; four power switches *S _{P}*,

3.5
$$\frac{d{i}_{L}}{dt}=\frac{{V}_{IN}-{V}_{Oi}}{L},$$

3.6
$$\frac{d{i}_{L}}{dt}=-\frac{{V}_{Oi}}{L},$$

where *i* equals 1 or 2. Compared with two traditional buck converters, the number of inductors being used is halved. Although the number of power switches is not reduced, the cost effectiveness can still be observed when more subconverters are incorporated.

The third type of topology for SIMO power converters is noninverting buck–boost topology, which achieves both step-up and step-down voltage conversions. As shown in Figure 3.4a, the two subconverters share the inductor *L* and power switches *S _{P}*,

Figure 3.3 (a) Power stage architecture and (b) timing diagram of single-inductor multiple-output buck converter.

In addition to these three topologies, there are also other topologies that can be used in SIMO power converters. For example, inverting buck–boost topology allows the generation of negative output voltages. When combined with the aforementioned topologies, both positive and negative output voltages can be implemented. As a result, it leads to SIMO converters with bipolar power outputs (Ki and Ma 2001, Ma et al. 2001b).

Figure 3.4 (a) Power stage architecture and (b) timing diagram of single-inductor multiple-output noninverting buck–boost converter.

Historically, based on the inductor current, the operation mode for SIMO power converters can be categorized into two types: DCM (Ki and Ma 2001, Ma et al. 2001a, 2003b, Sze et al. 2008) and CCM (Belloni et al. 2008, Goder and Santo 1997, Li 2000, May et al. 2001). This section addresses both in due course, using a single-inductor dual-output (SIDO) boost topology as an example.

Figure 3.5 (a) Power stage architecture and (b) inductor current waveform of a single-inductor multiple-output boost converter operating in discontinuous conduction mode.

The typical inductor current waveform in DCM operation is shown in Figure 3.5. At the beginning of each phase, the inductor is charged. The charge process ends when *D*_{1i}*T* expires, followed by a discharge period. Instead of occupying the rest of the phase, the discharge period, *D*_{2i}*T*, ends once the inductor current drops to zero. After it, the inductor current stays at zero until the next phase is enabled. Since each subconverter only operates within its own phase, no two adjacent phases are overlapped, thereby eliminating the potential cross-regulation effect.

While the DCM operation can effectively suppress cross-regulation, it has certain drawbacks at heavy load conditions. With the same input/output voltages and load current, in order to deliver the same amount of charge with the same switching frequency, the peak inductor current value in DCM operation is usually much higher than in CCM. Hence, under heavy load conditions, DCM operation leads to large voltage/current ripples and switching noise.

Alternatively, another operation mode for SIMO power converters is CCM. As shown in Figure 3.6, the inductor is charged from the beginning of each phase. This charge process continues until the time period *D*_{1i}*T* expires, where *i* equals 1 or 2. Then, the discharge period *D*_{2i}*T* is enabled until the discharge phase ends. The inductor current charge and discharge actions are repeated in each phase, thereby delivering the desired power from input to the corresponding output. Since the next phase starts immediately after the current phase expires, the inductor current is kept continuous during the phase transition periods. Such type of operation scheme is thus called CCM.

Figure 3.6 Inductor current waveform of continuous conduction mode operation.

Due to the continuous conduction property, the inductor current is always maintained above zero. As a result, compared to the DCM operation, the CCM operation facilitates lower inductor current ripples, which in turn reduces output voltage ripples. Moreover, since the inductor current never goes to zero in CCM, the potential negative/reverse inductor current, which may occur in DCM operations, is avoided, thereby improving the power efficiency. From the circuit design perspective, the zero current detector and active diodes can be obviated. The circuit complexity and design challenge are both reduced.

However, CCM operation also incurs some drawbacks. Due to the continuous conduction property, the inductor current at the end of each phase is uncertain. As a result, the initial value of the inductor current to the second subconverter is dependent to the end value of the first one. If a sudden load change occurs in one phase, it will inevitably affect the subsequent phases, causing severe cross-regulation problems (Ma et al. 2003b).

In order to receive the benefits from both CCM and DCM operation schemes, the PCCM was proposed for SIMO power converters (Ma et al. 2002, 2003a). In the PCCM mode, as depicted in Figure 3.7 and similar to a CCM one, the inductor current of a SIMO converter always stays greater than a predetermined DC value *I _{dc}*, thus reducing the inductor current ripples. This is achieved by shorting the inductor with the aid of a freewheel switch

Figure 3.7 (a) Power stage architecture and (b) inductor current waveform of a single-inductor dual-output boost converter operating in pseudo-continuous conduction mode.

Despite the aforementioned advantages of PCCM operation, there remain some drawbacks. To avoid cross-regulation, the freewheel switching current level *I _{dc}* has to be chosen to satisfy the largest load current among all the outputs. If the value of

Figure 3.8 IL during pseudo-continuous conduction mode operation in unbalanced load condition.

To resolve the problems of traditional PCCM, adaptive PCCM operation schemes are developed (Zhang and Ma 2010, 2011, 2012b, Zheng et al. 2010). By adaptively adjusting the freewheel switching durations and the freewheel current level *I _{dc}*, conduction power loss can be significantly reduced. Moreover, by switching

Figure 3.9a models a freewheel switching loop. The resistance of the freewheel switch, *R _{ON}*, and the DCR of the inductor,

3.7
$${I}_{L}(t)=\{\begin{array}{cc}\hfill {I}_{dc}\cdot {e}^{\frac{-{R}_{EQ}}{L}[t-({D}_{11}+{D}_{21})\cdot {T}_{1}}]& ({D}_{11}+{D}_{21})\cdot T\le t\le \frac{T}{2},\hfill \\ \hfill {I}_{dc}\cdot {e}^{\frac{-{R}_{EQ}}{L}\left[t-\left(\frac{1}{2}+{D}_{12}+{D}_{22}\right)\cdot T\right]}& \left(\frac{1}{2}+{D}_{11}+{D}_{21}\right)\cdot T\le t\le T\hfill \end{array}.$$

Consequently, the conduction power loss by *S _{fw}* is derived as

3.8
$${P}_{C}={\displaystyle \sum _{i=1}^{n}\frac{{I}_{dc}^{2}L}{2T}}\left(1-{e}^{\frac{2{R}_{EQ}}{L}\cdot {D}_{fwi}T}\right),$$

which reveals that the loss is highly related to *I _{dc}* and the freewheel switching period.

Figure 3.9 (a) Circuit model and (b) the inductor current waveform of the freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

In addition to the conduction loss, a freewheel switch induces two types of switching losses: the *V*–*I* overlap power loss and the gate-drive power loss. The cause of *V*–*I* overlap power loss is illustrated in Figure 3.10b. Due to the parasitic capacitors (*C _{GD}* and

Figure 3.10 (a) Circuit model and (b) key waveforms for switching power loss. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

The process ends when *V _{gate}* becomes zero at

3.9
$${E}_{on}=\frac{1}{2}({V}_{\mathrm{max}}-{V}_{IN})\cdot {I}_{dc}\cdot ({t}_{IR}+{t}_{VF}),$$

where *t _{IR}* and

3.10
$${E}_{off}=\frac{1}{2}({V}_{\mathrm{max}}-{V}_{IN})\cdot {I}_{dc}\cdot ({t}_{VR}+{t}_{IF}),$$

where *t _{VR}* and

3.11
$${P}_{VI}=\frac{1}{2}({V}_{\text{max}}-{V}_{IN})\cdot {I}_{dc}\cdot ({t}_{IR}+{t}_{VF}+{t}_{VR}+{t}_{IF})\cdot n\cdot {f}_{sw},$$

where *f _{sw}* is the switching frequency of the converter.

Another major switching power loss is the gate-drive power loss. This involves the charge/discharge processes on gate capacitors *C _{GD}* and

3.12
$${P}_{DRV}=({C}_{GD}\cdot {V}_{\mathrm{max}}^{2}={G}_{GS}\cdot {V}_{IN}^{2})\cdot n\cdot {f}_{sw}.$$

The total switching power loss of *S _{fw}*, thus, can be denoted as

3.13
$${P}_{SW}=\left[\frac{1}{2}({V}_{\mathrm{max}}-{V}_{IN})\cdot {I}_{dc}\cdot ({t}_{IR}+{t}_{VF}+{t}_{VR}+{t}_{IF})+({C}_{GD}\cdot {V}_{\mathrm{max}}^{2}+{C}_{GS}\cdot {V}_{IN}^{2})\right]\cdot n\cdot {f}_{sw}.$$

In conclusion, to achieve high efficiency in a SIMO converter operating in PCCM, the conduction and switching losses of the freewheel switch should be jointly minimized. These power losses are highly related to switching frequency of *S _{fw}*, freewheel switching current

To identify the optimal operation point, Figure 3.11 illustrates the inductor current *I _{L}* in different operation conditions. The proposed adaptive PCCM operation scheme aims to provide a universal method to maintain this optimization in different load conditions. It should be noted that in any case each freewheel switching period should not be too short in order to prevent the converter from entering CCM. Neither should it be too long to cause large conduction loss. This is easy to achieve in balanced load conditions such as in Figure 3.11a. However, in unbalanced load conditions as in Figure 3.11b, due to the fixed phase durations, the freewheel switching period for the light-load output (

Figure 3.11 Inductor current waveform in pseudo-continuous conduction mode with (a) balanced loads, (b) unbalanced loads, (c) lowered Idc, and (d) adaptively controlled phase durations and Idc. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

The adaptive PCCM operation scheme with distributed freewheel switching is illustrated in Figure 3.12. Initially, the two phases of a SIDO converter are set equally as *T*/2, with a preset freewheel switching current at *I _{dc}.* The duration of Σ

3.14
$$\sum {D}_{Ki}T={\displaystyle \sum _{k=1}^{2}{D}_{ki}T=({D}_{1i}+{D}_{2i})T.}$$

Figure 3.12 Adaptive pseudo-continuous conduction mode operation scheme with distributed freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

If the load current *I*_{LOAD1} of subconverter 1 suddenly increases (case (ii) in Figure 3.12), Σ*D*_{k1}T is extended by Δ*DT* to accommodate this load power increase, resulting in a decreased freewheel switching duration in Φ_{1}. The two freewheel switching periods are then equalized by adjusting the phase durations Φ_{1} and Φ_{2} in case (iii). Since this average freewheel switching duration is smaller than the optimal value, the *I _{dc}* level is gradually increased to prolong the freewheel switching periods. Thus, the phase adjustment and

3.15
$$\frac{{D}_{1i}}{{D}_{2i}}=\frac{{m}_{2i}}{{m}_{1i}},$$

where *m*_{1i} and *m*_{2i} are the slopes of *I _{L}* and can be defined as

3.16
$$\{\begin{array}{c}\hfill {m}_{1i}=\frac{{V}_{IN}}{L}\\ \hfill {m}_{2i}=\frac{{V}_{Oi}-{V}_{IN}}{L}\end{array}.$$

On the other hand, the total charge delivered to the *i*th output per switching cycle is calculated as

3.17
$${Q}_{i}={I}_{dc}\cdot {D}_{2i}T+\frac{{m}_{2i}}{2}\cdot {({D}_{2i}T)}^{2}.$$

In steady state, it equals to the total charge demanded by the load *I _{LOADi}*, which gives

3.18
$${Q}_{i}={I}_{LOADI}\cdot T.$$

Figure 3.13 IL with distributed freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

Substituting Equation 3.18 into Equation 3.17 gives

3.19
$${D}_{2i}T=\frac{\sqrt{{I}_{dc}^{2}+2{m}_{2i}T\cdot {I}_{LOADi}-{I}_{dc}}}{{m}_{2i}}.$$

Based on Equations 3.15 and 3.19, the adaptive adjustment on each phase duration follows

3.20
$${\Phi}_{i}=\frac{{m}_{1i}+{m}_{2i}}{{m}_{1i}\cdot {m}_{2i}}\left(\sqrt{{I}_{dc}^{2}+2{m}_{2i}T\cdot {I}_{LOADi}}-{I}_{dc}\right)+{D}_{fw}T.$$

Alternatively, unified freewheel switching can be implemented, where the freewheel switching only occurs once per switching cycle. According to Equation 3.13, the switching power loss of *S _{fw}* can be reduced (Zhang and Ma 2011). This saving can be significant when the number of the subconverters in a SIMO converter is large.

Figure 3.14 Adaptive pseudo-continuous conduction mode operation scheme with unified freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

Here, a SIDO converter is employed as an example. If *I*_{LOAD1} suddenly increases from the steady state in case (i) in Figure 3.14, the corresponding phase duration of Φ_{1} is extended by Δ*D*_{1}*T* to allow more inductor current to be delivered to *V*_{O1}, thereby stabilizing *V*_{O1}. Because of using the same start and end levels of the *I _{dc}*, Φ

In addition, the freewheel switching current level *I _{dc}* also needs to be adjusted to maintain the optimal freewheel switching duration. In the proposed operation scheme, if the monitored freewheel switching duration is shorter than the desired value (cases (ii) and (iii) in Figure 3.14), the freewheel switching current will be gradually increased from

3.21
$${\Phi}_{i}=\frac{{m}_{1i}+{m}_{2i}}{{m}_{1i}\cdot {m}_{2i}}\left(\sqrt{{I}_{dc}^{2}+2{m}_{2i}T\cdot {I}_{LOADi}}-{I}_{dc}\right).$$

Figure 3.15 IL with unified freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

The proposed adaptive PCCM operations schemes are suitable for both digital and analog implementations. As digital design is usually portable to technology scaling and backed up by well-designed electronic design automation (EDA) tools, it always carries a great commercialization potential. Hence, a digital implementation is introduced first using the distributed freewheel switching scheme as major control algorithm. On the other hand, in many cases, analog approach can be very efficient in the aspects of silicon and power consumption. An analog implementation using unified freewheel switching scheme is, thus, discussed as well. In general, the proposed schemes are flexible to either digital or analog processing and can be virtually implemented in any fabrication processes.

Figure 3.16 shows the system block diagram of a SIDO boost converter, with the control scheme proposed in Section 3.6.2.1. The operation can be described with reference to Figure 3.17. Consider a SIMO converter has *n* subconverters. Initially, the phase period for each subconverter and freewheel switching *I _{dc}* levels are set equal (Φ

Figure 3.16 Block diagram of an adaptive pseudo-continuous conduction mode single-inductor dual-output boost converter with digital distributed freewheel switching. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

Such a freewheel switching duration *D _{fwi}T* (1 ≤

Figure 3.17 Implementation of the digital controller with timing diagram. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

3.22
$${\Phi}_{i}=({D}_{1i}+{D}_{2i}+{D}_{avg})T.$$

In practice, the *D _{avg}T* should not be too long in order to reduce conduction loss according to Equation 3.8. If it is longer than a predefined limit

The adaptive PCCM operation scheme with unified freewheel switching is demonstrated through an analog implementation. In addition to the error amplifiers *EA _{i}* to determine the peak inductor current for each subconverter, the analog controller includes an online analog charge meter to adaptively adjust

During the discharge period of *D*_{2i}*T* in subconverter *i* (*i* = 1 or 2), *C _{dc}* in Figure 3.18 is charged by a constant current

3.23
$${I}_{ch}\cdot ({D}_{21}T+{D}_{22}T)={I}_{dch}\cdot {D}_{fw}T.$$

*V _{dc}* keeps constant and an optimal freewheel switching duration can be achieved by setting an appropriate

3.24
$${I}_{ch}\cdot ({D}_{21}^{\text{'}}T+{D}_{22}^{\text{'}}T)>{T}_{dch}\cdot {D}_{fw}^{\text{'}}T.$$

Consequently, *V _{dc}* is increased to ${V}_{dc}^{\text{'}}$

3.25
$${I}_{ch}\cdot ({D}_{21}^{"}T+{D}_{22}^{"}T)<{I}_{dch}\cdot {D}_{fw}^{"\text{\'}}T,$$

leading to a lower *I _{dc}* level. On the other hand, when a load change occurs in the foregoing phase (Figure 3.19b),

Figure 3.18 Circuit detail of single-inductor dual-output converter with proposed analog controller. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

After the *V _{dc}* level is stabilized, the phase duration Φ

Figure 3.19 Vdc adjustment with load variation occurring in (a) the last phase and (b) the foregoing phase. (From Zhang, Y. and Ma, D., J. Analog Integr. Circuits Signal Process., 72(2), 419, August 2012b.)

In this section, two adaptive PCCM operation schemes with the respective distributed and unified freewheel switching schemes were discussed. Compared with conventional PCCM operations, the phase durations and *I _{dc}* level can be adaptively modulated, thereby maintaining optimal freewheel switching in various load conditions. As a result, power loss due to freewheel switching can be significantly reduced while retaining low cross-regulation effect. In addition, the two proposed operation schemes were implemented by both digital and analog methods. The advantages for each implementation method are also discussed respectively.

For the digital implementation, as most of the control circuits consist of the robust digital circuits, the system robustness across the process, voltage, and temperature (PVT) variations can be significantly improved. Moreover, with the development of modern VLSI techniques, digital circuits usually consume less silicon area compared with analog circuit counterparts.

On the other hand, by using the analog implementation method, the *I _{dc}* level and phase durations for adaptive PCCM operation can be accurately fine-tuned. The adjustment resolution is thus well improved, resulting in more accurate control scheme. Based on the specific application background, the digital and analog circuit implementation, as well as the distributed/unified freewheel switching, can also be combined in different ways to define the most appropriate adaptive PCCM operation scheme for SIMO converters.

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Ma D., W.-H. Ki, C.-Y. Tsui, and P. K. T. Mok, A 1.8V single-inductor dual-output switching converter for power reduction techniques, in IEEE Symposium on VLSI Circuits, Kyoto, Japan, June 14–16, 2001a, pp. 137–140.

Ma D., W.-H. Ki, C.-Y. Tsui, and P. K. T. Mok, Single-inductor multiple-output switching converters with bipolar outputs, in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Sydney, New South Wales, Australia, May 6–9, 2001b, pp. 301–304.

Ma D., W.-H. Ki, C.-Y. Tsui, and P. K. T. Mok, Single-inductor multiple-output switching converters with time-multiplexing control in discontinuous conduction mode, IEEE J. Solid State Circuits, 38(1), 89–100, 2003b.

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Sze N.-M., F. Su, Y.-H. Lam, W.-H. Ki, and C.-Y. Tsui, Integrated single-inductor dual-input dual-output boost converter for energy harvesting applications, in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Seattle, WA, May 18–21, 2008, pp. 2218–2221.

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Zhang Y., Single-inductor multiple-output power converters: Architectures, control techniques and applications, PhD dissertation, The University of Texas at Dallas, Richardson, TX, 2013.

Zhang Y., R. Bondade, D. Ma, and S. Abedinpour, An integrated SIDO boost power converter with adaptive freewheel switching technique, in Energy Conversion Congress and Exposition (ECCE), Atlanta, GA, September 12–16, 2010, pp. 3516–3522.

Zhang Y. and D. Ma, Digitally controlled integrated pseudo-CCM SIMO converter with adaptive freewheel current modulation, in IEEE Applied Power Electronics Conference and Exposition (APEC), Palm Springs, CA, February 21–25, 2010, pp. 284–288.

Zhang Y. and D. Ma, Integrated SIMO DC-DC converter with on-line charge meter for adaptive PCCM operation, in Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS), Rio de Janeiro, Brazil, May 15–18, 2011, pp. 245–248.

Zhang Y. and D. Ma, Input-self-biased transient-enhanced maximum voltage tracker for low-voltage energy-harvesting applications, IEEE Trans. Power Electron., 27(5), 2227–2230, 2012a.

Zhang Y. and D. Ma, Adaptive pseudo-continuous conduction mode operation schemes and circuit designs for single-inductor multiple-output switching converters, J. Analog Integr. Circuits Signal Process., 72(2), 419–432, August 2012b.

Zheng C. and D. Ma, Design of a monolithic automatic substrate/supply multiplexer for DVS-enabled adaptive power converters, IEEE Trans. Circuits Syst. II, Express Briefs, 58(6), 376–380, 2011.