1. Introduction
The use of high-performance, power-hungry mobile devices has increased recently, prompting the need for longer battery life [
1,
2]. Accordingly, power management integrated circuits (PMICs) for mobile devices are becoming important. PMICs consist of a linear regulator, a switched capacitor (SC) converter, and a switched inductor (SI) converter [
3,
4]. Although linear regulators offer the advantage of low output voltage ripple, they have low power efficiency [
5,
6,
7,
8]. In contrast, SC converters have high power density with better power efficiency than linear regulators, but they suffer from severe degradation of efficiency when the conversion ratio of the SC converter differs from a pre-defined value [
9,
10,
11,
12]. Furthermore, when the load current (
ILOAD) increases, which is referred to as a heavy load condition, SC converters require many large external capacitors. Therefore, neither linear regulators nor SC converters are good candidates for powering high performance loading blocks that require a large
ILOAD. On the other hand, a SI converter with an external inductor is an efficient solution in heavy load conditions [
13,
14,
15,
16]. Buck, boost, and buck-boost SI converters exist for generating lower, higher, and lower or higher output voltage (
VO), respectively, compared with the battery voltage (
VIN).
In the SI converter, there are two representative power losses, as shown in
Figure 1. One is the switching loss (
PSW) which is proportional to the switching frequency. When the switching frequency is fixed, the
PSW is a constant independent of the
ILOAD. The other is the conduction loss (
Pcond). Since the
Pcond is proportional to the square of the current, the
Pcond is dominant in heavy load conditions. Therefore, reducing
Pcond is important for improving power efficiency when
ILOAD is large.
However, due to a large inductor current (
iL), under heavy load conditions, these efficient SI converters also suffer from significant conduction loss (
PDCR) dissipated at a parasitic DC resistance (
RDCR) of a small inductor for size-limited mobile devices as shown in
Figure 2. This large
PDCR causes a severe thermal problem as well as low power efficiency in heavy load conditions.
PDCR is expressed as follows:
where
iL,RMS,
IL, and Δ
iL are the root-mean-square value, the DC value, and the ripple of the
iL, respectively. Since the small inductor for the miniaturized mobile device can have much larger
RDCR than the on-resistance of switches, reducing
PDCR can achieve a significant improvement in power efficiency. To minimize the
PDCR, reducing
iL,RMS is the only solution when a large
RDCR of the small inductor is used as shown in Equation (1). In particular, as the inductor with larger
RDCR than the on-resistance of the switch is adopted, the efficiency improvement due to low
iL,RMS is significantly increased.
There are some alternative topologies that can reduce
iL,RMS in a SI converter. For example,
Figure 3a shows a multi-level structure with an additional flying capacitor that reduces Δ
iL, thereby improving power efficiency in light or medium load conditions [
17,
18]. However, under heavy loads, since
IL is much larger than Δ
iL, the reduction of
PDCR is limited. Alternatively,
Figure 3b shows a multi-phase structure that can reduce
IL and can result in increased power efficiency compared with the multi-level structure in heavy load conditions. However, it requires an additional inductor that is larger and more expensive than other passive components [
19,
20,
21]. Furthermore, both the multi-level and the multi-phase structures require complex balancing circuits, as shown in
Figure 3.
To resolve these issues, this paper proposes and analyzes a new type of hybrid switched inductor capacitor (SIC) converter with energy transfer media (ETM) using an additional flying capacitor. The topologies with the ETM provide improved efficiency by lowering IL owing to an additional current path in heavy load conditions.
The topologies with the proposed ETM are introduced in
Section 2. In
Section 3 and
Section 4, the operation principle and a detailed conduction loss analysis of both the buck and buck-boost topologies are provided. In
Section 5, different examples of extension to other topologies are explained and discussed. The simulation results for verification are presented in
Section 6. Finally, a brief concluding summary is given in
Section 7.
2. Energy Transfer Media
A hybrid SIC converter that possesses the advantages of both a SC converter and a SI converter is an attractive solution [
22,
23,
24,
25,
26,
27,
28,
29,
30]. However, it is complicated to design because of the many complex combinations of power switches and flying capacitors. Also, various factors such as conversion ratios, balancing circuits, and power loss should be considered. To make it easy to design, and to reduce
PDCR at the same time, this paper proposes an ETM that can be easily implemented with all types of non-isolated converters, such as buck, boost, and buck-boost topologies, with high efficiency under heavy load conditions. An ETM has been used previously to reduce only Δ
iL [
29,
30]. However, similar to a multi-level converter, this structure is not effective at improving power efficiency under heavy load conditions. Therefore, we propose an ETM that uses an additional flying capacitor to obtain high efficiency in heavy load conditions, as shown in
Figure 4.
The ETM uses one external flying capacitor (
CF) and three power switches (S
M1–S
M3). This approach offers the advantage of inserting the capacitor current path into the output current path (
C-path) as well as the inductor current path (
L-path). This ETM with dual current paths can be applied to conventional non-isolated topologies by simply cascading the ETM, as shown in
Figure 5.
Figure 5a is a conceptual structure showing that the ETM can be applied to conventional converter topologies.
Figure 5b–d show examples of applying the ETM to buck, boost, and buck-boost converters, respectively. This paper analyzes buck type and buck-boost type topologies with ETMs as examples and discusses possible extensions to other topologies.
3. Buck Converter with Energy Transfer Media
Figure 5b shows a buck converter with ETM (BKETM), which is composed of power switches S
1–S
2 and S
M1–S
M3, one inductor (
L), one flying capacitor (
CF), and one output capacitor (
CO). The BKETM uses two operating modes (Φ
1, Φ
2), as shown in
Figure 6a. The operation waveforms of the BKETM are shown in
Figure 6b.
In Φ
1, S
1 and S
M2 are turned on, and S
2, S
M1, and S
M3 are turned off. At this time,
iL is built up with a slope of 2(
VIN −
VO)/
L and is delivered to the output. In Φ
2, S
2, S
M1, and S
M3 are turned on, and S
1 and S
M2 are turned off. While
iL is de-energized with a slope of −
VO/
L, it is also delivered to the output. In the meantime, the capacitor current
iC of
CF flows to the output, while the voltage of
CF is charged to
VIN −
VO. To derive a conversion ratio (
MBK), applying the voltage sec balance to the inductor with duty cycle
D is expressed as follows:
Simplifying Equation (2),
MBK is given by:
The MBK of the BKETM from Equation (3) has a value between 0 and 1 as D varies from 0 to 1, which is the same as the range of a conventional buck converter (CBK). Therefore, in spite of the SIC converter, the BKETM behaves like a CBK without the limit of the conversion ratio.
To obtain the average value of the
C-path current (
IC,Φ2) delivered to the output in Φ
2, we also apply charge balance to
CF as shown below:
Simplifying Equation (4), IC,Φ2 is given by
Applying the charge balance to the output capacitor CO,
Substituting Equation (5) into Equation (6),
IL can be expressed with
ILOAD as shown below:
For the CBK,
IL is always the same as
ILOAD [
3,
4,
13,
14,
15,
16]. In contrast, for the proposed BKETM,
IL is
ILOAD divided by (1 +
D). As
MBK increases,
IL decreases. Therefore,
IL always has a smaller value than
ILOAD due to the two current paths (
L-path and
C-path). As
IL decreases,
PDCR also is reduced compared to that of the CBK. To compare the total conduction loss with that of the CBK, we assume that since the parasitic resistance (
RESR) of the flying capacitors is typically much smaller than other resistances, the loss of
RESR can be ignored for simplicity. Also, the on-resistance of each switch is assumed to be the same as
RON. Thus, the total conduction loss (
Pcond,CBK) of the CBK is expressed as follows:
On the other hand, the total conduction loss (
Pcond,BKETM) of the BKETM is as follows:
For the relative comparison with CBK, the ratio between
Pcond,CBK and
Pcond,BKETM is expressed as:
Figure 7 depicts the value calculated by Equation (13) versus the conversion ratio
MBK for different
RDCR. It shows that
Pcond,BKETM is lower than
Pcond,CBK across a wide range of
MBK values. As described by Equation (7), the total conduction loss decreases because
IL is reduced as
MBK increases. Also, the larger the
RDCR, the lower the
Pcond,BKETM is compared with
Pcond,CBK. Therefore, BKETM is a useful topology for step-down when a small inductor with a large
RDCR is used in heavy load conditions.
4. Buck-Boost Converter with Energy Transfer Media
Since the boost converter with the ETM shown in
Figure 5c has been previously described in detail in [
27], this paper focuses on the buck-boost converter with ETM (BBETM) shown in
Figure 5d. It is composed of power switches S
1–S
4, S
M1–S
M3, one inductor (
L), one flying capacitor (
CF), and one output capacitor (
CO). The BBETM also uses two operating modes (Φ
1, Φ
2), as shown in
Figure 8a. Its operation waveforms are shown in
Figure 8b.
In Φ1, S1 and S3 are turned on while iL increases with a slope of VIN/L and is delivered to the output. At the same time, SM1 and SM3 turn on, and iC flows to the output through the C-path, while the voltage of CF is charged to VIN − VO. With a conventional buck-boost (CBB) converter, current cannot be delivered to the output while iL is building up. The ability of the BBETM to transfer the energy to the output during iL build-up is one of the main differences between the BBETM and a CBB converter. Owing to this operation, the output delivery current (iD) in the BBETM is continuous, resulting in a small output voltage ripple (∆VO). In Φ2, S2, SM2, and SM3 turn on, and iL is delivered to the output.
For the BBETM conversion ratio (
MBB), applying the voltage sec balance to the inductor based on the operation is expressed as follows:
Simplifying Equation (14),
MBB is given by:
MBB of the BBETM from Equation (15) has a value between 0.5 and infinity as D varies from 0 to 1. This means that the BBETM can operate for step-up and step-down output voltages. Since the conversion ratio is limited to less than 0.5, this approach is not appropriate for applications with a low conversion ratio. However, it offers several advantages compared with a CBB converter.
First, similar to the buck type converter, the BBETM
IL is reduced compared with that of a CBB converter. To analyze this, the average value of the
C-path current (
IC,Φ1) in Φ
1 can be obtained by applying charge balance to the
CF as shown below:
Simplifying Equation (16), IC,Φ1 is given by
Applying the charge balance to CO,
Substituting Equation (17) into Equation (18),
IL can be expressed with load current (
ILOAD) as shown below:
Due to the two current paths in the ETM, the BBETM
IL is as low as
MBBILOAD, while the CBB
IL is (1 +
MBB)
ILOAD [
4]. Therefore, the BBETM
PDCR can be reduced. To compare the total conduction loss with that of the CBB, the on-resistance of each switch is assumed to be the same as
RON, and the total conduction loss (
Pcond,CBB) of the CBB is expressed as follows:
In contrast, the total conduction loss (Pcond,BBETM) of the BBETM is expressed as
For the relative comparison with the CBB, the ratio between Pcond,CBB and Pcond,BBETM for the BBETM is expressed as
Figure 9 depicts the values of Equation (24) versus the conversion ratio
MBB for different
RDCR values, showing that the
Pcond,BBETM is lower than the
Pcond,CBB for a wide range of
MBB values. This finding demonstrates that the BBETM is more efficient than CBB due to the dual current paths. Also, it shows that the larger the
RDCR, the lower
Pcond,BBETM is, compared with
Pcond,CBB. Therefore, the BBETM is useful for step-up and step-down applications when a small inductor with a large
RDCR is used in heavy load conditions.
7. Conclusions
In this paper, an ETM was proposed to make a promising hybrid switched inductor capacitor converter easier to design for heavy load conditions. New topologies with ETM, which generate dual current paths, were analyzed and compared with conventional topologies that have a single current path. Owing to the dual current paths (L-path and C-path), all of the topologies with the ETM shared the common advantage of reduced inductor current. Since it significantly decreases conduction loss dissipated at a considerable parasitic DC resistance of the inductor, the heating issue can be resolved at the same time as the power efficiency is improved, which was discussed with buck and buck-boost converters with ETMs as examples. Moreover, the buck-boost converter with ETM has continuous output delivery current, resulting in much smaller output voltage ripple than that of a conventional buck-boost converter. Also, a multi-phase converter and single-inductor multiple-output converter with several ETMs were proposed and simulated. The multi-phase converter with ETM offered the additional advantage of separating the switching frequency between the input frequency and the output frequency to further reduce the output ripple voltage. Additionally, the SIMO converter with ETM achieved a small output voltage ripple, similar to that of a buck-boost converter with ETM, due to the continuous output delivery current. In summary, the ETM can be implemented easily by combining with conventional topologies, and it has several merits such as reduced inductor current, small output voltage ripple, and independent frequency control. The proposed ETM can be applied to various non-isolated topologies as a promising solution for use in heavy load conditions with a small inductor.