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1304 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014
A FVF LDO Regulator With Dual-Summed
Miller Frequency Compensation for Wide
Load Capacitance Range Applications
Xiao Liang Tan, Student Member, IEEE, Kuan Chuang Koay, Member, IEEE,
Sau Siong Chong, Student Member, IEEE, and P. K. Chan, Senior Member, IEEE
Abstract—This paper presents a proposed Flipped Voltage Fol-
lower (FVF) based output capacitorless low-dropout (OCL-LDO)
regulator using Dual-Summed Miller Frequency Compensation
(DSMFC) technique. Validated by UMC 65-nm CMOS process,
the simulation results have shown that the proposed LDO regu-
lator can be stabilized by a total compensation capacitance
of 8 pF for a load capacitance ranging from 10 pF to 10
nF. It consumes 23.7 A quiescent current with a 1.2 V supply
voltage. With a dropout voltage of 200 mV, the LDO regulator can
support a maximum 50 mA load current. It can settle in less than
1.7 s with a 1% accuracy for the whole range. The proposed
LDO regulator is comparable to other reported works in terms of
figure-of-merit (FOM). Most significantly, it can drive the widest
range of and achieve the highest ratio with
respect to the counterparts.
Index Terms—DSMFC, FVF, LDO regulator, Miller compensa-
tion, wide load capacitance range.
I. INTRODUCTION
VOLTAGE regulators have been widely used to supply
various function blocks in battery powered devices.
A LDO regulator featuring a simple structure with fast re-
sponse and low noise characteristics is very popular in power
management IC design [1]. However, the LDO regulators
relying on a F level off-chip capacitor to maintain stable
operation will limit their fully integration ability for modern
System-on-Chips (SoC) [2]–[6]. As such, the output capacitor-
less LDO (OCL-LDO) regulators have received much attention
for fully on-chip applications.
OCL-LDO regulators have been recently reported in
[7]–[17]. Among these designs, the Flipped Voltage Follower
(FVF) based LDO regulators [8], [11]–[14] are attractive in
terms of simplicity, stability and fast transient responses. In
[8], the FVF structure is implemented as drivers for the output.
It gives a very fast response with a recovering time of 0.54
ns. However, the quiescent current in this LDO regulator is 6
mA. In addition, the LDO regulator is stabilized by a 600 pF
on-chip decoupling capacitor. This results in large power and
silicon area consumptions. In [11], a Single-Transistor-Control
LDO regulator based on FVF structure is proposed. It has been
proven that the LDO regulator is stable without an off-chip
capacitor. In [12], a direct voltage spike detection scheme
Manuscript received August 23, 2013; revised December 03, 2013, January
06, 2014; accepted January 12, 2014. Date of publication March 25, 2014; date
of current version April 24, 2014.
The authors are with the School of Electrical and Electronic Engi-
neering, Nanyang Technological University, 639798 Singapore (e-mail:
tanx0074@e.ntu.edu.sg; koay0013@e.ntu.edu.sg; chon0157@e.ntu.edu.sg;
epkchan@ntu.edu.sg).
Digital Object Identifier 10.1109/TCSI.2014.2309902
is adopted in the FVF structure to momentarily increase the
quiescent current during load current switching. Hence, the
transient response of the regulator is improved. However,
both topologies [11], [12] suffer from low loop gain due to its
simple folded structure [13]. As a result, an additional gain
stage has been added in the feedback loop to boost the loop
gain in [13] for improvement of both load and line regulations.
Due to the additional gain stage, a Miller compensation capac-
itor is required for circuit stability purpose at low quiescent
power.
However, the conventional Miller compensation typically
supports small load capacitors. The LDO regulator in [13]
is only able to drive a maximum 50 pF load capacitor with
a minimum 3 mA load current at V. To further
increase the load capacitance driving capability, either the
compensation capacitor or the minimum load current must
be increased to achieve a stable operation. This restricts its
application at the circuits with load capacitance starting from
few ten pF to few hundred pF. However, for some digital circuit
applications [18] that require the LDO regulator to drive the
on-chip capacitance of 3 nF or more. This creates a design
challenge on the FVF OCL-LDO regulators using standard
Miller compensation technique in the context of low quiescent
power. In [14], based on a FVF output driving stage, an active
compensation scheme is implemented which can drive a load
capacitance up to 1 nF. However, several poles and zeros
are within the unity gain bandwidth frequency , thus
leading to complicated pole-zero tracking. Furthermore, the
LDO regulator may be susceptible to process and temperature
variations since the stability is very much dependent on the
poles’ and zeros’ locations.
In view of that, a Dual-Summed Miller Frequency Compen-
sation (DSMFC) technique is implemented in a FVF based LDO
regulator topology [19]. The LDO regulator has been demon-
strated in a very wide load capacitance range. Not only does
the added Miller compensation stage form the dominant pole
together with the conventional Miller capacitor, it also shifts
the non-dominant pole(s) to a higher frequency. In the reported
dual-summed Miller compensated LDO regulator [19], a low
output impedance power transistor driver [20] is realized as
the second non-inverting gain stage to improve the loop gain.
Turning to the DSMFC network, the inverting driving transistor
for the second Miller amplifier is biased by a high impedance
current source with an open loop topology. To ensure a reliable
dc operating region of the additional Miller stage, the power
transistor has to be sized larger at the expense of larger silicon
area so as to reduce the voltage swing at the Miller node.
1549-8328 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
TAN et al.: FVF LDO REGULATOR 1305
Based on the scheme in [19], an improved FVF based LDO
regulator using the DSMFC technique is proposed in this paper.
In Section II, the frequency response of the proposed LDO reg-
ulator is analyzed at different load capacitor and current
conditions. Besides, the detailed analysis for phase margin
(PM), damping factor and gain margin (GM) is presented.
Effect of PM and GM with respect to the load capacitors is also
investigated. The simulated results and discussions of key pa-
rameters are given in Section III. In Section IV, a comparison
with other reported OCL-LDO regulators is given. Conclusions
are drawn in Section V.
II. PROPOSED FVF LDO REGULATOR WITH DSMFC
The schematic of the proposed LDO regulator is shown in
Fig. 1(a). The main loop contains a folded FVF gain stage,
a non-inverting gain stage and a power MOS transistor. The
LDO regulator is compensated using a DSMFC block (dash en-
closed area). It contains a standard Miller compensation capac-
itor and an additional Miller compensation stage (
and ). Different from [19], the DSMFC in the proposed
LDO regulator is biased using a passive resistor . This re-
alization permits a reliable DC operating point to be achieved in
absence of high impedance node. As such, the power transistor
can be sized smaller with respect to that in [19].
With the DSMFC technique, the dominant pole is formed
through the summing Miller effect which offers better stability.
Besides, when comparing with Single Miller Compensation
(SMC) counterpart, the DSMFC also shifts the non-dominant
pole(s) to a higher frequency, especially under the following
three conditions: (i) large with low , (ii) large with
moderate , and (iii) small with low . Since the DSMFC
technique addresses the conservative stability issue for both
small and large , the proposed LDO regulator can achieve
driving capability for a wide load capacitance range across the
whole load current range.
The control voltage for is generated through a symmet-
rical OTA amplifier which is shown in Fig. 1(b). Since the max-
imum load capacitor is in an nF range, to reduce the settling
time from overshoot, an overshoot reduction branch (
and ) is implemented to increase the sinking current momen-
tarily.
A. Stability Analysis
To analyze the stability of the proposed LDO regulator, the
small-signal model depicted in Fig. 1(c) is investigated. It is ob-
tained by breaking the feedback loop at the output branch as
shown in Fig. 1(a). It is noted that denotes the transcon-
ductance whereas and are the equivalent output resis-
tance and lumped output parasitic capacitance of the i-th gain
stage, respectively. and are the 1st and 2nd Miller
compensation capacitors. is the effective output resistance
which includes the output resistance of power transistor and the
loading resistance . is the load capacitance which has a
value ranging from 10 pF to 10 nF.
Fig. 1. (a) Schematic of the proposed FVF based LDO regulator with DSMFC
indicate the loop breaking point). (b) Control voltage
generator. (c) Small-signal model of the proposed FVF LDO regulator.
(1)
The transfer function is derived with the following assump-
tions: (i) and ; (ii)
and . It is obtained and expressed by (1), in
which is the dc loop gain and are the three zeros.
Based on the design parameters, locate at high frequencies,
thus they can be ignored in the following analysis. In addition,
1306 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014
TABLE I
POLES AND ZERO LOCATIONS FOR SIX CASES
Fig. 2. Loop gain of the proposed FVF LDO regulator with poles and zero
locations for (a) large , (b) small .
the loop gain transfer function has two real poles - .
Therefore, it can be simplified in the form as
-
(2)
Since the load capacitor varies from 10 pF to 10 nF with the
load current switching between 0 and 50 mA, the stability of the
OCL-LDO regulator is discussed at six different cases that deal
with the load capacitor corners at different load currents. They
are given as follows:(1) Large with low , (2) Large
with moderate , (3) Large with high (4) Small with
low , (5) Small with moderate , (6) Small with high
.
The poles and zeros locations for six cases are summarized
in Table I and their relative locations are shown in Fig. 2(a) and
Fig. 3. Simulated open-loop gain and phase responses at different for (a)
nF and (b) pF.
(b) for large and small , respectively. The loop gain transfer
function shows that the first case denotes the system with four
real poles whereas the other five cases denote the system having
two real poles plus one pair of complex poles. Each case is ex-
plained as follows:
Case 1: Large With Low : In this case, both power tran-
sistor’s output resistance and the equivalent load circuit
resistance are high. As a result, . Due to a
TAN et al.: FVF LDO REGULATOR 1307
Fig. 4. Simulated (a) Phase Margin, (b) Gain Margin and (c) Unity Gain Frequency as a function of at different using DSMFC.
Fig. 5. Simulated (a) Phase Margin, (b) Gain Margin and (c) Unity Gain Frequency as a function of at different using SMC.
small bias current in is still fairly large (around 17 k
). It forms a low frequency dominant pole with the large load
capacitor . The second pole is located at a lower frequency
than that of the zero, contributing a partial cancellation effect.
In addition, due to the DSMFC, the third pole is pushed
to a higher frequency by an extra frequency quantifying term,
. As for , the gain of the last stage is small due to
small . Hence, the Miller effect arising from the of the
power transistor is negligible, which leads to a small . There-
fore, is also located at a high frequency.
Case 2: Large With Moderate : The loop gain is the
highest in this range because of large and moderate .
The stability of the LDO regulator is at its worst condition. The
dominant pole of the system is formed by the Miller compen-
sation capacitor . More importantly, similar to Case 1, an
additional term, , is generated for defining
complex poles’ frequency in the DSMFC scheme. As a result,
the complex poles are shifted to a higher frequency which im-
proves both the PM and GM. The stability of the regulator is
achieved.
Case 3: Large With High : In this case, is ap-
proaching to its minimum value because of small and
small . This results in a small gain for the power transistor
gain stage. The two Miller compensation effects are close to
each other and form the dominant pole together. The second
pole and zero ( is around 2 times of ) exhibit a good can-
cellation. The complex poles are located at higher frequency due
to large .
Case 4: Small With Low : Under this condition,
no longer forms a low frequency pole. The dominant pole is gov-
erned by two Miller compensation capacitors ( and ).
A good pole and zero cancellation is also achieved in this case.
Similar to Case 2, the complex poles are shifted to a higher fre-
quency by the additional term generated by the DSMFC. The
stability of the LDO regulator is ensured.
Case 5: Small With Moderate : Similar to Case 2, the
dominant pole is created by the standard Miller capacitor .
Due to the small , the complex poles are located at high fre-
quency which will not affect the stability of the LDO regulator
in this case.
Case 6: Small With High : Similar to Case 5, it is ap-
parent that the stability of the LDO regulator at this condition
can easily be achieved due to large and small .
Fig. 3(a) and (b) depict the open loop gain and phase re-
sponses at mA, 5 mA, and 50 mA for
nF and pF, respectively. It can be seen that the sim-
ulated results match with the analysis. It also demonstrates that
the proposed FVF LDO regulator can achieve stability for both
large and small corners at different load currents. The PM,
GM and unity gain frequency across the whole load capacitor
range with different load currents are shown in Fig. 4. It can
be observed that the LDO regulator with DSMFC technique
achieves a minimum PM of 50 and a minimum GM of 8 dB.
For benchmark comparison, the SMC for this LDO regulator
topology without using the second Miller amplifier is applied.
The total compensation capacitance in the proposed LDO reg-
ulator and the SMC LDO regulator are sized to be the same (8
pF). Fig. 5 depicts the PM, GM and unity gain frequency simu-
lation results. As can be seen from Fig. 5(a), based on a 50 PM,
the SMC regulator is stable to support a load capacitor ranging
from 10 pF to 250 pF. Moreover, when comparing the unity
gain frequency simulation results in Figs. 4(c) and 5(c), the pro-
posed LDO regulator using the DSMFC technique provides a
larger unity gain frequency with respect to that of SMC LDO
regulator. This suggests that the speed will be faster in the pro-
posed LDO regulator.
Based on the above analysis and simulation results, the pro-
posed FVF LDO regulator using DSMFC technique is able to
maintain stable operation over the whole load capacitance range
of 10 pF–10 nF under the load current varying from 0 to 50
1308 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014
mA. Particularly, the DSMFC shows a significant improvement
under three conditions: (i) large with low , (ii) large
with moderate , and (iii) small with low . This extends
the load capacitance range because it addresses the conservative
stability issue for both small and large .
B. Phase Margin Under Variations
As can be seen in Fig. 4(a), at small condition, the PM
plot shows a “quadratic” behavior. When increases, the PM
drops from 83 to around 60 and then increases again. If
continues to increase, the PM will drop again. The phenomenon
is due to shifting of the pole when varies from small to large
values. The analysis can be divided into two parts: (i) complex
pole region for small and (ii) real pole region for large .
Region i: In this region, owing to small , the dominant
pole is formed by the two Miller compensation capacitors (
and ). It is independent of and gives a constant unity
gain frequency as follows:
(3)
In addition, the loop system gives a pair of complex poles
which are given by
(4)
It can be seen that the location of the complex poles is in-
versely proportional to . As increases, the complex poles’
frequency decreases and appears to be closer to the unit gain fre-
quency. As a consequence, the PM is reduced and the stability
of the LDO regulator becomes worse. This explains why the PM
plot in Fig. 4(a) shows a continuous drop first when is less
than 250 pF.
Region ii: For large , the output capacitor also plays a role
in the dominant pole formation. The dominant pole is given as
-
(5)
which leads to a dependent unity gain frequency as follows:
(6)
Since the zero generated from the DSMFC is fixed at
(1) and the second pole locates at a lower
times) frequency, the loop phase response gives a
small peak around the zero location. Based on the reason, when
unity gain frequency continues to reduce as increases, the
PM will increase and then drop again, depending on the relative
location of the unity gain bandwidth and the fixed zero .
TABLE II
DAMPING FACTOR AND GM FOR CASES EXHIBITING COMPLEX POLE PAIR
C. Damping Factor and Gain Margin Under Variations
Damping factor is critical for the LDO regulator stability
when a pair of complex poles exist in the loop gain transfer
function (case 2 to case 6 in Table I). Consider the second-order
terms in (2) with a standard form as
(7)
where is the damping factor and is the frequency of the
complex poles.
Although the DSMFC increases the frequency of the com-
plex poles which in turn improves the PM and GM, the of the
complex poles should be designed properly to avoid large fre-
quency peaking and maintain a good GM. If it is assumed that
the second pole and the zero generated by the DSMFC cancel
each other, based on [21], the relationship between and PM as
well as and GM in a second-order system is approximately as
follows:
(8)
(9)
From (8) and (9), a large increases the GM but it gives a
large negative phase shift which reduces the PM. On the other
hand, a small reduces the GM and makes a sharp phase drop
which can lead to a 0 PM.
Based on transfer function in (1), the general expression for
the in the second-order system defined in (7) is obtained as
(10), shown at the bottom of the page.
(10)
TAN et al.: FVF LDO REGULATOR 1309
TABLE III
MINIMUM DAMPING FACTOR AND MINIMUM GM WITH THEIR RESPECTIVE LOCATIONS
It is noted that the GM without taking log function is
. Therefore, the and for 5 cases
exhibiting a complex pole pair (case 2–case 6 in Table I) are
summarized in Table II. For case I in Table I (large , low
), the system displays four real poles, thus it is not included
in Table II and the respective analysis.
From Table II, when increases, the observation is in the
following. (i) For low and small (case 4), increases. (ii)
For moderate (case 2 and case 5), will reduce first and then
increase again. (iii) For high (case 3 and case 6), decreases.
Therefore, the minimum for low occurs at pF
whereas for high , the minimum occurs at nF. For
moderate , the minimum occurs at middle range. The
minimum value can be approximated as
(11)
which occurs at
(12)
Based on the above analytical expressions, the minimum
for different conditions and their respective
location are summarized in Table III. They are
governed by the design parameters in which the denoted sym-
bols have their usual meanings.
Consider GM of the LDO regulator depicted in Table II, when
increases, it follows the same trend as that of under low,
moderate and high cases. Therefore, (i) At low , the min-
imum GM occurs at pF. (ii) At high , the minimum
GM occurs at nF. (iii) At moderate , the minimum
GM occurs at middle range. The minimum GM
for three different conditions and their respective location
are also summarized in Table III. Turning to the
GM plot of the proposed LDO regulator in Fig. 4(b), at ,
the minimum GM location is at pF. On the other hand,
at and 50 mA, the minimum GM location is at
nF. This matches the minimum GM location analysis for low
and high conditions, respectively.
At moderate , through derivation and Binomial approxima-
tions, the minimum GM (without taking log function) is approx-
imated as
(13)
which occurs at
(14)
To demonstrate the analysis with an example, at
mA, the design parameters are given as follows:
pF, pF, S, mS,
S, k , and . Using (14), it gives
a of 2.06 nF. The GM plot in Fig. 4(b) also shows
that the minimum GM occurs around nF. This validates
that the analytical expression for the minimum GM location cor-
relates well with the simulation result.
D. Sizing of and
The dimensions of the two Miller compensation capacitors
are depending on the gain of the main loop and the dual-summed
amplifier. To analyze the influence, two cases of and
are discussed and compared with the nominal case. It is assumed
that the nominal case is at and the total sum is kept
at a constant (8 pF in this design).
Case I: . For large under low (case 1 in
Table I), a large degrades the stability of the LDO regu-
lator. This is because large gives a lower frequency that
leads to a poor PM. Under moderate (case 2 in Table I), the
Miller effect is strong because of large . The stability of the
LDO regulator is improved. For small under low and mod-
erate (case 4 and case 5 in Table I), large improves the
stability of the LDO regulator due to a stronger pole splitting
effect. This occurs when the gain of the second stage plus the
power transistor gain is larger than the gain of the dual-summed
amplifier, which is especially true under low and moderate .
As for high for both small and large (case 3 and case 6 in
Table I), the stability improvement is small due to a small power
transistor gain. This results in a similar Miller compensation ef-
fect for and .
Case II: . Under this case, the LDO regulator
stability is in opposite effect from those described in Case I
. Therefore, it is not repeated here.
Based on the analysis in Case I and Case II, the relative PM
and GM with reference to the nominal case of is
summarized in Table IV when and change their values
in different combinations. The symbol “ ” represents PM and
GM increase whereas the symbol “ ” represents PM and GM
decrease with respect to the nominal case that .
1310 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014
TABLE IV
RELATIVE PM AND GM FOR DIFFERENT COMBINATIONS WITH
REFERENCE TO NOMINAL CASE
TABLE V
PM AND GM FOR DIFFERENT COMBINATIONS
Table V gives the simulated PM and GM for the capacitor pair
( ) which corresponds to the design values of (5 pF, 3
pF), (4 pF, 4 pF) and (3 pF, 5 pF). For example one, at
mA (low ) and pF (small ), when pF,
pF, both PM and GM are larger than that of nominal
case ( pF, pF). For example two, at
mA (low ) and nF (large ), when pF,
pF, both PM and GM are smaller than the nominal
case. This confirms that the simulation results on the size of
and correlate well with the expected behavior as indicated
in Table IV.
III. SIMULATION RESULTS AND DISCUSSIONS
The proposed FVF LDO regulator is realized in a UMC
65-nm CMOS process. The compensation capacitors and
are each in 4 pF. It consumes a quiescent current of 23.7
A at typical process and room temperature with 1.2 V voltage
supply. The LDO regulator provides a 1 V output voltage with
a maximum of 50 mA load current. More importantly, the LDO
regulator is able to drive a load capacitor range of 10 pF–10
nF with good transient response. Fig. 6 shows the transient
responses for the LDO regulator with full current step (0 to
50 mA) at four different values. When the load current
switches between 0 and 50 mA with a 100 ns edge time, the
undershoots are 41 mV, 40 mV, 46 mV and 58 mV whereas the
overshoots are all close to 19 mV for pF, 100 pF, 1 nF
and 10 nF, respectively.
To demonstrate the robustness of the proposed design,
Table VI lists the PM and GM, quiescent current , load
regulation, power supply rejection (PSR) and the load transient
responses of the LDO regulator under extreme temperatures
and process corners. Except the PM and GM, all the other pa-
rameters are obtained with pF. The PM and GM are
simulated across the whole load capacitance range and current
range. The minimum values or worst case values are obtained
and presented in Table VI. For the load transient responses, two
different load current switching steps (0 to 50 mA, and 1 mA
to 50 mA) are used.
From Table VI, it can be concluded that the proposed LDO
regulator is stable even under process and temperature varia-
Fig. 6. Transient simulation results for 0 to 50 mA at pF, 100 pF, 1
nF and 10 nF ( time delay is introduced to differentiate the plot).
TABLE VI
PERFORMANCE SUMMARY UNDER PROCESS AND TEMPERATURE CORNERS
tions with sufficient PM and GM ( dB). Moreover,
the LDO regulator’s transient performance does not change sig-
nificantly for different corners, especially when switches be-
tween 1 mA to 50 mA.
IV. PERFORMANCE COMPARISON
Performance comparison between the proposed LDO regu-
lator with other reported OCL-LDO regulators is presented in
Table VII.
To compare the load capacitance driving ability and the
frequency compensation efficiency, the maximum load capaci-
tance to the total compensation capacitance ratio
is introduced. As can be seen from Table VII, with the DSMFC
TAN et al.: FVF LDO REGULATOR 1311
TABLE VII
PERFORMANCE COMPARISON WITH THE REPORTED OCL-LDO REGULATORS
technique, the proposed LDO regulator achieves the widest
load capacitance range and the highest ratio.
To compare the load transient performance, the OCL-LDO
regulator figure-of-merit (FOM) [13] is adopted. It is given by
(15)
where K is defined as the edge time ratio. In Table VII, the
smallest edge time (100 ps in [8]) is used as the reference while
the others are normalized values. To get a fair comparison, all
the parameters of the proposed LDO regulator is simulated at
pF. Furthermore, some of the LDO regulators [12],
[13] were tested with some amount of minimum loading current.
Therefore, two FOMs are obtained for the proposed FVF LDO
regulator. The first one utilizes a load current switching from 0
to 50 mA and vice versa, and the second one is based on the
load current switches between 1 mA to 50 mA. From Table VII,
it can be observed that the proposed LDO regulator achieves
a comparable or better FOM when compared with those of re-
ported OCL-LDO regulators. It also gives reasonable and good
results for other performances like load regulation, line regula-
tion, settling time and PSR.
Comparing with the original LDO regulator [19] with
wide load capacitance range driving capability, the proposed
topology displays better transient performance due to a smaller
power transistor, a simple non-inverting gain stage, smaller
compensation capacitors and an increased quiescent power.
V. CONCLUSION
A FVF based LDO regulator with Dual-Summed Miller Fre-
quency Compensation is presented. Implemented with a simple
resistive-loaded inverting amplifier, the DSMFC not only forms
the low frequency dominant pole together with the conventional
Miller compensation, it also shifts the non-dominant pole(s) to
a higher frequency, especially under low and moderate load
currents. The detailed stability analysis and simulation inves-
tigations have demonstrated that the proposed LDO regulator
topology can support wide load capacitance range (10 pF to 10
nF) for different load current conditions whilst maintaining very
good transient performance. It reaches a comparable or better
FOM and achieves the highest ratio with respect
to other reported OCL-LDO regulator topologies. Therefore, it
is useful for wide load capacitance range applications.
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for SoC with q-reduction,” IEEE J. Solid-State Circuits, vol. 42, no. 3,
pp. 658–664, Mar. 2007.
[10] R. J. Milliken, J. Silva-Martinez, and E. Sanchez-Sinencio, “Full
on-chip CMOS low-dropout voltage regulator,” IEEE Trans. Circuits
Syst. I, Reg. Papers, vol. 54, no. 9, pp. 1879–1890, Sep. 2007.
[11] T. Y. Man, K. N. Leung, C. Y. Leung, P. K. T. Mok, and M. Chan, “De-
velopment of single-transistor-control LDO based on flipped voltage
follower for SoC,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55,
no. 5, pp. 1392–1401, Jun. 2008.
[12] P. Y. Or and K. N. Leung, “An output-capacitorless low-dropout regu-
lator with direct voltage-spike detection,” IEEE J. Solid-State Circuits,
vol. 45, no. 2, pp. 458–466, Feb. 2010.
[13] G. J. and K. N. Leung, “A 6- W Chip-Area-Efficient Output-Capac-
itorless LDO in 90-nm CMOS Technology,” IEEE J. Solid-State Cir-
cuits, vol. 45, no. 9, pp. 1896–1905, Sep. 2010.
[14] S. Lai and P. Li, “A fully on-chip area-efficient CMOS low-dropout
regulator with fast load regulation,” Analog Integr. Circuits Signal
Process., vol. 72, pp. 433–450, 2012.
[15] E. N. Y. Ho and P. K. T. Mok, “A capacitor-less CMOS active feedback
low-dropout regulator with slew-rate enhancement for portable on-chip
application,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 57, no. 2,
pp. 80–84, Feb. 2010.
[16] C. Zhan and W. H. Ki, “An output-capacitor-free adaptively biased
low-dropout regulator with subthreshold undershoot-reduction for
SoC,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 5, pp.
1119–1131, May 2012.
[17] S. S. Chong and P. K. Chan, “A 0.9- A quiescent current output-ca-
pacitorless LDO regulator with adaptive power transistors in 65-nm
cmos,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 60, no. 4, pp.
1072–1081, Apr. 2013.
[18] M. Luders, B. Eversmann, D. Schmitt-Landsiedel, and R. Brederlow,
“Fully-integrated LDO voltage regulator for digital circuits,” in Proc.
Adv. Radio Sci., 2011, pp. 263–267.
[19] K. C. Koay, S. S. Chong, and P. K. Chan, “A FVF based output ca-
pacitorless LDO regulator with wide load capacitance range,” in Proc.
IEEE Int. Symp. Circuits Syst. (ISCAS), May 2013, pp. 1488–1491.
[20] Y. Tian and P. K. Chan, “Design of high-performance analog circuit
using wideband gm-enchanced MOS composite transistor,” IEICE
Trans. Electron., vol. E93-C, pp. 1199–1208, 2010.
[21] C. Zhan and W. H. Ki, “Output-capacitor-free adaptively biased low-
dropout regulator for system-on-chips,” IEEE Trans. Circuits Syst. I,
Reg. Papers, vol. 57, no. 5, pp. 1017–1028, May 2010.
Xiao Liang Tan was born in Chongqing, China. He
received the B.Eng. (hons.) degree from Nanyang
Technological University (NTU), Singapore, in
2011, where he is currently working toward the
Ph.D. degree in the School of Electrical and Elec-
tronic Engineering.
His research interests include design of analog
integrated circuits for low-dropout regulators,
voltage references, as well as design of process,
supply voltage and temperature (PVT) compensation
system for digital LSIs.
Kuan Chuang Koay was born in Malaysia. He
received the B.Eng. (hons) degree from Nanyang
Technological University (NTU), Singapore, in
2012, where he is currently working towards the
Ph.D. degree in School of Electrical and Electronic
Engineering.
His research interests include frequency compen-
sation techniques for low-dropout regulators and de-
sign of sensor interface IC.
Sau Siong Chong was born in Malaysia. He received
the B.Eng. (hons) degree from Nanyang Technolog-
ical University (NTU), Singapore, in 2009, where
he is currently working towards the Ph.D. degree in
School of Electrical and Electronic Engineering.
His research interests include design of analog in-
tegrated circuits and frequency compensation tech-
niques for low-voltage low-power multistage ampli-
fiers and low-dropout regulators.
Pak Kwong Chan was born in Hong Kong. He
received the B.Sc. (hons) degree from University of
Essex, Essex, U.K., in 1987, the M.Sc. degree from
University of Manchester, Institute of Science and
Technology, U.K., in 1988, and the Ph.D. degree
from University of Plymouth, U.K., in 1992.
From 1989 to 1992, he was a Research Assistant
with University of Plymouth, working in the area
of MOS continuous-time filters. In 1993, he joined
Institute of Microelectronics (IME), Singapore
as a Member Technical Staff, where he designed
high-performance analog/mixed-signal circuits for integrated systems and
CMOS sensor interfaces for industrial applications. In 1996, He was a Staff
Engineer with Motorola, Singapore where he developed the magnetic write
channel for Motorola 1st generation hard-disk preamplifier. He joined Nanyang
Technological University, Singapore in 1997, where he is an Associate Pro-
fessor in the School of Electrical and Electronic Engineering. Besides, he is
an IC Design Consultant to local and multi-national companies. He conducted
numerous IC design short courses to the IC companies and design centers. He
served as a Guest Editor for 2011 and 2012 Special Issues in Journal of Circuits,
Systems and Computers. His current research interests include sensor circuits
and systems, mixed-mode circuits and systems, precision analog circuits, ultra
low-voltage low-power circuits as well as power management IC for integrated
sensors and system-on-chip.

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Published_Paper_TCASI

  • 1. 1304 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014 A FVF LDO Regulator With Dual-Summed Miller Frequency Compensation for Wide Load Capacitance Range Applications Xiao Liang Tan, Student Member, IEEE, Kuan Chuang Koay, Member, IEEE, Sau Siong Chong, Student Member, IEEE, and P. K. Chan, Senior Member, IEEE Abstract—This paper presents a proposed Flipped Voltage Fol- lower (FVF) based output capacitorless low-dropout (OCL-LDO) regulator using Dual-Summed Miller Frequency Compensation (DSMFC) technique. Validated by UMC 65-nm CMOS process, the simulation results have shown that the proposed LDO regu- lator can be stabilized by a total compensation capacitance of 8 pF for a load capacitance ranging from 10 pF to 10 nF. It consumes 23.7 A quiescent current with a 1.2 V supply voltage. With a dropout voltage of 200 mV, the LDO regulator can support a maximum 50 mA load current. It can settle in less than 1.7 s with a 1% accuracy for the whole range. The proposed LDO regulator is comparable to other reported works in terms of figure-of-merit (FOM). Most significantly, it can drive the widest range of and achieve the highest ratio with respect to the counterparts. Index Terms—DSMFC, FVF, LDO regulator, Miller compensa- tion, wide load capacitance range. I. INTRODUCTION VOLTAGE regulators have been widely used to supply various function blocks in battery powered devices. A LDO regulator featuring a simple structure with fast re- sponse and low noise characteristics is very popular in power management IC design [1]. However, the LDO regulators relying on a F level off-chip capacitor to maintain stable operation will limit their fully integration ability for modern System-on-Chips (SoC) [2]–[6]. As such, the output capacitor- less LDO (OCL-LDO) regulators have received much attention for fully on-chip applications. OCL-LDO regulators have been recently reported in [7]–[17]. Among these designs, the Flipped Voltage Follower (FVF) based LDO regulators [8], [11]–[14] are attractive in terms of simplicity, stability and fast transient responses. In [8], the FVF structure is implemented as drivers for the output. It gives a very fast response with a recovering time of 0.54 ns. However, the quiescent current in this LDO regulator is 6 mA. In addition, the LDO regulator is stabilized by a 600 pF on-chip decoupling capacitor. This results in large power and silicon area consumptions. In [11], a Single-Transistor-Control LDO regulator based on FVF structure is proposed. It has been proven that the LDO regulator is stable without an off-chip capacitor. In [12], a direct voltage spike detection scheme Manuscript received August 23, 2013; revised December 03, 2013, January 06, 2014; accepted January 12, 2014. Date of publication March 25, 2014; date of current version April 24, 2014. The authors are with the School of Electrical and Electronic Engi- neering, Nanyang Technological University, 639798 Singapore (e-mail: tanx0074@e.ntu.edu.sg; koay0013@e.ntu.edu.sg; chon0157@e.ntu.edu.sg; epkchan@ntu.edu.sg). Digital Object Identifier 10.1109/TCSI.2014.2309902 is adopted in the FVF structure to momentarily increase the quiescent current during load current switching. Hence, the transient response of the regulator is improved. However, both topologies [11], [12] suffer from low loop gain due to its simple folded structure [13]. As a result, an additional gain stage has been added in the feedback loop to boost the loop gain in [13] for improvement of both load and line regulations. Due to the additional gain stage, a Miller compensation capac- itor is required for circuit stability purpose at low quiescent power. However, the conventional Miller compensation typically supports small load capacitors. The LDO regulator in [13] is only able to drive a maximum 50 pF load capacitor with a minimum 3 mA load current at V. To further increase the load capacitance driving capability, either the compensation capacitor or the minimum load current must be increased to achieve a stable operation. This restricts its application at the circuits with load capacitance starting from few ten pF to few hundred pF. However, for some digital circuit applications [18] that require the LDO regulator to drive the on-chip capacitance of 3 nF or more. This creates a design challenge on the FVF OCL-LDO regulators using standard Miller compensation technique in the context of low quiescent power. In [14], based on a FVF output driving stage, an active compensation scheme is implemented which can drive a load capacitance up to 1 nF. However, several poles and zeros are within the unity gain bandwidth frequency , thus leading to complicated pole-zero tracking. Furthermore, the LDO regulator may be susceptible to process and temperature variations since the stability is very much dependent on the poles’ and zeros’ locations. In view of that, a Dual-Summed Miller Frequency Compen- sation (DSMFC) technique is implemented in a FVF based LDO regulator topology [19]. The LDO regulator has been demon- strated in a very wide load capacitance range. Not only does the added Miller compensation stage form the dominant pole together with the conventional Miller capacitor, it also shifts the non-dominant pole(s) to a higher frequency. In the reported dual-summed Miller compensated LDO regulator [19], a low output impedance power transistor driver [20] is realized as the second non-inverting gain stage to improve the loop gain. Turning to the DSMFC network, the inverting driving transistor for the second Miller amplifier is biased by a high impedance current source with an open loop topology. To ensure a reliable dc operating region of the additional Miller stage, the power transistor has to be sized larger at the expense of larger silicon area so as to reduce the voltage swing at the Miller node. 1549-8328 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
  • 2. TAN et al.: FVF LDO REGULATOR 1305 Based on the scheme in [19], an improved FVF based LDO regulator using the DSMFC technique is proposed in this paper. In Section II, the frequency response of the proposed LDO reg- ulator is analyzed at different load capacitor and current conditions. Besides, the detailed analysis for phase margin (PM), damping factor and gain margin (GM) is presented. Effect of PM and GM with respect to the load capacitors is also investigated. The simulated results and discussions of key pa- rameters are given in Section III. In Section IV, a comparison with other reported OCL-LDO regulators is given. Conclusions are drawn in Section V. II. PROPOSED FVF LDO REGULATOR WITH DSMFC The schematic of the proposed LDO regulator is shown in Fig. 1(a). The main loop contains a folded FVF gain stage, a non-inverting gain stage and a power MOS transistor. The LDO regulator is compensated using a DSMFC block (dash en- closed area). It contains a standard Miller compensation capac- itor and an additional Miller compensation stage ( and ). Different from [19], the DSMFC in the proposed LDO regulator is biased using a passive resistor . This re- alization permits a reliable DC operating point to be achieved in absence of high impedance node. As such, the power transistor can be sized smaller with respect to that in [19]. With the DSMFC technique, the dominant pole is formed through the summing Miller effect which offers better stability. Besides, when comparing with Single Miller Compensation (SMC) counterpart, the DSMFC also shifts the non-dominant pole(s) to a higher frequency, especially under the following three conditions: (i) large with low , (ii) large with moderate , and (iii) small with low . Since the DSMFC technique addresses the conservative stability issue for both small and large , the proposed LDO regulator can achieve driving capability for a wide load capacitance range across the whole load current range. The control voltage for is generated through a symmet- rical OTA amplifier which is shown in Fig. 1(b). Since the max- imum load capacitor is in an nF range, to reduce the settling time from overshoot, an overshoot reduction branch ( and ) is implemented to increase the sinking current momen- tarily. A. Stability Analysis To analyze the stability of the proposed LDO regulator, the small-signal model depicted in Fig. 1(c) is investigated. It is ob- tained by breaking the feedback loop at the output branch as shown in Fig. 1(a). It is noted that denotes the transcon- ductance whereas and are the equivalent output resis- tance and lumped output parasitic capacitance of the i-th gain stage, respectively. and are the 1st and 2nd Miller compensation capacitors. is the effective output resistance which includes the output resistance of power transistor and the loading resistance . is the load capacitance which has a value ranging from 10 pF to 10 nF. Fig. 1. (a) Schematic of the proposed FVF based LDO regulator with DSMFC indicate the loop breaking point). (b) Control voltage generator. (c) Small-signal model of the proposed FVF LDO regulator. (1) The transfer function is derived with the following assump- tions: (i) and ; (ii) and . It is obtained and expressed by (1), in which is the dc loop gain and are the three zeros. Based on the design parameters, locate at high frequencies, thus they can be ignored in the following analysis. In addition,
  • 3. 1306 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014 TABLE I POLES AND ZERO LOCATIONS FOR SIX CASES Fig. 2. Loop gain of the proposed FVF LDO regulator with poles and zero locations for (a) large , (b) small . the loop gain transfer function has two real poles - . Therefore, it can be simplified in the form as - (2) Since the load capacitor varies from 10 pF to 10 nF with the load current switching between 0 and 50 mA, the stability of the OCL-LDO regulator is discussed at six different cases that deal with the load capacitor corners at different load currents. They are given as follows:(1) Large with low , (2) Large with moderate , (3) Large with high (4) Small with low , (5) Small with moderate , (6) Small with high . The poles and zeros locations for six cases are summarized in Table I and their relative locations are shown in Fig. 2(a) and Fig. 3. Simulated open-loop gain and phase responses at different for (a) nF and (b) pF. (b) for large and small , respectively. The loop gain transfer function shows that the first case denotes the system with four real poles whereas the other five cases denote the system having two real poles plus one pair of complex poles. Each case is ex- plained as follows: Case 1: Large With Low : In this case, both power tran- sistor’s output resistance and the equivalent load circuit resistance are high. As a result, . Due to a
  • 4. TAN et al.: FVF LDO REGULATOR 1307 Fig. 4. Simulated (a) Phase Margin, (b) Gain Margin and (c) Unity Gain Frequency as a function of at different using DSMFC. Fig. 5. Simulated (a) Phase Margin, (b) Gain Margin and (c) Unity Gain Frequency as a function of at different using SMC. small bias current in is still fairly large (around 17 k ). It forms a low frequency dominant pole with the large load capacitor . The second pole is located at a lower frequency than that of the zero, contributing a partial cancellation effect. In addition, due to the DSMFC, the third pole is pushed to a higher frequency by an extra frequency quantifying term, . As for , the gain of the last stage is small due to small . Hence, the Miller effect arising from the of the power transistor is negligible, which leads to a small . There- fore, is also located at a high frequency. Case 2: Large With Moderate : The loop gain is the highest in this range because of large and moderate . The stability of the LDO regulator is at its worst condition. The dominant pole of the system is formed by the Miller compen- sation capacitor . More importantly, similar to Case 1, an additional term, , is generated for defining complex poles’ frequency in the DSMFC scheme. As a result, the complex poles are shifted to a higher frequency which im- proves both the PM and GM. The stability of the regulator is achieved. Case 3: Large With High : In this case, is ap- proaching to its minimum value because of small and small . This results in a small gain for the power transistor gain stage. The two Miller compensation effects are close to each other and form the dominant pole together. The second pole and zero ( is around 2 times of ) exhibit a good can- cellation. The complex poles are located at higher frequency due to large . Case 4: Small With Low : Under this condition, no longer forms a low frequency pole. The dominant pole is gov- erned by two Miller compensation capacitors ( and ). A good pole and zero cancellation is also achieved in this case. Similar to Case 2, the complex poles are shifted to a higher fre- quency by the additional term generated by the DSMFC. The stability of the LDO regulator is ensured. Case 5: Small With Moderate : Similar to Case 2, the dominant pole is created by the standard Miller capacitor . Due to the small , the complex poles are located at high fre- quency which will not affect the stability of the LDO regulator in this case. Case 6: Small With High : Similar to Case 5, it is ap- parent that the stability of the LDO regulator at this condition can easily be achieved due to large and small . Fig. 3(a) and (b) depict the open loop gain and phase re- sponses at mA, 5 mA, and 50 mA for nF and pF, respectively. It can be seen that the sim- ulated results match with the analysis. It also demonstrates that the proposed FVF LDO regulator can achieve stability for both large and small corners at different load currents. The PM, GM and unity gain frequency across the whole load capacitor range with different load currents are shown in Fig. 4. It can be observed that the LDO regulator with DSMFC technique achieves a minimum PM of 50 and a minimum GM of 8 dB. For benchmark comparison, the SMC for this LDO regulator topology without using the second Miller amplifier is applied. The total compensation capacitance in the proposed LDO reg- ulator and the SMC LDO regulator are sized to be the same (8 pF). Fig. 5 depicts the PM, GM and unity gain frequency simu- lation results. As can be seen from Fig. 5(a), based on a 50 PM, the SMC regulator is stable to support a load capacitor ranging from 10 pF to 250 pF. Moreover, when comparing the unity gain frequency simulation results in Figs. 4(c) and 5(c), the pro- posed LDO regulator using the DSMFC technique provides a larger unity gain frequency with respect to that of SMC LDO regulator. This suggests that the speed will be faster in the pro- posed LDO regulator. Based on the above analysis and simulation results, the pro- posed FVF LDO regulator using DSMFC technique is able to maintain stable operation over the whole load capacitance range of 10 pF–10 nF under the load current varying from 0 to 50
  • 5. 1308 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014 mA. Particularly, the DSMFC shows a significant improvement under three conditions: (i) large with low , (ii) large with moderate , and (iii) small with low . This extends the load capacitance range because it addresses the conservative stability issue for both small and large . B. Phase Margin Under Variations As can be seen in Fig. 4(a), at small condition, the PM plot shows a “quadratic” behavior. When increases, the PM drops from 83 to around 60 and then increases again. If continues to increase, the PM will drop again. The phenomenon is due to shifting of the pole when varies from small to large values. The analysis can be divided into two parts: (i) complex pole region for small and (ii) real pole region for large . Region i: In this region, owing to small , the dominant pole is formed by the two Miller compensation capacitors ( and ). It is independent of and gives a constant unity gain frequency as follows: (3) In addition, the loop system gives a pair of complex poles which are given by (4) It can be seen that the location of the complex poles is in- versely proportional to . As increases, the complex poles’ frequency decreases and appears to be closer to the unit gain fre- quency. As a consequence, the PM is reduced and the stability of the LDO regulator becomes worse. This explains why the PM plot in Fig. 4(a) shows a continuous drop first when is less than 250 pF. Region ii: For large , the output capacitor also plays a role in the dominant pole formation. The dominant pole is given as - (5) which leads to a dependent unity gain frequency as follows: (6) Since the zero generated from the DSMFC is fixed at (1) and the second pole locates at a lower times) frequency, the loop phase response gives a small peak around the zero location. Based on the reason, when unity gain frequency continues to reduce as increases, the PM will increase and then drop again, depending on the relative location of the unity gain bandwidth and the fixed zero . TABLE II DAMPING FACTOR AND GM FOR CASES EXHIBITING COMPLEX POLE PAIR C. Damping Factor and Gain Margin Under Variations Damping factor is critical for the LDO regulator stability when a pair of complex poles exist in the loop gain transfer function (case 2 to case 6 in Table I). Consider the second-order terms in (2) with a standard form as (7) where is the damping factor and is the frequency of the complex poles. Although the DSMFC increases the frequency of the com- plex poles which in turn improves the PM and GM, the of the complex poles should be designed properly to avoid large fre- quency peaking and maintain a good GM. If it is assumed that the second pole and the zero generated by the DSMFC cancel each other, based on [21], the relationship between and PM as well as and GM in a second-order system is approximately as follows: (8) (9) From (8) and (9), a large increases the GM but it gives a large negative phase shift which reduces the PM. On the other hand, a small reduces the GM and makes a sharp phase drop which can lead to a 0 PM. Based on transfer function in (1), the general expression for the in the second-order system defined in (7) is obtained as (10), shown at the bottom of the page. (10)
  • 6. TAN et al.: FVF LDO REGULATOR 1309 TABLE III MINIMUM DAMPING FACTOR AND MINIMUM GM WITH THEIR RESPECTIVE LOCATIONS It is noted that the GM without taking log function is . Therefore, the and for 5 cases exhibiting a complex pole pair (case 2–case 6 in Table I) are summarized in Table II. For case I in Table I (large , low ), the system displays four real poles, thus it is not included in Table II and the respective analysis. From Table II, when increases, the observation is in the following. (i) For low and small (case 4), increases. (ii) For moderate (case 2 and case 5), will reduce first and then increase again. (iii) For high (case 3 and case 6), decreases. Therefore, the minimum for low occurs at pF whereas for high , the minimum occurs at nF. For moderate , the minimum occurs at middle range. The minimum value can be approximated as (11) which occurs at (12) Based on the above analytical expressions, the minimum for different conditions and their respective location are summarized in Table III. They are governed by the design parameters in which the denoted sym- bols have their usual meanings. Consider GM of the LDO regulator depicted in Table II, when increases, it follows the same trend as that of under low, moderate and high cases. Therefore, (i) At low , the min- imum GM occurs at pF. (ii) At high , the minimum GM occurs at nF. (iii) At moderate , the minimum GM occurs at middle range. The minimum GM for three different conditions and their respective location are also summarized in Table III. Turning to the GM plot of the proposed LDO regulator in Fig. 4(b), at , the minimum GM location is at pF. On the other hand, at and 50 mA, the minimum GM location is at nF. This matches the minimum GM location analysis for low and high conditions, respectively. At moderate , through derivation and Binomial approxima- tions, the minimum GM (without taking log function) is approx- imated as (13) which occurs at (14) To demonstrate the analysis with an example, at mA, the design parameters are given as follows: pF, pF, S, mS, S, k , and . Using (14), it gives a of 2.06 nF. The GM plot in Fig. 4(b) also shows that the minimum GM occurs around nF. This validates that the analytical expression for the minimum GM location cor- relates well with the simulation result. D. Sizing of and The dimensions of the two Miller compensation capacitors are depending on the gain of the main loop and the dual-summed amplifier. To analyze the influence, two cases of and are discussed and compared with the nominal case. It is assumed that the nominal case is at and the total sum is kept at a constant (8 pF in this design). Case I: . For large under low (case 1 in Table I), a large degrades the stability of the LDO regu- lator. This is because large gives a lower frequency that leads to a poor PM. Under moderate (case 2 in Table I), the Miller effect is strong because of large . The stability of the LDO regulator is improved. For small under low and mod- erate (case 4 and case 5 in Table I), large improves the stability of the LDO regulator due to a stronger pole splitting effect. This occurs when the gain of the second stage plus the power transistor gain is larger than the gain of the dual-summed amplifier, which is especially true under low and moderate . As for high for both small and large (case 3 and case 6 in Table I), the stability improvement is small due to a small power transistor gain. This results in a similar Miller compensation ef- fect for and . Case II: . Under this case, the LDO regulator stability is in opposite effect from those described in Case I . Therefore, it is not repeated here. Based on the analysis in Case I and Case II, the relative PM and GM with reference to the nominal case of is summarized in Table IV when and change their values in different combinations. The symbol “ ” represents PM and GM increase whereas the symbol “ ” represents PM and GM decrease with respect to the nominal case that .
  • 7. 1310 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014 TABLE IV RELATIVE PM AND GM FOR DIFFERENT COMBINATIONS WITH REFERENCE TO NOMINAL CASE TABLE V PM AND GM FOR DIFFERENT COMBINATIONS Table V gives the simulated PM and GM for the capacitor pair ( ) which corresponds to the design values of (5 pF, 3 pF), (4 pF, 4 pF) and (3 pF, 5 pF). For example one, at mA (low ) and pF (small ), when pF, pF, both PM and GM are larger than that of nominal case ( pF, pF). For example two, at mA (low ) and nF (large ), when pF, pF, both PM and GM are smaller than the nominal case. This confirms that the simulation results on the size of and correlate well with the expected behavior as indicated in Table IV. III. SIMULATION RESULTS AND DISCUSSIONS The proposed FVF LDO regulator is realized in a UMC 65-nm CMOS process. The compensation capacitors and are each in 4 pF. It consumes a quiescent current of 23.7 A at typical process and room temperature with 1.2 V voltage supply. The LDO regulator provides a 1 V output voltage with a maximum of 50 mA load current. More importantly, the LDO regulator is able to drive a load capacitor range of 10 pF–10 nF with good transient response. Fig. 6 shows the transient responses for the LDO regulator with full current step (0 to 50 mA) at four different values. When the load current switches between 0 and 50 mA with a 100 ns edge time, the undershoots are 41 mV, 40 mV, 46 mV and 58 mV whereas the overshoots are all close to 19 mV for pF, 100 pF, 1 nF and 10 nF, respectively. To demonstrate the robustness of the proposed design, Table VI lists the PM and GM, quiescent current , load regulation, power supply rejection (PSR) and the load transient responses of the LDO regulator under extreme temperatures and process corners. Except the PM and GM, all the other pa- rameters are obtained with pF. The PM and GM are simulated across the whole load capacitance range and current range. The minimum values or worst case values are obtained and presented in Table VI. For the load transient responses, two different load current switching steps (0 to 50 mA, and 1 mA to 50 mA) are used. From Table VI, it can be concluded that the proposed LDO regulator is stable even under process and temperature varia- Fig. 6. Transient simulation results for 0 to 50 mA at pF, 100 pF, 1 nF and 10 nF ( time delay is introduced to differentiate the plot). TABLE VI PERFORMANCE SUMMARY UNDER PROCESS AND TEMPERATURE CORNERS tions with sufficient PM and GM ( dB). Moreover, the LDO regulator’s transient performance does not change sig- nificantly for different corners, especially when switches be- tween 1 mA to 50 mA. IV. PERFORMANCE COMPARISON Performance comparison between the proposed LDO regu- lator with other reported OCL-LDO regulators is presented in Table VII. To compare the load capacitance driving ability and the frequency compensation efficiency, the maximum load capaci- tance to the total compensation capacitance ratio is introduced. As can be seen from Table VII, with the DSMFC
  • 8. TAN et al.: FVF LDO REGULATOR 1311 TABLE VII PERFORMANCE COMPARISON WITH THE REPORTED OCL-LDO REGULATORS technique, the proposed LDO regulator achieves the widest load capacitance range and the highest ratio. To compare the load transient performance, the OCL-LDO regulator figure-of-merit (FOM) [13] is adopted. It is given by (15) where K is defined as the edge time ratio. In Table VII, the smallest edge time (100 ps in [8]) is used as the reference while the others are normalized values. To get a fair comparison, all the parameters of the proposed LDO regulator is simulated at pF. Furthermore, some of the LDO regulators [12], [13] were tested with some amount of minimum loading current. Therefore, two FOMs are obtained for the proposed FVF LDO regulator. The first one utilizes a load current switching from 0 to 50 mA and vice versa, and the second one is based on the load current switches between 1 mA to 50 mA. From Table VII, it can be observed that the proposed LDO regulator achieves a comparable or better FOM when compared with those of re- ported OCL-LDO regulators. It also gives reasonable and good results for other performances like load regulation, line regula- tion, settling time and PSR. Comparing with the original LDO regulator [19] with wide load capacitance range driving capability, the proposed topology displays better transient performance due to a smaller power transistor, a simple non-inverting gain stage, smaller compensation capacitors and an increased quiescent power. V. CONCLUSION A FVF based LDO regulator with Dual-Summed Miller Fre- quency Compensation is presented. Implemented with a simple resistive-loaded inverting amplifier, the DSMFC not only forms the low frequency dominant pole together with the conventional Miller compensation, it also shifts the non-dominant pole(s) to a higher frequency, especially under low and moderate load currents. The detailed stability analysis and simulation inves- tigations have demonstrated that the proposed LDO regulator topology can support wide load capacitance range (10 pF to 10 nF) for different load current conditions whilst maintaining very good transient performance. It reaches a comparable or better FOM and achieves the highest ratio with respect to other reported OCL-LDO regulator topologies. Therefore, it is useful for wide load capacitance range applications. REFERENCES [1] G. A. Rincon-Mora, Analog IC Design With Low-Dropout Regula- tors. New York, NY, USA: McGraw-Hill, 2009. [2] G. Rincon-Mora and P. E. Allen, “A low-voltage, low quiescent cur- rent, low drop-out regulator,” IEEE J. Solid-State Circuits, vol. 33, no. 1, pp. 36–44, Jan. 1998. [3] M. Al-Shyoukh, H. Lee, and R. Perez, “A transient-enhanced low-qui- escent current low-dropout regulator with buffer impedance attenua- tion,” IEEE J. Solid-State Circuits, vol. 42, no. 8, pp. 1732–1742, Aug. 2007. [4] Y. H. Lam and W. H. Ki, “A 0.9 V 0.35 m adaptively biased CMOS LDO regulator with fast transient response,” in Proc. ISSCC Dig. Tech. Papers, 2008, pp. 442–626. [5] K. N. Leung and Y. S. Ng, “A CMOS low-dropout regulator with a mo- mentarily current-boosting voltage buffer,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 9, pp. 2312–2319, Sep. 2010. [6] M. Ho, K. N. Leung, and K. L. Mak, “A low-power fast-transient 90-nm low-dropout regulator with multiple small-gain stages,” IEEE J. Solid-State Circuits, vol. 45, no. 11, pp. 2466–2475, Nov. 2010. [7] K. N. Leung and P. K. T. Mok, “A capacitor-free CMOS low-dropout regulator with damping-factor-control frequency compensation,” IEEE J. Solid-State Circuits, vol. 38, no. 10, pp. 1691–1702, Oct. 2003. [8] P. Hazucha, T. Karnik, B. A. Bloechel, C. Parsons, D. Finan, and S. Borkar, “Area-efficient linear regulator with ultra-fast load regulation,” IEEE J. Solid-State Circuits, vol. 40, no. 4, pp. 933–940, Apr. 2005.
  • 9. 1312 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 61, NO. 5, MAY 2014 [9] S. K. Lau, P. K. T. Mok, and K. N. Leung, “A low-dropout regulator for SoC with q-reduction,” IEEE J. Solid-State Circuits, vol. 42, no. 3, pp. 658–664, Mar. 2007. [10] R. J. Milliken, J. Silva-Martinez, and E. Sanchez-Sinencio, “Full on-chip CMOS low-dropout voltage regulator,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 9, pp. 1879–1890, Sep. 2007. [11] T. Y. Man, K. N. Leung, C. Y. Leung, P. K. T. Mok, and M. Chan, “De- velopment of single-transistor-control LDO based on flipped voltage follower for SoC,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 5, pp. 1392–1401, Jun. 2008. [12] P. Y. Or and K. N. Leung, “An output-capacitorless low-dropout regu- lator with direct voltage-spike detection,” IEEE J. Solid-State Circuits, vol. 45, no. 2, pp. 458–466, Feb. 2010. [13] G. J. and K. N. Leung, “A 6- W Chip-Area-Efficient Output-Capac- itorless LDO in 90-nm CMOS Technology,” IEEE J. Solid-State Cir- cuits, vol. 45, no. 9, pp. 1896–1905, Sep. 2010. [14] S. Lai and P. Li, “A fully on-chip area-efficient CMOS low-dropout regulator with fast load regulation,” Analog Integr. Circuits Signal Process., vol. 72, pp. 433–450, 2012. [15] E. N. Y. Ho and P. K. T. Mok, “A capacitor-less CMOS active feedback low-dropout regulator with slew-rate enhancement for portable on-chip application,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 57, no. 2, pp. 80–84, Feb. 2010. [16] C. Zhan and W. H. Ki, “An output-capacitor-free adaptively biased low-dropout regulator with subthreshold undershoot-reduction for SoC,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59, no. 5, pp. 1119–1131, May 2012. [17] S. S. Chong and P. K. Chan, “A 0.9- A quiescent current output-ca- pacitorless LDO regulator with adaptive power transistors in 65-nm cmos,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 60, no. 4, pp. 1072–1081, Apr. 2013. [18] M. Luders, B. Eversmann, D. Schmitt-Landsiedel, and R. Brederlow, “Fully-integrated LDO voltage regulator for digital circuits,” in Proc. Adv. Radio Sci., 2011, pp. 263–267. [19] K. C. Koay, S. S. Chong, and P. K. Chan, “A FVF based output ca- pacitorless LDO regulator with wide load capacitance range,” in Proc. IEEE Int. Symp. Circuits Syst. (ISCAS), May 2013, pp. 1488–1491. [20] Y. Tian and P. K. Chan, “Design of high-performance analog circuit using wideband gm-enchanced MOS composite transistor,” IEICE Trans. Electron., vol. E93-C, pp. 1199–1208, 2010. [21] C. Zhan and W. H. Ki, “Output-capacitor-free adaptively biased low- dropout regulator for system-on-chips,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 5, pp. 1017–1028, May 2010. Xiao Liang Tan was born in Chongqing, China. He received the B.Eng. (hons.) degree from Nanyang Technological University (NTU), Singapore, in 2011, where he is currently working toward the Ph.D. degree in the School of Electrical and Elec- tronic Engineering. His research interests include design of analog integrated circuits for low-dropout regulators, voltage references, as well as design of process, supply voltage and temperature (PVT) compensation system for digital LSIs. Kuan Chuang Koay was born in Malaysia. He received the B.Eng. (hons) degree from Nanyang Technological University (NTU), Singapore, in 2012, where he is currently working towards the Ph.D. degree in School of Electrical and Electronic Engineering. His research interests include frequency compen- sation techniques for low-dropout regulators and de- sign of sensor interface IC. Sau Siong Chong was born in Malaysia. He received the B.Eng. (hons) degree from Nanyang Technolog- ical University (NTU), Singapore, in 2009, where he is currently working towards the Ph.D. degree in School of Electrical and Electronic Engineering. His research interests include design of analog in- tegrated circuits and frequency compensation tech- niques for low-voltage low-power multistage ampli- fiers and low-dropout regulators. Pak Kwong Chan was born in Hong Kong. He received the B.Sc. (hons) degree from University of Essex, Essex, U.K., in 1987, the M.Sc. degree from University of Manchester, Institute of Science and Technology, U.K., in 1988, and the Ph.D. degree from University of Plymouth, U.K., in 1992. From 1989 to 1992, he was a Research Assistant with University of Plymouth, working in the area of MOS continuous-time filters. In 1993, he joined Institute of Microelectronics (IME), Singapore as a Member Technical Staff, where he designed high-performance analog/mixed-signal circuits for integrated systems and CMOS sensor interfaces for industrial applications. In 1996, He was a Staff Engineer with Motorola, Singapore where he developed the magnetic write channel for Motorola 1st generation hard-disk preamplifier. He joined Nanyang Technological University, Singapore in 1997, where he is an Associate Pro- fessor in the School of Electrical and Electronic Engineering. Besides, he is an IC Design Consultant to local and multi-national companies. He conducted numerous IC design short courses to the IC companies and design centers. He served as a Guest Editor for 2011 and 2012 Special Issues in Journal of Circuits, Systems and Computers. His current research interests include sensor circuits and systems, mixed-mode circuits and systems, precision analog circuits, ultra low-voltage low-power circuits as well as power management IC for integrated sensors and system-on-chip.