1. IC Design of
Power Management Circuits (I)
Wing-Hung Ki
Integrated Power Electronics Laboratory
ECE Dept., HKUST
Clear Water Bay, Hong Kong
www.ee.ust.hk/~eeki
International Symposium on Integrated Circuits
Singapore, Dec. 14, 2009

2. Tutorial Content
1. Switching Converters: Fundamentals and Control
2. Switching Converters: IC Design
3. Switching Converters: Stability and Compensation
4. Fundamentals of Bandgap References
5. Development of Integrated Charge Pumps
6. Introduction to Low Dropout Regulators
Ki
2

3. Part I
Switching Converters:
Fundamentals and Control
Ki
3

4. Content
Steady State Analysis
Lossless elements
Buck, boost, buck-boost power stages
Volt-second balance
Continuous conduction mode
Discontinuous conduction mode
Ringing suppression
Pseudo-continuous conduction mode
Efficiency
Performance Evaluation Parameters
Control Topologies
PWM voltage mode control
PWM current mode control
Ki
Single-Inductor Multi-Input Multi-Output Converters
4

5. Linear Regulator has Low Efficiency
Idd
MN
IQ1
IQ2
VREF
Vdd
EA
Vo
IQ3
Io
R1
bVo
R2
C
RL
power converter
Efficiency of linear regulator is not high:
η=
Ki
Po
VI
V
Io
V
= o o = o
< o <1
Pin VddIdd Vdd Io + IQ Vdd
Can one design a power converter with efficiency close to 1?
5

6. Switches as Lossless Components
A power converter with high efficiency needs lossless components.
Reactive elements: capacitors, inductors
Active elements: switches
L
C
−
store &
relax
store &
relax
PC = 0
Ki
+
Vsw
Isw
PL = 0
+
Vsw
Isw
−
switch open
switch closed
Psw = Vsw×Isw
= Vsw×0
=0
Psw = Vsw×Isw
= 0×Isw
=0
6

7. Switching Converter: Heuristic Development (1)
Vo = Vdd
Vo
Vdd
RL
t
No regulation
SW1
Vdd
Vo
Vdd
Vo = DVdd
RL
t
duty ratio = D
Ki
Load cannot accept a
pulsating supply voltage
7

8. Switching Converter: Heuristic Development (2)
Vo
L
SW1
Vdd
C
Vx
Vdd
Ki
Vo
L
SW1
SW2
RL
C
Add a lossless filter to
achieve small ripple voltage,
but …
when switch is off, inductor
current cannot change
instantaneously and cause
spark (volt-second balance).
Vdd
Vo = DVdd
RL
Add a second switch that operates complementarily to arrive at
a functional switching converter.
t
8

9. Buck, Boost and Buck-Boost Converters (1)
Vx
SW1
Vdd
SW2
Vo
L
C
RL
Buck
Vx
L
Vdd
Vo
SW2
SW1
C
SW1
Vdd
Ki
Vo
SW2
L
C has to be in parallel with RL for
filtering, leaving three ways to place
L, SW1 and SW2 between Vdd and RL.
RL
Boost
Vx
One L and one C gives a second
order switching converter.
Three types of converters:
Step-down: buck
Step-up: boost
Step-up/down: buck-boost
(Boost-buck, or Cuk, is a 4th order
converter)
Buck-boost
C
RL
9

10. Buck, Boost and Buck-Boost Converters (2)
state 1
Vx
MN
Vdd
L
i
D1
C
state 2
RL
L
Vx
i
MN
state 1
Vo
D1
C
RL
Boost
MN
Vdd
Ki
state 1
SW1 is the controlling switch that
determines the duty ratio D, while SW2
provides a path for the inductor
current i to flow when SW1 is off.
Buck
state 2
Vdd
Vo
Vx
D1
Vo
i
L
state 2
C
RL
Buck-Boost
SW1 can be a power NMOS (MN). If
power PMOS is used, the phase has to
be reversed.
To prevent i from going negative, SW2
is usually implemented by a diode
(D1), but the forward drop gives a low
efficiency.
Note that Vo of buck-boost is negative.
10

11. I-V Relations of C and L
The I-V characteristics of a capacitor and an inductor are described by
ic = C
dv c
dt
ic
C
+
vc
i
v =L
di
dt
+
L
v
−
−
Approximations are very useful in many calculations:
ic = C
ΔVc
Δt
v =L
Δi
Δt
For sinusoidal steady state, the phasor relations are:
zc =
Ki
vc
1
=
ic
jωC
z =
v
= jω L
i
11

12. Volt-Second Balance
Switching actions cause ripples for both inductor current (i ) and
capacitor voltage (vc). In the steady state, both quantities return
to the same value after one cycle.
i
+ v
V (S1 )
= m1
L
−
di
dt
⇒ ΔI =
i
ΔI
I
L
v =L
V (S2 )
= −m2
L
V
Δt
L
0A
t1
t2
(or DT) (or D ' T)
Inductor current has to obey volt-second balance (VS balance):
V (S1)×t1 + V (S2)×t2 = 0
⇒
m1t1 = m2t2
or
m1D = m2D’
It is used to compute the conversion ratio M = Vo/Vdd.
Ki
12

13. Inductor, Input, Switch, Diode and Tail Currents
i
Consider the buck converter:
idd
is
L
Vx
MN
Vdd
i
D1
id
it
Vo
ic
Io
C
RL
Input current idd: current through Vdd
idd
is
Switch current is: i in State 1
Diode current id: i in State 2; even if diode
is implemented by NMOS switch
Tail current it: current through the
combination of C and RL.
id
Capacitor current ic: ac part of tail current
Load current io: averaged tail current
Ki
it
Io
13

14. Continuous Conduction Mode
The converter is operating in continuous conduction mode (CCM)
if the inductor current is always larger than zero.
Boost converter
(Step-up)
Buck converter
(Step-down)
Vdd
Vo
+V −
S1
S2
m1D = m2D’
⇒ (Vdd-Vo)D = VoD’
⇒ M=
Ki
V0
=D
Vdd
Vdd
Buck-boost converter
(Step-up/down)
Vo
+V −
S1
S2
m1D = m2D’
⇒ VddD = (Vo-Vdd)D’
⇒ M=
V0
1
=
Vdd 1 − D
Vdd
Vo
S1
+
V
−
S2
m1D = m2D’
⇒ VddD = -VoD’
⇒ M=
V0
−D
=
Vdd 1 − D
14

15. Discontinuous Conduction Mode
When the switching converter is operation in CCM, one switching
cycle has two states S1 and S2. When the load current becomes
smaller and smaller, eventually the inductor current would fall to
zero, and the converter then operates in discontinuous conduction
mode (DCM) with a third state S3. During D3T, all switches are open.
V (S1 )
= m1
L
V (S2 )
= −m2
L
V (S3 )
=0
L
i
ΔI
i =0
DT
D2 T
D3 T
VS balance becomes:
m1D = m2D2
Ki
15

16. Ringing Suppression
When both switches are open, L,
C and the parasitic capacitor Cx
at Vx form a resonance circuit
that leads to serious ringing.
Vx
Vdd
SW2
i
Cx
SW3
Vx
Vo
L
SW1
We may add a small switch to
short the inductor when SW1
and SW2 are both off [Jung 99].
Vdd
C
RL
SW2
Vo
L
SW1
Cx
C
RL
i
Vdd
Vo
Ki
Vx
Vx
16

17. Pseudo-Continuous Conduction Mode
By increasing the size of the ringing suppression switch, a switching
converter may work in pseudo-continuous mode (PCCM). It was first
employed in a single-inductor dual-output (SI-DO) converter to
increase the current handling capability [Ma 03b]. When both SW1
and SW2 are open, the freewheel switch SWFW is closed to allow
free-wheeling of i at Ipccm.
SWFW
L
Vx
SW1
Vdd
Vo
i
SW2
C
i
Ipccm
RL
0
Ki
17

18. Efficiency of Buck Converter
Rs
Idd
Io
L
S1
Vdd
Vo
R
S2
Rd
C
RL
η=
Po
VI
= o o
Pdd VddIdd
For an ideal buck converter working in CCM, the conversion ratio M
is Vo/Vdd = D, and Io:Idd = 1:D, giving η=1. If conduction loss is
accounted for, then Io/Idd is still 1/D, but M is modified as M=ηD,
with
P
1
η= o =
R + DR s + D 'R d
Pdd
1+
RL
Ki
18

19. Efficiency of 2nd Order Converters
By accounting for conduction losses due to switch, diode and inductor
series resistance (Rs, Rd and R , respectively), the efficiencies of buck,
boost and buck-boost converters are computed as [Ki 98]
1
R + DR s + D 'R d
1+
RL
Buck:
Boost:
ηboost =
Buck-boost:
Ki
ηbuck =
ηbuck −boost =
1
1 R + DR s + D 'R d
1+ 2
RL
D'
1
1 R + DR s + D 'R d
1+ 2
RL
D'
19

20. Performance Evaluation Parameters
For a good voltage regulator, the output voltage should remain
constant even the input voltage, load current or temperature changes.
Steady state parameters:
Line regulation
Load regulation
Temperature coefficient
Small signal parameters:
Power supply rejection
Output impedance
Transient parameters:
Line transient (settling times)
Load transient (settling times)
Reference tracking time
Ki
20

21. Line Regulation
Line regulation is the change of Vo w.r.t. the change in Vdd:
line reg. =
=
ΔVo
ΔVdd
in mV / V
ΔVo / Vo
ΔVdd
in % / V
Switching converters are non-linear circuits for large signal changes,
and hand analysis is impossible. It could be obtained by simulation.
In datasheets, line regulation is usually measured.
Ki
21

22. Power Supply Rejection
For a good switching converter (also for bandgap reference and
linear regulator), the output voltage should be a weak function w.r.t.
the supply voltage. Hence, a small signal parameter, the power
supply rejection, gives good indication of line regulation.
Power supply rejection (PSR) is the small signal change of Vo w.r.t.
the small signal change in Vdd.
vo
v dd
In transfer function form:
PSR =
In dB:
PSR = 20 × log
v dd
vo
Usually |vo/vdd| < 1, but we customarily give a positive PSR in dB.
Note:
Ki
Line reg. ≈ PSR × ΔVdd
22

23. Load Regulation and Output Impedance
Load regulation is the change of Vo w.r.t. the change in Io:
load reg. =
=
ΔVo
ΔIo
in mV / mA
ΔVo / Vo
ΔIo
in % / mA
In datasheets, load regulation is usually measured.
In the small signal limit, load regulation is the output impedance:
Ro =
Ki
dVo
dIo
in Ω
23

24. Temperature Coefficient
Temperature coefficient (TC) is the change of a parameter X w.r.t.
the change in T, and is a large signal parameter:
TC =
=
ΔX X(T2 ) − X(T1 )
=
ΔT
T2 − T1
in [X] / o C
ΔX / X
ΔT
in ppm / o C
TC could be positive or negative.
Ki
24

25. PWM Voltage Mode Control (1)
A regulated switching converter consists of the power stage and
the feedback circuit.
MP
Vo
L
Vg
MN
RL
ck
C
R1
CMP
Q
R
Q
va
EA
A(s)
S
va
bVo
Vref
ramp
Q
R2
va
Q
ramp
ck
Ki
For a buck converter, if an on-chip charge pump is not available,
then the NMOS power switch is replaced by a PMOS power switch.
25

26. PWM Voltage Mode Control (2)
The output voltage Vo is scaled down by the resistor string R1 and
R2. The scale factor is b = R2/(R1+R2).
The scaled output voltage bVo is compared to the reference
voltage Vref to generate a lowpass filtered voltage Va through the
compensator A(s).
At the start of the clock, the SR latch is set and the switch MP is
turned on, starting the duty cycle. A sawtooth waveform (ramp)
synchronized with the clock ramps up.
When the ramp reaches the level of Va (trip point), the SR latch is
reset, terminating the duty cycle.
Ki
When the SR latch is set, i ramps up. When the SR latch is reset,
i ramps down. In the steady state, i returns to the same level at
the start of every clock cycle.
26

27. PWM Feedback Action
For stability, the control loop has to have negative feedback.
Assume Vo drops suddenly due to change in load or disturbance
⇒ error voltage Verr = (Vref–bVo) becomes larger
⇒ Va = A(f)(Vref–Vo) also becomes larger
⇒ with a higher Va, it takes the ramp longer to reach Va
⇒ duty ratio D is temporarily increased
⇒ more current is dumped into the load
⇒ Vo rises accordingly and eventually settles to the original
value
Note that A(s) is the frequency response of the compensator,
not of the op amp Aop(s).
Ki
27

28. PWM Current Mode Control
A current mode controlled switching converter is realized by replacing
the fixed voltage ramp with the inductor current ramp.
L
MP
Vo
i
Vdd
RL
MN
C
R1
CMP
Q
R
Q
va
EA
A(s)
S
Vdd
ck
Vref
R2
current
sensor
i /N
va
NR f
Ki
bVo
i Rf
28

29. Sub-harmonic Oscillation and Slope Compensation
Output of EA Va cannot change in one cycle. If inductor current is
perturbed by an amount of ΔI1, oscillation occurs if
ΔI2
−m2
=
> 1 ⇔ D > 0.5
m1
ΔI1
Ia = Va / R f
D < 0.5
Ia = Va / R f
D > 0.5
−m2
m1
ΔI1
ΔI2
ΔI1
m1
−m2
ΔI2
To prevent oscillation, employ slope compensation by adding a negative
slope to Ia (i.e., Va) to suppress the change in ΔI2.
Ia = Va / R f
−mc
m1
Ki
ΔI1
m − m2
m
ΔI2
= c
< 1 ⇔ mc > 2
mc + m1
2
ΔI1
−m2
ΔI2
29

30. Current Mode PWM with Compensation Ramp
In practice, the output of EA (Va) should not be tempered, and a
compensation ramp of +mc is added to m1 instead.
L
MP
Vo
i
Vdd
RL
MN
C
R1
CMP
Q
(m1 + mc )R f
va
Ki
EA
A(s)
S
−(m2 − mc )R f
vb
DT
R
Q
va
bVo
Vref
Vdd
R2
i /N
ck
V2I
vb
NR f
ramp from OSC
compensation
ramp
30

31. Synchronous Rectification
To eliminate loss due to forward diode drop, the power diode is
replaced by a power NMOS MN, and the scheme is known as
synchronous rectification. To eliminate short-circuit loss of MP and
MN, a break-before-make (BBM) buffer is used.
L
MP
Q, VP
i
Vdd
RL
MN
C
VP
VN
BBM
Buffer
Ki
Q
R
Q
S
Additional logic is needed
for DCM operation.
Q
(ck)
VN
φ1
φ2
φ1 =
VP
φ2
Non-overlapping φ1 and φ2
φ1
φ2 = VN
31

32. Multiple-Output Converters
Consider two boost converters that operate in deep DCM:
L
i1
Vdd
Vo1
S1
S0
C1
i1
R L1
T
2T
T
2T
L
i2
Vdd
Ki
Vo2
S2
S0
i2
R L2
C2
32

33. Single-Inductor Multiple-Output Converters
Time-multiplexing allows sharing one inductor and diverting the
inductor current to two or more outputs [Ma 03a]:
Vo1
S1
L
C1
i
R L1
i
Vdd
T
S0
Vo2
S2
C2
Ki
2T
R L2
33

34. SIMO Converter in PCCM
To handle large load currents, raise the inductor current floor to
operate in PCCM. Add a free-wheeling switch (SFW) to short the
inductor when the inductor current reaches Ipccm [Ma 03b].
SFW
Vo1
S1
L
C1
i
R L1
i
T
S0
Vo2
S2
C2
Ki
2T
T
Vdd
2T
i
R L2
Ipccm
34

35. SI-MIMO Converter
Some applications need two converters in series with reduce efficiency.
Vbat
Vload
Vsrc
Energy-harvesting
source
Boost 1
Rechargeable
battery
Boost 2
Load
Reorganize by using a SI-DIDO converter that needs only one inductor
[Lam 04b], [Lam 07b], [Sze 08].
Vbat
Vbat
Vload
Vsrc
Ki
Energy-harvesting
source
SI-DIDO boost
Load
Rechargeable
battery
35

36. Development of SI-MO and SI-MIMO Converters
The recent years sees active R&D activities of SI-MO and SI-MIMO
switching converters for low power applications. It is important to
recognize the contribution of the first developers.
The idea of SI-MO converters was first conceived in [Goder 97], and
only boost sub-converters were considered.
An SI-DO converter with buck-boost sub-converters was discussed in
[Ma 97] to demonstrate the switching flow graph modeling method.
SI-DO converters became commercial products [MAX 98, UCC 99].
The concept of SI-MO was reinvented [Li 00, Ma 00, Ma 01, May
01]. [Ma 01] stressed the importance of DCM operation for reducing
cross-regulation. A systematic classification is discussed in [Ki 01].
DCM operation is extended to PCCM operation in [Ma 02].
The concept of SI-MIMO was conceived [Lam 04, Lam 07].
Ki
36

37. References: Switching Converter Fundamentals
Books:
[Brown 01] M. Brown, Power Supply Cookbook, EDN, 2001.
[Erickson 01] R. W. Erickson and D. Maksimovic, Fundamentals of Power
Electronics, 2nd Edition, Springer Science, 2001.
[Kassakian 91] J. G. Kassakian, M. F. Schlecht and G. C. Verghese, Principle
of Power Electronics, Addison Wesley, 1991.
[Krein 98] P. E. Krein, Elements of Power Electronics, Oxford, 1998.
Papers:
[Jung 99] S. H. Jung et. al., "An integrated CMOS DC-DC converter for
battery-operated systems," IEEE Power Elec. Specialists Conf.,
pp. 43–47, 1999.
[Ki 98]
Ki
W. H. Ki, "Signal flow graph in loop gain analysis of DC-DC PWM
CCM switching converters," IEEE TCAS-1, pp.644-655, June
1998.
37

38. References: Early Development of SI-MIMO Converters (1)
[Goder 97] D. Goder and H. Santo, “Multiple output regulator with time sequencing,” US
Patent 5,617,015, April 1, 1997.
[Ma 97]
[MAX 98]
"MAX685: Dual-output (positive and negative) DC-DC converter for CCD and
LCD", Maxim Datasheet, 1998.
[UCC 99]
"UCC3941: 1V synchronous boost converter," Datasheet, Unitrode
Semiconductor Products, Jan. 1999.
[Li 00]
T. Li, "Single inductor multiple output boost regulator," US Patent 6,075,295,
June 13, 2000.
[Ma 00]
Ki
Y. H. Ma and K. M. Smedley, "Switching flow-graph nonlinear modeling
method for multistate-switching converters," IEEE Trans. on Power Elec.,
pp.854–861, Sept., 1997.
D. Ma and W. H. Ki, "Single-inductor dual-output integrated boost converter
for portable applications," 4th Hong Kong IEEE Workshop on SMPS, pp. 4251, Nov. 2000.
38

39. References: Early Development of SI-MIMO Converters (2)
[Ma 01a]
D. Ma, W. H. Ki, C. Y. Tsui and P. Mok, "A single-inductor dual-output
integrated DC/DC boost converter for variable voltage scheduling",
IEEE/ACM Asia South Pacific Design Automation Conf., LSI University Design
Contest, pp.19–20, Jan. 2001.
[May 01]
[Ma 01b]
D. Ma, W. H. Ki, P. Mok and C. Y. Tsui, "Single-inductor multiple-output
switching converters with bipolar outputs", IEEE Int'l. Symp. on Circ. and
Syst., pp. III-301 - III-304, Sydney, May 2001.
[Ma 01c]
D. Ma, W. H. Ki, C. Y. Tsui and P. Mok, "A 1.8V single-inductor dual-output
switching converter for power reduction techniques," IEEE Symp. on VLSI
Circ., Kyoto, Japan, pp. 137-140, June 2001.
[Ki 01]
W. H. Ki and D. Ma, "Single-inductor multiple-output switching converters",
IEEE Power Elec. Specialists Conf., Vancouver, Canada, pp.226–231, June
2001.
[Ma 02]
Ki
M. W. May, M. R. May and J. E. Willis, "A synchronous dual-output switching
dc-dc converter using multibit noise-shaped switch control," IEEE Int’l SolidState Circ. Conf., pp.358–359, Jan 2001.
D. Ma, W.H. Ki, and C.Y. Tsui, "A pseudo-CCM / DCM SIMO switching
converter with freewheel switching", IEEE Int'l Solid–State Circ. Conf., San
Francisco, pp.390–391+476. Feb. 2002.
39

40. References: Early Development of SI-MIMO Converters (3)
[Ma 03a]
[Ma 03b]
D. Ma, W. H. Ki and C. Y. Tsui, "A pseudo-CCM/DCM SIMO switching
converter with freewheel switching," IEEE J. of Solid-State Circ., pp. 10071014, June 2003.
[Lam 03]
Y. H. Lam, W. H. Ki, C. Y. Tsui and P. Mok, "Single-inductor dual-input dualoutput switching converter for integrated battery charging and power
regulation," IEEE Int'l. Symp. on Circ. and Syst., Bangkok, Thailand, pp.
III.447-III.450, May 2003.
[Lam 04]
H. Lam, W. H. Ki, C. Y. Tsui and D. Ma, "Integrated 0.9V charge-control
switching converter with self-biased current sensor," IEEE Int'l Midwest
Symp. on Circ. & Sys., pp.II.305–II.308, July 2004.
[Koon 05]
S. C. Koon, Y. H. Lam and W. H. Ki, "Integrated charge-control singleinductor dual-output step-up/step-down converter," IEEE Int'l. Symp. on
Circ. and Syst., Kobe, Japan, pp. 3071-3074, May 2005.
[Lam 07]
Y. H. Lam, W. H. Ki and C. Y. Tsui, "Single-inductor multiple-input multipleoutput switching converter and method of use," US Patent 7,256,568, Aug
14, 2007.
[Ma 09]
Ki
D. Ma, W. H. Ki, C. Y. Tsui and P. Mok, "Single-inductor multiple-output
switching converters with time-multiplexing control in discontinuous
conduction mode," IEEE J. of Solid-State Circ., pp. 89-100, Jan. 2003.
D. Ma, W. H. Ki, and C. Y. Tsui, "Single-inductor multiple-output switching
converters in PCCM with freewheel switching," US Patent 7,432,614, Oct. 7,
2008.
40