AN-1269: Designing an Inverting Power Supply Using the ADP2441/ADP2442...

AN-1269
APPLICATION NOTE
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Designing an Inverting Power Supply Using the ADP2441/ADP2442
Synchronous Step-Down DC-to-DC Regulators
by Kevin Tompsett and Ricky Yang
INTRODUCTION
Applications such as bipolar amplifiers, optical modules,
CCD bias, and OLED displays usually require a negative output voltage from a positive input voltage. Designers of power
management systems need versatile switching controllers and
regulators that allow them to solve these power management
challenges. The ADP2441/ADP2442 switching regulators from
Analog Devices, Inc., provide synchronous buck functionality.
This ranges from a 36 V input voltage down to 0.6 V output
voltage at up to 1 A with a switching frequency range from
300 kHz to 1 MHz.
Although targeted for synchronous step-down applications, the
versatility of the ADP2441/ADP2442 allows these parts to realize
an inverting buck boost topology, which can generate a negative
output voltage from a positive input voltage, without additional
cost, component count, or solution size.
These parts utilize synchronous topology, which gives higher
efficiency at a full load and lower noise at a light load operation
than an asynchronous part. If higher efficiency at a low load
is desired, the ADP2441 has a pulse skip mode (PSM). The
ADP2442 can operate in forced constant current mode (CCM)
for lower noise at low load or with PSM enabled.
This application note describes how to implement the
ADP2441/ADP2442 in a synchronous inverting buck boost
topology to generate negative output voltages from positive
input power supplies. In addition, some design challenges and
possible solutions are addressed. For a faster design time, the
ADIsimPower design tool can be used. This tool uses far more
sophisticated design equations and methods to create a robust
design that meets the requirements under all conditions almost
instantaneously. It is available for download via the ADIsimPower
product page or directly via ADP244x Inverting Buck Boost
Designer.
Rev. 0 | Page 1 of 8
AN-1269
Application Note
TABLE OF CONTENTS
Introduction ...................................................................................... 1
Input Capacitor Selection .................................................................5
Revision History ............................................................................... 2
Compensation Selection ...................................................................6
Buck Boost Topology Basics ........................................................... 3
Enable Signal Level Shifting .............................................................6
Implementation with the ADP2441/ADP2442.............................. 3
Reduce VOUT Over Shoot Before Start Up ......................................7
Output Voltage Setting ..................................................................... 4
Conclusion..........................................................................................8
Inductor Selection ............................................................................ 4
References ...........................................................................................8
Ramp Compensation ....................................................................... 4
Related Links ......................................................................................8
Output Capacitor Selection ............................................................. 5
REVISION HISTORY
7/14—Revision 0: Initial Version
Rev. 0 | Page 2 of 8
Application Note
AN-1269
BUCK BOOST TOPOLOGY BASICS
IMPLEMENTATION WITH THE ADP2441/ADP2442
The simplified buck boost topology is shown in Figure 1. The
topology consists of an inductor, two power switches operating
out of phase from one another, and input/output capacitors.
To implement the buck boost topology inverting power supply
application by using the ADP2441/ADP2442 synchronous buck
regulator, take into consideration some design restrictions as
listed in Table 1.
Figure 2 and Figure 3 show the current flow path during the on
time and off time, respectively. During the on time, Switch S1 is
on, S2 is off, and the current is flowing from the input capacitor,
charging the inductor while the output capacitor provides
energy to the load. During off time, Switch S1 is off, Switch S2
is on, and the current flows from the inductor to the load while
charging the output capacitor.
Note that the current flows from ground to VOUT, which results
in negative output voltage.
S2
RLOAD
11888-001
COUT
Figure 1. Buck Boost Topology
S2
COUT
11888-002
Figure 2. Current Flow Path During On Time
S1
L
CVCC
VOUT
CIN1
COUT
RLOAD
11888-003
CIN
VIN
S2
RF2
The steady state conversion ratio can be written per Equation 1
by applying the principles of inductor voltage-second balance
and capacitor charge balance on the topology. The dc inductor
current value, IL, in CCM is specified in Equation 2, and the
inductor ripple current, ∆IL, is shown in Equation 3.
IL =
I OUT
1− D
−V × (1 − D )
∆I L = OUT
L × f SW
FB
RC1 CC1
Figure 3. Current Flow Path During Off Time
VOUT
−D
=
VIN
1− D
RF1
(1)
(2)
(3)
Rev. 0 | Page 3 of 8
VIN
COMP
CC2
EN
CBST
VIN
ADP2441/
ADP2442
SW
CC
L1
COUT1
PGND
–VOUT
CVCC 2
VCC
D1
COUT2
J2
H
RFREQ
L
CSS
Figure 4. Inverting Buck Boost Topology Implemented
with the ADP2441/ADP2442
11888-004
VIN
ADP2441/
ADP2442
4.5 V
20 V
1.2 A/1.2 A
To convert the synchronous buck regulator into the buck boost
topology, the inductor and output capacitor are connected
similar to the buck topology. Note that the ground and the
output voltage points are reversed as shown in Figure 4.
RLOAD
BST
L
CIN
VOUT
SYNC/
MODE/
SS/TRK
S1
VCC
VIN
>
<
<
FREQ
L
CIN
VOUT
Device
Parameters
VUVLO
VMAX
IOCP
The minimum input voltage of the buck boost circuit must be
higher than the UVLO voltage of the ADP2441/ADP2442, which
has the typical value of 4.5 V to get the regulator to work. The
sum of the maximum input voltage and the absolute value of
the output voltage must be lower than the maximum operation
input voltage of the regulators, VMAX, which has the typical value
of 20 V. In addition, make sure the inductor peak current is
smaller than the OCP trigger point of the regulator with
accommodation for inductance tolerance.
AGND
S1
Voltage and Current
VIN_MIN
VIN_MAX + |VOUT|
IL_PEAK (IL_peak not = IOUT)
PGOOD
VIN
Table 1. Design Restrictions
AN-1269
Application Note
OUTPUT VOLTAGE SETTING
The output voltage is set by an external resistive divider. The
resistor values are calculated using
RTOP = RBOTTOM ×
VOUT − 0.6
(4)
0.6
To limit the output voltage accuracy degradation due to the FB
bias current (0.1 µA maximum) to less than 0.5% (maximum),
ensure that RBOTTOM < 30 kΩ.
over a wider range of duty cycle than could be achieved with
the old style fixed ramp compensation that many chips use. To
choose an inductor that will be current-mode stable first,
choose an inductor using Equation 5. Then check that Qn
calculated using Equation 8 is between 0.2 and 0.9 at both
minimum and maximum VIN. Equation 8 is based on Ridley’s
work in his An Accurate and Practical Small-Signal Model for
Current-Mode Control paper (see the References section).
Qn = 1/(π × (0.5 − D + 0.33 × fSW × L/(D × VIN))
(8)
Table 2 lists the recommended resistor divider for various
output voltages.
where:
fSW is the switching frequency.
Table 2. Resistor Divider for Difference Output Voltage
The peak inductor current is calculated by adding the dc component and half of the peak-to-peak inductor ripple current.
RTOP ± 1% (kΩ)
10
20
47.5
10
22
28
35.7
RBOTTOM ± 1% (kΩ)
10
10
15
2.21
3
1.47
1.5
I PEAK = I AVG +
The inductor value is determined by the operating frequency,
input voltage, and inductor ripple current. Using a smaller
inductance leads to a faster transient response, but degrades
efficiency due to a larger inductor ripple current. Using a larger
inductance value leads to a smaller ripple current and better
efficiency, but results in a slower transient response.
Taking into account this maximum peak inductor current, the
application space of the ADP2441/ADP2442 in the inverting
buck boost topology for common input voltages at 600 kHz
switching frequency is shown in Figure 5 with the assumption
that the peak-to-peak inductor ripple current is 40% of the
inductor average current.
1.4
MAXIMUM OUTPUT CURRENT (A)
As a guideline, the inductor ripple current (∆IL) is typically set
to 30% of the maximum inductor average current, IAVG. The
inductor value is calculated using the following equation:
(5)
where:
VIN is the input voltage.
D is the duty cycle:
D=
VOUT
VOUT + VIN
I AVG
1.2
VIN = 5V (ADP2441/ADP2442)
VIN = 12V (ADP2441/ADP2442)
VIN = 15V (ADP2441/ADP2442)
1.0
0.8
0.6
0.4
0.2
(6)
0
–30
KRP is the chosen current ripple percentage. A good rule of
thumb is around 30%.
IAVG is the average inductor current:
I
= OUT
1− D
(9)
The peak inductor current is also the peak current in the
internal power switch, which is the sense element used to
determine whether to induce current limit. To avoid premature
current limit, the peak inductor current should not exceed the
OCP threshold current, IOCP, of the devices.
INDUCTOR SELECTION
VIN × D
L=
K RP × I AVG × f SW
I AVG × K RP
2
–25
–20
–15
–10
OUTPUT VOLTAGE (V)
–5
0
11888-005
VOUT (V)
−1.2
−1.8
−2.5
−3.3
−5
−12
−15
Figure 5. Application Space for Common Input Voltage at fSW = 600 kHz
(7)
fSW is the switching frequency.
RAMP COMPENSATION
The saturation current of the inductor must be larger than the
peak inductor current. For ferrite core inductors with a steep
saturation characteristic, the saturation current rating of the
inductor should be higher than the current limit threshold for
the IC. This prevents the inductor from saturating during
normal operation.
As with all current mode converters, the ADP2441/ADP2442 in
an inverting buck boost topology require ramp compensation to
assure current mode stability. The ADP2441/ADP2442 use an
innovative adaptive ramp scheme that is dependent on duty
cycle. This results in an ideal ramp compensation amplitude
Rev. 0 | Page 4 of 8
Application Note
AN-1269
OUTPUT CAPACITOR SELECTION
INPUT CAPACITOR SELECTION
The output voltage of the inverting buck boost tends to be
noisier than a buck converter. This is because unlike a buck
converter, the output current is discontinuous in the inverting
buck boost topology. The fast rise and fall times of Switch S2
result in noise spikes on the output voltage as the current in S2
is ramped up quickly from 0 to IL and back to 0. This makes it
very important to use low ESR, MLCC capacitors and good
layout techniques to reduce parasitic inductance.
The input current is also discontinuous in the inverting buck
boost topology. Therefore, the fast rise and fall times of Switch
S1 result in noise spikes on the input rail as the current in S1 is
ramped up quickly from 0 to IL and back to 0. This makes it
very important to use low ESR, MLCC capacitors, and good
layout techniques to reduce parasitic inductance.
Equation 10 gives an estimated value of the minimum
capacitance required to keep the output voltage ripple within
an allowable range.
(10)
where:
∆VRIPPLE is the allowable output ripple voltage.
ESR is the total equivalent series resistance of the output
capacitors.
IPEAK is the inductor peak current.
(12)
where:
IAVG is the average inductor current.
ESRC IN is the equivalent series resistance of the input
capacitors.
To achieve as low output ripple voltage as possible, MLCC
capacitors that have very low ESR values are recommended. The
rms current rating of the selected output capacitors should be
larger than the values calculated using Equation 11.
I RMS _ C OUT =
(11)
At least one 10 µF ceramic capacitor is recommended; place it
as close to PVIN pin as possible. The rms current of the selected
input capacitor should be greater than the value calculated in
Equation 13.
2
D 2 × I OUT
 2
∆I 2 
I RMS _ C IN =  I OUT
+ L  × D +
12 
1− D

(13)
Although the majority of the capacitance on the input voltage
rail is referenced to system ground, an additional input
decoupling capacitor placed from the input voltage to the GND
pin of ADP2441/ADP2442 can reduce the output voltage ripple
and improve the transient response as shown in Figure 6.
VIN
CVCC
RC1 CC1
VIN
FB
COMP
CC2
EN
BST
RF1
CBST
VIN
ADP2441/
ADP2442
SW
CC
L1
COUT1
PGND
–VOUT
SYNC/
MODE/
SS/TRK
RF2
VCC
CIN1
AGND
CVCC 2
VCC
D1
COUT2
J2
H
RFREQ
L
CSS
Figure 6. Inverting Buck Boost Topology with Input Decoupling Capacitor
from VIN to GND Pin
Rev. 0 | Page 5 of 8
11888-006
2
2
 I OUT × D  × (1 − D ) + ∆I L × (1 − D ) + I 2 × D


OUT
12
 1− D 
I AVG × D
f SW × (0.05 × VIN − I PEAK × ESRC IN )
FREQ
f SW
I OUT × D
× ( ∆VRIPPLE − I PEAK × ESR )
C IN =
PGOOD
COUT ≈
Equation 12 calculates the minimum input capacitance
assuming energy depletion of the input capacitor during
on time is no more than 5% of the input voltage.
AN-1269
Application Note
Use the following design guidelines to calculate the values of the
compensation network components.
COMPENSATION SELECTION
The control-to-output transfer function of the power stage in
buck boost topology can be written in the form:
•
Set the cross frequency, fC, between fP and 1/3 of fZ1
fC =

 

s
s
1 −
 

 2 × π × f  × 1 + 2π × f 
Z1  
Z2 

GVD (s) = K ×


s
1 +

 2 ×π × fP 
•
(14)
RC =
f C × VOUT
(19)
K × f P × g m × 0.6
where:
gm is the transconductance of the internal error amplifier
with a typical value of 250 µS.
R is the load resistor.
Ri is the current sense gain with a typical value of 0.49 V/A.
•
2
(1 − D ) × R
2 ×π × L × D
Place the compensation zero at 1/2 of the power stage pole, fP
CC1 =
The transfer function GVD(s) has one right-half-plane-zero
(RHPZ), fZ1; one zero, fZ2; and one pole, fP. The values of the
zero and pole are:
•
CC2 =
(15)
1
1+ D
fP =
2 × π × R × COUT
(20)
D×L
(21)
(1 − D )2 × R × RC
ENABLE SIGNAL LEVEL SHIFTING
(16)
2 × π × RESR × COUT
2 × R × CCOUT
(1 + D ) × RC
Place the compensation pole at the RHPZ fZ1
The ADP2441/ADP2442 have an EN pin to enable and disable
the regulator. However, in the inverting buck boost application,
the IC is referenced to the negative output voltage instead of the
system ground. Once the chip is enabled, pulling the enable pin
to ground will not turn the IC off because the voltage from the
enable pin to AGND of the IC will be equal to VOUT.
(17)
where:
RESR is the equivalent series resistance of the output capacitor.
One of the possible solutions for this issue is to use NPN and
PNP transistors and several resistors to level shift the enable
level as shown in Figure 7.
Note that the precision enable feature of the ADP2441/ADP2442
is lost when the level shifting circuit is used. If the enable
function is not needed, simply connect the EN pin to the input
voltage as shown in Figure 4.
VIN
CVCC
RF1
RC1 CC1
FB
COMP
ADP2441/
ADP2442
VIN
EN
FREQ
OFF
PGOOD
ON
CC2
VIN
SW
CC
L1
COUT1
PGND
–VOUT
CVCC 2
VCC
D1
COUT2
J2
H
RFREQ
L
CSS
Figure 7. EN Level Shifting Circuit for Inverting Buck Boost Topology
Rev. 0 | Page 6 of 8
11888-007
EN
RF2
CBST
BST
CIN
VCC
AGND
CIN1
VIN
SYNC/
MODE/
SS/TRK
fZ2 =
(18)
Calculate the RC value using the equation:
where:
R × (1 − D )
K=
Ri × (1 + D )
f Z1 =
f P × f Z1
Application Note
AN-1269
This issue can be seen in all buck regulators when they are used
to perform the inverting buck boost topology described herein
and it is very hard to eliminate the issue completely. One
solution is to put a Schottky diode on the output of the
converter. This diode reduces the positive voltage somewhat
and prevents any silicon diodes in the ADP2441/ADP2442
regulator or any load components from turning on and causing
problems. Another solution is to reduce the resistance of the
feedback resistor divider until the voltage drop across the
resistor divider is lower than the forward voltage of the body
diode of the low-side MOSFET. Then, the shutdown current
flows through the resistor divider instead of the body diode as
shown in Figure 10 and the positive voltage on the PGND pin
can be reduced to an acceptable value.
VOUT OVER SHOOT BEFORE STARTUP
When using the synchronous buck regulator as an inverting
buck boost topology, one common issue is that the output
voltage starts off positive before the regulator is enabled as
shown in Figure 8.
T
500mV
0V 2
ADP2441/ADP2442
CH2 1.0V BW
M2.00ms
A CH2
–2.72V
11888-008
VIN
VIN
CIN
L
SW
Figure 8. VOUT Ramps Up Before Startup
RTOP
ADP2441/ADP2442
VIN
VIN
CIN
SW
FB
COUT
RBOTTOM
PGND
VOUT
11888-010
This positive output voltage is caused by the shutdown current
of the regulator and any other chips connected to the negative
rail, flowing from the PGND pin of the IC through the body
diode of the low-side MOSFET and back to the system ground
as shown in Figure 9. The body diode of the low-side MOSFET
is that which clamps the VOUT at the forward voltage of the body
diode with a typical value of around 500 mV.
Figure 10. Current Flows Through the Feedback Resistor Divider
Figure 11 shows the result of reducing the resistance of the
resistor divider. The positive VOUT voltage decreases from
500 mV to 180 mV.
T
L
RTOP
FB
COUT
180mV
PGND
VOUT
11888-009
0V 2
RBOTTOM
Because VOUT is connected to the PGND pin of the regulator
which is actually the reference point for the internal circuits like
UVLO, the positive voltage shown in the PGND pin decreases
the UVLO threshold voltage. The regulator may fail to start up
when the input voltage is very close to the UVLO threshold
voltage of the regulator, which has a typical value of 4.0 V.
CH2 1.0V BW
M2.00ms
A CH2
–2.72V
11888-011
Figure 9. Current Flows Through Body Diode of Low Side MOSFET
Figure 11. Reduce VOUT Ramp Up by Decreasing the Resistance of the
Feedback Resistor Divider
The drawback of this solution is that the quiescent current
of the system increases because the current flowing through the
feedback resistor is higher. This increased quiescent current can
reduce the efficiency at light loads quite a bit, though the actual
power loss is quite small.
Rev. 0 | Page 7 of 8
AN-1269
Application Note
CONCLUSION
REFERENCES
The ADP2441/ADP2442 can be used successfully in the inverting buck boost topology resulting in a simple, inexpensive,
and small solution for creating a negative rail. In addition to
detailing all of the necessary design equations, this application
note provides a simple EN level shifting circuit when the
enable/disable functionality is needed. Also, the potential
start-up issue inherent with the inverting buck boost topology
is avoided with two simple solutions.
R. B. Ridley. An Accurate and Practical Small-Signal Model for
Current-Mode Control. Ridley Engineering Inc. 1999.
By following the design equations and suggestions in this
application note, the system designer can ensure a robust
design that satisfies all their requirements.
RELATED LINKS
Resources
ADP2441
ADP2442
AN-1083
AN-1168
ADP244x Inverting Buck
Boost Designer
Description
Data Sheet, 36 V, 1 A, Synchronous Step-Down DC-to-DC Regulator
Data Sheet, 36 V, 1 A, Synchronous Step-Down DC-to-DC Regulator with External Clock Synchronization
Application Note, Designing an Inverting Buck Boost Using the ADP2300 and ADP2301 Switching Regulators
Application Note, Designing an Inverting Power Supply Using the ADP2384/ADP2386 Synchronous Step-Down
DC-to-DC Regulators
ADIsimPower Design Tool
©2014 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
AN11888-0-7/14(0)
Rev. 0 | Page 8 of 8
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