Sepic Converter Design and Operation

Submitted 5/1/14 in partial completion of the requirements for a

BS degree from WPI

By
Gregory Sharp

Advisor: Alex Emanuel

Table of contents
I) Abstract
II) Introduction
III) Topology
a) Operation
b) Specifications
c) Duty Cycle Calculations
d) Inductor Calculations
e) Simulation results
IV) Potentiometer Controlled PWM
a) PWM Demonstration
b) Circuit diagram
c) Simulation results
V) Feedback Controlled PWM
a) Feedback Flowchart
b) Feedback Results at Various Levels of Gain
VI) Summary
VII) References

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Table of Figures
Fig 3.1 SEPIC operation
Fig 3.2 SEPIC Simulation
Fig 3.3 Graph of Vout and Pulse
Fig 3.4 Graph of ICout, IL1 and Pulse
Fig 3.5 Graph of Vout
Fig 3.6 Graph of Pout and Pin
Fig 3.7 Graph of Vout, D and VCin with Vin=10V
Fig 4.1 Graph of Triangle wave and Sinusoidal control wave
Fig 4.2 Graph of controlled square wave
Fig 4.3 Labelled schematic of SEPIC converter using a potentiometer to control PWM.
Fig 4.4 Graph of 555 and Triangle wave
Fig 4.5 Graph of Comparator output to MOSFET, Triangle Wave and Potentiometer Control Signal
Fig 5.1 Flow chart for feedback operation
Fig 5.2 Graph of Vout, as Vin increases. Gain is almost zero
Fig 5.3 Graph of Vout, as Vin increases. Gain is too low
Fig 5.4 Graph of Vout, as Vin increases. Gain is too high
Fig 5.5 Graph of Vout, as Vin increases. Gain is at a good value

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I) Abstract
The purpose of this project was to design and optimize a SEPIC dc/dc converter (Single
Ended Primary Inductance Converter). The SEPIC converter allows a range of dc voltage to be
adjusted to maintain a constant voltage output. This project talks about the importance of dc-dc
converters and why SEPIC converters are used instead of other dc-dc converters. This project
also goes into detail about how to control the output of the converter with either a potentiometer
or feedback to show how it can be implemented in a circuit. From this project, one learns dc-dc
converter optimization and control.

II) Introduction
Circuits run best with a steady and specific input. Controlling the input to specific subcircuits is crucial for fulfilling design requirements. AC-AC conversion can be easily done with a
transformer; however dc-dc conversion is not as simple. Diodes and voltage bridges are useful
for reducing voltage by a set amount, but can be inefficient. Voltage regulators can be used to
provide a reference voltage. Additionally, battery voltage decreases as batteries discharge which
can cause many problems if there is no voltage control. The most efficient method of regulating
voltage through a circuit is with a dc-dc converter. There are 5 main types of dc-dc converters.
Buck converters can only reduce voltage, boost converters can only increase voltage, and buckboost, Ck, and SEPIC converters can increase or decrease the voltage.
Some applications of converters only need to buck or boost the voltage and can simply
use the corresponding converters. However, sometimes the desired output voltage will be in the
range of input voltage. When this is the case, it is usually best to use a converter that can
decrease or increase the voltage. Buck-boost converters can be cheaper because they only require
a single inductor and a capacitor. However, these converters suffer from a high amount of input
current ripple. This ripple can create harmonics; in many applications these harmonics
necessitate using a large capacitor or an LC filter. This often makes the buck-boost expensive or
inefficient [2]. Another issue that can complicate the usage of buck-boost converters is the fact
that they invert the voltage. Ck converters solve both of these problems by using an extra
capacitor and inductor. However, both Ck and buck-boost converter operation cause large
amounts of electrical stress on the components, this can result in device failure or overheating.
SEPIC converters solve both of these problems [2].

III) Topology
a) Operation:
All dc-dc converters operate by rapidly turning on and off a MOSFET, generally with a
high frequency pulse. What the converter does as a result of this is what makes the SEPIC
converter superior. For the SEPIC, when the pulse is high/the MOSFET is on, inductor 1 is
charged by the input voltage and inductor 2 is charged by capacitor 1. The diode is off and the
output is maintained by capacitor 2. When the pulse is low/the MOSFET is off, the inductors
output through the diode to the load and the capacitors are charged. The greater the percentage of
time (duty cycle) the pulse is low, the greater the output will be. This is because the longer the
inductors charge, the greater their voltage will be. However, if the pulse lasts too long, the
capacitors will not be able to charge and the converter will fail as shown in Fig 3.6.

Fig 3.1 SEPIC operation [4]

Fig 3.2 SEPIC Simulation

Fig 3.3 Graph of Vout and Pulse

This graph shows the output ripple as a function of the input square wave.

Fig 3.4 Graph of ICout, IL1 and Pulse

This graph shows the ripple in the inductors and how the output capacitor charges and discharges
based on the pulse.
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b) Specifications:
The converter should meet certain standards
6V<Vin<18V
Vout=10V
Iout=1A
Fsw=50 kHz
An acceptable output current ripple is io, pp< 0.5 A
An acceptable output voltage ripple is Vo, pp< 0.1 V

c) Duty Cycle Calculation:

The amount that the SEPIC converters step up or down the voltage depends primarily on the
Duty Cycle and the parasitic elements in the circuit.
The output of an ideal SEPIC converter is
D * Vi
Vo
1 D
However, this does not account for losses due to parasitic elements such as the diode drop VD.
These make the equation:

D * Vi
1 D
This becomes
Vo VD
D
Vi Vo VD
Vo VD

The maximum Duty Cycle will occur when the input voltage is at the minimum. If VD=.5V, the
Duty Cycle is

10V .5V
.64
6V 10V .5V
The minimum Duty cycle will occur when the input voltage is at the maximum.
D min

D min

10V .5V
.37
18V 10V .5V

d) Inductor Calculation:
In theory, the larger the inductors are the better the circuit will operate and reduce the
ripple. However, larger inductors are more expensive and have a larger internal resistance. This
greater internal resistance will make the converter less efficient. Creating the best converter
requires choosing inductors that are just large enough to keep the voltage and current ripple at an
acceptable amount.
L

Vi min ( D max)
(6V )(.63)

151.2uH
io max f sw
(.5 A)(50kHz)

Inductors with low internal resistance and around 150uH will be ideal for both of the inductors in
the circuit.

e) Simulation Results:
SEPIC WITH PARASITICS
V
1
0
10
RL1 1
1.5
.07
L1
1.5
2
150u IC=0
S
2
0
20
0
SWK
.MODEL
SWK VSWITCH (RON=.2 ROFF=1MEG VON=1
VOFF=0)
VP
20
0
PULSE (0
10
0
1n
1n
.01045m
.02m)
RCl 2
2.5
.08
C1
2.5
3
10u
IC=0
L2
3
3.5
150u IC=0
RL2 3.5
0
.07
D
3
4
Dix
.MODEL
Dix
D (RS= .07 BV=480
N=.01)
C2
4
4.5
100u IC=0
RC2 4.5
0
.08
R
4
0
10
.PROBE
.TRAN
.005 .1
.099 10u
UIC
.END

Fig 3.5 Graph of Vout

Fig 3.6 Graph of Pout and Pin

This graph shows that the efficiency of the Converter=Pin/Pout= .91

SEPIC AVERAGED MODEL WITH PARASITICS AND D INCREASING FROM 0 TO 1

VC
30
0
PWL (0, 0 100m, 1)
D increasing from 0 to 1
V
1
0
10
L1
1
1.5
150u IC=0
RL1 1
2
.3
VD
2
3
0
E
3
20
Value= {(1-V(30))/V(30)*V(5)}
MOSFET V=Vo*(1-D)/D
VF
20
0
0
C1
3
3.5
1u
IC=0
RC1 3.5
4
.08
L2
4
4.5
150u IC=0
RL2 4.5
0
.3
G
4
5
Value={((1-V(30))/(V(30)*V(30)))*I(VF)} Diode I =Iin*(1-D)/D2
C2
5
5.5
100u IC=0
RC2 5.5
0
.08
R
5
0
10
.PROBE
.TRAN
0
.1
0
10u
UIC
.END

Fig 3.7 Graph of Vout, D and VCin with Vin=10V

This graph shows that as D increases from 0 to 1, Vout increases exponentially, reaching Vin
around D=.5. When D gets too high, VCin cannot stay charged and this causes Vout to drop as
well.

IV) Potentiometer Controlled PWM

The SEPIC converter is able to either increase or decrease an input voltage by controlling
the Duty Cycle of a pulse to the MOSFET. One way to do that is to directly control the Duty
cycle using a potentiometer. There are some applications for which this control method is
suitable but it is insufficient for many other applications.
In order to drive the MOSFET, a pulse is needed. A 555 timer is used to produce a square
wave with a set frequency and a Duty cycle50%. However, the duty cycle from the 555 cannot
be easily changed without switching resistors. In addition, the SEPIC requires a duty cycle below
50% to buck the voltage when the input voltage is low. The pulse width will need to be modified
separately from the 555 because the 555 cannot change or produce a duty cycle less than 50%.
First a resistor and a capacitor are used in lowpass to produce a triangle wave from the square
wave output of the 555. Afterwards, this is sent to the negative pin of a comparator. The positive
pin of the comparator receives a controlled voltage signal. Whenever the controlled voltage is
greater than the triangle wave, the comparator will output voltage and otherwise it will be off.
The greater this signal, the greater the duty cycle of the comparator output will be. One way to
control this signal is to step down voltage using a potentiometer. Luckily, this signal can be kept
in the same range as the triangle wave by using the same input that drives the 555 timer. The
duty cycle will not change when the input or the output voltage changes which means there is
full control of how much the SEPIC steps up or down the voltage. This has both advantages and
disadvantages for the circuit.
Full control of the circuit can be useful. The potentiometer allows the SEPIC to output a
wide range of voltage from a wide range of input. This could be useful in battery applications
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that need to run on various levels of power. One example would be a flashlight with adjustable
brightness. This SEPIC converter could allow it to run on a large range of power with greater
efficiency than simply reducing the voltage with a potentiometer to control the output. However,
this control method does have its drawbacks.
Most applications of the SEPIC converter control the voltage automatically. The problem
with relying on controlling the input for circuit control is that there is no circuit feedback. When
using a potentiometer, the only way to maintain the correct output is to watch the output and
adjust accordingly. Visual feedback is only useful in certain circumstances. Usually it is best to
use the SEPIC converter to hold a single output without the need for control when using a SEPIC
as part of a large circuit.

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a) PWM Demonstration

Fig 4.1 Graph of Triangle wave and Sinusoidal control wave

Fig 4.2 Graph of controlled square wave

This graph shows the resulting output of the comparator with the inputs shown in Fig 4.1. The
pulse is high when the control signal is greater than the triangle wave. This results in a higher
duty for high control signals.

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b) Circuit Diagram

Fig 4.3 Labelled schematic of SEPIC converter using a potentiometer to control PWM.

c) Simulation Results

Fig 4.4 Graph of 555 and Triangle wave

This is the output of the 555 with the triangle wave produced by the capacitor in lowpass.

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Fig 4.5 Graph of Comparator output to MOSFET, Triangle Wave and Control Signal from Potentiometer

This graph shows that the comparator turns on soon after the triangle wave falls below the
control signal (which is a simulation error) and turns off immediately when the triangle wave
rises above the signal.

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V) Feedback Controlled PWM

While a potentiometer allows for control of the SEPIC converter output during operation,
it is unable to hold a constant output with a variable input that changes. This is used in the
majority of SEPIC converter applications which require automation to correct an input voltage.
The simplest way to maintain a constant output is to use a feedback loop that will change the
output automatically instead of by manual control (using visual feedback from a voltmeter). The
feedback loop should be able to increase the duty cycle to raise the output when the output is too
low and decrease it when the output is too high. To do this, the output will need to be compared
to a reference voltage which remains constant even if the input changes. The error between the
output and the reference voltage is then amplified and added to a set bias voltage. The resulting
voltage is then used as the control voltage for PWM. When the output is too low, the amplified
error increases which causes the control voltage to increase. The increase in control voltage
increases the duty cycle until the output is correct. When the output is too high, the amplified
error becomes negative which decreases the duty cycle to correct output. Both of these scenarios
work together to constantly make slight adjustments to the duty cycle so that the output remains
stable. The simulations for feedback show how the output changes with the gain of the amplifier

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a) Feedback Flow Chart

Fig 5.1 Flow chart for feedback operation

b) Feedback Results at Various Levels of Gain

SEPIC AVERAGED MODEL WITH FEEDBACK
Gain
Feedback loop
Ve
30
0
10
Ee
33
0
Value={(1+7*(V(30,0)-V(5,0)))}
Eb
34
0
Value={.5*(1+(V(30,0)+V(33,0))/10)}
SEPIC averaged model
V
.5
0
0
VC
1
.5
PWL(0,0 100m, 20)
L1
1
1.5
150u IC=0
RL1 1
2
.07
VD
2
3
0
E
3
20
Value={(V(34,0)-1)/V(34,0)*V(5,0)}
VF
20
0
0
C1
3
3.5
1u
IC=0
RC1 3.5
4
.08
L2
4
4.5
150u IC=0
RL2 4.5
0
.07
G
4
5
Value={(V(34,0)-1)/(V(34,0)*V(34,0))
C2
5
5.5
100u IC=0
RC2 5.5
0
.08
R
5
0
10
.PROBE
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Gain*(Vref-Vo)= Gain*Error
this value equals D

.TRAN
.END

.1

10m

UIC

Fig 5.2 Graph of Vout, as Vin increases. Gain is almost zero

This graph shows that if the gain of the amplifier is around zero, Vout is uncontrolled.

Fig 5.3 Graph of Vout, as Vin increases. Gain is too low

This graph shows that if the gain of the amplifier is too low, Vout is controlled, but too high.
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Vin=6V=Minimum
Fig 5.4 Graph of Vout, as Vin increases. Gain is too high

This graph shows that if the gain of the amplifier is too high, the converter cannot boost
sufficiently and Vout does not reach 10V until after Vin is greater than the minimum value.

Vin=6V=Minimum
Fig 5.5 Graph of Vout, as Vin increases. Gain is at a good value

This graph shows that with the correct amount of gain, Vout will be at the correct value as long
as Vin is greater than the minimum value.
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VI) Summary
Most battery operated circuits require dc-dc conversion to maintain full operation. In
most circumstances that require stepping up and down the input voltage, SEPIC converters are
worth the price of the extra inductor and capacitor for the efficiency and stable operation they
provide. While this project does go into detail about simulation results for the SEPIC converter,
the physical potentiometer controlled SEPIC converter built was unsuccessful. Additionally, a
cost benefit analysis to determine peak efficiency with the cheapest cost for the inductors and
capacitors was never done. These are both things that could have been done with extra time and
group members. From this project, one learns dc-dc converter optimization and control.

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VII) References
1. Falin, Jeff. Designing DC/DC converters based on SEPIC topology 2008, Texas
Instruments. December 2013 <http://www.ti.com/lit/an/snva168e/snva168e.pdf>
2. Dr. Ridly, Ray. Analyzing the Sepic Converter 2006, Ridley Engineering. March 2014
<http://www.switchingpowermagazine.com/downloads/Sepic%20Analysis.pdf>
3. Durn, E. Sidrach-de-Cardona, M. Galn, J. Andjar, J.M. Comparative Analysis of BuckBoost Converters used to obtain I-V Characteristic Curves of Photovoltaic Modules April 2014
<http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04592243>

Pictures from
[4] Wikipedia user Mclausma <http://en.wikipedia.org/wiki/File:S1_open.jpg>
<http://en.wikipedia.org/wiki/File:S1_closed.jpg>

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