calculations for single ended primary inductor converter

1. Department of Electrical & Computer Engineering
ECE 573: Power Electronics
ECE 573 power electronics
SEPIC Analysis
primary-inductor converter
of professor: Dr. Akram Abu
Single-ended primary
under the guidance o
2014
Abu-Aisheh,Ph.D
ANANTHALAKSHMI ADAPA
12/8/2014

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Table of Contents
SINGLE-ENDED PRIMARY-INDUCTOR CONVERTER
1. Abstract 2
2. overview 3
3. difference between converters 4
4. methodology 5
Continuous mode operation 6
5. practical design 7
Calculation considerations 7
Output voltage 8
L & C Voltages 8
Voltage Ripple 9
Diode current 9
MOSFET selection 10
Isolation 10
6. Results and Observation 11
LT Spice designing 11
7. disadvantages 13
8. refrences 13

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Abstract:
The single-ended primary-inductance converter (SEPIC) is a DC/DC-converter that provides a positive
regulated output voltage from an input voltage that varies from above to below the output voltage. This
type of conversion is handy when the designer uses voltages (e.g.,12 V) from an unregulated input
power supply such as a low-cost wall wart. Unfortunately, the SEPIC is difficult to understand and
requires two inductors, making the power-supply footprint quite large. Recently, several inductor
manufacturers began selling off-the-shelf coupled inductors in a single package at a cost only slightly
higher than that of the comparable single inductor. The coupled inductor not only provides a smaller
footprint but also, to get the same inductor ripple current, requires only half the inductance required for
a SEPIC with two separate inductors. This article explains how to design a SEPIC converter with a
coupled inductor.
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Overview:
Single-ended primary-inductor converter (SEPIC) is a type of DC-DC converter allowing the
electrical potential (voltage) at its output to be greater than, less than, or equal to that at its input; the
output of the SEPIC is controlled by the duty cycle of the control transistor.
A SEPIC is essentially a boost converter followed by a buck-boost converter, therefore it is similar to
a traditional buck-boost converter, but has advantages of having non-inverted output (the output has
the same voltage polarity as the input), using a series capacitor to couple energy from the input to
the output (and thus can respond more gracefully to a short-circuit output), and being capable of true
shutdown: when the switch is turned off, its output drops to 0 V, following a fairly hefty transient
dump of charge.
SEPICs are useful in applications in which a battery voltage can be above and below that of the
regulator's intended output. For example, a single lithium ion battery typically discharges from 4.2
volts to 3 volts; if other components require 3.3 volts, then the SEPIC would be effective.

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Different converters showing line current waveform, DCM self-PFC and power
level
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Methodology
A converter similar to the Cuk is the single-ended primary inductance converter (SEPIC), as shown in
Fig. below. The SEPIC can produce an output voltage that is either greater or less than the input but with
no polarity reversal. To derive the relationship between input and output voltages, these initial
assumptions are made:
1. Both inductors are very large and the currents in them are constant.
2. Both capacitors are very large and the voltages across them are constant.
3. The circuit is operating in the steady state, meaning that voltage and current
waveforms are periodic.
4. For a duty ratio of D, the switch is closed for time DT and open for (1 _ D)T.
5. The switch and the diode are ideal.

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Continuous mode action:
A SEPIC is said to be in continuous-conduction mode ("continuous mode") if the current through the
inductor L1 never falls to zero. During a SEPIC's steady-state operation, the average voltage across
capacitor C1 (VC1) is equal to the input voltage (Vin). Because capacitor C1 blocks direct current
(DC), the average current across it (IC1) is zero, making inductor L2 the only source of load current.
Therefore, the average current through inductor L2 (IL2) is the same as the average load current and
hence independent of the input voltage
When switch turned on:
When switch S1 is turned on, current IL1 increases and the current IL2 increases in the negative
direction. (Mathematically, it decreases due to arrow direction.) The energy to increase the
current IL1 comes from the input source. Since S1 is a short while closed, and the instantaneous
voltage VC1 is approximately VIN, the voltage VL2 is approximately −VIN. Therefore, the capacitor C1
supplies the energy to increase the magnitude of the current in IL2 and thus increase the energy
stored in L2. The easiest way to visualize this is to consider the bias voltages of the circuit in a d.c.
state, then close S1.
When switch turn off
When switch S1 is turned off, the current IC1 becomes the same as the current IL1, since inductors do
not allow instantaneous changes in current. The current IL2 will continue in the negative direction, in
fact it never reverses direction. It can be seen from the diagram that a negative IL2 will add to the
current IL1 to increase the current delivered to the load. Using Kirchhoff's Current Law, it can be
shown that ID1 = IC1 - IL2. It can then be concluded, that while S1 is off, power is delivered to the load
from both L2 and L1. C1, however is being charged by L1 during this off cycle, and will in turn
recharge L2 during the on cycle.

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The practical design
Calculations
By considering
Vin = 12V
D = 0.6
Fs = 200KHz
L1 = L2 = 3.36μH

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C1 = C2 = 5.26μF
I0 = 5A
output voltage
the output voltage can be determined using the formula below
8
ݒ0 = ܸ௦ ൬
ܦ
1 − ܦ
൰ = 12 ൬
Ͳ.6
1 − Ͳ.6
൰ = 18ܸ
L and C voltages:
average inductor current, which is also the average source current will be calculated for calculating L
and C values
The average current in L1 is determined from
ܫ௅ଵ =
ܸ0 × ܫ0
ܸ௦
=
18 × 5
12
= 7.5ܣ
Now
Δ݅௅ଶ = Δ݅௅ଵ =
ܸ௦ × ܦ
ܮଵ × ܨ
=
12 × Ͳ.6
3.36 × 1Ͳି଺ × 2ͲͲ,ͲͲͲ
= 1Ͳ.72ܣ
Resulting the maximum and minimum current magnitudes in L1 are
ܫ௅ଵ,௠௔௫ = ܫ௅ଵ +
Δ݅௅ଵ
2
= 7.5 + ൬
1Ͳ.72
2
൰ = 12.86ܣ
ܫ௅ଵ,௠௜௡ = ܫ௅ଵ −
Δ݅௅ଶ
2
= 7.5 −
1Ͳ.72
2
= 2.14 ܣ
For the current in L2, the average is the same as the output current Io = 5 A. The variation
in IL2 is determined
ܫ௅ଶ,௠௔௫ = 5 +
1Ͳ.72
2
= 7.144ܣ
ܫ௅ଶ,௠௜௡ = 5 −
1Ͳ.72
2
= 2.86ܣ
The variation in iL1 when the switch is closed is found from

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ܸ௅ଵ = ܸ௅ଶ = ܸ௦ = ܮଵ ൬
Δ݅௅ଵ
ܦܶ
൰ = 3.36 × 1Ͳି଺ ൬
1Ͳ.72 × 2ͲͲ,ͲͲͲ
Ͳ.6
൰ = 12ܸ
The output stage consisting of the diode, C2, and the load resistor is the same
as in the boost converter, so the output ripple voltage is
ܸ௅ଶ = ܸ஼ଵ = ܸ௦ = 12ܸ
Voltage Ripple:
Kirchhoff’s voltage law applied to the circuit assuming no voltage ripple across the
capacitors, shows that the voltage across the switch when it is open is Vs + Vo. the
maximum reverse bias voltage across the diode when it is off is also Vs+ Vo. The output
stage consisting of the diode, C2, and the load resistor is the same as in the boost converter,
so the output ripple voltage is
By calculating
మ
௏ೄோ = 3.6Ω
ܴ = ௏బ
Δܸ0 = Δܸ௖ଶ = ௏బ×஽
ோ஼మி = ଵ଼×0.଺
ଷ.଺×ହ.ଶ଺×ଶ00,000 = 2.85ܸ
Diode current
Applications of Kirchhoff’s current law show that the diode and switch currents are
iD = 7.5 +10 = 17.5A when switch open
iD = 0 when switch closed
and
isw = 0 when switch open
isw = 17.5A when switch closed

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ଶ × ܴ஽ௌ,௢௡ × ܦெ௔௫ ൯ + (ܸௌ + ܸ0) × ܫொଵ × ൬
10
and switch voltage stress can be calculated as
ܸௌௐ,ௌா௉ூ஼ =
ܸ௦
1 − ܦ
=
12
1 − Ͳ.6
= 3Ͳ
Power MOSFET
The MOSFET peak current is
ܫொଵ,௠௔௫ = ܫ௅ଵ,௠௔௫ + ܫ௅ଶ,௠௔௫ = 12.86 + 7.84 = 2Ͳ.7ܣ
and the RMS current is
by considering VD = 0.5
ܫொଵ,௥௠௦ = ܫ0 ቌඨ
(ܸ௢ + ܸ௦ + ܸ஽) × (ܸ0 + ܸ஽)
ଶ ቍ = 2.916ܣ
ܸ௦
The rated drain voltage for the MOSFET must be higher than VIN+VOUT. RDS(ON) = 8 mΩ
and QGD = 10 nC is selected in this design. The gate drive current IG is taken 0.3A. The
estimated power loss is:
ܲொଵ = ൫ ܫொଵ
ܳீ஽ × ܨ
ܫீ
൰ = 44.78ܹ
Isolation:
Taking Isolated Single Ended Primary Inductance converters (Isolated SEPIC) are good choice
that can be used in high step-up photovoltaic applications. This type of converters has
advantages such as: 1- same input and output voltage polarity, 2- low input current ripple, 3-
Possibility of having multiple outputs, 4- Possibility of working in both step-up and step-down
modes, 5- Low amount of EMI due to low input current ripple and 6-Electrical isolation between
input and output
Simulation of SEPIC

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Disadvantages:
1. Like buck–boost converters, SEPICs have a pulsating output current. The similar Cuk
converter does not have this disadvantage, but it can only have negative output polarity,
unless the isolated Cuk converter is used.
2. Since the SEPIC converter transfers all its energy via the series capacitor, a capacitor
with high capacitance and current handling capability is required.
3. The fourth-order nature of the converter also makes the SEPIC converter difficult to
control, making them only suitable for very slow varying applications.
References:
1. Power Electronics text book by Daniel W. Hart
2. http://en.wikipedia.org/wiki/Single-ended_primary-inductor_converter
3. analysis of a SEPIC by Texas Instruments
4. high performance DC-DC controllers by liner technology
5. Analyzing the Sepic Converter by Dr. Ray Ridley, Ridley Engineering
6. Fundamentals of Power Electronics By Robert W. Erickson, Dragan Maksimovic