ET4384
Design of Low power Supplies
Assignment on
DESIGN OF DIFFERENT TOPOLOGIES OF
SMPS
Submitted on 13.03.2014
By
Rizwan Rafique Syed (4333861)
Shihabudheen Kavungal Kolparambath (4310411)
2
Table of Contents
Problem Content Page No
Introduction 3
Problem Statement 3
A Possible topologies 3
A1 Lowest Frequency in BCM Mode 4
B Calculation details for different topologies 4
C Preferred topology when 28
D Preferred topology when 28
Conclusion 30
References 30
List of Tables
Table Content Page No
1 Summary of Down converter parameters when 27
2 Summary of Up converter parameters when 27
3 Summary of Flyback converter parameters when 28
4 Summary of Down converter parameters when 29
5 Summary of Up converter parameters when 29
6 Summary of Flyback converter parameters when 30
3
INTRODUCTION
There are several topologies associated with SMPS. However this assignment discusses three basic
topologies. i.e., Buck (Forward) Converter, Boost (Downward) Converter and Buck-Boost (Fly back)
Converter. Each topology can be operated in different modes according to the requirement/
application.
To select the best topology for a given requirement, it is essential to know the operation, pros &
cons of a particular topology. Following factors are considered for selection of SMPS.
1. The output voltage is lower/higher than input voltage
2. The magnitude of output current
3. Switching at fixed/variable frequency
4. Cost
5. Size of component
6. Isolation requirement
7. Losses & Efficiency
8. EMI Level
9. Output Ripple
In the assignment, we will investigate the three topologies in continuous, discontinuous and
boundary condition mode as per the customer requirement considering the above factors and hence
a choice will be made for selection of the SMPS for the problem requirement.
PROBLEM STATEMENT
Design a switched mode power supply rail with , given that the available input voltages
are . The limit of output current is given as .
Assumptions
Series resistance of coil is related to self-inductance as √ , where in and
in when varies very much within one switching cycle,
Diode is assumed to have no forward voltage drop and no losses
Ringing time is neglected
Fixed frequency operation,
SOLUTION
A. The possible topologies
The required voltage is 12V while the input voltages available are 5V & 48V. As a preliminary survey
without analysing any selection factors, following combinations are possible.
Step up 5V to 12V using a Up converter-CCM, DCM & BCM
Step down 48V to 12V using a Down converter- CCM, DCM & BCM
4
Step up 5V to 12V using a Flyback converter- CCM, DCM & BCM
Step down 48V to 12V using a Flyback converter- CCM, DCM & BCM
A1. Lowest frequency in BCM mode
The main advantage of using SMPS in BCM mode is that the frequency can be varied according to
the variation in the input voltage and load. It is also important to mention that the switching losses
and core losses increases with increase in frequency. Therefore, designer will have a tendency to
decrease the frequency at High power and low input voltage. However, the reduction in frequency is
restricted to audible frequency (20Hz-20 kHz). BCM should be kept above the highest audible
frequency value. Therefore, In order to make switching inaudible to humans at a safe side, the
lowest frequency should be well above 20 kHz, so that component tolerance should not bring the
frequency to or near to the highest audible frequency. In this assignment, we have considered 25kHz
as the lowest possible frequency.
Note: If the designer is using components with small tolerance limit, the lowest frequency could be
selected near to highest audible frequency accordingly.
B. Calculation details for different topologies
This part of the assignment investigates the topologies discussed in A with facts & figures. Following
parameters are calculated for these topologies in different conduction mode.
a. Inductance value, L
b. Series resistance of coil, RL
c. Effective value of current through the coil,
d. Losses in the inductor, and
e. Effective value of current through the switch,
f. Losses in the switch,
g. Total Losses in the converter and efficiency
Given data
Available FET’s 50V/RDSon-0.02Ω, 100V/RDSon-0.05Ω, 200V/RDSon-0.1Ω
Assumptions
Series resistance of coil is related to self-inductance as √ , where in and in when varies very much within one switching cycle,
Diode is assumed to have no forward voltage drop and no losses
Ringing time is neglected
5
Fixed frequency operation,
No correction required for inductor value.
In case of voltage inversion, sign of voltage may be neglected.
FET losses-Only conduction losses are considered
COMPONENT SELECTION
The main components in the Converter considered in this assignment are Diode, Switch, Inductor
and Capacitor. Since design and selection of diode and capacitor are not covered in this assignment,
we will focus only on Inductor and Switch. Inductance of Inductor is calculated based on formula,
which will be calculated in the subsequent session. The available switch is FETs 50V/RDSon-0.02Ω,
100V/RDSon-0.05Ω, 200V/RDSon-0.1Ω. The selection of switch is based on maximum voltage that
will appear across the switch during turn off. Therefore the switch selection is as follows
a. Down Converter- FETs 50V/RDSon-0.02Ω , since Vin =48V is the maximum voltage across
switch
b. Up Converter- FETs 50V/RDSon-0.02Ω , since Vout =12V is the maximum voltage across
switch
c. Flyback Converter with input voltage as 5V- FETs 50V/RDSon-0.02Ω , since Vin+Vout
=5+12=17V is the maximum voltage across switch
d. Flyback Converter with input voltage as 48V-FETs 100V/RDSon-0.05Ω , since Vin+Vout
=48+12=60 V is the maximum voltage across switch
I. DOWN CONVERTER
a. CCM Mode
The duty cycle in continuous conduction mode is given by
The minimum value of inductance so that current will not go to discontinuous conduction mode is
(
)
The series resistance of the inductor is approximated as
√
√
6
The size of the coil is determined by inductance value and the maximum energy that has to be
stored. Therefore, which determines the storage capacity is calculated as
The variation of current in one switching cycle is given by
Since the losses in the circuit are analysed using the RMS values, RMS value of current through the
coil can be found using
Similarly, current through the switch is calculated as
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is very less, core losses are neglected.
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
7
Efficiency
b. DCM Mode
The relationship between input and output voltage in DCM mode is given by
Assuming we get
The maximum value of L is calculated as
( )
The series resistance of the inductor is approximated as
√
, which determines the storage capacity is calculated as
The variation of current in one switching cycle is given by
The effective value of current through inductor is given by
8
The RMS value of current through switch is calculated
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 8A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
c. BCM Mode
Neglecting dead time, duty cycle under all circumstances is
9
Since , maximum current through coil can be calculated as
In BCM mode, is varying according to the input voltage. , at any is given by
The minimum value of frequency is given by
( )
Considering , the maximum inductor value can be calculated as
( )
The series resistance of the inductor is approximated as
√
The effective value of current through inductor is given by
The variation of current in one switching cycle is given by
The RMS value of current through switch is calculated
10
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 8A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
II. BOOST CONVERTER
a. CCM Mode
The duty ratio is given by
The minimum value of L in order to guarantee continuous mode of operation is given by
11
The series resistance of the inductor is approximated as
√
The peak inductor current is calculated as
The variation of current in one switching cycle is given by
Since losses are our main concern, the RMS value of coil current can be calculated using the below
equation.
For the switch, calculation of RMS current yields,
Now the losses can be calculated from RMS current
12
Since the variation of current in switching cycle is very less, core losses is neglected.
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
b. DCM Mode
In DCM mode, the duty cycle is given by
Assuming
The maximum value of L is calculated as
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
√
13
The variation of current in one switching cycle is given by
The RMS value of current through the inductor can be calculated using
The effective value of current through the switch is calculated using the formula
(
)
(
)
Therefore,
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 19.2A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
14
c. BCM Mode
The duty ratio is given by
In BCM mode, is varying according to the input voltage. , at any is given by
The maximum inductance value corresponding to the lowest frequency is given by
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
The variation of current in one switching cycle is given by
The RMS value of current through the inductor can be calculated using
15
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 19.2A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
III. FLYBACK CONVERTER (Input is 5V, while output is 12V)
a. CCM Mode
The duty ratio is given by
16
The minimum value of L in order to guarantee continuous mode of operation is given by
(
)
(
)
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
The variation of current in one switching cycle is given by
The RMS value of current through the inductor can be calculated using
(
)
(
)
(
)
(
)
The RMS value of current through the switch can be calculated using
(
)
(
)
17
(
)
(
)
Now the coil losses can be calculated from RMS current
Since the variation of current in switching cycle is less, core loss is neglected.
While the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
b. DCM Mode
The duty cycle in DCM mode is given by
The maximum value of value of inductance is given by
(
)
18
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
√
√
The variation of current in one switching cycle is given by
The RMS value of current through coil is
The RMS value of current through switch is
Now the losses can be calculated from RMS current
19
Since the variation of current in switching cycle is 27.2A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
Efficiency
c. BCM Mode
The duty ratio in BCM mode
In BCM mode, is varying according to the input voltage. , at any is given by
(
)
The maximum inductance value corresponding to the lowest frequency is given by
(
)
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
20
(
)
The variation of current in one switching cycle is given by
The RMS value of current through coil is
The RMS value of current through switch is
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 27.2A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Total Converter losses with 50V FET
21
Efficiency
IV. FLYBACK CONVERTER (Input is 48V, while output is 12V)
a. CCM Mode
The duty ratio is given by
The minimum value of L in order to guarantee continuous mode of operation is given by
(
)
(
)
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
The variation of current in one switching cycle is given by
22
The RMS value of current through the inductor can be calculated using
(
)
(
)
(
)
(
)
The RMS value of current through the switch can be calculated using
(
)
(
)
(
)
(
)
Now the coil losses can be calculated from RMS current
Since the variation of current in switching cycle is very less, core losses is neglected
while the conduction losses in the switch is calculated as
Note that here for FET 100V as voltage appearing across switch during turn off is
60V and hence available option is 100V FET
Total Converter losses with 100V FET
Efficiency
23
b. DCM Mode
The duty cycle in DCM mode is given by
The maximum value of value of inductance is given by
(
)
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
√
√
The variation of current in one switching cycle is given by
The RMS value of current through coil is
24
The RMS value of current through switch is
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 10A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Note that here for FET 100V as voltage appearing across switch during turn off is
60V and hence available option is 100V FET
Total Converter losses with 100V FET
Efficiency
c. BCM Mode
The duty ratio in BCM mode
25
In BCM mode, is varying according to the input voltage. , at any is given by
(
)
The maximum inductance value corresponding to the lowest frequency is given by
(
)
(
)
The series resistance of the inductor is approximated as
√
The peak value of current through the coil is given by
(
)
The variation of current in one switching cycle is given by
The RMS value of current through coil is
The RMS value of current through switch is
26
Now the losses can be calculated from RMS current
Since the variation of current in switching cycle is 10A, core losses = winding losses
Now the conduction losses in the switch is calculated as
Note that here for FET 100V as voltage appearing across switch during turn off is
60V and hence available option is 100V FET
Total Converter losses with 100V FET
Efficiency
The table below depicts the summary of above calculations.
27
Table 3: Summary of Down converter parameters when
Down Converter
CCM DCM BCM
Duty Cycle 0.25 0.25 0.25
Lmin for CCM and Lmax for DCM (µH) 225.00 11.25 45.00
RL (ohm) 0.071 0.016 0.032
Ipeak (A) 4.20 8.00 8.00
Ripple Current d(IL) 0.40 8.00 8.00
IL,RMS (A) 4.00 4.62 4.62
Isw,RMS 2.00 2.31 2.31
Pcoil,loss (W) 1.14 0.34 0.68
Psw,loss (50V)-R=0.02 0.08 0.11 0.11
Psw,loss (100V)-R=0.05 0.20 0.27 0.27
Psw,loss (200V)-R=0.1 0.40 0.53 0.53
Total converter Loss with 50V FET 1.22 0.79 1.46
Total converter Loss with 100V FET 1.34 0.61 0.95
Total converter Loss with 200V FET 1.54 0.87 1.21
Efficiency in % 97.52 98.39 97.04
Table 3: Summary of Up converter parameters when
Up Converter
CCM DCM BCM
Duty Cycle 0.58 0.58 0.58
Lmin for CCM and Lmax for DCM (µH) 30.38 1.52 6.08
RL (ohm) 0.026 0.006 0.012
Ipeak (A) 10.08 19.20 19.20
Ripple Current d(IL) 0.96 19.20 19.20
IL,RMS (A) 9.60 11.09 11.09
Isw,RMS 7.34 8.47 8.47
Pcoil,loss (W) 2.41 0.72 1.44
Psw,loss (50V)-R=0.02 1.08 1.43 1.43
Psw,loss (100V)-R=0.05 2.69 3.58 3.58
Psw,loss (200V)-R=0.1 5.38 7.17 7.17
Total converter Loss with 50V FET 3.49 2.87 4.31
Total converter Loss with 100V FET 5.10 4.30 5.02
Total converter Loss with 200V FET 7.79 7.89 8.60
Efficiency in % 93.23 94.36 91.77
28
Table 3: Summary of Flyback converter parameters when
Up-Down Converter for 5V Up-Down Converter for 48V
CCM DCM BCM CCM DCM BCM
Duty Cycle 0.71 0.71 0.71 0.20 0.20 0.20
Lmin for CCM and Lmax for DCM (µH) 25.95 1.30 5.19 192.00 9.60 38.40
RL (ohm) 0.024 0.005 0.011 0.066 0.015 0.029
Ipeak (A) 25.16 27.20 27.20 5.25 10.00 10.00
Ripple Current d(IL) 1.36 27.20 27.20 0.50 10.00 10.00
IL,RMS (A) 13.60 15.70 15.70 5.00 5.77 5.77
Isw,RMS 11.43 13.19 13.19 2.24 2.58 2.58
Pcoil,loss (W) 4.47 1.33 2.67 1.64 0.49 0.98
Psw,loss (50V)-R=0.02 2.61 3.48 3.48 0.10 0.13 0.13
Psw,loss (100V)-R=0.05 6.53 8.70 8.70 0.25 0.33 0.33
Psw,loss (200V)-R=0.1 13.06 17.41 17.41 0.50 0.67 0.67
Total converter Loss with 50V FET 7.08 6.15 8.81 1.74 0.62 1.11
Total converter Loss with 100V FET 11.00 10.04 11.37 1.89 1.31 2.29
Total converter Loss with 200V FET 17.54 18.74 20.07 2.14 1.16 1.65
Efficiency in % 87.14 88.65 84.49 96.20 97.34 95.44
C. From the table 1,2 &3 shown above and the calculation, for the given problem/application,
Buck converter operating in DCM is preferred over any other topologies. This is due to the fact
that the losses are minimum/efficiency is maximum for this topology. The higher efficiency is
due to the following reasons.
a. The inductor value is less as compared to other modes in Buck Converter. This results in
reduced series resistance and hence reduced coil loss.
b. The voltage appearing across the switch during turn off is 48V,neglecting transients/over
voltage condition, FET of 50V can be selected for the design. Besides, The resistance of
this switch is less compared to other switch reducing the conduction losses.
c. Although core loss is neglected in CCM mode, despite the addition of core losses in
DCM, DCM mode is still having the highest efficiency due to the fact that the inductance
and hence series resistance is much lower in DCM mode compared to CCM mode
D. When the minimum output current is changed from 0.2A to 1A, the preferred topology would
be down or forward converter in CCM mode. Table 4,5 &6 gives the complete details when
This is again due to the higher efficiency/low losses. The change in efficiency when
changes are due to the following reasons.
a. The inductance value is reduced from as is a function of
in CCM mode given by the formula
In this formula, we can find that
29
Since coil resistance is related to inductance by √ , thus coil resistance
reduces, which in turn reduces the coil losses ( . Therefore overall converter
efficiency is increased.
b. In CCM mode, is very less compared to other modes.
Therefore core loss is assumed to be zero which in turn reduces the total loss and hence
increases the efficiency.
Table 4: Summary of Down converter parameters when
Down Converter
CCM DCM BCM
Duty Cycle 0.25 0.25 0.25
Lmin for CCM and Lmax for DCM (µH) 45.00 11.25 45.00
RL (ohm) 0.032 0.016 0.032
Ipeak (A) 5.00 8.00 8.00
Ripple Current d(IL) 2.00 8.00 8.00
IL,RMS (A) 4.04 4.62 4.62
Isw,RMS 2.02 2.31 2.31
Pcoil,loss (W) 0.52 0.34 0.68
Psw,loss (50V)-R=0.02 0.08 0.11 0.11
Psw,loss (100V)-R=0.05 0.20 0.27 0.27
Psw,loss (200V)-R=0.1 0.41 0.53 0.53
Total converter Loss with 50V FET 0.60 0.79 1.46
Total converter Loss with 100V FET 0.72 0.61 0.95
Total converter Loss with 200V FET 0.93 0.87 1.21
Efficiency in % 98.76 98.39 97.04
Table 5: Summary of Up converter parameters when
Up Converter
CCM DCM BCM
Duty Cycle 0.58 0.58 0.58
Lmin for CCM and Lmax for DCM (µH) 6.08 1.52 6.08
RL (ohm) 0.012 0.006 0.012
Ipeak (A) 12.00 19.20 19.20
Ripple Current d(IL) 4.80 19.20 19.20
IL,RMS (A) 9.70 11.09 11.09
Isw,RMS 7.41 8.47 8.47
Pcoil,loss (W) 1.10 0.72 1.44
Psw,loss (50V)-R=0.02 1.10 1.43 1.43
Psw,loss (100V)-R=0.05 2.74 3.58 3.58
Psw,loss (200V)-R=0.1 5.49 7.17 7.17
Total converter Loss with 50V FET 2.20 2.87 4.31
Total converter Loss with 100V FET 3.84 4.30 5.02
Total converter Loss with 200V FET 6.59 7.89 8.60
Efficiency in % 95.62 94.36 91.77
30
Table 6: Summary of Flyback converter parameters when
Up-Down Converter for 5V Up-Down Converter for 48V
CCM DCM BCM CCM DCM BCM
Duty Cycle 0.71 0.71 0.71 0.20 0.20 0.20
Lmin for CCM and Lmax for DCM (µH) 5.19 1.30 5.19 38.40 9.60 38.40
RL (ohm) 0.011 0.005 0.011 0.029 0.015 0.029
Ipeak (A) 71.40 27.20 27.20 6.25 10.00 10.00
Ripple Current d(IL) 6.80 27.20 27.20 2.50 10.00 10.00
IL,RMS (A) 13.62 15.70 15.70 5.05 5.77 5.77
Isw,RMS 11.44 13.19 13.19 2.26 2.58 2.58
Pcoil,loss (W) 2.00 1.33 2.67 0.75 0.49 0.98
Psw,loss (50V)-R=0.02 2.62 3.48 3.48 0.10 0.13 0.13
Psw,loss (100V)-R=0.05 6.55 8.70 8.70 0.26 0.33 0.33
Psw,loss (200V)-R=0.1 13.10 17.41 17.41 0.51 0.67 0.67
Total converter Loss with 50V FET 4.62 6.15 8.81 0.85 0.62 1.11
Total converter Loss with 100V FET 8.55 10.04 11.37 1.01 1.31 2.29
Total converter Loss with 200V FET 15.10 18.74 20.07 1.26 1.16 1.65
Efficiency in % 91.21 88.65 84.49 97.95 97.34 95.44
Conclusion
This assignment investigates the variable topologies in Switched mode power supply. The design of
SMPS for this assignment was based on factors like component selection and Converter losses, with
many factors neglected for the ease of calculation and to reduce the complexity. However, actual
design involves many factors, some of which are listed below.
a. The design of each component, including Capacitor, Diode, Switch and Inductor
b. Level of EMI
c. Output ripple and ripple rejection
d. Switching losses in the Switches, Diode losses etc.
e. Ringing time
f. Transient conditions like variation in input voltage, load variation etc.
g. Turns ratio in case of fly back converter
h. And most importantly the cost
References
1. Ir. Frans Pansier (2014). Lecture Notes, Introduction to SMPS topologies, chapter 1,2,3,4 & 5.
ET 4384, Design of low power supplies
2. Mohan Undeland and Robbins. Power Electronics-Converters, Application and Design(2nd
edition), Wiley Publications