The document summarizes the internship work of analyzing and modeling a DC/DC buck converter. Key points: 1) The intern designed a buck converter with a 5V load using a 20V source and an analog control system. Simulations were done in MATLAB. 2) Components like inductor, capacitor, controller gain were calculated. Simulation results showed the control system ensured a steady 5V output. 3) A circuit layout was designed but not realized due to lack of components. An Arduino-based approach was explored but not fully implemented. 4) The internship provided hands-on experience in power electronics design from modeling to implementation that will help in future academic pursuits.

1. REPORT – Analysis and Modelling of
DC/DC Buck converter
Tomsk State University of Control Systems & Radioelectronics,
Tomsk, Russia.
Faculty Mentor
Mihalchenko Sergey G.
Mentor
Denis Pakhmurin
Submitted by
Anirudh Shandilya Annavajhala
Bachelors in Electronics and Instrumentation
SRM University
Chennai, 603203
India

2. Acknowledgement –
I thank Mr. Mihalchenko Sergey G. for guiding me through the
internship patiently. I also thank Mr. Denis Pakhmurin for taking time
from his busy schedule to help and see us around. I would also like to
extend my gratitude to International relations office, TUSUR especially
Mr. Gennady Kobzev and Mrs. Maria Afanasyeva for making
arrangements to make our stay as comfortable as possible. At the end
of the note I thank TUSUR for giving us this wonderful opportunity to
explore and learn. I am also grateful to all the others who helped and
guided us and let us use their laboratories and equipment.

3. Overview of DC/DC Buck Converter –
Buck converter is DC voltage step-down transformer and current step
– up transformer. The output voltage is a function of input voltage and
the duty cycle of the gating pulse. DC voltage can also controlled by
using linear voltage regulators such as IC of 78xx series. But these
voltage regulators waste a significant amount of energy when used for
higher power load. But Buck converters on the other hand provide
95% efficiency and are used for loads like DC motors.
Integral parts of a Buck converter –
 Power source
 Mosfet
 Inductor
 Capacitor
 Load
 Control System
Types of Control system –
 Analog Control system
 Digital Control system
Integral parts of Analog Control system –
 Controller
 Saw-tooth Generator
 Comparator or PWM Generator
Types of conduction –
 Continuous conduction Mode (large “L”)
 Discontinuous conduction Mode (smaller “L”)

4. Mathematical Modelling –
For the mathematical modelling “State Space Method” is used. Buck
converter exhibits 2 states so state space modelling is done for these
2 states separately.
The ON state is when gate of mosfet receives digital ‘1’, and OFF state
is when is gate is given logic ‘0’.
The state space is represented in the form of –
For Buck converter the values of state space variables are -
X(t) = [IL; Vc]
Y(t) = Vo
A = [0, -1/L; 1/C, -1/Ro*C]
B = [1/L; 0]
C = [0, 1]
D = [0]
The above values can be obtained by applying Kirchhoff Voltage Law
& Kirchhoff Current Law.

5. Determining the values of Inductor –
For ON state,
We know that,
So,
For OFF state,
As Vg = 0. So,
When we plot the change in current,
By using this formula we can determine the value of Inductor.

6. My task for the internship –
My task for the internship –
 To design a buck converter for a 5 volts load using 20 volts as
source.
 To design the analog control system for the same.
 To physically realise the entire model on PCB.
Designing the Buck converter –
Specifications of my circuit –
 Input voltage = 20 volts
 Output voltage = 5 volts
 Duty cycle = Output voltage / Input voltage = (5/20)*100 = 25%
 Time period (Ts) = 0.00001 sec or 100KHz (freq)
 Delta IL = 1mA
 Ro = 2.5 ohms
Calculating Inductance –
By using the formula above the calculated inductance = 18.75mH.
Calculating Capacitance –
L and C pair act as low pass filter to the buck converter. Low pass filter
is employed to ground the higher frequency voltages and let only low
frequency voltage appear as output. The cut-off frequency of the low
pass filter is kept at a value very low compared to the time period or
the switching frequency of the converter. This is done to make sure
that there are lowest possible ripples in the output.
For my specifications the cut-frequency I selected = 1Khz
Cut-off frequency for a low pass filter = fc = 1/(2*pi*R*C)
= C = 1/(2*pi*R*fc)

7. By using the formula above the calculated capacitance = 60uF.
Modelling of converter in MATLAB Simulink –
The circuit was modelled using MATLAB Simulink, “Powerlib”. The
modelling was done for both ideal switching and not-ideal switching.
Circuit for ideal switching -
Graph for ideal switching –

8. As we can see for ideal switching output voltage reaches 5 volts in 0.06
seconds. But ideal switching does not take into account the mosfet &
diode internal resistance.
Circuit for non-ideal switching -
Graph for non-ideal switching-

9. For non-ideal switching the output voltage never reaches the specified
value (5 volts) at this duty of 25%. So we need to employ a control
system to change the duty cycle accordingly to ensure that 5 volts is
obtained at the output.
Designing the analog control system –
 MATLAB was used to simulate the BUCK converter with the
control system, and analyse the response.
Circuit for non-ideal switching & control system –
Note -
 The saw-tooth generator used generated a saw-tooth wave of
specified frequency between 1 & -1. Hence the arithmetic
operation to bring it between 0 and 10 accepted by the circuit.
 The “Saturation” block used is to limit the output of the
controller beyond a -1 and 11.

10. Graph for non-ideal switching & control system –
 Output voltage and currents graphs
 Output power graph

11.  Total power loss graph (in %)
We observe 3 things here –
 The voltage reaches the specified value (5 volts)
 It takes in about 0.005 seconds which is 90% of the time taken
on open loop to reach the set-point.
 The power loss is very less, i.e. only during the ON period we can
see that the power loss is about 5%.
Note-
 The controller used is P controller. The value of proportional gain
was experimentally found i.e. 135.
 The value of inductance was changed to 20mH and capacitance
to 100uF as these values provided the best results in terms of
response time and overshoot.

12. PWM generation –
 The output of the P controller is scaled between -1 and 11.
 This is done so avoid high output at t=0 as the error is maximum.
 The value -1 and 11 is used as saw-tooth wave oscillates between
0 and 10, and avoid loss of data.
P controller and saw-tooth wave output graphs
 Now the saw-tooth generator output is subtracted from P
controller output (P controller – saw-tooth wave).
 Now this difference is fed to a comparator.
 If the difference is positive the comparator produces logic ‘1’ as
output and if the difference is negative the comparator produces
a logic ‘0’.

13. Difference and PWM graphs
 The first white line marks the point where the saw-tooth value
became less than the p controller value, hence the difference
becomes positive. So the gate receives a logic ‘1’.
 The second line marks the point when the difference becomes
negative and comparator outputs a logic ‘0’.

14. Physical realisation of the model –
Analysis of components of control system using MATLAB -
Parts of control system -
1. Subtractor – It subtracts the process variable which is the output
voltage of the comparator with the set point which in our case is
5 volts.
 It uses an op-amp for the same. The op-amp generates V1-V2 as
output.

15. 2. Controller – It gets the input from the subtractor. The output
generates here is proportional to the gain of this P controller.
 Op-amp is used to realise the controller and an inverter circuit is
used as the controller output is inverted.
 The first op-amp is the controller, the second is the inverter.
 The input voltage is 0.1 volt, and with a gain of 135 the output is
13.5 volts.

16. 3. Saw-Tooth Wave Generator – A 555 timer IC is used to generate
the saw-tooth wave.
 The value of the components is determined experimentally.

17. 4. Comparator – It gives logic ‘1’ output when the non- inverting
voltage goes above the inverting terminal, and vice versa.

18. Layout of the circuit –
The layout was made using “SPLAN” software.

19. Components purchased and used –

20. PCB layout –
The PCB layout was designed using Fritzing software.
The pcb was made on copper clad board, using the above layout
Due to lack of components the PCB couldn’t be used.

21. Buck converter using Arduino –
 Due to lack of time and components the entire modelling of the
Buck converter in Arduino couldn’t be finished.
 The program is under development.
 The Arduino will act on behalf of the entire control system.
 The plan is to use a mosfet gate driver which will be controller by
the PWM dedicated pin of Arduino Micro.
 I have already developed a basic program to generate PWM
waves for triggering of gate.
 An op-amp multiplier circuit was used to multiply the voltage to
drive the gate but due to slow response of the op-amp the
desired output couldn’t obtained.
Progress till now –
 A function generator was used to generate the pulses for the
gate, and circuit was connected.
 Accurate output was obtained.
 This was done to check of the value of L,C and right and to check
the open loop characteristics of the converter

22. Circuit of buck converter and output
Tasks remaining –
 Physical realisation of the model with analog/digital control
system
 Fabricating a device on a PCB.
Things learnt –
 Use of MATLAB for the modelling and analysis of Power circuits.
 Designing Buck converter, i.e. determining the correct values of
L, C etc.
 Designing control system, i.e. determining the value of controller
parameters.
 Ball parking of values, i.e. experimentally determining the value
of various components.
 Effect on the system when values of a certain components is
changed.
 Designing of Multiplier circuit to drive the gate (can be used for
lower frequency).

23. Conclusion –
The 4 weeks of training at Tomsk State University of Control systems
and Radio electronics has greatly benefited us in several ways. We
have learnt how to proceed when a task or a project is assigned to it.
We were also exposed to various ways of testing and modelling before
the implementation of the final circuit. As I plan to pursue Master in
Power Electronics this internship has played a very important role in
making me realise where I stand. I now know what should be done by
me to improve my skills and knowledge in this field. So that I can do
better and compete.
I will make sure that things I have learnt and seen here are passed on
to my colleagues and use this system as an analogy to develop our
own.
The training has also inculcated professionalism and dedication to
work in us. No textbook would have been able to do provide the
knowledge I have gained in just 4 weeks. It has proved to be an
important milestone in my academic life.