Download 1.2.4 Output Voltage Ripple

BUCK-BOOST CONVERTER
1.1 Introduction:
In a large number of industrial applications, it is required to convert a dc voltage to a
different dc voltage level, often with a regulated output. To perform this task, a dc-dc
converter is needed. A dc-dc converter directly converts a dc voltage of one level to another.
It can be used to step-down (buck), or step-up (boost) a dc voltage source. Higher switching
frequency would reduce the size of the filter used.
1.2 Basic Principle of Buck-Boost converter:
The buck-boost is a popular non-isolated inverting power stage topology, sometimes
called a step-up/down power stage. Power supply designers choose the buck-boost power stage
because the required output is inverted from the input voltage, and the output voltage can be
either higher or lower than the input voltage. The input current for a buck-boost power stage is
discontinuous, or pulsating, because of the power switch current that pulses from zero to IL
every switching cycle. The output current for a buck-boost power stage is also discontinuous
or pulsating because the output diode only conducts during a portion of the switching cycle.
Equivalent circuit
1.2.1 Analysis for the Switch Closed:
When the switch is closed, the voltage across the inductor is
The rate of change of inductor current is a constant, indicating a linearly increasing inductor
current. The preceding equation can be expressed as
1.2.2 Analysis for the Switch Open:
When the switch is open, the current in the inductor cannot change instantaneously,
resulting in a forward-biased diode and current into the resistor and capacitor. In this condition,
the voltage across the inductor is
Again, the rate of change of inductor current is constant, and the change in current is
1.2.3 Inductor Design
Power absorbed by the load must be the same as that supplied by the source.
Average source current is related to average inductor current by
Substituting for Vo derived above and solving for IL, we find
For continuous current, the inductor current must remain positive. To determine the boundary
between continuous and discontinuous current, Imin is set to zero resulting in
1.2.4 Output Voltage Ripple:
The output voltage ripple for the buck-boost converter is computed from the capacitor current
waveform.
The converter consists of dc input voltage source VS, controlled switch S, inductor L,
diode D, filter capacitor C, and load resistance R. With the switch on, the inductor current
increases while the diode is maintained off. When the switch is turned off, the diode provides
a path for the inductor current. Note the polarity of the diode that results in its current being
drawn from the output. The condition of a zero volt-second product for the inductor in steady
state yields
VS DT  Vo (1  D)T
Fig 1.3 Circuit diagram of buck boost converter
Hence, the dc voltage transfer function of the buck-boost converter is
V
D
MV  o  
VS
1 D
The output voltage VO is negative with respect to the ground. Its magnitude can be
either greater or smaller (equal at D = 0.5) than the input voltage as the name of the converter
implies. The value of the inductor that determines the boundary between the CCM and DCM
is
(1  D) 2 R
2f
DVo
Cmin 
Vr Rf
Lcric 
DESIGN PROBLEM:
Vs = 24 V
D = 0.4
R = 5 Ohm
L = 20 uH
C = 80 uF
f = 100 kHz
Limitation = 0 V to 36 V(by simulation)
Output Voltage:
Vo
D

VS
1 D
Vo = -16Volt.
Inductor Current:
VsD
IL =
(R∗(1−D)^2
= 5.33 A
Ripple current:
VsDT
IL=
L
=4.8 A
ILmax= IL +
ILmin=IL −
∆IL
∆IL
2
2
= 7.33 A
= 2.93 A
Output voltage ripple:
Vo=
D
RCF
= 0.01=1%
Inductor Design:
Type
: Power Inductor
Inductance
: 20uH
Maximum DC current
: 7.8Amps
Core Material
: Powdered Iron Core
Maximum DC resistance : 26mOhm
OPEN LOOP SIMULATION:
Fig 1.4 Open Loop Simulation of buck boost converter
Fig 1.5 Simulation results
CLOSED LOOP SIMULATION:
Fig 1.6 Output Voltage
PI CONTROLLER:(Tuning by trial and error method)
Kp
0.00022
0.0005
0.0005
0.0009
0.002
0.005
0.009
0.001
0.01




Ki
15
10
1
5
8
10
5
8
5
Peak overshoot
-34
-34
-34
-34
-34
-34
-34
-34
-34
Settling time
0.032
0.052
0.093
0.068
0.055
0.053
0.092
0.060
0.089
Thus if Kp, Ki values are increased or decreased Overshoot remains the same.
When Ki value is increased and Kp value decreased further Settling time decreases.
The above table is achieved by trial and error method.
To further decrease the peak overshoot Derivative controller can be added.
M-File Coding for Open loop Buck Boost Converter:
function my_ode()
global A D Cf Lf Vs
f = 100000;
R = 5;
Vo = 16;
Io = Vo/R;
Vs = 24;
D = Vo/(Vo+ Vs);
L = 20E-6;
C = 80E-6;
Lf = L*f;
Cf = C*f;
A = [0 -1/Lf; 1/Cf -1/(R*Cf)];
x0 = [D*Io; Vo];
tf = 50;
tic
[t,X] = ode23(@bukboost,[0 tf],x0);
toc;
IL = X(:,1);
VC = X(:,2);
subplot(2,1,1),plot(t,IL),grid
axis([0 tf 0 20])
title('Inductor Current')
subplot(2,1,2),plot(t,VC),grid
axis([0 tf 0 120])
title('Output Voltage')
xlabel('cycles')
end
function dx = bukboost(t, x)
global A D Cf Lf Vs
iL = x(1);
vC = x(2);
B = [(vC+Vs)/Lf; -iL/Cf];
u = 0.5*(1-sign(t-fix(t)-D));
dx=A*x+B*u;
end
Fig 1.7 Inductor Current and Capacitor Voltage
Tic starts a stopwatch timer to measure performance. The function records the internal time at execution
of the tic command. Display the elapsed time with the toc function.
APPLICATIONS:
Battery-powered systems:
In battery powered systems , where the input voltage can vary widely, starting at full charge
and gradually decreasing as the battery charge is used up. At full charge, where the battery voltage may
be higher than actually needed by the circuit being powered, a buck regulator would be ideal to keep
the supply voltage steady. However as the charge diminishes the input voltage falls below the level
required by the circuit, and either the battery must be discarded or re-charged; at this point the ideal
alternative would be the boost regulator. Hence buck boost converter will be the preferred choice
In Solar PV for MPPT:
Buck/Boost converters make it possible to efficiently convert a DC voltage to either a lower or
higher voltage. Buck/Boost converters are especially useful for PV maximum power tracking purposes,
where the objective is to draw maximum possible power from solar panels at all times, regardless of
the load.