DC/DC Converters: The Step up (Boost) Converter
Covered in Chapter 7 of Mohan, Undeland and Robbins
Topics
Circuit and Basic Operation
Continuous Mode Analysis
o Voltage Transfer Ratio
o Inductor Ripple Current
o Input Current
o Output Current and Voltage Ripple
o Capacitor Ripple Current
Discontinuous Mode Analysis
o Boundary Condition
o Duty cycle as a function of current (Constant Vo)
Circuit
Continuous Mode Boost Converter Waveforms
Switch
D.Ts
(1-D).Ts
On
Off
Ts
time
vL
Vd
Vo
time
Vd-Vo
iL
IL
IL
time
IDiode
IL
Average = Io
time
Continuous Mode Boost Converter Relationships (You must be able to derive)
Vd
Voltage Transfer Ratio: Vo
(1 D )
Inductor Peak to Peak Ripple Current:
Input Current I d
IL
IL
Vd .D.Ts
L
Io
(1 D )
Diode Current: Peak to Peak Ripple = I L
IL
2
IL
Peak to Peak Output Voltage Ripple (approximation) =
Io
(1 D )
I o .esr
(1 D )
Ripple Current Rating of the Output Capacitor
Electrolytic capacitors have a maximum ripple current rating and the output capacitor of
the boost converter is exposed to high ripple. The easiest way to determine the required
ripple rating of the output capacitor is to use the following relationships, which hold for
any waveform:
Ts
0
I rms
Ts
Ts
I dc
I 2 (t).dt
0
I rms
I (t).dt
Ts
I dc2
I ac2
I dc
2
I rms
I ac2
Use the general formula for rms to calculate the rms of the diode current waveform and
assume that the ac component of this goes into the capacitor while the dc component
flows into the load. Note if the inductor ripple is 20% or less then it can safely be
neglected when calculating the capacitor current.
If we neglect inductor ripple then the diode current components become:
( I diode ) rms
( I diode ) dc
( I diode ) ac
I L. 1 D
I L .(1 D )
( I diode ) 2rms
( I diode ) 2dc
Discontinuous Mode Boundary
Just as in the Boost case the boundary condition for discontinuous mode occurs when the
average inductor current IL is half of the inductor peak-to-peak ripple IL.
IL
2
Boundary occurs at I L
but the output current I o
so at the boundary I o
I oB
Vd .D.Ts
Vo .D.(1 D ).Ts
2L
2L
I d (1 D )
I L (1 D )
Vo .D (1 D ) 2 Ts
2L
Behaviour of Boost Converter in discontinuous mode
As in the buck converter discontinuous mode operation results in a higher than expected
output voltage for a given duty cycle. Conversely the duty cycle must be reduced in order
to maintain a given input to output voltage ration when the converter goes into
discontinuous mode.
Problem
You are required to design a boost converter to provide a constant 300V output from a
Fuel cell stack.
Fuel cell stack parameters:
Maximum Load: 50Amps
No Load Voltage: 100V
Full Load Voltage: 60V at 50Amps
The following design constraints are to be adhered to:
You may assume that the switch and diode are ideal but a switching frequency of
50kHz is to be used.
-The peak-to-peak inductor ripple current must not exceed 10% of the inductors
dc current rating.
-A number of 350V/1000uF capacitors are available and the minimum number of
these should be used for the output capacitance. The capacitors have the following
specifications:
Voltage: 350V max
Capacitance: 1000uF +/-10%
Ripple current rating: 4 Amps maximum
esr: 0.4 maximum
The converter is to be controlled by an integrated circuit control chip which is
capable of generating duty cycles in the range of 0.1 to 0.9
In discontinuous operation the boost converter characteristic is:
D
2 I o L Vo
TsVd Vd
1
1. Calculate the inductor value and current rating required.
2. Determine the amount of output capacitance required and worst-case output voltage
ripple
3. Determine the value of dummy load required to prevent overvoltage.