Formula Sheets: Choppers | Power Electronics - Electrical Engineering (EE) PDF Download

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P o w er Electronics: Chopp ers F orm ula Sheet for
Electrical GA TE
Step-Do wn (Buc k) Chopp er
• A v erage Output V oltage :
V
o
=DV
in
where V
o
is output v oltage, V
in
is input v oltage, D is dut y cycle (0=D=1 ).
• A v erage Load Curren t :
I
o
=
V
o
R
=
DV
in
R
where R is load resistance.
• Output V oltage Ripple :
?V
o
=
V
in
D(1-D)
8LCf
2
where L is inductor v alue, C is capacitor v alue, f is switc hing frequency .
• Inductor Curren t Ripple :
?I
L
=
V
in
(1-D)D
fL
Step-Up (Bo ost) Chopp er
• A v erage Output V oltage :
V
o
=
V
in
1-D
• A v erage Input Curren t :
I
in
=
V
o
I
o
V
in
=
I
o
1-D
where I
o
is output curren t.
• Inductor Curren t Ripple :
?I
L
=
V
in
D
fL
• Output V oltage Ripple :
?V
o
=
I
o
D
fC
Buc k-Bo ost Chopp er
• A v erage Output V oltage :
V
o
=-
D
1-D
V
in
(Negativ e sign indicates output v oltage p olarit y in v ersion.)
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P o w er Electronics: Chopp ers F orm ula Sheet for
Electrical GA TE
Step-Do wn (Buc k) Chopp er
• A v erage Output V oltage :
V
o
=DV
in
where V
o
is output v oltage, V
in
is input v oltage, D is dut y cycle (0=D=1 ).
• A v erage Load Curren t :
I
o
=
V
o
R
=
DV
in
R
where R is load resistance.
• Output V oltage Ripple :
?V
o
=
V
in
D(1-D)
8LCf
2
where L is inductor v alue, C is capacitor v alue, f is switc hing frequency .
• Inductor Curren t Ripple :
?I
L
=
V
in
(1-D)D
fL
Step-Up (Bo ost) Chopp er
• A v erage Output V oltage :
V
o
=
V
in
1-D
• A v erage Input Curren t :
I
in
=
V
o
I
o
V
in
=
I
o
1-D
where I
o
is output curren t.
• Inductor Curren t Ripple :
?I
L
=
V
in
D
fL
• Output V oltage Ripple :
?V
o
=
I
o
D
fC
Buc k-Bo ost Chopp er
• A v erage Output V oltage :
V
o
=-
D
1-D
V
in
(Negativ e sign indicates output v oltage p olarit y in v ersion.)
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• A v erage Input Curren t :
I
in
=
I
o
D
1-D
• Inductor Curren t Ripple :
?I
L
=
V
in
D
fL
• Output V oltage Ripple :
?V
o
=
I
o
D
fC
P erformance P arameters
– E?iciency :
? =
P
o
P
in
=
V
o
I
o
V
in
I
in
– Ripple F actor :
RF =
?V
o
/2
V
o( a vg)
– Minim um Inductance for Con tin uous Conduction :
L
min
=
(1-D)
2
R
2f
(Buc k), L
min
=
R(1-D)
2
D
2f
(Bo ost)
Switc h and Dio de Ratings
* P eak Switc h V oltage :
V
S( max)
=V
in
(Buc k), V
S( max)
=V
in
+V
o
(Bo ost, Buc k-Bo ost)
* A v erage Switc h Curren t :
I
S( a vg)
=DI
o
(Buc k), I
S( a vg)
=
I
o
1-D
(Bo ost, Buc k-Bo ost)
* P eak Dio de Curren t :
I
D( max)
=I
o
+
?I
L
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Key Notes
* Dut y Cycle : D =
T on
T
, where T =
1
f
is switc hing p erio d.
* Con tin uous vs. Discon tin uous Conduction : Dep ends on L , f , and load.
* Switc h T yp es : MOSFET s or IGBT s t ypically used for high-frequency switc hing.
* Assumptions : Ideal comp onen ts, negligible losses unless sp ecified.
* Units : Use SI units for GA TE (e.g., V , A , H , F , Hz ).
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