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CHOPPERS
οƒ˜ Transfer power from DC circuit to another DC circuit.
οƒ˜ Converts fixed voltage to variable voltage.
Application of Chopper
1.Speed control of DC Motor.
2.Positional control in robotics.
3.Regulated power supply (SMPS)
4.Input to Inverter.
5.Solar Power Converter.
Step Down Chopper
CH: - fully controlled switch
Operation: - Periodic
Time period: - T
Duty cycle: - Ton/T
Ton = DT
CH: - ON Vo=Vs
CH: - OFF Io=0/Vo=0
t
t
t
Buck Converter
S1 :- Fully Controlled Switch
-MOSFET(high frequency)/IGBT/SCR+Commutation Circuit
S2:- Uncontrolled Switch
:- provides free wheeling action (due to L)
DC Motor load
-Step down chopper with a freewheeling
diode.
Buck Converter
SW:-ON (0<t<DT)
Vo = Vs
Vs = 𝑖𝑅 + 𝐿
𝑑𝑖
𝑑𝑑
+ 𝐸
L :- charging
SW :- OFF (DT<t<T)
0 = 𝑖𝑅 + 𝐿
𝑑𝑖
𝑑𝑑
+ 𝐸
L:- discharging
πΌπ‘šπ‘Žπ‘₯ =
𝑉𝑠
𝑅
1βˆ’π‘’
βˆ’π‘‡π‘œπ‘›
𝜏
1βˆ’π‘’
βˆ’π‘‡
𝜏
βˆ’
𝐸
𝑅
𝛕 = time constant = L/R
πΌπ‘šπ‘–π‘› =
𝑉𝑠
𝑅
𝑒
π‘‡π‘œπ‘›
𝜏 βˆ’1
𝑒
𝑇
πœβˆ’1
βˆ’
𝐸
𝑅
T = time period
(Valid when 𝛕 ≀ T)
βˆ†I = ripple in inductor current = Imax – Imin
Ripple must be as low as possible
Maximum ripple in IL occurs if D = 0.5 (Buck Converter)
βˆ†I = Vs/4fL (assume 𝛕>>T)To reduce the ripple, f and L must be
highβˆ†πΌ =
𝑉𝑠
𝑅
1βˆ’π‘’
βˆ’π‘‡π‘œπ‘›
𝜏
1βˆ’π‘’
βˆ’π‘‡
𝜏
βˆ’
𝑒
π‘‡π‘œπ‘›
𝜏 βˆ’1
𝑒
𝑇
πœβˆ’1
=
𝑉𝑠
𝑅
(1βˆ’π‘’
βˆ’π‘‡π‘œπ‘›
𝜏 )
(1βˆ’π‘’
βˆ’π‘‡
𝜏 )
βˆ’
𝑒
βˆ’π‘‡
𝜏 (𝑒
π‘‡π‘œπ‘›
𝜏 βˆ’1)
(1βˆ’π‘’
βˆ’π‘‡
𝜏 )
=
𝑉𝑠
𝑅
1βˆ’π‘’
βˆ’π‘‡π‘œπ‘›
𝜏
1βˆ’π‘’
βˆ’π‘‡
𝜏
(1 βˆ’ 𝑒
βˆ’π‘‡
𝜏 βˆ— 𝑒
π‘‡π‘œπ‘›
𝜏 )
=
𝑉𝑠
𝑅
1βˆ’π‘’
βˆ’π‘‡π‘œπ‘›
𝜏
1βˆ’π‘’
βˆ’π‘‡
𝜏
(1 βˆ’ 𝑒
βˆ’π‘‡π‘œπ‘“π‘“
𝜏 )
Discontinuous Conduction
β€’ Current can become 0 for finite duration of time.
β€’ Boundary :- When current IL=0 only for an instant
of time.
β€’ For boundary :- Imin =0
β€’
𝑉𝑠
𝑅
𝑒
π‘‡π‘œπ‘›
𝜏 βˆ’1
𝑒
𝑇
𝜏 βˆ’1
= E/R
β€’ 𝑒
π‘‡π‘œπ‘›
𝜏 βˆ’ 1 =
𝐸
𝑉𝑠
𝑒
𝑇
𝜏 βˆ’ 1
β€’ π‘‡π‘œπ‘› = πœπ‘™π‘› 1 +
𝐸
𝑉𝑠
𝑒
𝑇
𝜏 βˆ’ 1

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Chopper

  • 1. CHOPPERS οƒ˜ Transfer power from DC circuit to another DC circuit. οƒ˜ Converts fixed voltage to variable voltage.
  • 2. Application of Chopper 1.Speed control of DC Motor. 2.Positional control in robotics. 3.Regulated power supply (SMPS) 4.Input to Inverter. 5.Solar Power Converter.
  • 3. Step Down Chopper CH: - fully controlled switch Operation: - Periodic Time period: - T Duty cycle: - Ton/T Ton = DT CH: - ON Vo=Vs CH: - OFF Io=0/Vo=0 t t t
  • 4. Buck Converter S1 :- Fully Controlled Switch -MOSFET(high frequency)/IGBT/SCR+Commutation Circuit S2:- Uncontrolled Switch :- provides free wheeling action (due to L) DC Motor load -Step down chopper with a freewheeling diode.
  • 5. Buck Converter SW:-ON (0<t<DT) Vo = Vs Vs = 𝑖𝑅 + 𝐿 𝑑𝑖 𝑑𝑑 + 𝐸 L :- charging SW :- OFF (DT<t<T) 0 = 𝑖𝑅 + 𝐿 𝑑𝑖 𝑑𝑑 + 𝐸 L:- discharging
  • 6. πΌπ‘šπ‘Žπ‘₯ = 𝑉𝑠 𝑅 1βˆ’π‘’ βˆ’π‘‡π‘œπ‘› 𝜏 1βˆ’π‘’ βˆ’π‘‡ 𝜏 βˆ’ 𝐸 𝑅 𝛕 = time constant = L/R πΌπ‘šπ‘–π‘› = 𝑉𝑠 𝑅 𝑒 π‘‡π‘œπ‘› 𝜏 βˆ’1 𝑒 𝑇 πœβˆ’1 βˆ’ 𝐸 𝑅 T = time period (Valid when 𝛕 ≀ T) βˆ†I = ripple in inductor current = Imax – Imin Ripple must be as low as possible Maximum ripple in IL occurs if D = 0.5 (Buck Converter) βˆ†I = Vs/4fL (assume 𝛕>>T)To reduce the ripple, f and L must be highβˆ†πΌ = 𝑉𝑠 𝑅 1βˆ’π‘’ βˆ’π‘‡π‘œπ‘› 𝜏 1βˆ’π‘’ βˆ’π‘‡ 𝜏 βˆ’ 𝑒 π‘‡π‘œπ‘› 𝜏 βˆ’1 𝑒 𝑇 πœβˆ’1 = 𝑉𝑠 𝑅 (1βˆ’π‘’ βˆ’π‘‡π‘œπ‘› 𝜏 ) (1βˆ’π‘’ βˆ’π‘‡ 𝜏 ) βˆ’ 𝑒 βˆ’π‘‡ 𝜏 (𝑒 π‘‡π‘œπ‘› 𝜏 βˆ’1) (1βˆ’π‘’ βˆ’π‘‡ 𝜏 ) = 𝑉𝑠 𝑅 1βˆ’π‘’ βˆ’π‘‡π‘œπ‘› 𝜏 1βˆ’π‘’ βˆ’π‘‡ 𝜏 (1 βˆ’ 𝑒 βˆ’π‘‡ 𝜏 βˆ— 𝑒 π‘‡π‘œπ‘› 𝜏 ) = 𝑉𝑠 𝑅 1βˆ’π‘’ βˆ’π‘‡π‘œπ‘› 𝜏 1βˆ’π‘’ βˆ’π‘‡ 𝜏 (1 βˆ’ 𝑒 βˆ’π‘‡π‘œπ‘“π‘“ 𝜏 )
  • 7. Discontinuous Conduction β€’ Current can become 0 for finite duration of time. β€’ Boundary :- When current IL=0 only for an instant of time. β€’ For boundary :- Imin =0 β€’ 𝑉𝑠 𝑅 𝑒 π‘‡π‘œπ‘› 𝜏 βˆ’1 𝑒 𝑇 𝜏 βˆ’1 = E/R β€’ 𝑒 π‘‡π‘œπ‘› 𝜏 βˆ’ 1 = 𝐸 𝑉𝑠 𝑒 𝑇 𝜏 βˆ’ 1 β€’ π‘‡π‘œπ‘› = πœπ‘™π‘› 1 + 𝐸 𝑉𝑠 𝑒 𝑇 𝜏 βˆ’ 1