# Chopper (DC to DC Converter)

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## Chopper

##### Chopper is a converter which is convert fixed DC to variable DC voltage .
• When output voltage is less then the input voltage its called Step-down chopper(Vo < Vs).
• When output voltage is greater  then the input voltage its called Step-up chopper(Vo > Vs).

#### Two types of Chopper.

1. Step-up Chopper (Boost Converter).
2. Step-Down Chopper (Buck Converter).

## Step-up Chopper (Boost Converter)

• Step-up chopper convert the low DC voltage to high DC voltage.
• Its also known as DC booster.
• When output voltage is less then the input voltage its called step-down chopper(Vo < Vs).
• We can use SCR , MOSFET , IGBT instead of CH(switch).
• Output voltage appear across R.
• Large capacity inductor is connected in series with the supply voltage. Booster Configuration is shown in fig:

#### Working:-

• At the first instant chopper switch is open.
• Now close the switch and current flowing through path Vs – L – CH – Vs. shown in fig 1:
• During this period inductor store the charge. that stored charge is given by the L(di / dt).
• After that at next instant open that switch again.
• Hence the current flowing through path during this mode is Vdc – L – D – R – Vdc. shown in fig 2:
• During this time inductor will dissipate the charge which it has store during first instant.
• Therefore, the output voltage is given by the summation of  supply voltage and the charge dissipated by the inductor both.
• Output voltage is given by  Vo = Vs + L(di / dt).

Total time (T) = Ton + Toff (chopping period)

During the period Ton ,

Won = voltage across L *average current through L * Ton

= Vs * ((I1 + I2)/2)*  Ton…………………………….equ(1)

During the period Toff,

Woff = voltage across L *average current through L * Toff

= (Vo-Vs) * ((I1 + I2)/2)*  Toff………………………..equ(2)

compare equ (1) & (2);

Vs * ((I1 + I2)/2)*  Ton =  (Vo-Vs) * ((I1 + I2)/2)*  Toff

Vs *Ton =  (Vo-Vs) * Toff

Vs *Ton =  Vo*Toff  -Vs *Toff

Vo*Toff = Vs *Ton + Vs *Toff

Vo*Toff = Vs(Ton+Toff)

Vo*Toff = Vs(T)

Vo = Vs*(T/Toff)

Vo = Vs *T/(T-Ton)

Vo = Vs(1/(1-α))………………………………….equ (3)

where,  (T/Ton)= α

• α is a ratio of Ton and T. its called Duty cycle.
• when value of α = 0 , output voltage = supply voltage.(Vs = Vo).
• by changing the value of α we can change value of output voltage.