Expression for The Output Voltage of Step Up Chopper

Expression for The Output Voltage of Step Up Chopper

Q. Describe stop up chopper with neat circuit diagram. Draw its input and output waveforms.

Q. Explain principle of step up chopper with neat be circuit diagram. Derive the expression of output voltage.

Assuming that the current ripple △I is small, i.e. assuming current i_o, to be constant, equal to I amp the energy input E_i to the inductor during the on time of chopper (mode I) will be,
   E_i  = V x I x T_ON

The energy E_O, delivered by the inductor to the load in mode II will be,

   E_O = (V_O  – V)I
x T_OFF

Where V_O , is the instantaneous load voltage.

In a system that has no losses, the energy stored by the inductor must be equal to the energy delivered by it to the load. Therefore

   E_i = E_O

   V x I x T_ON = (V_O – V) x I x T_OFF

   v_o = V T_ON/ T_OFF + V

   v_o = V (T_ON+T_OFF)/ T_OFF

   v_o = V(T)/ T_OFF = VxT/(T – T_ON)

   v_o= V/[1 – T_ON/T] = V(1 – D)

This is the desired expression.
As shown by Equation (2.8.4), the instantaneous load voltage will be dependent on the duty cycle D.

   For D = 0,  v_o = and for D = 1, v_o = ∞

In this way the load voltage of the step up chopper is greater than the input dc voltage and can be varied by varying the duty cycle D.
If a large capacitor C is connected across the load as shown by the dashed lines in Figure A . the output voltage will be continuous and v_o, would become equal to the average value V_Ldc.
Variation in Output Voltage :

Figure B shows the variation in the output voltage with the value of the duty cycle D.

D	vO	vO/V
0	V volts	1
0.2	1.25 V	1.25
0.4	1.66 V	1.66
0.6	2.5 V	2.5
0.8	5 V	5
0.9	10 V	10

Figure A

Waveforms :

The voltage waveforms at different points of the step up chopper are as shown in Figure B.

Figure B