Test: Steady State Time Domain Analysis of Type-A Chopper

Identification of DC-DC Converter:

• Buck converter: Inductor is connected in series with the combination of the capacitor and load resistor.
• Boost converter: Inductor is connected in series with the supply voltage source.
• Buck-Boost converter: Inductor is connected in parallel to the series-connected switch and supply voltage source.

In a Buck-Boost converter, the inductor stores the energy for T_ON time and release the energy for the time T_OFF
Given that, duty ratio (δ) = 0.6

⇒ T_ON = δT = 0.6 T
⇒ T_OFF = (1 – δ) T = 0.4 T
So, the inductor stores the energy for a time of 0.6 T and releases the energy for 0.4 T.
So, for one cycle, the increase in inductor current is corresponding to a time of (0.6 T – 0.4 T) = 0.2 T
Frequency (f) = 10 kHz
The time period for one cycle, 

The waveform of the inductor current is as shown below. 

From the waveform, rise in the inductor current for one cycle

Rise in the inductor current for 10 cycles = 0.1 × 10 = 1 A
Energy stored in the inductor for 10 cycles, 

The function of capacitor C across-load resistance R is to make the output voltage continuous.

For Buck Converter

The peak to peak ripple current is 

V_o = V_dc × T_on × f
f = 5 kHz, V_dc = 230 V, V_o = 180

but chopping period

blocking period of SCR
T_off = T – T_on = 0.2 – 0.156 = 0.04347 msec = 43.47 μsec

Ripple current in the chopper circuit :
Ripple current is the difference between maximum current (Imx) and minimum current (Imin) flowing through the chopper circuit in the steady-state operation of the chopper.
The ripple current of chopper operating in steady-state is given by

Where
α = duty cycle of the chopper, V_s = DC supply voltage, R = load resistance, T_a = time constant = L/R , and T = time period of the chopper 
From the above equation, we can observe per unit ripple current is only depends on the time constant (T_a), Time period (T), and duty cycle (α ).
Variation of ripple current with a duty cycle (α) and T/T_a ratio:
We can observe the variation of ripple current with duty cycle and T/T_a ration in the figure is shown below,

• From the above graph, the value of ripple current is increased with an increasing duty cycle (α) up to some instant where the value of α =0.5, and after that, it is decreasing.
• The maximum value of ripple current  is given at the value of α = 0.5
• The maximum value of the ripple current is increased with increasing T/T_a ratio but still, the max ripple current occurs at α = 0.5.