Boost converter

Question 1

What is the circuit for the boost converter?

Answer 1

[Picture5]

Question 2

What are the features of the circuit?

Answer 2

> The output voltage is higher than the input voltage

> All components are considered to be ideal

> The input current to the boost converter is continuous

Question 3

What happens when the switch is closed?

Answer 3

> The inductor is connected across the power supply

> The current will rise dramatically

Question 4

What is the equations for the voltage across the inductor when the switch is closed?

Answer 4

V_i = L(∆i_on / t_on)

V_i = L(∆i_on / KT_S)

Question 5

What happens when the switch is open?

Answer 5

> The inductor and the power supply are in series

> The voltage is higher

> The inductor discharges

Question 6

What is the equations for the voltage across the inductor when the switch is open?

Answer 6

V_L = L (∆i_off / t_off)

V_L = L (∆i_off / (1 - K)T_S)

Question 7

What is the relationship for the current when the switch is closed and open?

Answer 7

∆i_on = -∆i_off

Question 8

What is the voltage relationship equation?

Answer 8

1 / (1 - K) = V_O / V_i

Question 9

Derive the voltage relationship equation

Answer 9

[Picture6]

Question 10

What are the power relationships for an ideal boost converter?

Answer 10

P_in = P_out

P_out = I_OV_O

P_in = V_i × i_avg = V_i×I_i

I_OV_O = V_iI_i

V_O / V_i = I_i / I_O

Question 11

What is the current relationship equation?

Answer 11

1 / (1 - K) = I_i / I_O

Question 12

Draw the waveforms for inductor current, switch voltage, switch current, diode current

Answer 12

[Picture7]

Question 13

What is required to calculate the value of the inductor when the switch is closed?

Answer 13

> PWM Duty cycle

> Input voltage

> Switching frequency

> Input current change

Question 14

What is required to calculate the value of the inductor when the switch is open?

Answer 14

> PWM Duty cycle

> Input voltage

> Output voltage

> Switching frequency

> Input current change

Question 15

What is the assumption with C₀?

Answer 15

> That it is so large that it can be ignored.

> In real world examples, this is not the case

Question 16

What is the ∆Q for the time when the switch is closed?

Answer 16

∆Q = I₀KT_S = (I_OK) / f_S

Question 17

What are the equation to calculate C_O value? Derive it

Answer 17

C₀ = I_OK / (v_O×f_S)

C₀ = V_OK / (v_O×R× f_S)

Q = C_Ov_O

∆Q = (I_OK) / f_S

(I_OK) / v_Of_S = C_O

Question 18

What is the equation to calculate the output voltage ripple?

Answer 18

∆v_O / V_O = KT_S / C_OR

Question 19

What is the average voltage of the inductor?

Answer 19

0V

Question 20

What is the average switch voltage?

Answer 20

V_S = V_L + V_i = V_I