BUCK CONVERTER - Working - Circuit

In buck regulator, the average output voltage V_o is less than the input voltage V_s , hence the name ‘buck’.

Buck regulator circuit diagram is shown below.

The chopper CH is a switch like Bjt or Mosfet or Igbt etc.

Assumptions :-

(1) Let the value of capacitance be so large that the output voltage remains almost constant.

(2) The output current is constant and equal to I_o.

BUCK CONVERTER WORKING

Buck regulator operation can be divided into two modes.

Mode-1 :- ( 0 ≤ t ≤ T_on )

During this duration, chopper CH is ON and therefore freewheeling diode FD is reverse biased by the supply voltage V_S and therefore FD acts as an open switch. The circuit reduces to as shown below.

By KVL,

- V_s + V_L + V_o = 0

V_L = V_s - V_o

Inductor voltage :-

Since inductor current rises linearly therefore, inductor voltage is positive and constant having value V_s – V_o .

Capacitor current :-

i_c = i_L – I_o from the circuit.

Since I_o remains constant and i_L rises linearly from I_minto I_max therefore i_c rises linearly from I_min – I_o to I_max – I_o in T_on time.

Capacitor voltage | Output voltage :-

Let the initial voltage across capacitor be V_o. Therefore, the voltage across capacitor varies as per below given basic equation.

As i_cis linear therefore its integral will be parabolic and hence, capacitor voltage varies parabolically as shown in waveforms.

Buck Converter Waveforms :-

Mode-2 :- (T_on ≤ t ≤ T )

During this duration, chopper CH is OFF. Since inductor current cannot become zero immediately therefore , i_L flows through FD i.e FD acts as a closed switch. Equivalent circuit is shown below.

Inductor current decreases linearly from I_max to I_min i.e rate of change of inductor current is negative and hence voltage induced across inductor is of negative polarity and the inductor acts as a energy source.

Inductor voltage :-

i.e negative and constant value.

Capacitor current :-

i_c = i_L – I_o from the circuit.

Since I_o is constant and i_L decreases linearly from I_maxto I_min therefore i_c decreases linearly from I_max – I_o to I_min – I_o in T_off time.

Capacitor / Output voltage :-

The voltage across capacitor varies as per below given basic equation.

Capacitor voltage varies parabolically.

Condition for continuous inductor current and capacitor voltage.

The fall of inductor current is opposed by the inductive property of the inductor. Lower the value of inductance L , the more suddenly i_L decreases. Therefore, inductance must not be lower than a particular value. This particular value at which i_L waveform becomes just discontinuous is called critical inductance L_c .

L_c value can be obtained by making I_min=0. Its value is

Similarly, capacitance value must not be made below a particular value for continuous capacitance voltage waveform. This particular value is called critical capacitance C_c . Its value is