Boost regulator working principle

A Boost regulator is a switching DC-DC converter whose average output voltage is greater than the input: Va = Vs/(1 − k).

Circuit

        L    iL            Dm
 +Vs --uuuu---+----------->|---+-----+
              |                |     |
              Q (switch)       C   LOAD  Va
              |                |     |
 −  ----------+----------------+-----+

Working principle

Mode 1 (Q ON, 0 < t < t1 = kT): The inductor is connected across Vs. Inductor current rises linearly from I1 to I2 and energy is stored. Dm is reverse biased; C supplies the load.

Vs = L·ΔI/t1   →  t1 = L·ΔI/Vs

Mode 2 (Q OFF, t1 < t < T): The inductor voltage reverses and adds to Vs. Current flows through Dm to C and the load; iL falls from I2 to I1.

Vs − Va = −L·ΔI/t2   →  t2 = L·ΔI/(Va − Vs)

Waveforms

Q   |‾‾‾‾‾|___|‾‾‾‾‾|___
    0    kT   T
iL  |    /\     /\        I2 (peak)
    |   /  \   /  \
    |__/    \_/    \_     I1
iD  |      |\_   |\_      (only when Q is OFF)
vC  |~~~~~~~~~~~~~~~~      Va with ripple ΔVc

Expressions

Output voltage:

Vs·t1 = (Va − Vs)·t2
Vs·kT = (Va − Vs)(1 − k)T
Va = Vs/(1 − k)

Peak-to-peak inductor ripple current:

ΔI = Vs·t1/L = Vs·k/(f·L)
   = Vs(Va − Vs)/(f·L·Va)

Capacitor ripple voltage: during t1 the capacitor alone supplies Ia:

ΔVc = Ia·t1/C = Ia·k/(f·C)

Currents: Is = Ia/(1 − k) (ideal, Pin = Pout); I2 = Is + ΔI/2, I1 = Is − ΔI/2.

Critical values:

Lc = k(1 − k)R/(2f),   Cc = k/(2fR)

Advantages: steps up voltage without a transformer; input current is continuous. Disadvantages: high peak current in the switch; output is very sensitive to k as k → 1.