Boost

Part 14 · Voltage Regulation

Key point: the switch node is ground, then \(V_{\mathrm{OUT}}\). Input current is the inductor triangle. Output current is the pulse into COUT.

\(D = 1 - V_{\mathrm{in}}/V_{\mathrm{out}}\). \(\Delta i_L = V_{\mathrm{in}} D /(L f_{\mathrm{sw}})\). Axes stay at −4…40 V and 0…8 A.

1
Input is the triangle. Output is the pulse.
Preset 12 → 24 V at 1.5 A, 10 µH, 250 kHz. D is 50.0 %. SW is 0, then 24 V. Δi_L is 2.40 A. I_L,pk is 4.20 A. I_IN average is 3.00 A. i_IN is the inductor current the whole cycle. i_OUT flows only while Q2 is on.
2
D is 66.7 %. The output pulse is shorter.
Preset 12 → 36 V at 1.5 A, 10 µH, 250 kHz. D is 66.7 %. SW is 0, then 36 V. Δi_L is 3.20 A. I_L,pk is 6.10 A. I_IN average is 4.50 A. Q1 stays on longer, so Q2 has less of the cycle to dump L into COUT.
3
Δi_L falls to 0.51 A.
Preset 12 → 24 V at 1.5 A, 47 µH, 250 kHz. D stays 50.0 %. Δi_L is 0.51 A. I_L,pk is 3.26 A. I_IN average stays 3.00 A. The triangle is shorter. The input is still continuous, and the output is still a pulse.
4
f_sw is 500 kHz. SW is still 0 and 24 V.
Preset 12 → 24 V at 1.5 A, 10 µH, 500 kHz. D stays 50.0 %. Δi_L is 1.20 A. I_L,pk is 3.60 A. I_IN average stays 3.00 A. f_sw is 500 kHz. Raising frequency shrinks the triangle. It does not change the switch-node levels.
5
Δi_L is clamped at 1.48 A.
Preset 12 → 24 V at 0.4 A, 10 µH, 250 kHz. D is 50.0 %. The sketch clamps Δi_L to 1.48 A. I_L,pk is 1.54 A. I_IN average is 0.80 A. The inductor would go discontinuous. The drawing keeps the triangle above zero.

Q2 is drawn as a FET. A diode there has the same current timing. While Q1 is on, the load runs from COUT alone. Dead time, the right-half-plane zero, and the output capacitor loop come later. The gold dash on i_IN is peak inductor current. The Y axes do not rescale.

Switch node, then the two currents

SW is fixed at −4 to 40 V. Currents are fixed at 0 to 8 A. Two cycles.

\(V_{\mathrm{IN}}\) (V) \(V_{\mathrm{OUT}}\) (V) \(I_{\mathrm{OUT}}\) (A) \(L\) (µH) \(f_{\mathrm{sw}}\) (kHz)

Q1 on

Synchronous boost. Amber i_IN is the triangle. Green i_OUT is the pulse.

0.00 µs

Switch node · −4 to 40 V

i_IN · amber · continuous · gold dash is I_L,pk · 0 to 8 A

i_OUT · green · rectified · 0 to 8 A

Duty D—

Δi_L—

I_L,pk—

I_IN avg—

f_sw—