Buck

Part 13 · Voltage Regulation

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

\(D = V_{\mathrm{out}}/V_{\mathrm{in}}\). \(\Delta i_L = V_{\mathrm{in}} D(1-D)/(L f_{\mathrm{sw}})\). Axes stay at −4…28 V and 0…6 A.

1
Input is a pulse. Output is the triangle.
Preset 12 → 5 V at 2 A, 4.7 µH, 250 kHz. D is 41.7 %. SW is 12 V, then 0. Δi_L is 2.48 A. I_L,pk is 3.24 A. I_IN average is 0.83 A. i_IN flows only while Q1 is on. i_OUT is the inductor current.
2
D is 75.0 %. The 12 V pulse is wider.
Preset 12 → 9 V at 2 A, 4.7 µH, 250 kHz. D is 75.0 %. Δi_L is 1.91 A. I_L,pk is 2.96 A. I_IN average is 1.50 A. SW is still 12 V, then 0. Q1 stays on for more of the cycle, so the input pulse is wider.
3
Δi_L falls to 0.53 A.
Preset 12 → 5 V at 2 A, 22 µH, 250 kHz. D stays 41.7 %. Δi_L is 0.53 A. I_L,pk is 2.27 A. I_IN average stays 0.83 A. The input pulse is shorter in amps. It is still a pulse.
4
f_sw is 500 kHz. SW is still 12 V and 0.
Preset 12 → 5 V at 2 A, 4.7 µH, 500 kHz. D stays 41.7 %. Δi_L is 1.24 A. I_L,pk is 2.62 A. I_IN average stays 0.83 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 0.93 A.
Preset 12 → 5 V at 0.5 A, 4.7 µH, 250 kHz. D is 41.7 %. The sketch clamps Δi_L to 0.93 A. I_L,pk is 0.96 A. I_IN average is 0.21 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. Dead time, \(R_{\mathrm{DS(on)}}\), and the input filter come later. The gold dash on i_IN is peak switch current. The Y axes do not rescale.

Switch node, then the two currents

SW is fixed at −4 to 28 V. Currents are fixed at 0 to 6 A. Two cycles.

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

Q1 on

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

0.00 µs

Switch node · −4 to 28 V

i_IN · amber · rectified · gold dash is I_L,pk · 0 to 6 A

i_OUT · green · continuous · 0 to 6 A

Duty D—

Δi_L—

I_L,pk—

I_IN avg—

f_sw—