Ćuk

Part 17 · Voltage Regulation

Key point: both port currents are inductor triangles. The output triangle is negative. The switch node is ground, then \(V_{\mathrm{IN}}+|V_{\mathrm{OUT}}|\).

\(|V_{\mathrm{out}}|/V_{\mathrm{in}} = D/(1-D)\). \(\Delta i_L = V_{\mathrm{in}} D /(L f_{\mathrm{sw}})\). Axes stay at −4…32 V and −4…4 A.

1
i_OUT sits below zero.
Preset 12 → −12 V at 1.5 A, 22 µH, 250 kHz. D is 50.0 %. SW is 0, then 24 V. Δi_L is 1.09 A. I_L,pk is 3.55 A. I_IN average is 1.50 A. i_IN is a triangle above zero. i_OUT is a triangle below zero.
2
Source above the rail. D is 42.9 %.
Preset 16 → −12 V at 1.5 A, 22 µH, 250 kHz. D is 42.9 %. SW is 0, then 28 V. Δi_L is 1.25 A. I_L,pk is 3.25 A. I_IN average is 1.13 A. Both traces are still triangles. i_OUT is still negative.
3
|VOUT| is above the source. D is 60.0 %.
Preset 8 → −12 V at 1.5 A, 22 µH, 250 kHz. D is 60.0 %. SW is 0, then 20 V. Δi_L is 0.87 A. I_L,pk is 4.19 A. I_IN average is 2.25 A. The switch-node high is still VIN+|VOUT|.
4
Δi_L falls to 0.51 A.
Preset 12 → −12 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 1.50 A. Both triangles get shorter. i_OUT stays negative. SW is still 0 and 24 V.
5
Δi_L is clamped at 0.93 A.
Preset 12 → −12 V at 0.25 A, 22 µH, 250 kHz. D is 50.0 %. The sketch clamps Δi_L to 0.93 A. I_L,pk is 0.96 A. I_IN average is 0.25 A. The inductors would go discontinuous. The drawing keeps both triangles off zero.

Coupling C carries the chopped current, so the cables stay triangles. I_L,pk is that internal peak. It is not a mark on the port charts. The inverting buck-boost makes the same negative rail with a pulse on each cable. The Y axes do not rescale.

Switch node, then the two currents

SW is fixed at −4 to 32 V. Currents are fixed at −4 to 4 A. Two cycles.

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

Q1 on

Ćuk. Amber i_IN is above zero. Green i_OUT is the same shape, below zero.

0.00 µs

Switch node · −4 to 32 V

i_IN · amber · continuous · −4 to 4 A

i_OUT · green · continuous · negative · −4 to 4 A

Duty D—

Δi_L—

I_L,pk—

I_IN avg—

f_sw—