Zeta

Part 18 · Voltage Regulation

Key point: the switch node is \(V_{\mathrm{IN}}\), then \(-V_{\mathrm{OUT}}\). Input current is a pulse. Output current is the L2 triangle. Same up-or-down job as SEPIC, with the quiet port on the load.

\(D = V_{\mathrm{out}}/(V_{\mathrm{in}}+V_{\mathrm{out}})\). \(\Delta i_L = V_{\mathrm{in}} D /(L f_{\mathrm{sw}})\). Axes stay at −16…16 V and 0…6 A.

1
Equal rails. The output is the triangle.
Preset 12 → 12 V at 1.5 A, 22 µH, 250 kHz. D is 50.0 %. SW is 12 V, then −12 V. Δi_L is 1.09 A. I_L,pk is 3.55 A. I_IN average is 1.50 A. i_IN is the pulse, and that pulse reaches I_L,pk. i_OUT is the L2 triangle.
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 16 V, then −12 V. Δi_L is 1.25 A. I_L,pk is 3.25 A. I_IN average is 1.13 A. The input is still a pulse. The output is still a triangle.
3
Source below the rail. D is 60.0 %.
Preset 8 → 12 V at 1.5 A, 22 µH, 250 kHz. D is 60.0 %. SW is 8 V, then −12 V. Δi_L is 0.87 A. I_L,pk is 4.19 A. I_IN average is 2.25 A. Duty crossed 50 %. The switch node still goes negative.
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. The output triangle is shorter. The input is still a pulse. SW is still 12 V and −12 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 the output triangle above zero.

SEPIC does this same up-or-down job and quiets the input instead. The negative switch-node level is this cell. Coupling C carries current that is not on these charts. 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 −16 to 16 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

Zeta. Amber i_IN is the pulse. Green i_OUT is the L2 triangle.

0.00 µs

Switch node · −16 to 16 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—