Inverting buck-boost

Part 15 · Voltage Regulation

Key point: the switch node is \(V_{\mathrm{IN}}\), then \(-V_{\mathrm{OUT}}\). Both cables carry a pulse. This cell makes a negative rail.

\(|V_{\mathrm{out}}|/V_{\mathrm{in}} = D/(1-D)\). \(\Delta i_L = V_{\mathrm{in}} D /(L f_{\mathrm{sw}})\). Axes stay at −28…20 V and 0…8 A.

1
Both currents are pulses.
Preset 12 → −12 V at 1.5 A, 10 µH, 250 kHz. D is 50.0 %. SW is 12 V, then −12 V. Δi_L is 2.40 A. I_L,pk is 4.20 A. I_IN average is 1.50 A. i_IN flows only while Q1 is on. i_OUT flows only while Q2 is on.
2
D is 66.7 %. SW reaches −24 V.
Preset 12 → −24 V at 1.5 A, 10 µH, 250 kHz. D is 66.7 %. SW is 12 V, then −24 V. Δi_L is 3.20 A. I_L,pk is 6.10 A. I_IN average is 3.00 A. Q1 stays on longer, so the pulse into −VOUT is the short part of the cycle.
3
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 pulses are shorter in amps. Both cables are still pulses.
4
f_sw is 500 kHz. SW is still 12 V and −12 V.
Preset 12 → −12 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 1.50 A. f_sw is 500 kHz. Raising frequency shrinks the pulses. It does not change the switch-node levels.
5
Δi_L is clamped at 1.48 A.
Preset 12 → −12 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 0.40 A. The inductor would go discontinuous. The drawing keeps the pulses 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. This is the inverting cell, not a four-switch buck-boost. Ćuk does the same negative rail with both ports continuous. 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 −28 to 20 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

Inverting buck-boost. Amber i_IN and green i_OUT are both pulses, on opposite halves.

0.00 µs

Switch node · −28 to 20 V

i_IN · amber · rectified · 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—