Power · voltage-mode boost

Boost crossover window

Key point: two ordinary placement rules can leave a CCM boost with no crossover to aim at. Not a worse one. None. Drag \(L\). This page is here to show that squeeze the Analog Intuition way — a picture you can poke — not to replace a compensator CAD.

Along the way

1
Why a slider instead of a paper. The algebra is real, and it overwhelms most readers on sight. The move here is the same as every other lab on this site: one chart, one knob, a bound you can see. Feel \(L\) close the band. Then you already know what the equations were trying to say.
2
The ceiling everyone quotes. A CCM boost has a right-half-plane zero. Ask for more output and the switch stays on longer, so the rectifier is disconnected longer — the rail dips first. TI SLVA633 and Ridley both cap crossover at about \(f_{\mathrm{RHPZ}}/5\), and \(f_{\mathrm{RHPZ}}=V_{\mathrm{IN}}^2/(2\pi L P_{\mathrm{OUT}})\). No \(f_{\mathrm{sw}}\) in that. Bigger \(L\) drops the ceiling as \(1/L\).
3
The floor fewer people watch. Voltage-mode still has the LC pair (\(L_e=L/D'^2\), so a few microhenries look huge to the loop). Crossing before you have passed that resonance means closing the loop through ~180° you have not recovered. Same app note: \(f_c\) at least twice \(f_0\). That floor rises only as \(1/\sqrt{L}\).
4
They do not move together. Ceiling falls twice as fast as the floor rises (log axes). Set them equal and the band pinches shut at \(L_{\mathrm{crit}}=(V_{\mathrm{IN}}V_{\mathrm{OUT}}/(10\,P_{\mathrm{OUT}}))^2 C\). That 10 is just the two rule-of-thumb factors \(2\times5\). Past it, those two inequalities have an empty set. The quiet, low-ripple inductor is often the part that did it.
5
Switching faster does not reopen it. Hit faster fsw · still shut. The dashed \(f_{\mathrm{sw}}/10\) line jumps; the wedge does not. Ripple and EMI care about \(f_{\mathrm{sw}}\). This window does not.
6
Everyday path: current-mode, and let the CAD do the arithmetic. Most Analog Devices boosts are current-mode. The inner current loop takes the LC pair out of the voltage loop, so SLVA636 drops the “twice resonance” floor. You still respect the RHP zero — you just always have a (slower) target. LTpowerCAD sizes \(L\), \(C\), and compensation for a given ADI part and shows the Bode. That is the tool you ship with. Background: AN-149 (loop compensation of switchers).

This lab plots TI’s voltage-mode placement rules from SLVA633 (rules 7 and 8). The default 9–16 V → 48 V, 120 W, 100 µF rail is the numerical example in Philip Bassett’s write-up. The shut point is those two heuristics meeting — not a law that the converter cannot be stabilized some other way. Current-mode is that other way.

Vin, low line (V) Vout (V) Pout (W) Cout (µF) fsw (kHz)

L (µH)

Voltage-mode window is open.

Valid \(f_c\) vs inductance · worst corner (low line, full load)

Floor 2\(f_0\) —

Ceiling \(f_{\mathrm{RHPZ}}/5\) —

Window —

\(L_{\mathrm{crit}}\) —

Ripple ratio \(\Delta i/I_L\) —

\(f_{\mathrm{RHPZ}}\) —

Resonance \(f_0\) —

\(f_{\mathrm{sw}}/10\) —

\[ f_{\mathrm{RHPZ}}=\frac{V_{\mathrm{IN}}^2}{2\pi L P_{\mathrm{OUT}}},\quad f_0=\frac{D'}{2\pi\sqrt{LC}},\quad L_{\mathrm{crit}}=\left(\frac{V_{\mathrm{IN}}V_{\mathrm{OUT}}}{10\,P_{\mathrm{OUT}}}\right)^2 C \]

Try it: start on 4.7 µH · window open — teal band, about 2.75–4.57 kHz. Switch to 15 µH · no target. The band is gone. Then faster fsw · still shut: dashed line moves, wedge does not. Last, current-mode · ceiling only — the green floor disappears and you have a (slow) number to give the compensator again. That last view is the world Analog Devices current-mode boosts and LTPowerCAD live in.

When you are done looking

Current-mode boost controllers are easier to compensate because the current loop already removed the LC double pole. Analog Devices’ design tool LTpowerCAD handles that math behind the scenes for a chosen part: pick the IC, set the rail, and read the Bode instead of intersecting two inequalities by hand.

Start here: LTpowerCAD download · AN-149 · loop compensation · Boost timing & ripple (this site — the power-stage waveforms, not the loop).