Why switch

Part 11 · Voltage Regulation

Key point: linear heat is \((V_{\mathrm{in}}-V_{\mathrm{out}})I\). A switcher moves that energy in packets. The η knob is the heat that remains.

\(P_{\mathrm{load}}=V_{\mathrm{out}}I\). \(P_{\mathrm{lin}}=(V_{\mathrm{in}}-V_{\mathrm{out}})I\). Buck \(D=V_{\mathrm{out}}/V_{\mathrm{in}}\).

1
Linear heat is 17.4 W.
Preset 12 → 3.3 @ 2 A. Pload is 6.60 W. Linear heat is 17.4 W. η linear is 27.5 %. Switcher heat is 574 mW. Buck D is 27.5 %. Rose is (Vin−Vout)I. Gold, at 92%, is 574 mW. Linear heat is (Vin−Vout)I. Switcher heat is the η knob.
2
η linear stays 27.5 %.
Preset Same rails · 0.5 A. Pload is 1.65 W. Linear heat is 4.35 W. η linear is 27.5 %. Switcher heat is 143 mW. Buck D is 27.5 %. 0.5 A is a quarter of 2 A, and linear heat is a quarter of 17.4 W. η linear stays 27.5 %. Linear heat is (Vin−Vout)I. Switcher heat is the η knob.
3
Switcher heat is 1.65 W.
Preset η 80%. Pload is 6.60 W. Linear heat is 17.4 W. η linear is 27.5 %. Switcher heat is 1.65 W. Buck D is 27.5 %. The η knob moved the gold bar from 574 mW to 1.65 W. Linear heat is still 17.4 W. Linear heat is (Vin−Vout)I. Switcher heat is the η knob.
4
Linear heat is 1.00 W.
Preset 12 → 11.5 V. Pload is 23.0 W. Linear heat is 1.00 W. η linear is 95.8 %. Switcher heat is 2.00 W. Buck D is 95.8 %. D and η linear are both 95.8 %. Linear heat is under the switcher. A 0.5 V drop is where an LDO still wins on heat. Drop is small. Linear heat is under the switcher.
5
Buck D is not a buck.
Preset 5 → 12 V. Pload is 12.0 W. Linear heat is n/a (no boost). η linear is —. Switcher heat is 1.33 W. Buck D is not a buck. The right-hand circuit is a boost. Boost steps up and quiets the input. Flyback isolates and quiets neither. An LDO cannot boost. Buck D does not apply.

Ideal switches skip the linear term. Real heat is \(R_{\mathrm{DS(on)}}\), gate charge, and the magnetics, rolled into the η knob. Part 5d is the switching loss. Min on-time and EMI come later. A tiny drop, or a rail that cannot take ripple, stays an LDO.

Linear heat vs a switcher

Teal is load power. Rose is linear heat. Gold is switcher heat at the η knob.

\(V_{\mathrm{IN}}\) (V) \(V_{\mathrm{OUT}}\) (V) \(I_{\mathrm{load}}\) (A) Switcher η (%)

Left: series pass. Right: a buck while \(V_{\mathrm{OUT}} < V_{\mathrm{IN}}\), a boost when it is not.

#	Cluster	Job	Quiet port
13	Buck	always down	output
14	Boost	always up	input
15	Inverting buck-boost	negative rail	neither
16	SEPIC	up or down	input
17	Ćuk	negative, quiet cables	both
18	Zeta	up or down	output
19	Flyback	isolated	neither

Power · teal load under the heat · rose linear, gold switcher

P_load—

P_lin heat—

η linear—

P_sw heat—

Buck D—

\(P_{\mathrm{load}}=V_{\mathrm{out}}I\)

→ —

\(P_{\mathrm{lin}}=(V_{\mathrm{in}}-V_{\mathrm{out}})I\)

→ —

\(D_{\mathrm{buck}}=V_{\mathrm{out}}/V_{\mathrm{in}}\)

→ —