Energy packets

Part 4 · Voltage Regulation

Key point: average power is energy per unit time. A tall short pulse and a lower steady flow deliver the same joules when the areas match.

Both charts use a fixed 80 µs window. The lab forces \(D = P_{\mathrm{avg}}/P_{\mathrm{hi}}\), so the areas stay matched.

1
Almost a steady flow.
6.00 W average, 7.00 W pulses, 50 kHz. Duty is 85.7%. Each packet is on for 17.14 µs and carries 120.00 µJ.
2
Taller and narrower, same joules.
Same 6.00 W and 50 kHz. Pulse height 24.0 W. Duty falls to 25.0%, on-time to 5.00 µs. The packet is still 120.00 µJ.
3
Faster rate, smaller packets.
250 kHz, still 6.00 W and 24.0 W. Period is 4.00 µs, on-time 1.00 µs. Each packet is 24.00 µJ. The average line does not move.
4
More average power widens the pulse.
12.0 W average, still 24.0 W pulses, back at 50 kHz. Duty is 50.0%, on-time 10.00 µs. Each packet is 240.00 µJ. The ramp gets steeper with it.

Ideal rectangles. No switch, no inductor. Over one period the steady line at \(P_{\mathrm{avg}}\) delivers the same joules as one packet. Next is the device that actually routes those packets.

Pulsed versus steady

Fixed 80 µs window · areas stay matched

Average power \(P_{\mathrm{avg}}\) (W) Pulse height \(P_{\mathrm{hi}}\) (W) Pulse rate \(f\) (kHz)

Power · blue packet · teal is the steady \(P_{\mathrm{avg}}\)

Energy · blue steps versus the teal ramp

\(P_{\mathrm{avg}}\)—

\(P_{\mathrm{hi}}\)—

Duty \(D\)—

\(T_{\mathrm{on}}\)—

Period \(T\)—

\(E_{\mathrm{packet}}\)—

\(E_{\mathrm{pkt}} = P_{\mathrm{hi}}\,T_{\mathrm{on}}\)

→ —

\(P_{\mathrm{avg}} = E_{\mathrm{pkt}}/T\)

→ —

\(D = P_{\mathrm{avg}}/P_{\mathrm{hi}}\)

→ —