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6.334 Lecture Notes: Intro to DC/DC

Brief alt
Small hand-drawn node diagram showing three labelled branches converging at a single point, with arrows indicating direction.
Detailed figure description
A small hand-drawn node diagram showing three straight branch lines converging at a single central junction. One branch comes from the upper-left, one from the lower-right, and one from the lower-left; each branch has a short arrow near the junction pointing toward the junction. Each arrow is labeled with a Greek lambda: the upper-left branch is labeled \(\lambda_n\), the right branch is labeled \(\lambda_1\), and the lower-right branch is labeled \(\lambda_2\). There are small dotted marks drawn near one branch to indicate continuation or additional branches beyond the three shown. The sketch is compact and positioned near the top-right of the page.
First Averaged circuit rules
KCL
KCL applied to time-average branch quantities (cons. charge).
The same is true for KVL.
So for a power converter in Periodic Steady State:
- Average KCL\[ \sum_d \langle \lambda_d \rangle = 0 \]
- Average KVL\[ \sum_k \langle V_k \rangle = 0 \]
- Capacitor in P.S.S.\[ \langle \lambda_C \rangle = 0 \]
- Inductor in P.S.S.\[ \langle V_L \rangle = 0 \]
- If system lossless (cons. of energy)\[ \langle P_{in} \rangle = \langle P_{out} \rangle \]
