# Circuits and Electronics

Massachusetts Institute of Technology

This course is designed to serve as a first course in an undergraduate electrical engineering (EE), or electrical engineering and computer science (EECS) curriculum. The course introduces the fundamentals of the lumped circuit abstraction. Topics covered include: resistive elements and networks; independent and dependent sources; switches and MOS transistors; digital abstraction; amplifiers; energy storage elements; dynamics of first- and second-order networks; design in the time and frequency domains; and analog and digital circuits and applications. Design and lab exercises are also significant components of the course. The course content was created collaboratively by Profs. Anant Agarwal and Jeffrey H. Lang.

• ##### Introduction and Lumped Abstraction
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Basic Circuit Analysis Method (KVL and KCL mMethod)
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Superposition, Thevenin and Norton
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### The Digital Abstraction
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Inside the Digital Gate
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Nonlinear Analysis
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Incremental Analysis
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Dependent Sources and Amplifiers
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### MOSFET Amplifier Large Signal Analysis, Part 1
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### MOSFET Amplifier Large Signal Analysis, Part 2
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Amplifiers - Small Signal Model
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Small Signal Circuits
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Capacitors and First-Order Systems
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Digital Circuit Speed
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### State and Memory
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Second-Order Systems, Part 1
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Second-Order Systems, Part 2
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Sinusoidal Steady State
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### The Impedance Model
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Filters
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### The Operational Amplifier Abstraction
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Operational Amplifier Circuits
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Op Amps Positive Feedback
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Energy and Power
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Energy, CMOS
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.

• ##### Violating the Abstraction Barrier
Anant Agarwal

We revisit the shortest paths problem, considering the case where the input is a directed minor-free graph with negative arc lengths (but no negative-length cycles).In Lecture 14, we saw almost-linear-time algorithms for the case of planar and bounded-genus graphs. Currently, comparable bounds for minor-free graphs are not known. We shall discuss Goldberg's algorithm, a shortest-path algorithm for general graphs with integer lengths, whose running time depends logarithmically on the magnitude of the largest negative arc length. By exploiting separators (Lecture 6), it runs faster on minor-free graphs than on general graphs, but it still requires superlinear time.