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NAS Revision Guide

The document provides concise revision notes on network analysis and synthesis, covering key concepts such as Hurwitz polynomials for stability, graph theory including Thevenin and Norton equivalents, and Laplace transforms for transient analysis. It also details two-port network parameters (Z, Y, h, ABCD) and synthesis techniques for filters, including band-pass and high-pass filters. Essential formulas and theorems are highlighted for effective understanding and application in network analysis.

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19 views1 page

NAS Revision Guide

The document provides concise revision notes on network analysis and synthesis, covering key concepts such as Hurwitz polynomials for stability, graph theory including Thevenin and Norton equivalents, and Laplace transforms for transient analysis. It also details two-port network parameters (Z, Y, h, ABCD) and synthesis techniques for filters, including band-pass and high-pass filters. Essential formulas and theorems are highlighted for effective understanding and application in network analysis.

Uploaded by

dark030bro
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Network Analysis and Synthesis - Concise Revision Notes

Q1 + Basics

- Hurwitz Polynomial: All first-column elements of Routh array must be positive. No sign change = stable.
- Causal System: Output depends only on present/past input.
- Port Parameters: h <-> Y <-> Z conversions are common. Remember conversion formulas.
- Laplace Transform of Piecewise: Use u(t-a) shifting and linearity.
- f-cut set: Minimal set of edges that disconnect graph.
- f-tie set: Loops formed by adding a link to a tree.

Unit I: Graph Theory & Thevenin

- Tree: Acyclic subgraph with all nodes.


- Tie-set Matrix: Rows = loops; Columns = branches.
- Cut-set Matrix: Rows = minimal cuts; Columns = branches.
- Thevenin: Open-circuit voltage (Voc), equivalent resistance (Rth).
- Norton: Short-circuit current (Isc), Rn = Voc/Isc.

Unit II: Laplace & Transients

- Laplace of Triangular: Use basic Laplace pairs + shifting.


- Initial Value Theorem: f(0+) = lim(s->infinity)[sF(s)]
- Final Value Theorem: f(infinity) = lim(s->0)[sF(s)] if poles in LHP
- RC Transient: V(t) = V0(1 - e^(-t/RC))
- L inductor: i(t) continuity; C capacitor: v(t) continuity

Unit III: Two-Port Networks

- Z-parameters: V1 = Z11*I1 + Z12*I2, V2 = Z21*I1 + Z22*I2


- Y-parameters: I1 = Y11*V1 + Y12*V2, I2 = Y21*V1 + Y22*V2
- h-parameters: V1 = h11*I1 + h12*V2, I2 = h21*I1 + h22*V2
- ABCD: [V1; I1] = [A B; C D] * [V2; -I2]
- Cascading: ABCD matrices multiply directly

Unit IV: Synthesis & Filters

- PR Function: Real part >= 0 in RHP; pole-zero symmetry; odd-degree numerator.


- Foster I: LC elements in parallel; use partial fraction.
- Cauer I: Use continued division; ladder network.
- Band-pass: Allows mid-range freq; blocks low/high.
- High-pass: Blocks low freq; passes high freq.

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