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Block Diagram Representation

ELEC 312

Systems I

Circuit Diagrams

A drawing describing the structure of a network along with the nature and function of its elements

The input and the output are physical quantities, i.e., voltages and currents

Shows nature of elements: active (independent sources, op amp) passive (resistors, capacitors, inductors)

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Block Diagrams

A drawing describing the terminal properties of a network, i.e., the relationship between its input and its output

Gives no information about the structure

The input and the output are arbitrary signals related in some specified way.

May be physical quantities, but not necessary.

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Intermediate Level Diagrams

Focus not on the physical elements, but on their mathematical functions they perform

Resistors are (scalar) multipliers

Inductors and capacitors are differentiators and integrators

Signals are arbitrary functions related by a set of equations that follow from the rules of interconnection of the elements

Elementary Operation Blocks

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Top Level Diagrams For frequency-domain analysis, a system is

represented as a block with an input, an output, and a transfer function (assuming LTI systems)

Three basic configurations for system interconnection: cascade, parallel, feedback

For state-space analysis, a system is represented as a signal-flow graph

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Signal Flow Graph

consists of nodes interconnected by arcs or branches

Node a dot labeled with a signal

Arc a directed line segment labeled with an operation or transfer function

performed on the signal

Input arc enters a node

Output arc leaves a node

Branching or summing performed at a node

Cascade Form

The result is obtained under no loading effect assumption.

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Parallel Form

Feedback Form

G(s)H(s) is called the open-loop transfer function, or loop gain.

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Example: Obtain a block diagram for the circuit shown using (a) vL(t) and (b) i(t) as the output.

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Example: Represent an arbitrary feedback system as a unity feedback system

Block Diagram Reduction

Procedure for moving blocks to create familiar forms

Complicated system with multiple subsystems can be represented in the most basic form

The goal is to represent a complex system with a single overall transfer function if possible

Four rules for basic block moves that can be made to create familiar forms

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Moving a summer to left of a block

Moving a summer to right of a block

Moving a pickoff to left of a block

Moving a pickoff to right of a block

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Example 5.1 (text): Reduce the following block diagram to a single transfer function.

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Example: Reduce the following block diagram to a single transfer function.

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Example: Reduce the following block diagram to a single transfer function.

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Example: Reduce the following block diagram to a single transfer function.

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