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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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