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The document discusses signal flow graphs (SFG), which provide a graphical representation of the relationship between variables in a system without needing to reduce block diagrams. An SFG consists of nodes and directed branches and can only represent linear systems. The basic elements of an SFG include branches, nodes, paths, loops, and different types of loops. Mason's gain formula is presented for calculating the transfer function of a system from its SFG. Examples are given to demonstrate how to derive an SFG from a block diagram and simultaneous equations, and how to use Mason's formula to solve for paths and loops.
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Lecture 10 11-signal_flow_graphs
This document provides an overview of signal flow graphs including:
- Definitions and terminology of signal flow graphs
- Examples of constructing signal flow graphs from equations and block diagrams
- Mason's gain formula for calculating the transfer function of a system from its signal flow graph representation in 3 sentences or less
- Examples are provided to demonstrate applying Mason's gain formula to calculate transfer functions from given signal flow graphs.
Signal flow graph
This document contains several examples of using Mason's Rule to calculate transfer functions from signal flow graphs. The examples demonstrate applying Mason's Rule to calculate loop gains, forward path gains, non-touching loops, and the overall transfer function. Signal flow graphs are constructed from block diagrams and the steps of Mason's Rule are systematically worked through.
Signal Flow Graph, SFG and Mason Gain Formula, Example solved with Masson Gai...
Basic Properties of SFG
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The document discusses signal flow graphs (SFG), which provide an alternative representation to block diagrams. SFGs depict the flow of signals through a system using directed branches connecting nodes. Important elements include input/output nodes, branches, loops, and path/loop gains. Mason's rule can be used to derive the transfer function of a system from its SFG. It involves calculating the determinant and individual path determinants based on loop gains. Examples show applying Mason's rule to calculate a transfer function and converting a block diagram into an equivalent SFG.
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This document provides an overview of signal flow graphs and Mason's rule for calculating transfer functions from such graphs. It begins with definitions of key signal flow graph concepts like nodes, branches, paths, and loops. It then gives examples of constructing signal flow graphs from sets of simultaneous equations and converting block diagrams. Mason's rule is explained as providing the transfer function from a single formula involving the forward path gains and graph determinants, avoiding successive block diagram reductions. Finally, the document works through two examples applying Mason's rule to calculate transfer functions from given signal flow graphs.
Signal flow graph
This document discusses signal flow graphs and Mason's rule for calculating transfer functions from such graphs. It defines key terms used in signal flow graphs like nodes, branches, paths, loops, and gains. Mason's rule is presented as a way to relate a signal flow graph to the simultaneous equations of the system to determine the overall transfer function T. The formula for T is given as the sum of the products of the forward path gains and the characteristic function Δ over the number of paths. An example is worked through to demonstrate applying Mason's rule.
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This document discusses block diagrams and signal flow graphs, which are useful tools for modeling control systems. It begins by explaining what block diagrams are and how they represent the components and signal flows in a system. Signal flow graphs are then introduced as a more compact way to determine the relationships between input and output variables using Mason's gain formula, without needing to reduce the diagram. The document provides examples of block diagram reductions and simple signal flow graphs. It concludes that block diagrams and signal flow graphs provide control engineers a better understanding of systems by describing the connections between components.
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This document discusses signal flow graphs and Mason's gain formula. It begins by explaining how to convert a block diagram into an equivalent signal flow graph by labeling summing points and take-off points, assigning nodes, and connecting nodes with associated gains. An example is provided. Mason's rule for reducing a signal flow graph to a transfer function is introduced. It uses the net gain formula that considers forward paths, loop gains, and non-touching loops. Another example applies Mason's rule to calculate the transfer function. In the end, some references on the topic are listed.
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This document provides an overview of signal flow graphs including:
- Definitions and terminology of signal flow graphs
- Examples of constructing signal flow graphs from equations and block diagrams
- Mason's gain formula for calculating the transfer function of a system from its signal flow graph representation in 3 sentences or less
- Examples are provided to demonstrate applying Mason's gain formula to calculate transfer functions from given signal flow graphs.
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This document contains several examples of using Mason's Rule to calculate transfer functions from signal flow graphs. The examples demonstrate applying Mason's Rule to calculate loop gains, forward path gains, non-touching loops, and the overall transfer function. Signal flow graphs are constructed from block diagrams and the steps of Mason's Rule are systematically worked through.
Signal Flow Graph, SFG and Mason Gain Formula, Example solved with Masson Gai...
Basic Properties of SFG
Definitions of SFG Terms
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Example solved with Masson Gain Formula
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The document discusses signal flow graphs (SFG), which provide an alternative representation to block diagrams. SFGs depict the flow of signals through a system using directed branches connecting nodes. Important elements include input/output nodes, branches, loops, and path/loop gains. Mason's rule can be used to derive the transfer function of a system from its SFG. It involves calculating the determinant and individual path determinants based on loop gains. Examples show applying Mason's rule to calculate a transfer function and converting a block diagram into an equivalent SFG.
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This document provides an overview of signal flow graphs and Mason's rule for calculating transfer functions from such graphs. It begins with definitions of key signal flow graph concepts like nodes, branches, paths, and loops. It then gives examples of constructing signal flow graphs from sets of simultaneous equations and converting block diagrams. Mason's rule is explained as providing the transfer function from a single formula involving the forward path gains and graph determinants, avoiding successive block diagram reductions. Finally, the document works through two examples applying Mason's rule to calculate transfer functions from given signal flow graphs.
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This document discusses signal flow graphs and Mason's rule for calculating transfer functions from such graphs. It defines key terms used in signal flow graphs like nodes, branches, paths, loops, and gains. Mason's rule is presented as a way to relate a signal flow graph to the simultaneous equations of the system to determine the overall transfer function T. The formula for T is given as the sum of the products of the forward path gains and the characteristic function Δ over the number of paths. An example is worked through to demonstrate applying Mason's rule.
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This document discusses block diagrams and signal flow graphs, which are useful tools for modeling control systems. It begins by explaining what block diagrams are and how they represent the components and signal flows in a system. Signal flow graphs are then introduced as a more compact way to determine the relationships between input and output variables using Mason's gain formula, without needing to reduce the diagram. The document provides examples of block diagram reductions and simple signal flow graphs. It concludes that block diagrams and signal flow graphs provide control engineers a better understanding of systems by describing the connections between components.
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This document discusses signal flow graphs and Mason's gain formula. It begins by explaining how to convert a block diagram into an equivalent signal flow graph by labeling summing points and take-off points, assigning nodes, and connecting nodes with associated gains. An example is provided. Mason's rule for reducing a signal flow graph to a transfer function is introduced. It uses the net gain formula that considers forward paths, loop gains, and non-touching loops. Another example applies Mason's rule to calculate the transfer function. In the end, some references on the topic are listed.
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This document discusses signal flow graphs and Mason's rule for analyzing control systems. It begins with an introduction to signal flow graphs and their basic components and terminology. It then explains Mason's rule, which provides a formula for reducing a signal flow graph to a single transfer function. The formula relates the graph to the simultaneous equations that can be written from it. The document provides an example of applying Mason's rule to calculate the transfer function of a sample signal flow graph. It demonstrates identifying forward paths, calculating loop transmittances, and determining the characteristic function and path determinants.
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The document discusses signal flow graphs (SFGs), which are diagrams that represent sets of simultaneous equations. SFGs consist of nodes connected by directed branches, with branches representing the flow of signals between nodes. Key terms are defined, such as transmittance (branch gain), paths, loops, and Mason's gain formula, which is used to reduce an SFG to a single transfer function. Examples are given of constructing SFGs from block diagrams, simultaneous equations, and differential equations. The document also discusses identifying loops and applying Mason's formula to solve problems represented by SFGs.
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1) The document discusses signal flow graphs, which provide a graphical representation of linear algebraic equations in a system. Nodes represent variables and branches show relationships.
2) It compares block diagrams and signal flow graphs, noting that signal flow graphs only need to be drawn once, saving time and space over repeatedly redrawing block diagrams.
3) Mason's gain formula allows directly calculating the overall transfer function of a system from its signal flow graph representation, without lengthy reduction steps.
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This document contains presentation slides on signal flow graphs (SFG). SFG is a graphical representation method for linear systems. Key points covered include:
- Definitions of SFG terminology like nodes, branches, forward paths and loops.
- Properties of SFG like it only applying to linear time-invariant systems.
- How to construct a SFG from system equations or a block diagram.
- Mason's gain formula for determining overall transfer function from a SFG.
- Converting between SFG and block diagrams.
- How feedback affects overall gain and stability of a system.
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This document provides an overview of signal flow graphs (SFG). It defines SFG as a graphical representation of linear systems, where each variable is represented by a node and transmissions are branches with arrows denoting signal flow direction. Key terms are defined, including input/output nodes, mixed nodes, transmittance, forward paths, loops, and path/loop gains. Properties and examples of SFG construction from equations and block diagrams are described. Mason's gain formula is introduced for determining overall transfer functions from SFGs. The effects of feedback on gain and stability are also briefly discussed.
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The document defines key terms used in signal flow graphs such as input/output nodes, forward/feedback paths, path/loop gains, and non-touching loops. It also provides Mason's rule for determining the transfer function of a system from its signal flow graph representation, which is defined as the ratio of the output to input with adjustments made for any feedback loops that touch the forward paths. Examples are also given of constructing signal flow graphs from block diagrams and applying Mason's rule to solve for various transfer functions.
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3. Common block diagram reduction techniques include combining blocks in cascade or parallel, moving summing or pickoff points, eliminating feedback loops, and swapping summing points.
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The document discusses signal flow graphs (SFGs), which are diagrams that represent sets of simultaneous equations. SFGs consist of nodes connected by directed branches, with branches representing the flow of signals between nodes. Key terms are defined, such as transmittance (branch gain), paths, loops, and Mason's gain formula, which is used to reduce an SFG to a single transfer function. Examples are given of constructing SFGs from block diagrams, simultaneous equations, and differential equations. The document also discusses identifying loops and applying Mason's formula to solve problems represented by SFGs.
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1) The document discusses signal flow graphs, which provide a graphical representation of linear algebraic equations in a system. Nodes represent variables and branches show relationships.
2) It compares block diagrams and signal flow graphs, noting that signal flow graphs only need to be drawn once, saving time and space over repeatedly redrawing block diagrams.
3) Mason's gain formula allows directly calculating the overall transfer function of a system from its signal flow graph representation, without lengthy reduction steps.
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This document contains presentation slides on signal flow graphs (SFG). SFG is a graphical representation method for linear systems. Key points covered include:
- Definitions of SFG terminology like nodes, branches, forward paths and loops.
- Properties of SFG like it only applying to linear time-invariant systems.
- How to construct a SFG from system equations or a block diagram.
- Mason's gain formula for determining overall transfer function from a SFG.
- Converting between SFG and block diagrams.
- How feedback affects overall gain and stability of a system.
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This document provides an overview of signal flow graphs (SFG). It defines SFG as a graphical representation of linear systems, where each variable is represented by a node and transmissions are branches with arrows denoting signal flow direction. Key terms are defined, including input/output nodes, mixed nodes, transmittance, forward paths, loops, and path/loop gains. Properties and examples of SFG construction from equations and block diagrams are described. Mason's gain formula is introduced for determining overall transfer functions from SFGs. The effects of feedback on gain and stability are also briefly discussed.
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This document provides an introduction to block diagram representation of control systems. It discusses how block diagrams provide a pictorial representation of the relationships between elements in a system using blocks and arrows. The blocks represent system elements or operations, and the arrows represent the direction of signal or information flow. Specific topics covered include summing points, takeoff points, examples of representing equations as block diagrams, and canonical forms.
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This document discusses signal flow graphs and Mason's gain formula for control systems. It begins by defining key terms used in signal flow graphs such as nodes, branches, transmittance, input/output nodes, paths, and loop gains. It then describes properties of signal flow graphs and how Mason's gain formula can be used to determine a system's transfer function from its signal flow graph. The document concludes by providing two example problems that demonstrate how to apply Mason's gain formula to calculate a system's overall transfer function.
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This document summarizes key concepts related to signal flow graphs (SFG). It defines the basic elements of an SFG including nodes, branches, input nodes, output nodes, mixed nodes, forward paths, and loops. It explains how to calculate the forward path gain as the product of branch transmittances along a forward path. It also describes Mason's Gain Formula for calculating the transfer function of a system represented by an SFG using determinants based on forward path gains and loop gains. Finally, it outlines the step-by-step process for applying Mason's Gain Formula which involves identifying forward paths and loops, calculating individual and combined loop gains, and determining the numerator and denominator determinants.
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This document provides an overview of signal flow graphs. It defines key concepts like nodes, branches, paths, loops, and loop gains. Examples are given to illustrate these concepts, such as a simple voltage-current-resistance circuit and its corresponding signal flow graph. Different types of nodes, paths, and loops are defined, including forward paths, self loops, and non-touching loops. The document serves as an introduction to representing physical systems as signal flow graphs.
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This document discusses techniques for reducing block diagrams and signal flow graphs that represent complex control systems composed of multiple interconnected subsystems into a single transfer function. It introduces block diagram elements like summing junctions and pickoff points used to represent interconnections. Three methods for reducing block diagrams to an equivalent transfer function are presented: cascade form, parallel form, and feedback form. Rules are provided for moving blocks around diagrams to establish these familiar forms. Signal flow graphs are introduced as an alternative representation and Mason's rule is outlined as a method for reducing a signal flow graph to a transfer function. Examples are worked through to demonstrate these reduction techniques.
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This document discusses signal flow graphs (SFG), which are a graphical technique used to analyze microwave networks in terms of reflected and transmitted waves. It introduces the basic components of SFGs, including nodes and branches, and how sources and loads are represented. The document outlines four rules for constructing and manipulating SFGs: the series rule, parallel rule, recursive rule, and node splitting rule. It provides examples of applying each rule. The document concludes by stating that SFGs can be used to derive expressions for input and output reflection coefficients Γin and Γout of microwave networks.
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This document contains a presentation on block diagram representation and reduction techniques. It discusses how block diagrams can be used to represent complex systems through interconnected blocks, each characterized by a transfer function. The key advantages and disadvantages of using block diagrams are outlined. The document then covers topics such as closed loop systems, drawing block diagrams, and provides step-by-step examples of applying block reduction techniques to derive an equivalent transfer function.
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This document outlines a lecture on block diagrams for a control systems engineering course. It begins with an introduction to block diagrams and their use in representing subsystems and combining multiple subsystems. It provides examples of subsystems for automobile control and antenna control. The document then discusses mathematical modeling of systems using transfer functions. It covers concepts such as cascaded systems, feedback forms, and simplifying block diagrams. Finally, it provides examples of simplifying complex block diagrams and modeling a shuttle pitch control system using block diagrams.
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The document defines key terms used in signal flow graphs such as input/output nodes, forward/feedback paths, path/loop gains, and non-touching loops. It also provides Mason's rule for determining the transfer function of a system from its signal flow graph representation, which is defined as the ratio of the output to input with adjustments made for any feedback loops that touch the forward paths. Examples are also given of constructing signal flow graphs from block diagrams and applying Mason's rule to solve for various transfer functions.
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Block diagram reduction techniques
1. Block diagrams can be used to model both simple and complex systems, and consist of multiple blocks connected to represent the system's functioning.
2. It is often necessary to reduce block diagrams by combining or rearranging blocks for easier analysis and calculation of the transfer function.
3. Common block diagram reduction techniques include combining blocks in cascade or parallel, moving summing or pickoff points, eliminating feedback loops, and swapping summing points.
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This document discusses techniques for reducing multiple subsystems to a single transfer function. It covers block diagram algebra and Manson's rule. Block diagram algebra can be used to reduce block diagrams representing cascaded, parallel, and feedback subsystems into equivalent single transfer functions. The key techniques are collapsing summing junctions and forming equivalent cascaded, parallel, and feedback systems. Signal-flow graphs also represent subsystems and can be reduced using Manson's rule by writing equations for each signal as the sum of incoming signals times their transfer functions. Examples demonstrate reducing various block diagrams and signal-flow graphs to equivalent single transfer functions.
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The document discusses steady-state error in control systems. It defines steady-state error as the difference between the input and output of a system as time approaches infinity. It describes how to evaluate steady-state error for different test inputs like step, ramp, and parabolic inputs. The steady-state error depends on factors like system configuration and number/type of poles in the closed-loop transfer function. Systems with integrators have zero steady-state error for step inputs, while more poles may be needed at the origin to achieve zero error for ramps and parabolas. The document also introduces static error constants which characterize the steady-state error.
Basic instrumentation
This document provides an overview of basic instrumentation used for measuring pressure, flow, level, temperature, and neutron flux. It discusses the general theory and operating principles of common pressure measurement devices like bourdon tubes, diaphragms, bellows and capsules. It also covers flow measurement techniques using devices like orifices, venturis and annubars. Level measurement using differential pressure cells and bubblers is described. Methods for measuring temperature with RTDs, thermocouples and thermostats are summarized. The document concludes with sections on neutron flux detection and basic control principles.
Some important tips for control systems
This document provides notes on control systems for a Bachelor of Engineering degree. It includes:
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2. A classification of control systems based on their method of analysis and design, type of signal, system components, and main purpose.
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One input voltage and three output voltage universal biquad filters with orth...
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01-05-2021_CS-EEE-A&B-SFG_synchros.pptx
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16 s1 ee2002_ld_multi-stage_differential_amplifiers_v1.3
This document is a lesson plan on multi-stage and differential amplifiers by Assoc Prof Zheng Yuanjin of Nanyang Technological University. It includes objectives, outlines the analysis of AC-coupled multi-stage amplifiers and differential amplifiers. It provides examples of a 3-stage amplifier and differential amplifier circuits. Key concepts covered are voltage gain, input and output resistances of multi-stage amplifiers, and differential and common mode gains of differential amplifiers. References and textbooks are listed for additional reading.
03-05-2021_CS-EEE-A&B-SFG_synchros.pptx
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Orientation Lectures - Department of ECEhttps://www.kluniversity.in › ece
S.No. Date Research Group Delivered by
1 18‑Jul‑20 SPRG Dr. N. Siddaiah
2 30‑Jul‑20 CSRG Dr. R. Revathi
3 1‑Aug‑20 MERG Mrs. Mariya Priyadarshini
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Faculty Orientation Workshop On SE (E&TC/Elex) Revised ...https://engg.kkwagh.edu.in › EC_FOW_report
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Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
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image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
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- 1. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Control Systems Signal Flow graphs
- 2. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Introduction • Block diagram is a pictorial representation of the sequence of events in a process • For complicated systems difficult to reduce block diagrams • Signal flow graph – a graphical representation of the relationship between variables – Provides relationship between system variables without the need for reduction
- 3. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Signal Flow Graph (SFG) Block Diagram to signal flow graph
- 4. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Signal Flow Graph (SFG) • A signal-flow graph is a diagram consisting of nodes that are connected by several directed branches and is a graph representation of a set of linear relation. • Only valid for linear system
- 5. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Basic elements of SFG • Branch: A unidirectional path segment • Nodes: The input and output points or junctions
- 6. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Basic elements of SFG Input Node Output Node Mixed Node
- 7. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION • Path: A branch or a continuous sequence of branches that can be traversed from one node to anther node. Basic elements of SFG 1. Forward Path 2. Feedback path
- 8. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION • Loop: A closed path that originates and terminates on the same node, and along the path no node is met twice. Basic elements of SFG
- 9. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION • Non-touching loops: If two loops do not have a common node. Basic elements of SFG
- 10. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Touching loops: Two touching loops share one or more common nodes. Basic elements of SFG
- 11. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Self loop: Path that originates and terminates at the same node. Basic elements of SFG
- 12. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Basic elements of SFG 1. Forward Path Gain: P1 = G1G2G3 P2 = G4 P3 = G1G2(-1)
- 13. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION 2. Feedback Path Gain: -G1H1 Basic elements of SFG In this case there is one loop or Feed back path
- 14. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Basic elements of SFG 3. Non-touching loop gain: Two Non-touching loops gain: G2H2H3 G2H2H7G7 G7H7H3 Three Non-touching loops gain: G2H2H3H7G7
- 15. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Basic elements of SFG )(sR )(sG )(sC )(sG )(sR )(sC block diagram: signal flow graph: In this case at each step block diagram is to be redrawn. That’s why it is tedious method. So wastage of time and space. Only one time SFG is to be drawn and then Mason’s gain formula is to be evaluated. So time and space is saved.
- 16. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Block Diagram to SFG
- 17. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Block Diagram to SFG
- 18. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION G4(s) Block Diagram to SFG E(s) x1 (s) x2 (s) Y(s) -H1(s) G1(s) G2(s) G3(s) -1 R(s) 1
- 19. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Block Diagram to SFG
- 20. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Block Diagram to SFG
- 21. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Mason’s gain formula The linear dependence (Gain) T i j between input variable x i and output variable x j is given by the following formula: k ijkijk ij P T
- 22. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Mason’s Gain Rule Mason’s gain rule is as follows: the transfer function of a system with signal-input, signal-output flow graphs is 332211 )( ppp sT Δ=1-(sum of all loop gains)+(sum of products of gains of all combinations if 2 non-touching loops)- (sum of products of gains of all combinations if 3 non-touching loops)+… A path is any succession of branches, from input to output, in the direction of the arrows, that does not pass any node more than once. A loop is any closed succession of branches in the direction of the arrows that does not pass any node more than once.
- 23. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Ex 1: Signal-Flow Graph Models
- 24. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION P 1 = G1G2G3G4 P 2 = G5G6G7G8 Ex 1: Signal-Flow Graph Models
- 25. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Individual loops L 1 = G2 H2 L 4 = G7 H7 L 3 = G6 H6 L 2= G3 H3 Pair of Non-touching loops L 1L 3 L 1L 4 L2 L3 L 2L 4 Ex 1: Signal-Flow Graph Models
- 26. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION ..)21(1( LiLjLkiLjLLL P R Y kk Y s( ) R s( ) G1 G2 G3 G4 1 L3 L4 G5 G6 G7 G8 1 L1 L2 1 L1 L2 L3 L4 L1 L3 L1 L4 L2 L3 L2 L4 Ex 1: Signal-Flow Graph Models
- 27. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Ex 2: SFG
- 28. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Ex 2: SFG Forward Paths P1 = G1G2G3G4G5G6 P2 = G1G2G7G6 P3 = G1G2G3G4G8
- 29. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION L 3 = -G 8 H 1 LOOPS L 2 = -G2 G 3G 4G 5 H2 Ex 2: SFG
- 30. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION L 4 = - G2 G 7 H2 L5 = -G 4 H 4 L1= -G 5 G 6 H 1 LOOPS Ex 2: SFG
- 31. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION L 7 = - G 1G2 G 7G 6 H3 L 6 = - G 1G2 G 3G 4G 8 H3 L 8= - G 1G2 G 3G 4G 5 G 6 H3 Ex 2: SFG LOOPS
- 32. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Ex 2: SFG Pair of 2 non-touching loops
- 33. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Pair of Non-touching loops L 4 L 5 L 3 L 7 L 4 L 5L 7 L 4L 5 L 3L 4
- 34. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Non-touching loops for paths ∆ 1 = 1 ∆ 2= -G 4 H4 ∆ 3= 1
- 35. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Signal-Flow Graph Models Y s( ) R s( ) P1 P2 2 P3 P1 G1 G2 G3 G4 G5 G6 P2 G1 G2 G7 G6 P3 G1 G2 G3 G4 G8 1 L1 L2 L3 L4 L5 L6 L7 L8 L5 L7 L5 L4 L3 L4 1 3 1 2 1 L5 1 G4 H4
- 36. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION Simultaneous equations to SFG 𝑦2 = 𝑡21 𝑦1 + 𝑡23 𝑦3 𝑦3 = 𝑡32 𝑦2 + 𝑡33 𝑦3 + 𝑡31 𝑦1 𝑦4 = 𝑡43 𝑦3 + 𝑡42 𝑦2 𝑦5 = 𝑡54 𝑦4 𝑦6 = 𝑡65 𝑦5 + 𝑡64 𝑦4
- 37. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION t21 t 23 t31 t32 t33 𝑦2 = 𝑡21 𝑦1 + 𝑡23 𝑦3 𝑦3 = 𝑡32 𝑦2 + 𝑡33 𝑦3 + 𝑡31 𝑦1 𝑦4 = 𝑡43 𝑦3 + 𝑡42 𝑦2 Simultaneous equations to SFG
- 38. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION 𝑦5 = 𝑡54 𝑦4 𝑦6 = 𝑡65 𝑦5 + 𝑡64 𝑦4 Simultaneous equations to SFG
- 39. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION After joining all SFG