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Engineering 1000 Chapter 6: Abstraction and Modeling

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Title: Engineering 1000 Chapter 6: Abstraction and Modeling


1
Engineering 1000 Chapter 6 Abstraction and
Modeling
2
Outline
  • Why is abstraction useful?
  • What are models?
  • how are models different from theory and
    simulation?
  • Examples from microelectronics
  • Types of model
  • finite element models
  • Approximations and responsibility

3
Abstraction
  • Abstraction has the same root meaning as the
    abstract of a report
  • to summarise and extract the essential elements
  • from the Oxford English Dictionary the act or
    process of separating in thought, of considering
    a thing independently of its associations
  • The purpose of abstraction is to enable the
    designer to consider the relative merits of
    several options without having to build
    prototypes of each one
  • By formulating the problem in the ways that we
    have already considered
  • especially the objective/function trees
  • we have already moved some way along the road
    to abstraction
  • the generation of multiple options is sometimes
    referred to as parsing

4
  • The advantage of the tree diagrams is that
    closely related issues are automatically
    identified
  • and some idea of their level has been obtained
  • this is effectively a second stage of abstraction
  • it is worth checking to see if objectives at the
    same level but on different branches of the tree
    can be achieved using a common method
  • In our objectives tree, we stopped one stage
    before developing ways of implementing those
    objectives
  • in abstraction, we now need to consider what
    these possible implementations will be
  • to do this we need to shuffle around concepts,
    find relations, identify commonalities, consider
    variations, ,
  • i.e. manipulate the elements of the problem
  • the textbook calls this the dimensions of
    variation
  • the statement-restatement technique was one way
    of achieving this

5
What is a Model?
  • A model is a representation or imitation of a
    real object
  • in engineering terms, a model is used because it
    enables predictions or calculations or in some
    other way makes the design process more
    convenient
  • often, the model is a mathematical description
    which can be manipulated by computer
  • but it can also be a physical model of an object,
    which maintains a desired characteristic (e.g.
    the shape of a car) but is in some way simpler
    than the real thing (e.g. no internal machinery)
  • Traditionally, models are small-scale versions of
    bridges, buildings, planes, etc.
  • which are tested in order to predict how the real
    structure would behave under appropriate
    conditions
  • this is not always easy because some effects do
    not scale linearly with distance (e.g. friction,
    fluid flow)

6
Models as Purposeful Representations
  • The textbook uses the words purposeful
    representation as a brief definition of a model
  • Models are used to assist the designers
    thinking, analyse potential designs, realise what
    is known or unknown, predict behaviour, identify
    connections, etc.
  • Models are typically used when the system is
    incompletely understood
  • the textbook also states that models are used for
    complex systems
  • However, we must distinguish here between
    physical models and computer-based models
  • physical models are indeed used for complex
    systems, and represent one of engineerings
    oldest tools
  • complex and understood systems are usually solved
    by simulation in computer-based approaches (see
    later for an example)

7
How is a Model Different from Theory?
  • A model is related to, but different from, a
    theoretical description of the object
  • the model may be based on theory
  • but may include non-ideal behaviours observed in
    experiments but not well explained by theory
  • theory may predict certain trends, but empirical
    numbers from experiments are included to get the
    calculated results to agree with the real results
  • The key difference is that a model must behave as
    nearly as possible the same way as the real thing
  • but it is not directly important whether the
    models behaviour is well predicted by theory
    it is the result that counts
  • a good theoretical basis is good however,
    because it will likely expand the range of
    conditions over which the model will work

8
How is a Model Different from Simulation?
  • A simulation is usually a technique for obtaining
    theoretical results in cases where the theory is
    mathematically tough to solve
  • so simulation is a practical way of solving the
    theoretical description
  • assuming you know the appropriate theory!
  • It can help to think of the difference between a
    model plane and a flight simulator!
  • We will illustrate these situations with an
    example from microelectronics

9
Microelectronic Circuit Design
  • The goal here is to predict as closely as
    possible the behaviour of a microelectronic
    circuit design before it is manufactured
  • e.g. amplifier gain, bandwidth, distortion, logic
    gate switching time
  • There are a number of levels which we must
    consider
  • the circuit operation
  • the components which make up the circuit
    (transistors, resistors, capacitors, diodes,
    interconnects)
  • the physical mechanisms within each of these
    components
  • the way in which the manufacturing process
    affects the behaviour
  • It is not always necessary for the designer to
    understand all of these levels in depth
  • but the computer software must assume this
    knowledge

10
SPICE Circuit Simulator
  • SPICE is a widely used circuit analysis package
    which allows the designer to connect electronic
    devices into a circuit
  • and predicts the response of the circuit under
    specified conditions
  • SPICE is a circuit simulator
  • it applies circuit analysis equations to the
    designed circuit to calculate currents and
    voltages as a function of time
  • for any condition, it may require a lot of
    calculations to reach a final answer where all
    the values are internally consistent
  • But how does SPICE know how a transistor
    behaves?

www.silvaco.com
11
SPICE Models
  • SPICE contains an analytical model of how every
    device behaves
  • analytical means mathematically solvable
  • There are numerous levels of models depending
    on how complex they are
  • i.e. how accurately they describe every aspect of
    the device behaviour, no matter how subtle
  • It is not directly important for SPICE models to
    be theoretically accurate
  • the basic characteristics are described by theory
  • but many complexities are based on observations
    of extensive experimental data
  • these are empirical or semi-empirical models
  • This is very important, because it means that the
    accuracy of your predictions are highly dependent
    on how much you know about the specific devices
    in your circuit

12
  • Microelectronic manufacturing fabs will measure
    thousands of devices in order to get accurate
    SPICE models
  • A widely used SPICE model for transistors is BSIM
    3.3
  • The better the theoretical framework, the more
    generally applicable will be the results
  • and the model can be refined

www.silvaco.com
13
Device Simulators
  • Most of the basic theory for semiconductor
    devices is well known
  • however, applying it to a realistic device is
    extremely complex (sound familiar? same as
    SPICE)
  • this is because the 3-D geometry of the devices
    and the any material layers they contain makes
    hand calculation impossible
  • Device simulators such as MEDICI sub-divide the
    device into elements which are simulated
    individually but consistently with neighbouring
    elements
  • elements are of varying size to capture details
    where needed but to save computation time
    elsewhere

www.avanticorp.com
14
  • As with all simulators, the results are only as
    good as your theoretical understanding of the
    situation
  • In the end, engineers like theory to the extent
    that it improves the models
  • but a design must still work even if there is no
    adequate theory
  • and so (good) models are of paramount importance

www.avanticorp.com
15
Computer-Aided Design (CAD)
  • Many engineering projects would be impossible to
    realise without CAD
  • CAD is rather a loose term which may range from
    fancy graphics packages to complex software
    suites including modelling and simulation
  • e.g. the 10 million transistors in the Pentium
    would not be feasible if paced and connected by
    hand (much is done with automatic layout)
  • A common tool for laying out chips is CADENCE
  • it contains a drawing package for defining
    metal, silicon, etc layers
  • a design rule checker
  • SPICE
  • automatic layout
  • standard cells
  • and numerous other tools

16
AutoCad
  • Another standard CAD package is AutoCad
  • which you will learn in part 2 of ENG1000
  • www.autodesk.com

17
Computer-Aided Manufacture (CAM)
  • The logical conclusion of CAD is CAM
  • and the two are often lumped together as CAD/CAM
  • By using the data generated by the CAD tools
    directly for controlling the machines
    manufacturing the item several benefits follow
  • speed
  • accuracy no (additional) errors introduced
  • flexibility
  • For example, we email output files from CADENCE
    to the chip manufacturing plant
  • one of the advantages of standardisation of
    information formats

18
Types of Model
  • Models can be categorised into three basic types
  • Iconic models
  • look identical to the finished object visually
    equivalent
  • e.g. maps, globes, computer graphics, physical
    models
  • but are incomplete in the sense that some
    information is lost
  • e.g. a 2-D representation of a 3-D object, no
    internal mechanics
  • Analogic models
  • are functionally equivalent to the object
  • so they behave like the real object, but not
    necessarily for the same reasons
  • e.g. the transistor models in SPICE, model
    aeroplane in a wind tunnel
  • Symbolic models
  • such as descriptions using mathematical (or
    chemical) equations
  • e.g. postscript representation of a font, x2 y2
    r2

19
Finite Element Models
  • The mesh used to analyse electronic devices in
    MEDICI is an example of a finite element model
    (FEM)
  • FEMs are used in many situations where the basic
    equations are known but are very difficult to
    solve in more than one dimension and for complex
    situations
  • heat flow (thermal conductivity) x (temperature
    gradient)
  • electrical currents as a function of electric
    field
  • fluid flow as a function of pressure gradients
  • stresses in complex surfaces
  • For each element the equations are solved
  • ensuring that conditions match at boundaries
    between adjacent elements
  • boundary conditions are satisfied

20
  • One general FEM solver is ANSYS
  • www.ansys.com

mesh
stresses
21
Approximations
  • It should be remembered at all times that models
    and simulations are all approximations to reality
  • they may use simplifying assumptions (i.e.
    models)
  • unknown effects cannot be included
  • equations may be solved by numerical methods,
    which do not yield exact results
  • often, models are only valid over a specific
    range of conditions, especially is they are
    semi-empirical (use measured data)
  • The engineer must understand
  • the theory, models, and techniques on which the
    solution is based
  • nature of the approximations used in the model
  • the situations for which the technique is valid
  • There is no substitute to experience with a
    particular modelling tool
  • often engineers know when a particular tool
    gives good or bad results

22
Responsibility
  • The performance of the design is engineers
    responsibility, regardless of how the design was
    carried out
  • errors in simulation or modelling are also the
    engineers responsibility, not that of the
    software vendor
  • From the PEO
  • The practice of professional engineering has
    become increasingly reliant on computers, and
    engineers use many computer programs that
    incorporate engineering principles and matters.
    Many of these programs are based upon or include
    assumptions, limitations, interpretations and
    judgments on engineering matters that were made
    by or on behalf of an engineer when the program
    was first developed. Therefore, it is often
    difficult to determine, just by using a program
    or by being given a description of its function,
    the engineering principles and matters it
    incorporates. The engineer must have a suitable
    knowledge of the engineering principles involved
    in the work being conducted, and is responsible
    for the appropriate application of these
    principles. When using computer programs to
    assist in this work, engineers should be aware of
    the engineering principles and matters they
    include, and are responsible for the
    interpretation and correct application of the
    results provided by the programs. Engineers are
    responsible for verifying that results obtained
    by using software are accurate and acceptable.
    Given the increasing flexibility of computer
    software, the engineer should ensure that
    professional engineering verification of the
    software's performance exists. In the absence of
    such verification, the engineer should establish
    and conduct suitable tests to determine whether
    the software performs what it is required to do.

23
Developing a Model
  • Developing good models is a difficult and
    time-consuming process
  • this is perhaps not surprising since the
    complexity of the situation is the likely reason
    for needing a model in the first place
  • a large proportion of engineering research is
    devoted to the development and improvement of
    models
  • How do you know its a good model?
  • ultimately, it must be verified by favourable
    comparison with a wide range of experimental
    results collected by different people under a
    variety of appropriate conditions
  • goodness depends on the requirements of the
    specific situation
  • by repeated successful trials, some measure of
    confidence can be established in the tool
  • a corollary is that software modelling tools are
    the domain of a few well-established companies in
    each engineering field

24
Summary
  • Theory, simulation, and modelling are tools to
    enable the engineer to understand and to predict
    the behaviour of proposed designs
  • without having to construct prototypes
  • The advantage is that various options can be
    considered and compared as efficiently as
    possible
  • The disadvantage is that no model/simulation/theor
    etical description is exact
  • It is the engineers responsibility to ensure
    that these tools are used appropriately

25
Homework
  • Read chapter 6 of the textbook and the case
    studies described in that chapter
  • Do problems 6.1 and 6.2

26
Exercise
  • Develop a simple model governing the number of
    economy-class seats in an aeroplane
  • as a function of other relevant factors (e.g.
    ticket price)
  • can you optimise the number?
  • What assumptions have you made in your model?
  • it is always important to state explicitly all
    your assumptions, so users of the model know if
    it is valid for their situation
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