Engineering 1000 Chapter 6: Abstraction and Modeling

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Engineering 1000Chapter 6 Abstraction and
Modeling
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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

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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

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• 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

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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)

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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)

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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

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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

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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

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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?

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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

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• 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

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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

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• 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
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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

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AutoCad

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

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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

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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

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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

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

mesh
stresses
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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

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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.

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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

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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

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Homework

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

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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