Lumped Ckt Abstraction

POWER OF ABSTRACTION

1. Engineering is purposeful use of science.
2. Science provides understanding of natural phenomena.
3. Scientific study involves experiment.
4. Scientific laws (concise statements or equations) explain experimental data.
5. Laws of physics abstract experimental data to practitioners
6. Practitioners use specific phenomena (without specifics of experiments & data that inspired laws)
7. Abstractions have goals.
8. Abstractions apply when appropriate constraints are met.

Eg: Newton’s laws of motion

1. Here simple statements relate dynamics of rigid bodies to their masses & external forces.
2. The laws apply under certain constraints (ex: when velocities are much smaller than speed of light.)
3. Scientific abstractions are simple & easy to use.
4. Scientific abstractions help us use properties of nature.

1. Electrical engg is purposeful use of Maxwell’s Equations (or Abstractions) for EMG phenomena.
2. To ease use of EMG, EE creates a new abstraction layer on top of Maxwell’s Equations
3. This abstraction is called ‘Lumped circuit abstraction’.
4. Lumped circuit abstraction connects physics & EE.
5. It makes EE an art of creating & exploiting successive abstractions to manage complexity of building useful electrical systems.

6. Abstraction makes building complex systems manageable.

Eg: force equation: F = ma.
1. With this we calculate acceleration (of a particle with a given mass) for an applied force.
2. Abstraction disregards size, shape, density, and temperature (properties immaterial to calculation of object’s acceleration.)
3. It ignores myriad details (of experiments & observations) that led to force equation.
4. Force equation is accepted as a given.

1. Laws & abstractions leverage/build upon past experience & work.
2. Over past century,a set of EE abstractions transformed physical sciences to engg - to build useful, complex systems.
3. Abstractions transform science to engg (and saves us from scientific minutiae)
4. Abstractions are derived through discretization discipline.
5. Discretization is called lumping.
6. A discipline is a self-imposed constraint.
7. Discipline of discretization states that
a. We choose to deal with discrete elements or ranges &
b. We ascribe a single value to each discrete element or range.
8. Discretization discipline ignores distribution of values within a discrete element.
9. Discretization discipline requires systems (built on this principle) operate within appropriate constraints so that single-value assumptions hold.
10. LCA (fundamental to EE) is based on lumping or discretizing matter.
11. Digital systems use digital abstraction.
12. Digital abstraction is based on discretizing signal values.
13. Clocked digital systems are based on discretizing both signals and time.
14. Digital systolic arrays are based on discretizing signals, time and space.


1. EE creates further abstractions to manage complexity of building large systems.
2. A lumped circuit element is an abstract representation (model) of material with complicated internal behavior.
3. A circuit often is an abstract representation of interrelated physical phenomena.
4. Operational amplifier is composed of primitive discrete elements
5. An opamp is a powerful abstraction that simplifies building of bigger analog systems.
6. Logic gate, digital memory, digital finite-state machine, and microprocessor are all abstractions developed to facilitate building complex computer & control systems.
7. Art of computer programming is creating successively higher-level abstractions from lower-level primitives.


1.2 LUMPED CIRCUIT ABSTRACTION
1. A lightbulb lights up when connected to battery (by pair of cables).
2. To know current flowing through bulb, we employ Maxwell’s equations.
3. We derive current by analysis of physical properties of bulb, battery, and cables.
4. This is a complicated process.
5. EEs do such computations to design more complex circuits (say with multiple bulbs & batteries.)
6. So how to simplify our task?
7. We observe that if we discipline ourselves to asking only simple questions, such as what is net current flowing through bulb, we can ignore internal properties of bulb and represent bulb as a discrete element.
8. Further, for purpose of computing current, we can create a discrete element known as a resistor and replace bulb with it.
9. We define resistance of bulb R to be ratio of voltage applied to bulb and resulting current through it.
10. In other words, R = V/I.
11. Notice that actual shape and physical properties of bulb are irrelevant provided it offers resistance R.
12. We were able to ignore internal properties and distribution of values inside bulb simply by disciplining ourselves not to ask questions about those internal properties.
13. In other words, when asking about current, we were able to discretize bulb into a single lumped element whose single relevant property was its resistance.
14. This situation is analogous to point mass simplification that resulted in force relation in Equation 1.1, where single relevant property of object is its mass.
15. As illustrated in Figure 1.5, a lumped element can be idealized to point
16. Terminal FIGURE where it can be treated as a black box accessible through a few terminals.
17. Behavior at terminals is more important than details of behavior internal to black box.
18. That is, what happens at terminals is more important than how it happens inside black box.
19. Said another way, black box is a layer of abstraction between user of bulb and internal structure of bulb.
20. Resistance is property of bulb of interest to us.
21. Likewise, voltage is property of battery that we most care about.
22. Ignoring, for now, any internal resistance of battery, we can lump battery into a discrete element called by same name supplying a constant voltage V, as shown in Figure 1.4b.
23. Again, we can do this if we work within certain constraints to be discussed shortly, and provided we are not concerned with internal properties of battery, such as distribution of electrical field.
24. In fact, electric field within a real-life battery is horrendously difficult to chart accurately.
25. Together, collection of constraints that underlie lumped circuit abstraction result in a marvelous simplification that allows us to focus on specifically those properties that are relevant to us.
26. Notice also that orientation and shape of wires are not relevant to our computation.
27. We could even twist them or knot them in any way.
28. Assuming for now that wires are ideal conductors and offer zero resistance,3 we can rewrite bulb circuit as shown in Figure 1.4b using lumped circuit equivalents for battery and bulb resistance, which are connected by ideal wires.
29. Accordingly, Figure 1.4b is called lumped circuit abstraction of lightbulb circuit.
30. If battery supplies a constant voltage V and has zero internal resistance, and if resistance of bulb is R, we can use simple algebra to compute current flowing through bulb as I = V/R.
31. Lumped elements in circuits must have a voltage V and a current I defined for their terminals.
32. 4 In general, ratio of V and I need not be a constant.
33. ratio is a constant (called resistance R) only for lumped elements that obey Ohm’s law.
34. 5 circuit comprising a set of lumped elements must also have a voltage defined between any pair of points, and a current defined into any terminal.
35. Furthermore, elements must not interact with each other except through their terminal currents and voltages.
36. That is, internal physical phenomena that make an element function must interact with external electrical phenomena only at electrical terminals of that element.
37. As we will see in Section 1.3, lumped elements and circuits formed using these elements must adhere to a set of constraints for these definitions and terminal interactions to exist.
38. We name this set of constraints lumped matter discipline.
39. lumped circuit abstraction Capped a set of lumped elements that obey lumped matter discipline using ideal wires to form an assembly that performs a specific function results in lumped circuit abstraction.
40. Notice that lumped circuit simplification is analogous to point-mass simplification in Newton’s laws.
41. Lumped circuit abstraction represents relevant properties of lumped elements using algebraic symbols.
42. For example, we use R for resistance of a resistor.
43. Other values of interest, such as currents I and voltages V, are related through simple functions.
44. ease of using algebraic equations in place of Maxwell’s equations to design and analyze complicated circuits will become much clearer in following chapters.
45. process of discretization can also be viewed as a way of modeling physical systems.
46. resistor is a model for a lightbulb if we are interested in finding current flowing through lightbulb for a given applied voltage.
47. It can even tell us power consumed by lightbulb.
48. Similarly, as we will see in Section 1.6, a constant voltage source is a good model for battery when its internal resistance is zero.
49. Thus, Figure 1.4b is also called lumped circuit model of lightbulb circuit.
50. Models must be used only in domain in which they are applicable.
51. For example, resistor model for a lightbulb tells us nothing about its cost or its expected lifetime.
52. primitive circuit elements, means for combining them, and means of abstraction form graphical language of circuits.
53. Circuit theory is a well established discipline.
54. With maturity has come widespread utility.
55. Language of circuits has become universal for problem-solving in many disciplines.
56. Mechanical, chemical, metallurgical, biological, thermal, and even economic processes are often represented in circuit theory terms, because mathematics for analysis of linear and nonlinear circuits is both powerful and well-developed.
57. For this reason electronic circuit models are often used as analogs in study of many physical processes.
58. Readers whose main focus is on some area of electrical engineering other than electronics should therefore view material in this