Difference between revisions of "Electronics primer"

Revision as of 16:23, 22 August 2012

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Overview: Should I read this thing?

This primer is intended to quickly get electronics newbies comfortable with circuit interpretation by providing clear definitions and systematic mathematical approaches, without unnecessary detail.

If you don’t feel comfortable defining an open or short circuit across arbitrary nodes, aren’t sure how to keep your voltage and current signs consistent, and perhaps even barely remember what series versus parallel means, then this guide is for you. You probably want to read all of it, preferably before the second lecture on electronics (lecture X). You’ll get more out of lecture if you’re not struggling with the basics.

If you do feel comfortable with the basic concepts and math in theoretical form, but have no clue how these relate to instruments, breadboards, and what leads are touching where, then you can probably skip this guide and focus your efforts on completing Module 0 instead.

References to the relevant sections of Agarwal and Lang (6.002 textbook, 2005 edition) are included for those seeking to further solidify their understanding.

Motivation: Where is this all leading and why should I care?

Circuit representations are useful for solving problems in many engineering domains -- electrical, mechanical, thermal, hydraulic, etc. Any system of linear ordinary differential equations is amenable to circuit analysis. For simplicity, we’ll start with circuit elements whose behavior is not frequency dependent, namely resistors and sources, and build up to more complex systems involving capacitors and inductors in lecture/lab and perhaps someday a subsequent primer.

Defining essential circuit elements and variables: v, i, R

Table 1 lists the name, symbol, constitutive relation and its graphical representation for each of four simple idealized elements: a voltage source, a current source, a conductor, and a resistor. Each constitutive equation and associated plot relate voltage (v) across an element and current (i) through that element.

Current reflects the flow rate of charge carriers such as electrons and by convention is positive in the direction of positive charge flow, which means the electrons are actually flowing in the negative direction. Voltage reflects the electrical potential difference between two points. The higher the voltage, the greater the current flow (always down the potential gradient, because electrons are attracted up the potential gradient) through a given element. To make circuit analysis tenable, each element is treated as having a uniform v and i.*

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Table 1 Equations below + symbols etc. (Graphs separately below so can be bigger?)

(1) v = V (2) i = I (3) v = iR (4) v = 0

An element is bracketed by terminals, one designated (+) and the other (-). Terminals may be shown as filled or open circles to indicate whether or not that terminal connects to another electrical element. (Open circles represent no connection.) Pairs of terminals are sometimes called ports, whether for a single element or across multiple elements. A port approach is particularly useful for abstracting away (black-boxing) multiple circuit elements and treating them as an equivalent element with defined inputs and/or outputs. We’ll discuss this further in section X. [Be sure to follow through – not super clear as yet.]

A voltage v and current i can be defined at any terminal. For terminals A and B, the element voltage $ v = v_A – v_B $ and the element current$ i = i_A = i_B $. Here, $ v_A $ and $ v_B $ are the absolute potentials (defined relative to a reference), and v is the potential difference between the two terminals.

[Sketch] Repeat resistor symbol, but include labels for terminals, v, and arrow for i.

Expanding upon Table 1,

1. An ideal voltage source maintains a set potential difference across its terminals no matter what current is being drawn through it. Thus, its voltage versus current graph is simply a horizontal line. A real source such as a battery does not exhibit this behavior. However, such non-ideal elements can be modeled as combinations of ideal linear elements, as described in section X.
2. Similarly, an ideal current source provides a set current no matter what potential difference exists across its terminals. Real sources include op-amps.
3. Resistance reflects the tendency of an element to draw current and also its tendency to dissipate energy. A linear resistor obeys Ohm’s law, v=iR, at any instant in time. Real resistors are well represented by the model resistor equation only so long as the current and voltage do not exceed their maximum combined ratings.
4. Ideal conductors have no resistance, meaning that no potential difference appears across them for any value of current flow through them. No voltage drop in turn results in no energy dissipation. Ideal conductors are a fine model for real wires.

Elements such as sources and resistors are connected at their terminals by wires in order to form circuits. To make circuit analysis tenable, elements are treated as interacting only through their terminals; in other words, electromagnetic fields associated with a given element are internal to it.* When this assumption does not hold, more complex elements called capacitors and inductors can be integrated into the circuit. (See section X.)

• Again, see Agarwal 1.3.

Two limiting cases of the resistor element are useful for solving circuit problems: the open circuit and the short circuit. Infinite resistance means that no current passes through that element; this is also called an open circuit across said element and is equivalent to an unconnected port. Zero resistance means no potential difference appears across the element; this is also called a short circuit across that element and is equivalent to an ideal wire.

[Sketches] Keep it simple: single voltage source and resistor. (1) open circle port parellel to resistor is open circuit, full potential difference across R, vAB = V (2) port parallel to resistor connected with a wire, short circuit, potential same everywhere, vAB=0
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