Circuit Design: Know It All

Darren Ashby, Bonnie Baker, Ian Hickman, Walt Kester, Robert Pease, Tim Williams, Bob Zeidman

• Publisher: Newnes
• Year: 2011
• ISBN:
  9780080949659
• Topic: Technology & Engineering
• Subtopic: Microelectronics
• Index: Technology & Engineering

The Newnes Know It All Series takes the best of what our authors have written to create hard-working desk references that will be an engineer's first port of call for key information, design techniques and rules of thumb. Guaranteed not to gather dust on a shelf!Electronics Engineers need to master a wide area of topics to excel. The Circuit Design Know It All covers every angle including semiconductors, IC Design and Fabrication, Computer-Aided Design, as well as Programmable Logic Design.

• A 360-degree view from our best-selling authors
• Topics include fundamentals, Analog, Linear, and Digital circuits
• The ultimate hard-working desk reference; all the essential information, techniques and tricks of the trade in one volume

Chapter 1

The Fundamentals

Mike Tooley, Darren Ashby and Robert Pease

1.1 Electrical Fundamentals

This chapter has been designed to provide you with the background knowledge required to help you understand the concepts introduced in the later chapters. If you have studied electrical science, electrical principles, or electronics then you will already be familiar with many of these concepts. If, on the other hand, you are returning to study or are a newcomer to electronics or electrical technology this chapter will help you get up to speed.

1.1.1 Fundamental Units

You will already know that the units that we now use to describe such things as length, mass and time are standardized within the International System of Units (SI). This SI system is based upon the seven fundamental units (see Table 1.1).

Table 1.1 SI units

Quantity	Unit	Abbreviation
Current	ampere	A
Length	meter	m
Luminous intensity	candela	cd
Mass	kilogram	kg
Temperature	Kelvin	K
Time	second	s
Matter	mol	mol

1.1.2 Derived Units

All other units are derived from these seven fundamental units. These derived units generally have their own names and those commonly encountered in electrical circuits are summarized in Table 1.2, together with the corresponding physical quantities.

Table 1.2 Electrical quantities

(Note that 0K is equal to −273°C and an interval of 1K is the same as an interval of 1°C.)

If you find the exponent notation shown in Table 1.2 a little confusing, just remember that V⁻¹ is simply 1/V, s⁻¹ is 1/s, m⁻² is 1/m⁻², and so on.

Example 1.1

The unit of flux density (the tesla) is defined as the magnetic flux per unit area. Express this in terms of the fundamental units.

Solution

The SI unit of flux is the weber (Wb). Area is directly proportional to length squared and, expressed in terms of the fundamental SI units, this is square meters (m²). Dividing the flux (Wb) by the area (m²) gives Wb/m² or Wb m⁻². Hence, in terms of the fundamental SI units, the tesla is expressed in Wb m⁻².

Example 1.2

The unit of electrical potential, the volt (V), is defined as the difference in potential between two points in a conductor, which when carrying a current of one amp (A), dissipates a power of one watt (W). Express the volt (V) in terms of joules (J) and coulombs (C).

Solution

In terms of the derived units:

Note that: Watts = Joules/seconds and also that Amperes × seconds = Coulombs.

Alternatively, in terms of the symbols used to denote the units:

One volt is equivalent to one joule per coulomb.

1.1.3 Measuring Angles

You might think it strange to be concerned with angles in electrical circuits. The reason is simply that, in analog and AC circuits, signals are based on repetitive waves (often sinusoidal in shape). We can refer to a point on such a wave in one of two basic ways, either in terms of the time from the start of the cycle or in terms of the angle (a cycle starts at 0° and finishes as 360°—see Figure 1.1). In practice, it is often more convenient to use angles rather than time; however, the two methods of measurement are interchangeable and it’s important to be able to work in either of these units.

Figure 1.1 One cycle of a sine wave voltage

In electrical circuits, angles are measured in either degrees or radians (both of which are strictly dimensionless units). You will doubtless already be familiar with angular measure in degrees where one complete circular revolution is equivalent to an angular change of 360°. The alternative method of measuring angles, the radian, is defined somewhat differently. It is the angle subtended at the center of a circle by an arc having length that is equal to the radius of the circle (see Figure 1.2).

Figure 1.2 Definition of the radian

You may sometimes find that you need to convert from radians to degrees, and vice versa. A complete circular revolution is equivalent to a rotation of 360° or 2π radians (note that π is approximately equal to 3.142). Thus, one radian is equivalent to 360/2π degrees (or approximately 57.3°). Try to remember the following rules that will help you to convert angles expressed in degrees to radians and vice versa:

• From degrees to radians, divide by 57.3.

• From radians to degrees, multiply by 57.3.

Example 1.3

Express a quarter of a cycle revolution in terms of:

(a) degrees;

(b) radians.

So...