Why is modulation needed? Though there are many reasons, for our purposes here there's
only one: to translate (move) a given signal's information to a different frequency. Why this
is necessary will become evident in the discussion that follows.

Wireline Effects on a DC Signal

Normally, people are inclined to think of data communications through a wire as being
instantaneous. This is because their observations are usually based on only short lengths of
wire and are focused on such effects as turning on a car's headlights, which seem to come
on "immediately." However, the transmission time from the moment the switch contacts
are made until current is flowing through the lamp filaments is definable. This is particularly
true of signals that have a fast rise (or fall) time such as data signals. Figure 7-1 illustrates
the waveforms, both ideal and real, for a simple-series circuit that consists of a load
(resistor), a source (battery), a switch, and a relatively long length of connecting wire. The
switch's ideal output is an abrupt change (called a step voltage). After a long length of wire
the end result is something less than abrupt.

Note: The following discussion of wireline changes involves basic electrical knowledge.
Skipping it will dilute your understanding of why modems are necessary but not what they
do. So if you have a limited electrical background (or none at all) you may want to skip to
the next section, "Sine Wave As a Carrier."

To see the reason for this output change, we must analyze the step voltage and understand
that any conductor, such as a wire, has an inductance and a capacitance and that the
longer the wire is, the greater the inductive and capacitive effects will be. Capacitance is
parallel (shunt) between the conductors. Figure 7-2 illustrates the lumped-constant
schematic. Lumped merely means that the inductance is distributed evenly throughout the
conductor. The state of being lumped is represented by the schematic symbol for an
inductor whose value represents the total inductance throughout the wire; the same is true
for the capacitor, a single symbol representing the lumped capacitance of a segment of line.

Observing the circuit that results from representing the lumped components shows it to be
a PI (looks like the PI symbol p) filter with multiple sections. Arranged as shown in figure 7-
2, it is a low-pass filter, meaning, of course, that high frequencies are attenuated, while the
lower frequencies have less attenuation.
Analyzing the signal of a unit step waveform is complex and involves the use of higher
mathematics. However, it should be easy to see that the unit step signal (the abrupt rise or
fall) can represent any on-off signal that periodically changes state, such as a square wave.
A square wave itself can be thought of as a sine wave whose period is the sum of one on
and one off state or two element times. The square wave's leading and falling edges for the
most part consist of the higher-frequency components. The level state is made up of the
lower-frequency components-primarily the fundamental sine wave. Developing a square
wave from the fundamental sine wave and its odd harmonics is performed by Fourier
analysis techniques (quite beyond the scope of this text) all that is necessary to know is that
the resultant square wave shape is formed by its low- and high-frequency components.

When a unit step voltage change or any other large swing in voltage levels occurs and a
device attempts to transmit these changes down a long metallic wireline, the line's lumped
capacitance and inductance and the line's copper losses (the DC resistance) combine to
reduce the output waveform's amplitude and attenuate its higher-frequency components.
The faster the rise time (or fall time) is, the greater the attenuation. Also, the metallic line
acts as a delay line. That is, the reactive time constants are different for different frequency
components of the square wave. This results in different parts of the waveform arriving at
different times. The net result is a distorted waveform. The attenuation for low- or high-frequency
components is called "amplitude distortion," and the different time constants result
in an effect called "phase distortion."

The number of decisions that a media can support in one second is called the "line modulation
rate" or "baud rate." You may determine a media's required baud rate by taking the
smallest element or symbol time that you wish to transmit (the quickest decision time) and
dividing this time into 1. A standard telephone wireline of 300 to 3,300 Hz is generally
capable of 1,200 baud. That is twelve hundred decisions a second. For duplex operation
this is six hundred decisions in both directions (adding up to twelve hundred). This is the
maximum that the media can support.

Sine Wave As a Carrier

The sine wave is used as a carrier because a sine wave cannot be "integrated" or "differentiated"
mathematically. Long wireline processes affect a square wave exactly as they affect a
process controller. Integration (the averaging of change over time) causes a square wave to
become a triangular waveform, while differentiation (the rate of change over time) on a
square wave causes it to become a peaked waveform. These processes do not affect a sine
waveform. Its amplitude can be reduced and the entire waveform shifted in phase, but the
sine wave's shape cannot be changed through a linear or passive device. The fact that a
sine wave cannot be integrated or differentiated by passive devices, that a square wave is
made up of a fundamental sine wave and its odd harmonics, and that an electrical line acts
as a low pass filter are actual physical phenomena, meaning, of course, that we may not
necessarily know why, but we can use the rules. Because a sine wave will retain its physical
waveform through linear processes it is used to "carry" digital information.