Table of Contents

# Frequency Ranges

The table shows the different frequency ranges used for communication along with the typical applications, propagation modes, and propagation issues.

Frequency Range | Type of Signal | |

Very low, low, and medium frequency: 3 kHz to 3 MHz | VLF LF MF | Very long-range communication, commercial AM radio. Ground waves circle the Earth. |

High frequency: 3 to 30 MHz | HF | Over-the-horizon communication, Signals reflect from ionosphere. |

Very high frequency:30 to 300 MHz | VHF | Mobile communication, TV and commercial FM . Line-of-sight required. |

Ultra high frequency: 300 MHz to 1 GHz | UHF | Mobile communication and TV. Line-of-sight required. |

Microwave: 1 to 30 GHz | MW | TV and telephone links, satellite links. Line-of-sight required. |

Millimeter wave: 30 to 100 GHz | mmW | Very short-range communication. Requires line-of-sight, high absorption in rain and fog. |

Note that propagation at the lower frequencies is characterized by reduced dependence on line of sight. Ground wave and ionospheric skip allow communication over very extended ranges. However, the lower fre- quencies are also characterized by narrow bandwidths. High percentage bandwidths create difficulties with antenna and amplifier performance. In general 10% bandwidth is fairly well behaved, and performance trade-offs are required for bandwidths greater than 10%.

VLF and LF links usually carry low-rate digital signals or Morse code, while MF links are wide enough to carry voice signals. Commercial AM radio is broadcast in the upper end of the MF frequency range. Above approximately 30 MHz, radio transmissions pass through the ionosphere, so higher frequency signals cannot propagate through ionospheric hops. They are dependent on line-of-sight or near line-of-sight propagation paths.

VHF and UHF transmissions can support enough bandwidth to carry not only voice and data, but also video signals—including commercial television broadcasts. Microwave frequencies are used to carry high information content signals in wide bandwidths. Wideband microwave point-to-point links carry large blocks of telephone signals, television signals, and wideband digital data. Communication satellite links are also at microwave.

RSGB Annotation | Frequency band |

L band | 1 to 2 GHz |

S band | |

C band | |

X band | |

Ku band | |

K band | |

Ka band | |

Q band | |

U band | |

V band | |

Microwave frequency bands, as defined by the Radio Society of Great Britain (RSGB)

# The Frequency Domain

It was shown over one hundred years ago by Baron Jean Baptiste Fourier that any waveform that exists in the real world can be generated by adding up sine waves. We have illustrated this in the Figure for a simple waveform composed of two sine waves. By picking the amplitudes, frequencies and phases of these sine waves correctly, we can generate a waveform identical to our desired signal.

Any real waveform can be produced by adding sine waves together.

Conversely, we can break down our real world signal into these same sine waves. It can be shown that this combination of sine waves is unique; any real world signal can be represented by only one combination of sine waves.

The relationship between the time and frequency domains.

a) Three- dimensional coordinates showing time, frequency and amplitude

b) Time domain view

c) Frequency domain view.

In the Figure a three dimensional graph of this addition of sine waves. Two of the axes are time and amplitude, familiar from the time domain. The third axis is frequency which allows us to visually separate the sine waves which add to give us our complex waveform. If we view this three-dimensional graph along the frequency axis we get the view in Figure b. This is the time domain view of the sine waves. Adding them together at each instant of time gives the original waveform.

However, if we view our graph along the time axis as in Figure c, we get a totally different picture. Here we have axes of amplitude versus frequency, what is commonly called the frequency domain. Every sine wave we separated from the input appears as a vertical line. Its height represents its amplitude and its position represents its frequency. Since we know that each line represents a sine wave, we have uniquely characterized our input signal in the frequency domain*. This frequency domain representation of our signal is called the spectrum of the signal. Each sine wave line of the spectrum is called a component of the total signal.

## The Need for Decibels

Since one of the major uses of the frequency domain is to resolve small signals in the presence of large ones, let us now address the problem of how we can see both large and small signals on our display simultaneously. Suppose we wish to measure a distortion component that is 0.1% of the signal. If we set the fundamental to full scale on a four inch (10 cm) screen, the harmonic would be only four thousandths of an inch (0.1 mm) tall. Obviously, we could barely see such a signal, much less measure it accurately. Yet many analyzers are available with the ability to measure signals even smaller than this. Since we want to be able to see all the components easily at the same time, the only answer is to change our amplitude scale. A logarithmic scale would compress our large signal amplitude and expand the small ones, allowing all components to be displayed at the same time.

The relationship between decibels, power and voltage.

Alexander Graham Bell discovered that the human ear responded logarithmically to power difference and invented a unit, the Bel, to help him measure the ability of people to hear. One tenth of a Bel, the deciBel (dB) is the most common unit used in the frequency domain today. A table of the relationship between volts, power and dB is given in the Figure. From the table we can see that our 0.1% distortion component example is 60 dB below the fundamental. If we had an 80 dB display as in thr Figure, the distortion component would occupy 1/4 of the screen, not 1/1000 as in a linear display.

It is very important to understand that we have neither gained nor lost information, we are just representing it differently. We are looking at the same three-dimensional graph from different angles. This different perspective can be very useful.

## Why the Frequency Domain?

Suppose we wish to measure the level of distortion in an audio oscillator. Or we might be trying to detect the first sounds of a bearing failing on a noisy machine. In each case, we are trying to detect a small sine wave in the presence of large signals. Figure A shows a time domain waveform which seems to be a single sine wave. But Figure B shows in the frequency domain that the same signal is composed of a large sine wave and significant other sine wave components (distortion components). When these components are separated in the frequency domain, the small components are easy to see because they are not masked by larger ones. The frequency domain’s usefulness is not restricted to electronics or mechanics. All fields of science and engineering have measurements like these where large signals mask others in the time domain. The frequency domain provides a useful tool in analyzing these small but important effects.

## The Frequency Domain: A Natural Domain

At first the frequency domain may seem strange and unfamiliar, yet it is an important part of everyday life. Your ear-brain combination is an excellent frequency domain analyzer. The ear-brain splits the audio spectrum into many narrow bands and determines the power present in each band. It can easily pick small sounds out of loud background noise thanks in part to its frequency domain capability. A doctor listens to your heart and breathing for any unusual sounds. He is listening for frequencies which will tell him something is wrong. An experienced mechanic can do the same thing with a machine. Using a screwdriver as a stethoscope, he can hear when a bearing is failing because of the frequencies it produces. So we see that the frequency domain is not at all uncommon. We are just not used to seeing it in graphical form. But this graphical presentation is really not any stranger than saying that the temperature changed with time like the displacement of a line on a graph.

## Spectrum Examples

Let us now look at a few common signals in both the time and frequency domains. In Figure 2a, we see that the spectrum of a sine wave is just a single line. We expect this from the way we constructed the frequency domain. The square wave in Figure 2b is made up of an infinite number of sine waves, all harmonically related. The lowest frequency present is the reciprocal of the square wave period. These two examples illustrate a property of the frequency transform: a signal which is periodic and exists for all time has a discrete frequency spectrum. This is in contrast to the transient signal in Figure 2c which has a continuous spectrum. This means that the sine waves that make up this signal are spaced infinitesimally close together.

Another signal of interest is the impulse shown in Figure 2d. The frequency spectrum of an impulse is flat, i.e., there is energy at all frequencies. It would, therefore, require infinite energy to generate a true impulse. Nevertheless, it is possible to generate an approximation to an impulse which has a fairly flat spectrum over the desired frequency range of interest. We will find signals with a flat spectrum useful in our next subject, network analysis.