### Introduction

This article will give you an introduction to some of the key terms used by spacecraft engineers when designing and analyzing antennas. While this article doesn’t require any prior knowledge of spacecraft engineering, some knowledge of circuit theory as well as mathematical concepts including logarithms and complex numbers are used.

This article is a bit of a work in progress that we’ll be adding to continuously, so there are a few sections that aren’t yet completed. These are marked with a [TBC] for “To Be Completed”.

##### Prerequisite Knowledge

### Background

This section will introduce many of the theoretical and conceptual terms you will come across on Crash Cube on pages related to antennas and electromagnetics.

##### Electric Field

An electric field, commonly abbreviated as an E-field, is a field generated by electrical charges (such as electrons) or by a magnetic field that changes with time. It is one half of the force of electromagnetism, one of the four fundamental forces of nature. The strength of an electric field (**E**) is given as the force (**F**) exerted per unit charge (**q**) and is often measured in units of volts per meter, or electric potential per distance. Electric field is a vector quantity, meaning that direction is important in determining its effect.

\overrightarrow{E} = \frac{\overrightarrow{F}}{q}

Dimensional Analysis:

\frac{Newton}{Coulomb} = \frac{N*m}{C*m} = \frac{J}{C*m} = \frac{V}{m}

Convention is to define electric field lines generated by a positive charge as emanating from the charge, outward.

##### Magnetic Field

A magnetic field, commonly abbreviated as an B-field, is one generated by a moving electric charges (such as an electric current) or by an electric field that changes with time. It is the other half of the force of electromagnetism along with the electric field.

It is convention to define the direction of the field as perpendicular to the direction of the current generating it, following the right-hand rule.

##### Electromagnetic Wave

An electromagnetic wave is a paired, sinusoidally oscillating electric field and magnetic field that travels through space, either through vacuum, air, or some other non-conducting material. In almost all typically used materials, including PCB substrates and vacuum, the electric and magnetic fields are perpendicular to both each other and the direction of travel of the wave. They follow the right hand rule such that the cross product of the E field and the B field is in the direction of propagation.

The direction of Figure 1 shows an illustration of an electromagnetic wave, with the electric field (**E**) in blue oscillating in the x-axis, the magnetic field (**B**) in red oscillating in the y-axis. The z-axis is the direction the wave is travelling in.

##### Polarization

An electromagnetic wave can oscillate in different axes, or multiple axes simultaneously. This is called the polarization, essentially how the wave oscillates in the plane perpendicular to its axis of propagation.

In Figure 1 for example, the electric field is oscillating in the x-axis. If the wave was projected into the x-y plane, the tip of the arrow would trace out a line over time, only moving in the x-axis. This is an example of linear polarization. If the ground is in the y-z plane in that image, this could also be called vertical polarization. If the wave was rotated 90 degrees to either side, it would be an example of horizontal polarization. It is also possible for a linearly polarized wave to be rotated at an arbitrary angle around the axis of propagation (z in this example).

A wave can also be polarized in more than one axis simultaneously. A common form of this in the space industry is circular polarization, in which the electric field oscillates in both the vertical and horizontal axis with the same magnitude, 90 degrees out of phase with each other. If the oscillations are of differing magnitudes or have different phasing, the polarization is called elliptical. Figure 2 shows an example of linear, circular, and elliptical polarization.

##### Frequency

The frequency of an electromagnetic wave is the rate at which the phase of the wave changes per time. All electromagnetic waves oscillate sinusoidally. Frequency is commonly measured in Hertz (abbreviated Hz), or cycles per second. In antenna engineering, however, it is also common to measure frequency using angular measurements, radians per second. Recall that for each 360° phase cycle of a sine wave, there are 2π radians. Frequency is often abbreviated using the symbol *f*.

##### Wavelength

The wavelength of an electromagnetic wave is the distance between the peaks of the wave, represented by the symbol *λ*. In vacuum, this is equal to the speed of light divided by the frequency.

\lambda_0 = \frac{c_0}{f}

The subscript 0 (often pronounced “naught”) is used to indicate that the wavelength is that measured in vacuum. In materials other than vacuum, the frequency of a wave remains the same. The wavelength, however, will change based on the material’s properties since the speed of light in a material other than vacuum is lower than the speed of light in vacuum.

**Modulation**

An electromagnetic wave is sinusoidal, but it is impossible to encode any information onto a pure sinusoid without changing it over time. By changing the sinusoid in some way that is detectable, we can encode information. Changes to the wave over time to encode information can take many forms, from changing the phase at specific intervals, to changing the frequency, to shutting the wave on and off. These changes, which can be decoded by a receiver as 0’s and 1’s, are called modulation.

##### Bandwidth

An unmodulated signal with one frequency appears as a single value on a frequency spectrum plot (see prerequisite reading #1). When a signal is modulated it is no longer a pure sinusoid, instead it’s power spreads out wider in the frequency spectrum in a manner that is dependent on the type of modulation that’s being used and the rate at which the signal is being modulated.

Bandwidth is the range of frequencies under which most of the power of the signal resides. It can be defined in a couple of ways most commonly 98% power (for signal bandwidths), -3 dB off-peak insertion loss (for filter bandwidths), or -10 dB return loss (for antenna bandwidths), but it’s possible to define it however is relevant to your specific application.

Essentially, it boils down to the difference between the minimum significant frequency component and the maximum frequency component of your signal. A modulated signal that has a minimum frequency component of 10 MHz and a maximum frequency component of 15 MHz has a bandwidth of 5 MHz.

Rather than defining a signal by the minimum and maximum frequency components, its common to describe it using the point in between them, called the center frequency, and the bandwidth (in this example 12.5 MHz and 5 MHz, respectively).

##### Decibels

Decibels, often abbreviated as dB, are a logarithmic unit of measurement for measuring relative quantities. Most often you’ll see them used to describe quantities like gain (dBi, decibels relative to an isotropic antenna), power (dBm, decibels relative to one milliwatt), or voltage (dBV, decibels relative to one volt), but it can be used to describe any measurement. The purpose of using decibels for many quantities in communications is twofold. First, they allow representations of both extremely large and extremely small values in a manner that’s easy to represent and perform mathematical operations with. Second,

For example, 50 mW can be represented as 17 dBm. If a 1 GHz signal is transmitted over 50 km, the amount of power at a receiver is 2.3*10^-14 of what was originally transmitted, or -106.4 dB. Rather than multiply these two numbers together to find the amount of power at the receiver (1.15*10^-9 mW), by using decibels the two values can simply be added together. This becomes far more convenient, especially when many different gains and losses need to be taken into account in an equation.

To convert a value *x* to decibels, for linear quantities such as voltage, use the following formula.

20\log_{10}x

For nonlinear quantities such as power or gain (which is itself a measure of relative power), use the following formula.

10\log_{10} x

##### Impedance

The impedance of an electromagnetic wave is the ratio between the amplitudes of its electric and magnetic fields. In a circuit, the impedance describes the ratio between the voltage and current of a wave travelling in the circuit. It is measured in units of ohms, similarly to resistance, and can be a complex value. Impedance is important because, as a wave reaches the boundary between two mediums or transmission lines (such as transitioning between a coaxial cable and a an antenna), if the impedances aren’t matched, some of the energy gets reflected resulting in inefficiencies.

The two relationships that impedance describes are related. If you wish to learn about them in more detail, check out Chapter 2 in [3], an excellent textbook on the fundamentals of electromagnetics.

##### VSWR and Reflection Coefficient

[TBC] – While we continue work on this article, here is an external link covering the concept we haven’t gotten around to yet.

https://www.electronics-notes.com/articles/antennas-propagation/vswr-return-loss/what-is-vswr.php

##### Directivity, Gain, Realized Gain

[TBC]

##### Radiation Pattern

When an antenna radiates, it does not do so equally in all directions. Based on the shape, size, and material composition of an antenna, the amplitudes of the fields radiated in different directions will be different. By plotting the strength of the fields relative to the direction in which they emanate, a radiation pattern can be generated. The radiation pattern is one of the most useful tools for an antenna engineer.

A radiation pattern can be generated for several different quantities, most of which are what is called far-field quantities, i.e. they are the values that would be measured if an observer was very far away from an antenna, such that the entire antenna essentially appears as a point source. Typical quantities measured using a radiation pattern are directivity, gain, realized gain, and axial ratio. An example of a 2D radiation pattern (normalized to the peak value, 9 dBi) is shown below in Figure 3.

### Further Reading

- [TBC]

### References

[1] – By SuperManu – Self, based on Image:Onde electromagnetique.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=2107870

[2] – R. Nave, *Classification of Polarization*. [Online]. Available: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polclas.html. [Accessed: 12-Jan-2021].

[3] – Ulaby, Fundamentals of Applied Electromagnetics

[4] – https://commons.wikimedia.org/wiki/File:Patch_antenna_pattern.gif

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