What is Amplitude Modulation?

In this next series of posts, we’re going to dive into the heart of the radio arts: modulation. Modulation is what make wireless communications possible. Over the years, many different ways to modulate signals have been created. The advent of digital electronics has brought along with it a slew of new digital modulation techniques as well.

In this post we’re going to dissect one of the oldest forms of modulation: amplitude modulation, or AM. It is also relatively easy to understand.

Why we Need Modulation

Our voice can only carry so far. Sound waves are quickly attenuated, and can’t be used to communicate over long distances. Electromagnetic (EM) waves however have the potential to travel very far with little energy. They also have the advantage of being much, much faster: EM waves travel at the speed of light. The basis of radio (for speech-based modes) is to translate our sound waves into electromagnetic waves, allowing our message to be sent over long distances in a very short amount of time.

Translating our sound waves to an electric signal is easy enough: this is the role of the microphone. Transforming an electronic signal to an EM waves requires an antenna. An electric signal is applied at the antenna, and the antenna radiates that signal as an EM wave. So just connecting a microphone to an antenna should give us the intended result right? Not exactly. Not all EM waves are equal. An EM wave’s fundamental characteristic is its frequency. A human’s voice can range from 20Hz to 20 000Hz in the audio spectrum. The microphone translates that 20Hz-20kHz audio wave into a 20Hz-20kHz electric signal, which, if it were connected to an antenna, would be translated into a 20Hz-20kHz EM wave. Unfortunately that EM wave would be very bad at its job, and few people would be able to receive the signal. The reason for this is that EM waves have fundamentally different characteristics depending on their frequency. The EM spectrum, or RF spectrum, can be divided into the following categories:

3kHz to 30kHz: Very Low Frequency (VLF)
30kHz to 300kHz: Low Frequency (LF)
300kHz to 3MHz: Medium Frequency (MF)
3MHz to 30MHz: High Frequency (HF)
30MHz to 300MHz: Very High Frequency (VHF)
300MHz to 3GHz: Ultra High Frequency (UHF)
3GHz to 30GHz: Super High Frequency (SHF)
30GHz to 300GHz: Extremely High Frequency (EHF)

If we were to directly hook up our microphone to an antenna, the resulting EM wave would fall into the VLF range. Unfortunately these frequencies are terrible for radio use. For best reception, the size of an antenna should be close to the EM wave’s wavelength: that means the lower the frequency, the bigger our antenna needs to be. VLF frequencies have wavelengths in the 10s of kilometers, making the required antennas physically impractical. Furthermore, these frequencies are extremely noisy and easily disturbed by weather and other natural phenomena.

If we want our signal to be received be someone, we need to shift its frequency up to an RF category that is well suited for radio, without losing the information the signal contains. This is called modulation.

At MF and higher, all frequencies have potential for radio use. Which one you choose will depend on the characteristic you are after. Want to send messages over the ocean? You should go for MF or HF. Want to communicate locally, or send digital data? Maybe VHF and higher is a better bet.

What is Modulation

At its heart, modulation is moving the original signal from audio range, also known as baseband, to a specific radio range. However, our initial audio signal already contains certain frequencies. These frequencies are what make up the actual message we want to send. To modulate a signal, we need to somehow shift that signal up to the wanted frequency while keeping the initial frequency(ies) intact. A modulated signal therefore has at least two frequencies:

the actual message’s frequency in the audio range: this is called the modulating frequency
and the required RF frequency: this is called the carrier frequency

This may sound complicated if you’ve never heard of the concept before, but it turns out there are several ways to achieve this. One of the first methods created was amplitude modulation. This technique involves having the audio frequency signal ride on the higher frequency carrier signal: the amplitude of the carrier signal will follow the amplitude of the modulating signal. Below you will find both the modulating signal and the carrier signal. The last diagram is of the amplitude modulated signal.

Notice how the two frequencies manifest themselves in the modulated signal. The top envelope of the AM signal carries the audio information. The bottom envelope carries an inverted version of the audio signal.

The Fundamentals of Amplitude Modulation

We’ve seen what an AM modulated signal looks like. Now, how do we create one? It’s time to dive into some math. Let $s_M$ be the modulating signal in the audio frequency range, and $s_C$ be the high frequency carrier. To keep things simple, we’ll make $s_M$ a sine wave:

$s_M = k_1 \sin(2\pi f_M t)$
$s_C = k_2 \sin(2\pi f_C t)$

As explained in the previous section, an AM signal involves the carrier frequency having its amplitude follow the modulating signal. What this means is that the carrier’s amplitude is not constant:

$s_{AM} = k(t) \sin(2 \pi f_C t)$

More specifically, its amplitude varies with the modulating signal:

$s_{AM} = k \sin(2\pi f_M t) \sin(2\pi f_C t)$

The above is simply a sine wave of frequency $f_C$ with an amplitude that is equal to $\sin(2\pi f_M t)$ . Amplitude modulation is simply multiplication. A variety of circuits can be used to perform this operation. These circuits are called mixers.

Practical AM – the Modulation Factor

There is a problem with the AM signal above. Notice how when the modulating signal crosses 0 volts, the AM signal is also equal to zero. After passing 0 volts, while the modulating audio signal goes negative, our AM signal jumps back up to positive values. The envelope of the signal doesn’t faithfully represent the modulating signal:

To fix this problem, all we need to do is some DC offset to the modulating signal. To keep the math simple, we’ll add a 1V DC offset. The goal is for the modulating signal to never go negative: $s_M = 1 + m \sin(2\pi f_M t)$ . The AM signal becomes:

$s_{AM} = [1 + m \sin(2\pi f_M t) ] sin(2\pi f_C t)$

Notice the $m$ factor in front of the $f_M$ sine wave. It can vary from 0 to 1. Mathematically, it is equal to the ratio of the maximum amplitude of the modulating signal to the maximum amplitude of the carrier:

$m = \frac{Modulating Amplitude}{Carrier Amplitude}$

The modulating signal’s amplitude must be smaller than the carrier amplitude, otherwise the resulting AM signal will be distorted: the modulation factor should not go over 1. The modulation factor tells us how much the AM signal’s amplitude varies with the modulating signal. It can be seen as the AM signal’s sensitivity to the modulating signal $s_M$ . A modulation factor of exactly one would result in an AM signal that reaches 0V when the modulation reaches its lowest peak:

However, a modulation factor greater than 1 distorts the AM signal: its envelope no longer resembles the modulating signal, and a part of the information is lost.

AM Signal Spectrum

If we analyze the AM signal more closely and look at its frequency spectrum, this is what we will see:

Notice that there are three spikes in the graph, one at $f_C - f_M$ , one at $f_C + f_M$ , and one at $f_C$ . Remember that what we want to send is the modulating frequency $f_M$ . This signal contains $f_M$ in the two spikes around $f_C$ , so the information is preserved. These spikes are called the sidebands, while $f_C$ is also called the center frequency.

The spectrum only shows three discrete frequencies because our audio modulating signal consisted of only one frequency: it was a pure sine wave. In reality, our vocal message will consist of many different frequencies in the audio range. These will show up as wide bands in the signal’s frequency spectrum, centered around the center frequency.

Such a signal can absolutely be sent on the air and exploited. In fact, it is still done so today: AM radio is still alive and well.

However, looking at the spectrum we can see that this method is perhaps not the most optimal. Our signal is preserved, but it is present in two sidebands. The AM signal also contains $f_C$ , which doesn’t contain any useful information, but yet takes up half the power of the signal. Having both sidebands also increases the space this signal takes up on the radio spectrum.

A variety of AM modulation schemes exist to try and make the AM signal take up less space on the RF spectrum and require less power. We’ll go over the most popular one: SSB modulation.

Making AM Leaner: Single-Sideband

SSB, or Single-Sideband, amplitude modulation is probably the most popular type of AM. It aims to solve the two problems seen in the previous section: big frequency spread on the RF spectrum, and high amounts of energy waster on just the carrier. To achieve this, a SSB AM signal simply gets rid of both the carrier frequency $f_C$ and one of the sidebands: either $f_C - f_M$ , called the lower sideband, or $f_C + f_M$ , called the higher sideband. The RF spectrum of an SSB signal where we have chosen to keep the lower sideband is:

A SSB signal requires only half the spectrum space the AM signal does. Furthermore, all the energy is dedicated to transmitting the information, and none of it is wasted on either duplicating the message or sending the carrier. This efficiency comes at a cost however. The most obvious drawback is the added complexity in creating an SSB signal. The other, less obvious drawback is that tuning in to a SSB signal is harder than for an AM signal, and requires an oscillator (BFO) with very good resolution. This makes SSB impractical for consumer use (such as music). It does see considerable professional use however: the army, ships, both military and civilian, and of course hams use it frequently. The RF spectrum is a vital and scarce natural resource, and modulation schemes that limit the RF space a signal requires are a necessity.

Conclusion

I hope this primer on amplitude modulation was helpful to you. I willingly omitted any details about the circuitry needed to modulate and demodulate signals here. Future articles will deal with this topic in length.