The Ups and Downs of Amplitude Modulation

May 24, 2023

An Introduction to the History, Principles and Applications of AM Radio

When you think of advancements in signal modulation, your mental time machine might go back to the turn of the 21^st century and LTE which was proposed by NTT DOCOMO as “Super 3G” in early 2004.¹ But over a hundred years earlier, on June 3^rd, 1900, in the city of São Paulo, Brazil, the Reverend Father Roberto Landell de Moura demonstrated the transmission of voice messages over a distance of 8 km using amplitude modulation.² Several months later, on December 23, 1900, Reginald Aubrey Fessenden successfully transmitted an amplitude-modulated signal approximately 1.6 km.³ Throughout the nearly 123 years since these transmissions occurred, arguably no modulation scheme has been of greater significance in world history than amplitude modulation (AM).

While AM is an inexpensive and simple way to transmit and receive signals over great distances, it is also susceptible to natural and man-made noise, which tend to be amplitude modulated as well. In this article, we first review the importance of some of the traditional frequency bands in which amplitude modulation has been utilized over the years and why it continues to be important today. Next, we describe the basic principles of amplitude modulation in both the time and frequency domains, enabling us to delve further into its advantages and disadvantages. Finally, we discuss modern modulation schemes for which amplitude modulation still plays a key role.

The Advent of AM Radio Communications

Much of the early work by pioneers attempting to amplitude modulate signals was performed on spark-gap-type wireless telegraph transmitters. One of the difficulties with this approach was in reliably achieving an adequate spark frequency to modulate. The development of the diode detector, as well as vacuum tube (“valve”) oscillator and amplifier technology during World War I advanced the design of transmitters and receivers significantly. Toward the end of 1915 in the UK, shortly after the development group at Brooklands headed by Charles Edmond Prince was relocated to Joyce Green at Kent, Prince’s team demonstrated one of the first documented AM CW uplinks to a flying aircraft.⁴ This demonstration was repeated in St. Omer, France in February 1916, when clear voice transmissions from the aircraft were received from 20 miles away.⁴

The airborne radio utilized was the Tuner Aircraft Valve Mk. I.⁵ This radio is believed to have covered the 300 to 800 meter band (375 kHz to 1 MHz) and used a single Q valve powered by a 6V battery for the filament and a 100V battery for the HT, or high tension.⁵ Understanding the significance of this capability, Prince remarked, “It seemed almost beyond hope to achieve really practical wireless telephony from an aeroplane, but the difficulties have been overcome, and the new [radio] set is by no means a toy, or only of scientific interest. A new and amazing power is conferred by it.”⁴

These early, successful developments of two-way AM CW communications in the medium frequency band were replicated in the HF and VHF bands in subsequent years, denoted by the channels labeled “AM Comms” in Figure 1. Amplitude modulated HF still finds broad usage and is very important when flying over the ocean because of its ability to propagate over long distances. AM has long been – and continues to be – utilized in the 118 to 137 MHz portion of the VHF band, which is allocated to aircraft communications.

Figure 1: Primary bands, frequencies and applications for which amplitude modulation has been utilized.

AM Broadcasting

Just as in two-way AM communications, the components available from the advancement of vacuum tube technology led to much higher power transmitters and much more sensitive receivers.

The U.S. Commerce Department began regulating AM broadcasting in the MF range in 1921, and the number of broadcasting stations grew to over 500 in the United States by the end of 1922.⁶ “By 1925, the [AM] ‘broadcast band’ consisted of the frequencies from 550 kHz to 1500 kHz, in ten kHz steps.”⁶ The current AM radio band extends from 530 kHz to 1700 kHz as shown in Figure 1. While factory-built radios were expensive, crystal radios were very inexpensive, could be built at home, and became very popular with the general public. American sportscaster and author Walter Lanier “Red” Barber once said, “People who weren’t around in the Twenties when radio exploded can’t know what it meant, this milestone for mankind. Suddenly, with radio, there was instant human communication. No longer were our homes isolated and lonely and silent. The world came into our homes for the first time. Music came pouring in. Laughter came in. News came in. The world shrank, with radio.”⁷

The transmission of amplitude-modulated, medium-frequency radio signals quickly reached the masses and has enjoyed tremendous success for nearly a century, until the present day, but particularly from the 1920’s through the 1940’s, known as the “Golden Age” of radio.

Also shown in Figure 1 are the traditional television bands and frequencies of operation as well as the channels contained within these bands. In broadcast television, the picture that appears on the television screen has been amplitude-modulated onto the carrier and transmitted over public airwaves to the viewer. The total bandwidth allocated for each VHF or UHF TV channel is 6 MHz.

Amplitude Modulation in the Time Domain

In the time domain, it is easy to see the trigonometry behind transmitting and receiving amplitude modulation. It is also not difficult to envision what an AM signal looks like in the time domain. The early radio communications pioneers sought to amplitude modulate a continuous wave (CW) carrier with the human voice and to demodulate this signal miles away, something that was referred to at the time as wireless telephony. Charles Prince’s team in the UK overcame the additional challenge of having the aircrew attempt to modulate the carrier in a very noisy and windy environment by inventing the throat microphone.⁸ Figure 2 shows a very simplified block diagram of a microphone (left) as the modulator of an AM transmitter along with its companion receiver and the mathematical equations describing the waveforms present at various stages of the Tx and Rx systems. Additionally, Figure 2 shows a notional AM waveform with the mathematical expressions for the envelope [x(t)] and the entire AM waveform itself [x(t)cos(ω₀t)] labeled on the diagram. The envelope [x(t)] appears as a solid line simply for clarity. The modulation itself is often referred to as the baseband signal, and the cosine waveform the local oscillator. In both the transmitter and receiver, the RF port of the mixer is connected to the antenna.

Figure 2: Simplified Tx and Rx block diagrams with waveform expressions and a time domain illustration of of x(t)cos(ω₀t).

There are several things to note about AM and its mathematical expressions, particularly as it is demodulated at the receiver. Perhaps the most interesting mathematical operation is that in “tuning” the receiver to the desired, precise AM “station,” or frequency (ω₀), we are left with a cosine squared function [cos²(ω₀t)]. As shown in Figure 2, we utilize the following trigonometric identity to change the form of the demodulated signal:

x(t)cos²(ω₀t) = x(t)[1/2 + cos²(2ω₀t)/2] = x(t)/2 + x(t)cos(2ω₀t)/2

Consequently, demodulation has yielded two separate signals, the mathematical expressions for which show that one is simply a scaled version of the original modulation (our desired, received signal), and the other is an AM signal that is exactly two times the frequency of the original transmission. Since the highest frequency of the modulation envelope [x(t)] is generally much less than the carrier frequency, a simple lowpass filter is needed to filter out the AM signal at 2ω₀t. Be mindful of the fact that this is a bit of an oversimplification to illustrate the mathematical principle behind AM demodulation.

Most often, the modulated envelope of the transmitted waveform first passes through a sensitive detector, or rectifier, such that the peaks of the carrier waveform are detected (rectified), reproducing the original modulation as a single-ended audio waveform. The composition of the simplest form of the lowpass filter that proceeds this detection/rectification process is a resistor and a capacitor.

Frequency conversion in receivers from ω₀ to some lower, intermediate frequency (IF) usually takes place before processing and demodulation. One of the primary reasons for converting to IF is that higher performance components are available at lower frequency, making it is easier to process and demodulate AM as well as other modulations. Receivers known for utilizing this principle of frequency conversion to IF, then processing and demodulating are known as superheterodyne receivers. The superheterodyne technique was invented by Edwin Howard Armstrong in 1919.⁹

Amplitude Modulation in the Frequency Domain

Understanding AM in the frequency domain is relatively straightforward thanks to the Fourier transform. Developed by French Mathematician, Jean-Baptiste Joseph Fourier, the Fourier transform can be used as the mathematical basis for transitioning a function from the time domain to the frequency domain. The Fourier transform F{cos(ω₀t)} becomes a function of ω, and is denoted X(ω). The step-by-step process of determining the Fourier transform of cos(ω₀t) is shown in Appendix A, and the result is shown below:

F{cos(ω₀t)} = π[δ(ω – ω₀) + δ(ω + ω₀)] => F{cos(2πf₀t)} = ½[δ(f – f₀) + δ(f + f₀)]

Due to the unique property of the Dirac delta function (δ), the resulting frequency domain representation is two impulses, the magnitude of each being 1/2, one located at f₀ and one at – f₀, as shown in Figure 3 below.

Figure 3: Frequency domain representation of cos(2πf₀t) as predicted by the Fourier transform using Dirac delta functions.

Since the Fourier transform is symmetric about the y-axis due to the fact that it’s defined over the interval – ∞ to +∞, we have an impulse frequency at a negative frequency. In reality, negative frequencies do not exist, and having an impulse there does not stand to reason, since an examination of any sinusoidal signal on a spectrum analyzer shows that the entire magnitude of the signal resides at +f₀.

The spectrum of the modulating signal x(t) can be arrived at if we simply consider this unique property of the Fourier transform that results in both positive and negative frequency components. Assume that our modulating signal x(t) is in the audio frequency range, 20 Hz to 15 kHz. There will be a symmetric distribution on the positive and the negative frequency side of the magnitude of the spectrum over that frequency range. Figure 4 shows a notional audio modulation spectrum.

Figure 4: Notational 20 Hz to 15 kHz audio modulation in the frequency domain.

Rather than a continuous audio spectrum, we could have made the audio a single frequency, say 10 kHz. That would be represented by a ½ amplitude impulse at – 10 kHz and a ½ amplitude impulse at + 10 kHz.

To create the modulated carrier waveform, the modulation x(t) is multiplied by the carrier waveform cos(ω₀t). The frequency convolution theorem states that “the multiplication of two signals in the time domain is equivalent to the convolution of their spectra in the frequency domain.”¹² Qualitatively, through convolution, the audio modulation spectrum shown in Figure 4, which is very near to, and symmetric about DC, is shifted because it is convolved with the carrier delta function, and now resides on either side of the carrier frequency. The spectra on either side of the carrier impulses are known as sidebands and this type of amplitude modulation is known as double-sideband (DSB) AM. Other forms of AM are double-sideband suppressed carrier (DSB-SC), which is more complex to receive, and single-sideband (SSB). The transmitted AM signal spectrum is shown in Figure 5.

Figure 5: Transmitted AM signal frequency domain spectrum showing the convolution of the modulation x(t) with cos(ω₀t).

What happens in the frequency domain on the receive side is very interesting. Remember, multiplication in the time domain is convolution in the frequency domain, and convolution with a delta function in the frequency domain results in a frequency shift. The frequency spectrum in Figure 5 is shifted up by f₀ and down by f₀, and is shown in Figure 6. Just as in the time domain (Figure 2) we have a low frequency component, and a component at 2f₀, the same is shown in the spectrum of Figure 5. Since 2f₀ is so much greater in frequency than the baseband modulation signal, the latter is very easy to separate with a lowpass filter.

Figure 6: Received AM signal spectrum after being multiplied by a local oscillator signal cos(ω₀t).

I AM, Therefore I Exist¹³

AM is ubiquitous. In this application note we reviewed the history of amplitude modulation, crediting several key pioneers important enough to have left an indelible mark on history. We also examined various applications in which AM has a strong foothold and appears to be here to stay, including aeronautical communication and broadcast. The time domain and frequency domain representations of AM signals were illustrated to explain the theory of how AM is created, transmitted, and received.

Many developments in the state of the art of electronics have occurred over the 100+ years since AM emerged. Using spark-gap generators for carrier frequencies gave way to vacuum tube oscillators. Eventually, most vacuum tubes (except for the very high-power broadcast station tubes) would be replaced by transistors. Since the 1950’s, billions of transistor radios have been sold. Over 50 years ago, in 1972, Motorola introduced the MC1496, a double balanced multiplier IC. This device can be used as an RF mixer, multiplier, or modulator and is capable of generating SSB (single-sideband) or DSB (double-sideband) AM signals. The MC1496 is also used for demodulation of SSB or DSB signals and for a multitude of other RF applications. Fast forward 50 years and today’s modern cell phone likely has 8 double balanced multipliers built right into the controller IC that take up less than 1/1000^th the space. AM remains a very important modulation scheme, not just due to its longevity, but because many of today’s more complex waveforms such as QAM (quadrature amplitude modulation) depend on it. We will address QAM specifically in a subsequent article.