## Wave Modulation: Placing sound, image or data on an electromagnetic wave (1/2)

http://www.dspguide.com/ch10/5.htm

"Audio signals are great for short distance communication; when you speak, someone across the room hears you. On the other hand, radio frequencies are very good at propagating long distances. For instance, if a 100 volt, 1 MHz sine wave is fed into an antenna, the resulting radio wave can be detected in the next room, the next country, and even on the next planet."

There is a technique that enables the "embedding" of an audio signal onto a radio frequency so that it can be propagated in long distances. It is called modulation.

"Modulation is the process of merging two signals to form a third signal with desirable characteristics of both. This always involves nonlinear processes such as multiplication; you can't just add the two signals together."

Two main schemes of modulation is amplitude modulation which generates the AM waves and frequency modulation which generates the FM waves.

## Amplitude Modulation

We saw in the section about "Microphones" how we can convert a sound to an electricity signal (specific voltage). Let us consider the audio signal that we see in the following image (all images that follow, unless othewise specified are derived from the link http://www.dspguide.com/ch10/5.htm).

The next image shows what we have chosen as the carrier wave. It is a sinusoidal wave. If someone tell us that we see 30 ups and downs in the image, can we calculate its frequency? Since the image shows 30 cycles in 1 millisecond, that means 30.000 cycles in a second or a frequency of 30KHz. Note that for AM radio stations, the carrier frequency is the frequency we select when choosing the radio station.

This chart which is said to be in the "time domain" can be transformed to a "frequency domain" chart. This would be a frequency versus amplitude chart, the following:

We see the frequency of the wave, which has the value of 30 KHz, being associated to its amplitude. In the case of the audio wave we have a group of frequencies that are in the range of 300Hz to 3KHz, as seen in the following image. We also see a variability of the amplitudes.

We will now proceed to wave multiplication, since modulation is performed in this way. Mathematics tell us that (as mentioned in the link above) "this results in an oscillatory waveform that has an instantaneous amplitude proportional to the original audio signal". Also, "in the jargon of the field, the envelope of the carrier wave is equal to the modulating signal". The envelope of the carrier is indicated with the dashed line in the following picture. The one after that represents the result of the multiplication, which corresponds to the AM signal.

As mentioned "this signal can be routed to an antenna, converted into a radio wave, and then detected by a receiving antenna." "A detector or demodulator circuit is then used to convert the AM waveform into the audio signal.

For those interested in the wonders of mathematics, the process of the multiplication generates two additional frequencies, two sidebands, as demonstrated in the following "frequency domain" chart.

What is interesting about that is that if we add up (algebrically) the carrier wave and the two sideband frequencies we will get the pattern of the AM wave. This is shown in a slide from this presentation (no 33) http://www.powershow.com/view/130476-N2IwO/Amplitude_Modulation_powerpoint_ppt_presentation

Let us consider the notion of “Bandwidth”.

This is calculated as follows: B=2 fm

It is the difference between the upper and lower sideband frequencies.

B= fUSB – fLSB

Here is an example from the same presentation.

An AM broadcasting station is transmitting on a frequency of 980 KHz.

It is allowed to transmit modulating frequencies up to 5kHz.

What are the sideband frequencies and total bandwidth?

The solution is found in the presentation.

Note that the first is the carrier frequency and the second is the frequency that will modulate the carrier, i.e. the audio signal.

Generally: Audio (0 - 4 kHz), Video (0 - 6 MHz).

Another case of modulation. Note the envelope with the dashed red line.

Slide source

https://en.wikibooks.org/wiki/Sound_Synthesis_Theory/Modulation_Synthesis

Figure 8.4 A time-domain plot of an amplitude-modulated signal. M(t), the sinusoidal 10hz modulator signal, C(t) the sinusoidal 220 Hz carrier signal, andA(t) the two combined using amplitude modulation.

## Amplitude modulation, an example of heterodyning

Heterodyning is equivalent to wave multiplication and generates lower frequencies (side bands) in the process.

Excerpt from http://www.informit.com/articles/article.aspx?p=24687&seqNum=5:
« The human voice, for example, can typically generate frequencies from 100Hz to 10,000Hz, for a bandwidth of 9,900Hz. But the ear does not require a vast range of frequencies to elicit meaning from ordinary speech; the vast majority of sounds we make that constitute intelligible speech fall between 250Hz and 3,400Hz. So, the phone company typically allotted a total bandwidth of 4,000Hz for voice transmission. »

We say that the signal produced by the human voice, this specific baseband signal, is « band-limited » to a few KHz.

If we want to transmit an electromagnetic wave of 1 KHz we will need a 300 Km antenna. For a practical size of 30cm we would have a 1 GHz wave, which is close to the frequency used by some mobile phone companies.

As mentioned in these MIT lecture notes : http://web.mit.edu/6.02/www/s2012/handouts/14.pdf
« Any baseband signal can be broken up into a weighted sum of sinusoids using Fourier decomposition (Chapter 13). If the baseband signal is band-limited, then there is a finite maximum frequency of the corresponding sinusoids. One can take this sum and modulate it on a carrier signal of some other frequency in a simple way: by just multiplying the baseband and carrier signal (also called “mixing”) ».

This process is also called heterodyning. As mentioned here https://fas.org/man/dod-101/navy/docs/es310/superhet.htm: "To heterodyne means to mix to frequencies together so as to produce a beat frequency, namely the difference between the two. Amplitude modulation is a heterodyne process: the information signal is mixed with the carrier to produce the side-bands. The side-bands occur at precisely the sum and difference frequencies of the carrier and information. These are beat frequencies (normally the beat frequency is associated with the lower side-band, the difference between the two)."

What Superheterodyning is
"When you use the lower side-band (the difference between the two frequencies), you are superheterodyning. Strictly speaking, the term superheterodyne refers to creating a beat frequency that is lower than the original signal."

Amplitude modulation is a heterodyne process (cf my site http://www2.information-book.com/physics/amplitude-modulation/)

As mentioned, it is a multiplication and it can be represented graphically as shown in the attached image which is slide 7 from this presentation http://www.powershow.com/view/130476-N2IwO/Amplitude_Modulation_powerpoint_ppt_presentation

We see that the baseline signal is m(t). Via a certain process it becomes g(t) and then a -g(t) appears as a « reflection » ! Then this envelop formed by those two is "filled" with the carrier frequency.

This mathematical process generates two sidebands, the two small waves in the second attached picture. What is interesting is that if you add carrier and sidebands you get the complex waveform.
http://www2.information-book.com/s/cc_images/teaserbox_2452243177.png?t=1439487268

Via this process, heterodyning can be used to generate lower frequencies from an original frequency.

In electronics this process can be performed by a frequency mixer. A diode can be used for this purpose as mentioned at this link. https://en.wikipedia.org/wiki/Frequency_mixer

## "Can we create a localized magnetic field to make a directional ELF EM spotlight per say?

Question from Physics Forum:

"I saw a compass with nothing around it for 20 or more feet. The compass needle oscillated between magnetic north and 90 degrees from its resting state, magnetic north, at about 1/3 of a hertz indefinitely but another compass 10 feet away did not. ELF waves are not directional so I thought somehow higher frequencies which are directional could be heterodyned into a localized magnetic field to make a directional ELF EM spotlight per say. The scientist or magician claimed he could do this on a much larger scale and turn the Earth into an NMR and ESR machine under its own magnetic field but this device helped with the signal to noise ratio. He did not explain how he projected directional ELF waves at a distance."

"And I don't think you can use beam forming with ELF waves either."