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| howto:hambasics:sections:wavemodulation [2020/10/07 08:04] – va7fi | howto:hambasics:sections:wavemodulation [2022/11/04 18:52] (current) – [AM] va7fi |
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| ====== Properties of Waves ====== | ====== Properties of Waves ====== |
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| Here we dive a little more deeply into waves and look at three ways that a "pure" radio wave (called the //carrier//) can be modulated to encode a voice signal (called the //baseband// signal): //AM, SSB, FM//. | Here we dive a little more deeply into waves and look at three ways that a "pure" radio wave (called the //carrier//) can be modulated to encode a voice signal (called the //baseband// signal): //AM, SSB, FM//. |
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| ===== Amplitude, Wavelength, Frequency, and Period ===== | ===== Amplitude, Wavelength, Frequency, and Period ===== |
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| Here's a good introductory video for this section:((Dave Castler makes his videos for American Licences, which don't completely match the Canadian licences, but the concepts are the same.)) | Here's a good introductory video for this section:((Dave Castler makes his videos for American Licences, which don't completely match the Canadian licences, but the concepts are the same.)) |
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| {{ youtube>lrfLk2kjwMc }} | {{ youtube>lrfLk2kjwMc }} |
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| Here are two moving waves. What's different about them? What's the same? | Here are two moving waves (press the play {{/play.png}} button on the bottom left corner of the picture). What's different about them? What's the same? |
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| Imagine that the dots moving up and down are creating the waves that are travelling to the right (as we'll see later, this is kind of like how radio waves are created). Here are a few things to notice: | Imagine that the dots moving up and down create the waves that are travelling to the right (as we'll see later, this is kind of like how radio waves are created). Here are a few things to notice: |
| - The Blue wave is twice as "tall" as the green wave. | - The Blue wave is twice as "tall" as the green wave. |
| - Both waves are travelling to the right at the same speed. | - Both waves are travelling to the right at the same speed. |
| To quantify these observations more precisely, let's look at a snapshot of both waves frozen in time. | To quantify these observations more precisely, let's look at a snapshot of both waves frozen in time. |
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| {{ :howto:hambasics:travelingwaves.png }} | {{ howto:hambasics:sections:travelingwaves.png }} |
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| * the //amplitude// is the vertical height from the centre of the wave to its highest (or lowest) point. <fc #0014a8>The blue wave has an amplitude of 2</fc> and the <fc #008000>green wave has an amplitude of 1</fc>. | * the //amplitude// is the vertical height from the centre of the wave to its highest (or lowest) point. <fc #0014a8>The blue wave has an amplitude of 2</fc> and the <fc #008000>green wave has an amplitude of 1</fc>. |
| When two waves overlap, they add up together at every point. Here, the <fc #4682b4>blue</fc> and <fc #008000>green</fc> waves are generated and add up together to form the <fc #ff0000>red</fc> wave. You can move the blue and green waves and see the result. To convince yourself that the red wave is really the sum of the blue and green waves, look at points <fc #4682b4>A</fc>, <fc #008000>B</fc>, and <fc #ff0000>C</fc>. You can move the blue or green waves by sliding their phase (<fc #4682b4>φ</fc> and <fc #008000>Φ</fc>) around. You'll see that point <fc #ff0000>C</fc> is always the sum of <fc #4682b4>A</fc> and <fc #008000>B</fc>. | When two waves overlap, they add up together at every point. Here, the <fc #4682b4>blue</fc> and <fc #008000>green</fc> waves are generated and add up together to form the <fc #ff0000>red</fc> wave. You can move the blue and green waves and see the result. To convince yourself that the red wave is really the sum of the blue and green waves, look at points <fc #4682b4>A</fc>, <fc #008000>B</fc>, and <fc #ff0000>C</fc>. You can move the blue or green waves by sliding their phase (<fc #4682b4>φ</fc> and <fc #008000>Φ</fc>) around. You'll see that point <fc #ff0000>C</fc> is always the sum of <fc #4682b4>A</fc> and <fc #008000>B</fc>. |
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| * the red wave is cancelled out?((Fun fact: This is how [[wp>Active_noise_control |noise cancelling headphones]] work. The headset has a microphone that picks up the noise, inverts the waves, and plays them back in the ear piece. The combination of the real life noise and the inverted noise being played in the speaker cancel out (somewhat).)) | * the red wave is cancelled out?((Fun fact: This is how [[wp>Active_noise_control |noise cancelling headphones]] work. The headset has a microphone that picks up the noise, inverts the waves, and plays them back in the ear piece. The combination of the real life noise and the inverted noise being played in the speaker cancel out (somewhat).)) |
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| If you press the play button on the bottom left corner, you'll see the blue wave travel to the right and the green wave travel to the left. The red wave oscillates up and down but doesn't travel anywhere. This is called a //standing wave//, which we'll see again later when we discuss SWR. | If you press the play button {{/play.png}} on the bottom left corner, you'll see the blue wave travel to the right and the green wave travel to the left. The red wave, which is the sum of the forward and reflected waves, oscillates up and down but doesn't travel anywhere, which means it's not going into the antenna. |
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| | While the animation is running, slowly decrease the amplitude of the reflected wave (<fc #008000>V<sub>B</sub></fc>) and you'll see that the red wave will start moving to the right. As you do that, notice how the SWR (Standing Wave Ratio) decreases toward 1:1. At this point, there is no reflected wave and all of the energy is going to the antenna (assuming no loss in the feedline). |
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| ====== Modulation ====== | ====== Modulation ====== |
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| For example, let's transmit a single audio note of <fc #ff0000>10 kHz</fc> at a radio frequency of <fc #4682b4>200 kHz</fc>.((Note that 200 kHz is lower than commercial AM broadcast and is **not** a ham radio frequency. I chose a ratio of 20:1 so we can see the effects on the graph)): | For example, let's transmit a single audio note of <fc #ff0000>10 kHz</fc> at a radio frequency of <fc #4682b4>200 kHz</fc>.((Note that 200 kHz is lower than commercial AM broadcast and is **not** a ham radio frequency. I chose a ratio of 20:1 so we can see the effects on the graph)): |
| {{ ..:am01.png }} | {{ am01.png }} |
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| Before we //modulate// the carrier, we raise the audio signal above zero to get an //envelope//: | Before we //modulate// the carrier, we raise the audio signal above zero to get an //envelope//: |
| {{ ..:am01b.png }} | {{ am01b.png }} |
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| Finally, we **multiply** the envelope and the carrier, which gives us a wave that has the same frequency as the carrier, but an amplitude that varies like the voice signal: | Finally, we **multiply** the envelope and the carrier, which gives us a wave that has the same frequency as the carrier, but an amplitude that varies like the voice signal: |
| {{ ..:am02.png }} | {{ am02.png }} |
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| So very roughly: | So very roughly: |
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| <WRAP center round important box 80%> | <WRAP center round important box 80%> |
| Let's pause for a minute and highlight that here, we are **multiplying** two waves together (not simply adding them). Later on, we'll see that the electronic component that does that is called a //mixer//, not to be confused with an sound mixer, which does do addition. | Let's pause for a minute and highlight that here, we are **multiplying** two waves together (not simply adding them). Later on, we'll see that the electronic component that does that is called a //mixer//, not to be confused with a sound mixer, which does do addition. |
| </WRAP> | </WRAP> |
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| This is absolutely **not** obvious but let's see why it's at least plausible. Imagine we start with the following three waves: | This is absolutely **not** obvious but let's see why it's at least plausible. Imagine we start with the following three waves: |
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| {{ ..:am03.png }} | {{ am03.png }} |
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| * An <fc #800000>LSB Wave</fc> oscillating at 190 kHz with an amplitude of 0.5 | * An <fc #800000>LSB Wave</fc> oscillating at 190 kHz with an amplitude of 0.5 |
| Now let's add them together. This is a bit of a mess, but let's look at specific places along the waves: | Now let's add them together. This is a bit of a mess, but let's look at specific places along the waves: |
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| {{ ..:am05.png }} | {{ am05.png }} |
| * at point A, all three waves align so the sum is: 0.5 + 1 + 0.5 = 2 | * at point A, all three waves align so the sum is: 0.5 + 1 + 0.5 = 2 |
| * at point B, the two side bands are opposite and cancel each other and only the carrier remains: 0 + 1 + 0 = 1 | * at point B, the two side bands are opposite and cancel each other and only the carrier remains: 0 + 1 + 0 = 1 |
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| The result is the same as final AM signal: | The result is the same as final AM signal: |
| {{ ..:am06.png }} | {{ am06.png }} |
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| Note that the carrier as a frequency of 200 kHz just like the original carrier, but the two side bands are 10 kHz lower and higher with half of the amplitude. Notice also how the <fc #800000>LSB Wave</fc> oscillates slower than the <fc #4682b4>Carrier Wave</fc>, while the <fc #008000>USB Wave</fc> oscillates faster. | Note that the carrier has a frequency of 200 kHz just like the original carrier, but the two side bands are 10 kHz lower and higher with half of the amplitude. Notice also how the <fc #800000>LSB Wave</fc> oscillates slower than the <fc #4682b4>Carrier Wave</fc>, while the <fc #008000>USB Wave</fc> oscillates faster. |
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| For example, the spectrum of our 10 kHz note transmitted over a 200 kHz carrier would look like this: | For example, the spectrum of our 10 kHz note transmitted over a 200 kHz carrier would look like this: |
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| {{ ..:am07.png?600 }} | {{ am07.png?600 }} |
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| All this is saying is that the radio signal is composed of three pieces: a signal at 190 kHz with an amplitude of 0.5, a signal at 200 kHz with an amplitude of 1, and another at 210 kHz with an amplitude of 0.5. | All this is saying is that the radio signal is composed of three pieces: a signal at 190 kHz with an amplitude of 0.5, a signal at 200 kHz with an amplitude of 1, and another at 210 kHz with an amplitude of 0.5. |
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| ...for LSB, the spectroscope would look like: | ...for LSB, the spectroscope would look like: |
| {{ ..:ssb01.png?600 }} | {{ ssb01.png?600 }} |
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| ...for USB, the spectroscope would look like: | ...for USB, the spectroscope would look like: |
| {{ ..:ssb02.png?600 }} | {{ ssb02.png?600 }} |
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| By itself, neither of these transmissions would carry the information we need (that the baseband signal was a 10 kHz note) since it's the difference between the sideband and the carrier that gives us that information. But if the receiver knows that this signal was generated by a transmitter at a frequency of 200 kHz, then the receiver can re-inject the missing carrier on its side. | By itself, neither of these transmissions would carry the information we need (that the baseband signal was a 10 kHz note) since it's the difference between the sideband and the carrier that gives us that information. But if the receiver knows that this signal was generated by a transmitter at a frequency of 200 kHz, then the receiver can re-inject the missing carrier on its side. |
| In reality, the voice we transmit contains a whole group of "notes" typically between 300 Hz and 3000 Hz (music could range between 20 Hz and 20,000 Hz). A typical voice signal (baseband) could look something like this:((The next few images are from [[wp>Single-sideband_modulation]])) | In reality, the voice we transmit contains a whole group of "notes" typically between 300 Hz and 3000 Hz (music could range between 20 Hz and 20,000 Hz). A typical voice signal (baseband) could look something like this:((The next few images are from [[wp>Single-sideband_modulation]])) |
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| {{ ..:ssb03.png }} | {{ ssb03.png }} |
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| So the AM signal would look like this: | So the AM signal would look like this: |
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| {{ ..:ssb04.png }} | {{ ssb04.png }} |
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| Notice how: | Notice how: |
| And finally, each individual sideband would look like this: | And finally, each individual sideband would look like this: |
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| {{ ..:ssb05.png }} | {{ ssb05.png }} |
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| Here's a screenshot of VA7FI's IC-7300 scope showing both modes on the same screen: | Here's a screenshot of VA7FI's IC-7300 scope showing both modes on the same screen: |
| {{ ..:scope01.png }} | {{ scope01.png }} |
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| The radio is tuned to 3.880 MHz (where no one is transmitting), but there are two neighbouring conversations going on: | The radio is tuned to 3.880 MHz (where no one is transmitting), but there are two neighbouring conversations going on: |
| For example, let's again transmit a single audio note of <fc #ff0000>10 kHz</fc> at a radio frequency of <fc #4682b4>200 kHz</fc> using FM this time instead of AM: | For example, let's again transmit a single audio note of <fc #ff0000>10 kHz</fc> at a radio frequency of <fc #4682b4>200 kHz</fc> using FM this time instead of AM: |
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| {{ ..:fm01.png }} | {{ fm01.png }} |
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| This time, we don't simply multiply the baseband signal to the carrier (as in AM). Instead, we "compress" and "stretch" the carrier (ie, modulate its frequency) based on the baseband signal. | This time, we don't simply multiply the baseband signal to the carrier (as in AM). Instead, we "compress" and "stretch" the carrier (ie, modulate its frequency) based on the baseband signal. |
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| {{ ..:fm02.png }} | {{ fm02.png }} |
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| Here, the math is a bit more involved and requires at least 1<sup>st</sup> year calculus to understand but in a nutshell, if the carrier is \$$ c(t) = \cos(2 \pi f_c t) \$$ and the baseband signal is \$$s(t)\$$, then the FM signal will be: | Here, the math is a bit more involved and requires at least 1<sup>st</sup> year calculus to understand but in a nutshell, if the carrier is \$$ c(t) = \cos(2 \pi f_c t) \$$ and the baseband signal is \$$s(t)\$$, then the FM signal will be: |
