howto:hambasics:sections:wavemodulation
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howto:hambasics:wavemodulation [2019/10/05 06:31] – ve7hzf | howto:hambasics:sections:wavemodulation [2020/11/08 15:48] – va7fi | ||
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- | ~~NOTOC~~ | + | ====== |
- | ====== | + | |
- | Here we dive a little more deeply into waves and look at three ways that a " | + | |
+ | Here we dive a little more deeply into waves and look at three ways that a " | ||
- | ====== Amplitude, Period, and Frequency ====== | + | But first, let's look at the general characteristics of a wave. |
- | Look at the following two waves. | ||
- | {{wave1.png? | + | ===== Amplitude, Wavelength, Frequency, and Period ===== |
+ | Here's a good introductory video for this section: | ||
- | At first look: | + | {{ youtube> |
- | - the first one is " | + | |
- | - the first one is also " | + | |
- | These two observations can be quantified very precisely as: | + | Here are two moving waves (press |
- | - the // | + | |
- | - the //period//: **horizontal** length of one complete cycle. | + | |
- | {{ wave3.png | + | {{ggb> |
- | So the previous two waves have: | ||
- | - Amplitude = 2, Period = 0.05 ms | ||
- | - Amplitude = 1, Period = 0.02 ms | ||
- | {{wave1.png? | + | 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 " | ||
+ | - Both waves are travelling to the right at the same speed. | ||
+ | - The Blue dot is moving up and down three times as fast as the green dot. | ||
+ | - The Blue wave is three times as compressed as the green wave. | ||
+ | To quantify these observations more precisely, let's look at a snapshot of both waves frozen in time. | ||
- | The amplitude is normally related to the strength of the signal (like the volume for sound). | + | {{ howto: |
- | Since the period | + | * the // |
+ | * the //wavelength// is the horizontal distance | ||
- | < | + | Now imagine that the animation is in super slow motion and that the waves are actually travelling at the speed of light, which is roughly 300,000,000 metres per second: How many times does each dot go up and down in one second? |
- | Let's pause for a minute here... | + | Another way of asking that question is: how many full cycles can you fit in 300,000,000 metres (since radio waves travel 300,000,000 metres each second). |
+ | * Since the blue wave has a wavelength of 2m, it'll take 150,000,000 cycles to reach 300,000,000 metres. That means that the blue dot oscillates at 150,000,000 cycles per second, or 150,000,000 Hz, or 150 Mhz | ||
+ | * Similarly, since the green wave has a wavelength of 6m, its frequency is 50 Mhz. | ||
- | In this course, we'll see a few formulas and it'll be tempting | + | So a quick way to relate the frequency \$f\$ (in MHz) and the wavelength \$\lambda\$ (in metres) is: |
- | Here: | + | <WRAP centeralign> |
- | * The period is the length of time it takes to complete one cycle and | + | \$$ \lambda = \frac{300}{f} \qquad \text{or} \qquad f = \frac{300}{\lambda}\$$ |
- | * The frequency is the number cycles in one second. | + | </ |
- | So: | + | Note that the reason we're using just 300, instead |
- | * if the period is half a second, we can fit 2 full cycles in one second. | + | |
- | * If the period is a quarter | + | |
- | * If the period is a tenth of a second, | + | |
- | * If the period is T seconds, | + | |
- | Right? | + | Now, here's a related question: how long does it take for each wave to complete one cycle? |
- | So for the previous two waves, the frequencies | + | * For the blue wave, we know that it oscillates 150,000,000 times / second, so only one of those time would take 150,000,000<sup>**th**</ |
- | - <latex>$$f = \frac{1}{0.05 \text{ ms}} = \frac{1}{0.00005 \text{ s}}$$</latex> = 20,000 Hz = 20 kHz | + | * Similarly, the green wave oscillates at 50,000,000 cycles per second, so only one of those cycle would take \$\frac{1}{50,000,000}\$ s or 2x10< |
- | | + | |
- | Recall that //Hz// means "cycle per seconds" | + | The time to complete one full cycle is called the //period (T)// and is the reciprocal |
- | Let's now look at three different ways to encode | + | <WRAP centeralign> |
+ | \$$T = \frac{1}{f} | ||
+ | </ | ||
+ | |||
+ | |||
+ | ===== Wave Addition ===== | ||
+ | |||
+ | When two waves overlap, they add up together at every point. | ||
+ | |||
+ | {{ggb> | ||
+ | |||
+ | |||
+ | Where do the blue and green waves need to be so that... | ||
+ | * the red wave is the biggest? | ||
+ | * the red wave is cancelled out?((Fun fact: This is how [[wp> | ||
+ | |||
+ | If you press the play button {{/ | ||
+ | |||
+ | While the animation is running, slowly decrease the amplitude of the reflected wave (<fc # | ||
+ | |||
+ | ====== Modulation ====== | ||
+ | Modulation is the process of " | ||
+ | |||
+ | {{ youtube> | ||
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{{ am02.png | {{ am02.png | ||
- | So: | + | So very roughly: |
**AM Radio Wave** = (<fc # | **AM Radio Wave** = (<fc # | ||
- | The incredible thing about the resulting AM broadcast is that the transmitted radio signal can also be seen as the //sum// of three pure sine wavesL | + | <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). | ||
+ | </ | ||
+ | |||
+ | The incredible thing about the resulting AM broadcast is that the transmitted radio signal can also be seen as the //sum// of three pure sine waves: | ||
**AM Radio Wave** = <fc # | **AM Radio Wave** = <fc # | ||
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* A <fc # | * A <fc # | ||
- | Now let's add them together: | + | Now let's add them together. This is a bit of a mess, but let's look at specific places along the waves: |
{{ am05.png | {{ am05.png | ||
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- | Note that the carrier | + | Note that the carrier |
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==== Frequency Spectrum ==== | ==== Frequency Spectrum ==== | ||
- | An easier way to represent a radio signal is using a // | + | An easier way to represent a radio signal is using a // |
+ | |||
+ | For example, the spectrum of our 10 kHz note transmitted over a 200 kHz carrier would look like this: | ||
{{ am07.png? | {{ am07.png? | ||
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* The two side bands are 10 kHz on each side of the carrier (same as the <fc # | * The two side bands are 10 kHz on each side of the carrier (same as the <fc # | ||
* Most of the power is going into transmitting the carrier, which in itself doesn' | * Most of the power is going into transmitting the carrier, which in itself doesn' | ||
- | * More fundamentally: | + | * More fundamentally: |
===== SSB ===== | ===== SSB ===== | ||
- | One way of saving power is to only transmit one of the side bands. | + | One way of saving power (and reduce bandwidth) |
...for LSB, the spectroscope would look like: | ...for LSB, the spectroscope would look like: | ||
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* It takes half the bandwidth. | * It takes half the bandwidth. | ||
- | Here's a screenshot of the scope from my IC-7300. | + | Here's a screenshot of VA7FI' |
{{ scope01.png | {{ scope01.png | ||
- | The radio is tuned to 3.880 MHz (where no one is transmitting), | + | The radio is tuned to 3.880 MHz (where no one is transmitting), |
+ | * one at 3.875 MHz using LSB, | ||
+ | * and another at 3.885 MHz using AM. | ||
+ | The scope shows the recent history of the radio signal (called // | ||
| | | | ||
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- | ====== FM ====== | + | ===== FM ===== |
- | FM stands for Frequency Modulation. | + | FM stands for //Frequency Modulation//. What this means is that the transmitted radio wave is obtained by changing the frequency of the carrier based on the audio signal. |
For example, let's again transmit a single audio note of <fc # | For example, let's again transmit a single audio note of <fc # | ||
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{{ fm02.png | {{ fm02.png | ||
- | Here, the math is a bit more involved and requires at least 1st year calculus to understand but in a nutshell, if the carrier is < | + | Here, the math is a bit more involved and requires at least 1< |
- | <latex>$$ \cos\Big(2 \pi f_c t + 2 \pi k \int_0^t s(\tau) d\tau\Big) $$</latex> | + | <WRAP centeralign> |
+ | \$$ \cos\Big(2 \pi f_c t + 2 \pi k \int_0^t s(\tau) d\tau\Big) | ||
+ | </WRAP> | ||
If this looks like Greek to you, don't worry; the math isn't important. | If this looks like Greek to you, don't worry; the math isn't important. | ||
- | ====== Optional Details | + | ===== Optional Details ===== |
For those interested in some of the mathematical details, see this [[wavemodulationmath |optional page]]. | For those interested in some of the mathematical details, see this [[wavemodulationmath |optional page]]. | ||
- | |< 100% 50% 50% >| | + | [[intro|{{/back.png }}]] [[mathbasics |{{ /next.png}}]] |
- | |[[sections# | + | |
howto/hambasics/sections/wavemodulation.txt · Last modified: 2022/11/04 18:52 by va7fi