howto:hambasics:sections:wavemodulation
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howto:hambasics:wavemodulation [2019/09/27 11:55] – ve7hzf | howto:hambasics:sections:wavemodulation [2020/11/08 15:24] – 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 three ways a " | + | |
+ | But first, let's look at the general characteristics of a wave. | ||
- | ====== Amplitude, Period, and Frequency ====== | ||
- | Look at the following two waves. | + | ===== Amplitude, Wavelength, Frequency, and Period ===== |
+ | Here's a good introductory video for this section: | ||
- | {{wave1.png? | + | {{ youtube> |
- | At first look: | + | Here are two moving waves (press |
- | - the first one is " | + | |
- | - the first one is also " | + | |
- | These two observations can be quantified very precisely as: | + | {{ggb> |
- | - the //amplitude//: **vertical** length from the centre of the wave to its highest (or lowest) point. | + | |
- | - the //period//: **horizontal** length of one complete cycle. | + | |
- | {{ wave3.png | ||
- | So the previous two waves have: | + | Imagine that the dots moving up and down create |
- | - Amplitude = 2, Period = 0.05 ms | + | - The Blue wave is twice as " |
- | - Amplitude = 1, Period = 0.02 ms | + | - 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. | ||
- | {{wave1.png? | + | To quantify these observations more precisely, let's look at a snapshot of both waves frozen in time. |
+ | {{ howto: | ||
- | The amplitude is normally related to the strength | + | * the //amplitude// is the vertical height from the centre |
+ | * the // | ||
- | Since the period | + | Now imagine that the animation |
- | < | + | 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. | ||
+ | * Similarly, since the green wave has a wavelength of 6m, its frequency is 50 Mhz. | ||
- | Let's pause for a minute here... | + | So a quick way to relate the frequency \$f\$ (in MHz) and the wavelength \$\lambda\$ (in metres) is: |
- | In this course, we'll see a few formulas and it'll be tempting to memorize them but let's instead understand what they really mean... | + | <WRAP centeralign> |
+ | \$$ \lambda = \frac{300}{f} \qquad \text{or} \qquad f = \frac{300}{\lambda}\$$ | ||
+ | </ | ||
- | Here: | + | Note that the reason we're using just 300, instead |
- | * The period is the length | + | |
- | * The frequency | + | |
- | So: | + | Now, here's a related question: how long does it take for each wave to complete |
- | * if the period is half a second, we can fit 2 full cycles in one second. | + | |
- | * If the period is a quarter of a second, the frequency is 4. | + | |
- | * If the period is a tenth of a second, the frequency is 10. | + | |
- | * If the period is T seconds, the frequency is $\frac{1}{T}$ ( $\frac{1}{0.5} = 2, \quad \frac{1}{0.25} = 4, \quad \frac{1}{0.1} = 10$ ) | + | |
- | Right? | + | * For the blue wave, we know that it oscillates 150,000,000 times / second, so only one of those time would take 150, |
+ | * Similarly, the green wave oscillates at 50,000,000 cycles per second, so only one of those cycle would take \$\frac{1}{50, | ||
- | So for the previous two waves, the frequencies would be: | + | The time to complete one full cycle is called |
- | - < | + | |
- | - < | + | |
- | Recall that //Hz// means "cycle per seconds" | + | <WRAP centeralign> |
+ | \$$T = \frac{1}{f} | ||
+ | </WRAP> | ||
- | Let's now look at three different ways to encode | + | |
+ | ===== 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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* at point E, the same as point A is happening | * at point E, the same as point A is happening | ||
- | Here they are again with the final transmitted wave: | + | The result is the same as final AM signal: |
{{ am06.png | {{ am06.png | ||
- | 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 | ||
{{ 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 // | ||
| | | | ||
^Symmetry |The signal is on the left (low side) of where the carrier would be (at 3.875 MHz) and varies with speech. |The signal has a strong, constant carrier in the centre, and two symmetrical sides that vary with speech. | | ^Symmetry |The signal is on the left (low side) of where the carrier would be (at 3.875 MHz) and varies with speech. |The signal has a strong, constant carrier in the centre, and two symmetrical sides that vary with speech. | | ||
- | ^Bandwidth |About | + | ^Bandwidth |About |
^Pauses |During pauses, no radio signal is transmitted. |During pauses, the carrier is still transmitted. | | ^Pauses |During pauses, no radio signal is transmitted. |During pauses, the carrier is still transmitted. | | ||
^Relationship |An AM signal can be understood in LSB mode because it contains the lower side band required. | ^Relationship |An AM signal can be understood in LSB mode because it contains the lower side band required. | ||
- | ====== 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 # | ||
- | {{ | + | {{ fm01.png |
This time, we don't simply multiply the baseband signal to the carrier (as in AM). Instead, we " | This time, we don't simply multiply the baseband signal to the carrier (as in AM). Instead, we " | ||
- | {{ | + | {{ 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