howto:hambasics:sections:wavemodulation
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howto:hambasics:wavemodulation [2019/09/27 11:41] – [Wave and Modulation] 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 time to complete one full cycle is called |
- | | + | |
- | | + | <WRAP centeralign> |
+ | \$$T = \frac{1}{f} \qquad | ||
+ | </WRAP> | ||
+ | |||
+ | |||
+ | ===== 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 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' | ||
+ | |||
+ | While the animation is running, slowly decrease the amplitude of the reflected wave (<fc # | ||
+ | |||
+ | ====== Modulation ====== | ||
+ | Modulation is the process of " | ||
+ | |||
+ | {{ youtube> | ||
- | Recall that //Hz// means "cycle per seconds" | ||
- | Let's now look at three different ways to encode a signal on a radio wave. | ||
===== AM ===== | ===== AM ===== | ||
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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 waves. This is absolutely **not** obvious so read on... | + | <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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* <fc # | * <fc # | ||
* <fc # | * <fc # | ||
+ | |||
+ | This is absolutely **not** obvious but let's see why it's at least plausible. | ||
{{ am03.png | {{ am03.png | ||
- | In this example, we have: | + | |
- | | + | |
* A <fc # | * A <fc # | ||
* A <fc # | * A <fc # | ||
- | To see why adding these three waves together | + | Now let's add them together. This is a bit of a mess, but let' |
{{ 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