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howto:hambasics:wavemodulation [2019/11/24 21:19] – [Amplitude, Period, and Frequency] ve7hzfhowto:hambasics:sections:wavemodulation [2022/11/04 18:52] (current) – [AM] va7fi
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 +====== Properties of Waves ======
  
-====== Wave and Modulation ====== +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//.  But first, let's look at the general characteristics of a wave+
  
 +But first, let's look at the general characteristics of a wave. 
  
-====== Amplitude, Period, and Frequency ====== 
  
-Look at the following two waves.  How are they different?+===== Amplitude, Wavelength, Frequency, and Period ===== 
 +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.))
  
-{{wave1.png?400}}{{wave2.png?400}}+{{ youtube>lrfLk2kjwMc }}
  
-At first sight: +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'the same?
-  - the first one is "taller" than the second one That is, it goes up and down higher and lower. +
-  - the first one is also "longer" than the second one.  That is, it stretches sideways more.  It'not as "tight".+
  
-These two observations can be quantified very precisely as: +{{ggb>/howto/hambasics/sections/travelingwave.ggb 800,250}}
-  - the //amplitude//: **vertical** height 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 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
-  - Amplitude = 2, Period = 0.05 ms +  - The Blue wave is twice as "tall" as the green wave
-  - 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?400}}{{wave2.png?400}}+To quantify these observations more precisely, let's look at a snapshot of both waves frozen in time.
  
 +{{ howto:hambasics:sections:travelingwaves.png }}
  
-The amplitude is normally related to the strength of the signal (like the volume for sound).+  * the //amplitude// is the vertical height from the centre of the wave to its highest (or lowestpoint.  <fc #0014a8>The blue wave has an amplitude of 2</fc> and the <fc #008000>green wave has an amplitude of 1</fc>
 +  * the //wavelength// is the horizontal distance of one full cycle.  <fc #0014a8>The blue wave has a wavelength of 2m </fc> and the <fc #008000>green wave has a wavelength of 6m</fc>.
  
-Since the period (//T//is the amount of time it takes to complete one cycle, and the frequency (//f//) is the number of cycles in one second, the period and the frequency are inverses of each other:+Now imagine that the animation is in super slow motion and that the waves are actually travelling at the speed of lightwhich is roughly 300,000,000 metres per second: How many times does each dot go up and down in one second?
  
-<latex> \qquad  $$f = \frac{1}{T}  \qquad  \Leftrightarrow   \qquad T = \frac{1}{f}$$</latex>+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.
  
-<box 80% blue> +So quick way to relate the frequency \$f\$ (in MHz) and the wavelength \$\lambda\$ (in metres) is:
-In this course, we'll see few formulas and it'll be tempting to memorize them but let's instead understand what they really mean... +
-</box>+
  
-For example: +<WRAP centeralign> 
-  * if the period is half a second, we can fit 2 full cycles in one second. +\$$ \lambda = \frac{300}{f} \qquad \text{or\qquad f = \frac{300}{\lambda}\$
-  * If the period is a quarter of a second, the frequency is 4. +</WRAP>
-  * 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?+Note that the reason we're using just 300, instead of 300,000,000 is that we've cancelled 6 of the zeros so that the frequency is in MHz instead of in Hz.
  
-So for the previous two wavesthe frequencies would be +Nowhere's a related questionhow long does it take for each wave to complete one cycle?
-  * <latex>$$f = \frac{1}{0.05 \text{ ms}} = \frac{1}{0.00005 \text{ s}}$$</latex> = 20,000 Hz = 20 kHz+
  
-  * <latex>$$f = \frac{1}{0.02 \text{ ms}} = \frac{1}{0.00002 \text{ s}}$$</latex= 50,000 Hz = 50 kHz+  * 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**</sup> of a second, or \$\frac{1}{150,000,000}\$ s or 6.67x10<sup>-9</sup> s or 6.67 ns.(("ns" means nanosecond. "Nano" means a billionth of ___)) 
 +  * 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<sup>-8</sups or 20 ns.
  
-Recall that //Hz// means "cycle per seconds" That's why when we divide a number of cycles by time, we get Hertz.+The time to complete one full cycle is called the //period (T)// and is the reciprocal of the frequency:
  
-Let's now look at three different ways to encode a signal on a radio wave.+<WRAP centeralign> 
 +\$$T = \frac{1}{f}  \qquad  \text{or}   \qquad f = \frac{1}{T}\$$ 
 +</WRAP>
  
-FIXME: add $f=\frac{c}{\lambda}$ 
  
-====== AM ======+===== Wave Addition ===== 
 + 
 +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>
 + 
 +{{ggb>/howto/hambasics/sections/waveaddition.ggb 800,500}} 
 + 
 + 
 +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>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).)) 
 + 
 +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. 
 + 
 +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).   
 + 
 +====== Modulation ====== 
 +Modulation is the process of "encoding" a message (be it voice or digital) onto a radio wave. 
 + 
 +{{ youtube>D9Oa6jaHwtA }} 
 + 
 + 
 +===== AM =====
  
 AM stands for //Amplitude Modulation// What this means is that the transmitted radio wave is obtained by changing the amplitude of a pure radio waves (the //<fc #4682b4>carrier</fc>//) based on an audio signal (the //<fc #ff0000>baseband</fc>//). AM stands for //Amplitude Modulation// What this means is that the transmitted radio wave is obtained by changing the amplitude of a pure radio waves (the //<fc #4682b4>carrier</fc>//) based on an audio signal (the //<fc #ff0000>baseband</fc>//).
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 **AM Radio Wave** = (<fc #ff0000>Audio Signal</fc> + 1) **×** <fc #4682b4>Carrier Wave</fc> **AM Radio Wave** = (<fc #ff0000>Audio Signal</fc> + 1) **×** <fc #4682b4>Carrier Wave</fc>
 +
 +<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 a sound mixer, which does do addition.  
 +</WRAP>
  
 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: 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:
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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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 ==== Frequency Spectrum ==== ==== Frequency Spectrum ====
  
-An easier way to represent a radio signal is using a //spectroscope//, which shows the frequency spectrum of a wave.  That is, instead of looking at the signal wave itself, the spectroscope shows the strength of each frequency that makes up the sum of the signal.  For example, the spectrum of our 10 kHz note transmitted over a 200 kHz carrier would look like this:+An easier way to represent a radio signal is using a //spectroscope//, which shows the frequency spectrum of a wave.  That is, instead of looking at the signal wave itself, the spectroscope shows the strength of each frequency that makes up the sum of the signal. 
 + 
 +For example, the spectrum of our 10 kHz note transmitted over a 200 kHz carrier would look like this:
  
 {{  am07.png?600  }} {{  am07.png?600  }}
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   * The two side bands are 10 kHz on each side of the carrier (same as the <fc #ff0000>baseband</fc> signal!).  It is that distance away from the carrier that represents the audio signal we want to recover.   * The two side bands are 10 kHz on each side of the carrier (same as the <fc #ff0000>baseband</fc> signal!).  It is that distance away from the carrier that represents the audio signal we want to recover.
   * Most of the power is going into transmitting the carrier, which in itself doesn't carry any information, so that's a bit of a waste of energy.   * Most of the power is going into transmitting the carrier, which in itself doesn't carry any information, so that's a bit of a waste of energy.
-  * More fundamentally: even though we say that the signal is transmitted at 200 kHz, in this example, it is really contained between 190 kHz and 210 kHz.  That is, it has a bandwidth of 20 kHz (210 kHz - 190 kHz).  This bandwidth is regulated and depends on the [[intro#full_frequency_list | band used]]. +  * More fundamentally: even though we say that the signal is transmitted at 200 kHz, in this example, it is really contained between 190 kHz and 210 kHz.  That is, it has a bandwidth of 20 kHz (210 kHz - 190 kHz).  This bandwidth is regulated and depends on the [[intro#full_frequency_list| band used]]. 
-====== SSB ======+ 
 +===== SSB =====
  
 One way of saving power (and reduce bandwidth) is to only transmit one of the side bands.  In this example, the radio would be tuned to 200 kHz, but... One way of saving power (and reduce bandwidth) is to only transmit one of the side bands.  In this example, the radio would be tuned to 200 kHz, but...
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   * It takes half the bandwidth.   * It takes half the bandwidth.
  
-Here's a screenshot of VE7HZF'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  }}
  
-The radio is tuned to 3.880 MHz (where no one is transmitting), but there are two different conversations going on: 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 //waterfall//) where the present is at the top and the past at the bottom.  Blue represent a weak signal strength and yellow or red represent a strong signal strength.  Here are some things to notice:+The radio is tuned to 3.880 MHz (where no one is transmitting), but there are two neighbouring conversations going on: 
 +  * 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 //waterfall//) where the present is at the top and the past at the bottom.  Blue represent a weak signal strength and yellow or red represent a strong signal strength.  Here are some things to notice:
  
 |               LSB (3.875 MHz)  ^   AM (3.885 MHz)   | |               LSB (3.875 MHz)  ^   AM (3.885 MHz)   |
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-====== FM ======+===== FM =====
  
 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.  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. 
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 {{  fm02.png  }} {{  fm02.png  }}
  
-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 <latex>$$ c(t) = \cos(2 \pi f_c t) $$</latex> and the baseband signal is <latex>$$s(t)$$</latex>, 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:
  
-<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.  The key concept to understand is that the highs and lows of the baseband signal are encoded in the horizontal compression (the frequency) of the radio wave:  When the baseband is high, the radio signal is more compressed (its frequency is higher), and when the baseband is low, the radio signal is more stretched out (its frequency is lower). If this looks like Greek to you, don't worry; the math isn't important.  The key concept to understand is that the highs and lows of the baseband signal are encoded in the horizontal compression (the frequency) of the radio wave:  When the baseband is high, the radio signal is more compressed (its frequency is higher), and when the baseband is low, the radio signal is more stretched out (its frequency is lower).
  
  
-====== 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]].
  
-[[sections |{{/back.png }}]] [[mathbasics |{{  /next.png}}]]+[[intro|{{/back.png }}]] [[mathbasics |{{  /next.png}}]]
  
howto/hambasics/sections/wavemodulation.1574659171.txt.gz · Last modified: 2019/11/24 21:19 by ve7hzf