Sawtooth wave

<h2 id="applications">Applications</h2>
<ul><li>Sawtooth waves are known for their use in <a href="/facts/Electronic_music/zfGNfUvR">electronic music</a>. The sawtooth and square waves are among the most common waveforms used to create sounds with subtractive <a href="/facts/Subtractive_synthesis/2Kk3TqUE">analog</a> and <a href="/facts/Virtual_analog/zPLLJXG5">virtual analog</a> music synthesizers.</li>
<li>Sawtooth waves are used in <a href="/facts/Switched-mode_power_supply/YKcyRBtP">switched-mode power supplies</a>. In the regulator chip the feedback signal from the output is continuously compared to a high-frequency sawtooth to generate a new duty cycle PWM signal on the output of the <a href="/facts/Comparator/jfk32rf6">comparator</a>.</li>
<li>In the field of computer science, particularly in automation and robotics, 
  
    
      
        
          s
          a
          w
          t
          o
          o
          t
          h
        
        (
        θ
        )
        =
        2
        arctan
        ⁡
        (
        tan
        ⁡
        (
        
          
            θ
            2
          
        
        )
        )
      
    
    {\displaystyle \mathrm {sawtooth} (\theta )=2\arctan(\tan({\frac {\theta }{2}}))}
  
 allows to calculate sums and differences of angles while avoiding discontinuities at 360° and 0°.</li>
<li>The sawtooth wave is the form of the vertical and horizontal <a href="/facts/Deflection_(physics)/ya8MwRG3">deflection</a> signals used to generate a <a href="/facts/Raster_graphics/HkXNc8oI">raster</a> on <a href="/facts/Cathode-ray_tube/8NVGx5C7">CRT</a>-based television or monitor screens. <a href="/facts/Oscilloscope/HMdD8XVk">Oscilloscopes</a> also use a sawtooth wave for their horizontal deflection, though they typically use <a href="/facts/Electrostatic/bxkuW6s4">electrostatic</a> deflection.
<ul><li>On the wave's "ramp", the magnetic field produced by the deflection yoke drags the <a href="/facts/Electron/L0KBo5cW">electron</a> beam across the face of the CRT, creating a <a href="/facts/Scan_line/3JEKoDRr">scan line</a>.</li>
<li>On the wave's "cliff", the magnetic field suddenly collapses, causing the electron beam to return to its resting position as quickly as possible.</li>
<li>The current applied to the deflection yoke is adjusted by various means (transformers, capacitors, center-tapped windings) so that the half-way voltage on the sawtooth's cliff is at the zero mark, meaning that a negative current will cause deflection in one direction, and a positive current deflection in the other; thus, a center-mounted deflection yoke can use the whole screen area to depict a trace. The horizontal frequency is 15.734 kHz on <a href="/facts/NTSC/HYWIvxCR">NTSC</a>, 15.625 kHz for <a href="/facts/PAL/t8TugcxK">PAL</a> and <a href="/facts/SECAM/vexpud7W">SECAM</a>.</li>
<li>The vertical deflection system operates the same way as the horizontal, though at a much lower frequency (59.94 Hz on <a href="/facts/NTSC/HYWIvxCR">NTSC</a>, 50 Hz for PAL and SECAM).</li>
<li>The ramp portion of the wave must appear as a straight line. If otherwise, it indicates that the current isn't increasing linearly, and therefore that the magnetic field produced by the deflection yoke is not linear. As a result, the electron beam will accelerate during the non-linear portions. This would result in a television image "squished" in the direction of the non-linearity. Extreme cases will show marked brightness increases, since the electron beam spends more time on that side of the picture.</li>
<li>The first television receivers had controls allowing users to adjust the picture's vertical or horizontal linearity. Such controls were not present on later sets as the stability of electronic components had improved.</li></ul></li></ul>
<h2 id="see-also">See also</h2>

<ul><li><a href="/facts/List_of_periodic_functions/v8MPIMjr">List of periodic functions</a></li>
<li><a href="/facts/Sine_wave/mD1CB09M">Sine wave</a></li>
<li><a href="/facts/Square_wave_(waveform)/h1cWR1KM">Square wave</a></li>
<li><a href="/facts/Triangle_wave/72BUtbRl">Triangle wave</a></li>
<li><a href="/facts/Pulse_wave/CEPen7fY">Pulse wave</a></li>
<li><a href="/facts/Sound/DlKXlPuF">Sound</a></li>
<li><a href="/facts/Wave/fU0HH6St">Wave</a></li>
<li><a href="/facts/Zigzag/xUtxcBah">Zigzag</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="/facts/Hugh_Montgomery_(mathematician)/k1VI3W69">Hugh L. Montgomery</a>; <a href="/facts/Robert_Charles_Vaughan_(mathematician)/djBcTCVL">Robert C. Vaughan</a> (2007). <i>Multiplicative number theory I. Classical theory</i>. Cambridge tracts in advanced mathematics. Vol. 97. pp. 536–537. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-521-84903-6.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Fourier Series-Triangle Wave - from Wolfram MathWorld". Mathworld.wolfram.com. 2012-07-02. Retrieved 2012-07-11. <a href="http://mathworld.wolfram.com/FourierSeriesTriangleWave.html" target="_blank">http://mathworld.wolfram.com/FourierSeriesTriangleWave.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Dave Benson. "Music: A Mathematical Offering" (PDF). Homepages.abdn.ac.uk. p. 42. Retrieved 26 November 2021. <a href="https://homepages.abdn.ac.uk/d.j.benson/pages/html/music.pdf" target="_blank">https://homepages.abdn.ac.uk/d.j.benson/pages/html/music.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Sawtooth wave open-in-new

Sawtooth wave