mirror of
https://github.com/noplacenoaddress/RNMnetwork.git
synced 2024-10-01 01:05:51 -04:00
746 lines
112 KiB
HTML
746 lines
112 KiB
HTML
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table tr th { border-bottom: 0px; }
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video { max-width: 100%; display: block; margin: 0px auto; }
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iframe { max-width: 100%; width: 100%; border: none; }
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html {
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padding-bottom: 100px;
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h1,
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h2,
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h3,
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h4,
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h5,
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margin-top: 1rem;
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<body class='typora-export'><div class='typora-export-content'>
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<div id='write' class=''><h1 id='circuitos-en-corriente-alterna-filtros-transformadores-formas-de-onda-no-sinusoidales'><span>Circuitos en corriente alterna. Filtros. Transformadores. Formas de onda no sinusoidales.</span></h1><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/simbolos_resistencias.jpg" referrerpolicy="no-referrer"></p><h4 id='21-circuitos-en-corriente-alterna'><span>2.1 Circuitos en corriente alterna.</span></h4><p><span>La ley de Ohm se aplica también a circuitos de </span><code>CA</code><span> siempre y cuando solo haya resistencias o elementos que se comporten como tales.</span></p><p><span>En el caso existan </span><a href='https://es.wikipedia.org/wiki/Inductor'><span>bobinas</span></a><span> encontraremos la llamada </span><a href='https://es.wikipedia.org/wiki/Reactancia_inductiva'><span>reactancia inductiva</span></a><span> y si hay </span><a href='https://es.wikipedia.org/wiki/Condensador_el%C3%A9ctrico'><span>condensadores</span></a><span> la </span><a href='https://es.wikipedia.org/wiki/Reactancia'><span>reactancia</span></a><span> </span><a href='https://github.com/redeltaglio/RNMnetwork/raw/master/es.telecomlobby.com/radio_aficion/Documentos/9_t3s2_c5_html_contex_1.pdf'><span>capacitiva</span></a><span>; las dos son consecuencia del desfase que se produce entre tensión y corriente.</span></p><h4 id='211-reactancia-inductiva'><span>2.1.1 Reactancia inductiva.</span></h4><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n7" cid="n7" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.505ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5527.1 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-263-TEX-I-1D44B" d="M42 0H40Q26 0 26 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434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D44B" xlink:href="#MJX-263-TEX-I-1D44B"></use></g><g data-mml-node="mi" transform="translate(861,-150) scale(0.707)"><use data-c="1D43F" xlink:href="#MJX-263-TEX-I-1D43F"></use></g></g><g data-mml-node="mtext" transform="translate(1392.5,0)"><use data-c="A0" xlink:href="#MJX-263-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1920.3,0)"><use data-c="3D" xlink:href="#MJX-263-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(2976.1,0)"><use data-c="A0" xlink:href="#MJX-263-TEX-N-A0"></use></g><g data-mml-node="mn" transform="translate(3226.1,0)"><use data-c="32" xlink:href="#MJX-263-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(3726.1,0)"><use data-c="1D70B" xlink:href="#MJX-263-TEX-I-1D70B"></use></g><g data-mml-node="mi" transform="translate(4296.1,0)"><use data-c="1D453" xlink:href="#MJX-263-TEX-I-1D453"></use></g><g data-mml-node="mi" transform="translate(4846.1,0)"><use data-c="1D43F" xlink:href="#MJX-263-TEX-I-1D43F"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><msub><mi>X</mi><mi>L</mi></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>2</mn><mi>π</mi><mi>f</mi><mi>L</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La oposición al paso de corriente alterna que presenta una bobina de inductancia </span><code>L</code><span> se llama reactancia inductiva </span><code>XL</code><span>. Si la tensión aplicada por el generador es </span><code>E</code><span>, la su frecuencia </span><code>f</code><span>, la oposición es explicada por la ecuación sobre escrita. </span></p><p><span>Si la </span><code>f</code><span> es </span><code>0</code><span> la </span><code>XL</code><span> también es </span><code>0</code><span> entonces la bobina se comporta como un conductor permitiendo el paso de la corriente. Mejor dicho </span><u><span>una bobina no se opone al paso de la corriente continua</span></u><span>.</span></p><h4 id='212-reactancia-capacitiva'><span>2.1.2 Reactancia capacitiva. </span></h4><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n11" cid="n11" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.717ex" height="5.052ex" role="img" focusable="false" viewBox="0 -1366.5 5620.7 2233" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.96ex;"><defs><path id="MJX-264-TEX-I-1D44B" d="M42 0H40Q26 0 26 11Q26 15 29 27Q33 41 36 43T55 46Q141 49 190 98Q200 108 306 224T411 342Q302 620 297 625Q288 636 234 637H206Q200 643 200 645T202 664Q206 677 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data-mml-node="mi" transform="translate(500,0)"><use data-c="1D70B" xlink:href="#MJX-264-TEX-I-1D70B"></use></g><g data-mml-node="mi" transform="translate(1070,0)"><use data-c="1D453" xlink:href="#MJX-264-TEX-I-1D453"></use></g><g data-mml-node="mi" transform="translate(1620,0)"><use data-c="1D436" xlink:href="#MJX-264-TEX-I-1D436"></use></g></g><rect width="2580" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><msub><mi>X</mi><mi>c</mi></msub><mtext> </mtext><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>π</mi><mi>f</mi><mi>C</mi></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Es la oposición </span><code>XC</code><span> al paso de </span><code>CA</code><span> que presenta un condensador </span><code>C</code><span>. A mayor </span><code>f</code><span> o mayor </span><code>C</code><span> del condensador corresponderá menor reactancia capacitativa y viceversa. Cuanto mayor sea </span><code>C</code><span> y </span><code>f</code><span> mayor intensidad de </span><code>CA</code><span> atraviesa el condensador. Si </span><code>f</code><span> es </span><code>0</code><span> </span><code>XC</code><span> es infinita porqué el condensador se comporta como un aislante, impidiendo el paso de corriente. </span></p><p><span>Un condensador se opone al paso de corriente continua.</span></p><h4 id='213-combinación-de-componentes-impedancia'><span>2.1.3 Combinación de componentes. Impedancia. </span></h4><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n15" cid="n15" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div class="md-rawblock-container md-math-container" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="13.127ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5802 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-265-TEX-I-1D44D" d="M58 8Q58 23 64 35Q64 36 329 334T596 635L586 637Q575 637 512 637H500H476Q442 637 420 635T365 624T311 598T266 548T228 469Q227 466 226 463T224 458T223 453T222 450L221 448Q218 443 202 443Q185 443 182 453L214 561Q228 606 241 651Q249 679 253 681Q256 683 487 683H718Q723 678 723 675Q723 673 717 649Q189 54 188 52L185 49H274Q369 50 377 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4T261 1Q258 1 243 1T201 2T142 2Q64 2 42 0Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D44D" xlink:href="#MJX-265-TEX-I-1D44D"></use></g><g data-mml-node="mtext" transform="translate(723,0)"><use data-c="A0" xlink:href="#MJX-265-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1250.8,0)"><use data-c="3D" xlink:href="#MJX-265-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(2306.6,0)"><use data-c="A0" xlink:href="#MJX-265-TEX-N-A0"></use></g><g data-mml-node="mi" transform="translate(2556.6,0)"><use data-c="1D445" xlink:href="#MJX-265-TEX-I-1D445"></use></g><g data-mml-node="mo" transform="translate(3537.8,0)"><use data-c="2B" xlink:href="#MJX-265-TEX-N-2B"></use></g><g data-mml-node="mi" transform="translate(4538,0)"><use data-c="1D457" xlink:href="#MJX-265-TEX-I-1D457"></use></g><g data-mml-node="mi" transform="translate(4950,0)"><use data-c="1D44B" xlink:href="#MJX-265-TEX-I-1D44B"></use></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>Z</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>R</mi><mo>+</mo><mi>j</mi><mi>X</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p> </p><p><span>Se oponen al paso de CA en los circuitos tanto resistencias, cuanto condensadores y bobinas.</span></p><p><span>La </span><a href='https://es.wikipedia.org/wiki/Impedancia'><span>impedancia</span></a><span> </span><code>Z</code><span> de un circuito es la suma de su resistencia </span><code>R</code><span> y su reactancia </span><code>X</code><span>. La letra </span><code>j</code><span> se trata da un </span><a href='https://es.wikipedia.org/wiki/N%C3%BAmero_imaginario'><span>número imaginario</span></a><span> ya que como hemos visto anteriormente para definir correctamente una reactancia, hay que tener en cuenta tanto su valor absoluto como el ángulo de desfase introducido por las bobinas y/o condensadores del circuito. Una impedancia, pues, debe definirse de tal forma que se conozca su magnitud y el desfasaje que produzca.</span></p><h4 id='2131-circuitos-serie'><span>2.1.3.1 Circuitos serie.</span></h4><p><img src="https://github.com/noplacenoaddress/RNMnetwork/raw/master/Images/circuito_resistencia.jpg" referrerpolicy="no-referrer"></p><p><span>Si intercalamos una resistencia en un circuito recurrido por CA la intensidad según la ley de Ohm es </span><code>I = E/R</code><span> y la tensión estará en fase con la intensidad.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_condensador.jpg" referrerpolicy="no-referrer"></p><p><span>La oposición que opone </span><code>C</code><span> a la </span><code>CA</code><span> se llama reactancia capacitiva, presenta menor resistencia al paso de la corriente cuando:</span></p><ul><li><span>su capacidad es alta.</span></li><li><span>aumenta la frecuencia de la corriente.</span></li></ul><p><span>Se produce un desfase en el que la intensidad </span><code>I</code><span> se adelanta a la tensión </span><code>E</code><span> en 90°.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_bobina.jpg" referrerpolicy="no-referrer"></p><p><span>La bobina </span><code>L</code><span> se opone al paso de </span><code>CA</code><span> a través de reactancia inductiva, proporcional al </span><a href='https://es.wikipedia.org/wiki/Coeficiente_(matem%C3%A1tica)'><span>coeficiente</span></a><span> de </span><a href='https://es.wikipedia.org/wiki/Autoinducci%C3%B3n'><span>autoinducción</span></a><span> </span><code>L</code><span> , a la </span><a href='https://es.wikipedia.org/wiki/Velocidad_angular'><span>pulsación</span></a><span> </span><code>ω</code><span> y por consiguiente a la frecuencia </span><code>f</code><span>. A mayor frecuencia de la </span><code>CA</code><span>, mayor reactancia inductiva. </span><code>L</code><span> se opone con más fuerza a los aumentos de la frecuencia se comporta de forma contraria al condensador, la tensión </span><code>E</code><span> se adelanta de 90° a la intensidad </span><code>I</code><span>.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_bobina_serie.jpg" referrerpolicy="no-referrer"></p><p><span>In un circuito con una resistencia y una bobina en </span><a href='https://es.wikipedia.org/wiki/Circuito_en_serie'><span>serie</span></a><span> como la resistencia no desfasa y la bobina si que lo hace predomina el efecto de </span><code>L</code><span>. El desfase en este caso es menor de 90° porqué interviene </span><code>R</code><span>.</span></p><p><span>Cuando hay condensadores, bobinas y resistencias en un circuito aparecen </span><a href='http://ingenieriaelectricafravedsa.blogspot.com/2014/11/tensiones-simples-y-compuestas.html'><span>tensiones combinadas</span></a><span> o de conjunto, intensidades combinadas o del conjunto e impedancias. </span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_condensador_serie.jpg" referrerpolicy="no-referrer"></p><p><span>En los circuitos </span><code>R-C</code><span> también hay caída de tensión menor de 90°. </span><code>R</code><span> aminora este desfase. La tensión del conjunto es la suma de la caídas en </span><code>R</code><span> y </span><code>C</code><span>.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_bobina_condensador_serie.jpg" referrerpolicy="no-referrer"></p><p><span>En serie </span><code>R-L-C</code><span> bobina y condensador ejercen efectos opuestos tanto en reactancia cuanto en caídas de tensión. La impedancia en este caso es la suma de la resistencia de </span><code>L</code><span> y </span><code>C</code><span>. La tensión total también es la suma de la caída de tensión en la </span><code>R</code><span> y la resultante en </span><code>L</code><span> y </span><code>C</code><span>. Los valores tensión aplicada se reparten en los distintos componentes </span><code>R</code><span>, </span><code>L</code><span> y </span><code>C</code><span> dependiendo del valor resistivo de cada una de ellas, en cada elemento </span><code>R</code><span>, </span><code>L</code><span> y </span><code>C</code><span> la tensión es el producto de intensidad por resistencia (o reactancia en los casos de </span><code>L</code><span> y </span><code>C</code><span>).</span></p><p><span>Los desfases dependen de los valores de </span><code>R</code><span>, </span><code>L</code><span> y </span><code>C</code><span> y son menores de 90°. Si la reactancia del condensador es mayor que la de la bobina, nos encontramos ante un </span><a href='https://www.fisicapractica.com/inductivos-alterna.php'><span>circuito inductivo</span></a><span>. Si predominan componentes capacitivas será un </span><a href='https://www.fisicapractica.com/capacitivos-alterna.php'><span>circuito capacitivo</span></a><span>. Si se compensan el circuito será </span><a href='http://www.proyecto987.es/corriente_alterna_6.html#Circuito_resistivo_puro'><span>resistivo puro</span></a><span>.</span></p><h4 id='2132-circuitos-en-paralelo'><span>2.1.3.2 Circuitos en paralelo</span></h4><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_bobina_paralelo.jpg" referrerpolicy="no-referrer"></p><p><span>Las caídas de tensión en </span><code>R</code><span> y </span><code>L</code><span> son iguales dependiendo con la tensión aplicada. La intensidad de línea </span><code>I</code><span> tiene que ser mayor que la que circula por cada rama, equivaliendo a la </span><a href='https://es.wikipedia.org/wiki/Teorema_de_Pit%C3%A1goras'><span>suma pitagórica</span></a><span> de ambas.</span></p><p><span>El desfase es también menor de 90° adelantándose </span><code>E</code><span> a </span><code>I</code><span>. Si la reactancia inductiva de la bobina es menor que la resistencia </span><code>R</code><span> la corriente va por la bobina: circuito inductivo.</span></p><p><span>Si la reactancia inductiva es mayor que la resistencia </span><code>R</code><span> la corriente va por la resistencia: el circuito es resistivo.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_condesador_paralelo.jpg" referrerpolicy="no-referrer"></p><p><span>Con la caída de tensión ocurre igual que en el caso anterior, pero referido a </span><code>R</code><span> y </span><code>C</code><span>, en el desfase, siempre menor de 90°, </span><code>C</code><span> hace que se adelante la intensidad </span><code>I</code><span> a la tensión </span><code>E</code><span>. </span></p><p><span>Si la reactancia capacitiva es menor que </span><code>R</code><span> la corriente va por </span><code>C</code><span>: circuito capacitivo.</span></p><p><span>Si la reactancia capacitiva es mayor que </span><code>R</code><span> la corriente va por </span><code>R</code><span>: circuito resistivo.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/circuito_resistencia_bobina_condensador_paralelo.jpg" referrerpolicy="no-referrer"></p><p><span>La tensión es la misma en cada rama. La intensidad es según la ley de Ohm la tensión dividida por la resistencia </span><code>R</code><span> o las reactancias </span><code>L</code><span> y </span><code>C</code><span>.</span></p><p><span>Si la reactancia de </span><code>C</code><span> es mayor que la de </span><code>L</code><span>: circuito inductivo.</span></p><p><span>Si predominan las componentes capacitivas: circuito capacitivo.</span></p><p><span>Si los componentes son iguales: circuito resistivo puro.</span></p><h4 id='22-circuitos-resonantes'><span>2.2 Circuitos resonantes. </span></h4><p><img src="https://upload.wikimedia.org/wikipedia/commons/f/f8/VariacionIZ.jpg" referrerpolicy="no-referrer"></p><p><span>Circuitos donde se igualen las reactancias inductivas y capacitivas a una determinada frecuencia, llamada </span><a href='https://es.wikipedia.org/wiki/Resonancia_el%C3%A9ctrica'><span>frecuencia de resonancia</span></a><span>:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block 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647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mtable"><g data-mml-node="mtr" transform="translate(0,89)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D453" xlink:href="#MJX-266-TEX-I-1D453"></use></g><g data-mml-node="mtext" transform="translate(550,0)"><use data-c="A0" xlink:href="#MJX-266-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1077.8,0)"><use data-c="3D" xlink:href="#MJX-266-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(2133.6,0)"><use data-c="A0" xlink:href="#MJX-266-TEX-N-A0"></use></g><g data-mml-node="mfrac" transform="translate(2383.6,0)"><g data-mml-node="mn" transform="translate(1652,676)"><use data-c="31" xlink:href="#MJX-266-TEX-N-31"></use></g><g data-mml-node="mrow" transform="translate(220,-929)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJX-266-TEX-N-32"></use></g><g data-mml-node="mi" transform="translate(500,0)"><use data-c="1D70B" xlink:href="#MJX-266-TEX-I-1D70B"></use></g><g data-mml-node="msqrt" transform="translate(1070,0)"><g transform="translate(853,0)"><g data-mml-node="mi"><use data-c="1D43F" xlink:href="#MJX-266-TEX-I-1D43F"></use></g><g data-mml-node="mi" transform="translate(681,0)"><use data-c="1D436" xlink:href="#MJX-266-TEX-I-1D436"></use></g></g><g data-mml-node="mo" transform="translate(0,109)"><use data-c="221A" xlink:href="#MJX-266-TEX-N-221A"></use></g><rect width="1441" height="60" x="853" y="849"></rect></g></g><rect width="3564" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>f</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mn>1</mn><mrow><mn>2</mn><mi>π</mi><msqrt><mi>L</mi><mi>C</mi></msqrt></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><code>L</code><span> es la autoinducción en henrios y </span><code>C</code><span> la capacidad en faradios. </span></p><p><span>Por debajo de la resonancia predomina el carácter inductivo porque la corriente pasará mejor por la bobina que por el condensador. Por encima el circuito será capacitivo porqu el condensador para estas frecuencias presenta menos dificultades al paso de la corriente.</span></p><p><span>La intensidad será por la ley de Ohm la tensión dividida pro la impedancia del conjunto </span><code>I=E/Z</code></p><h5 id='resonante-serie'><span>Resonante serie</span></h5><p><span>La tensión es la misma en los terminales de la autoinducción que en los terminales de la capacidad, se reduce al mínimo y la intensidad es máxima.</span></p><p><span>Se pueden conseguir corrientes muy elevadas haciendo que la resistencia sea muy pequeña y puede el circuito entregar tensiones mucho mayores que las que recibe.</span></p><p><span>La </span><a href='https://es.wikipedia.org/wiki/Resonancia#Curva_de_resonancia_universal'><span>curva de resonancia</span></a><span> nos dice que la corriente varía según sea la frecuencia. Al variar </span><code>R</code><span>, la frecuencia de resonancia no varía. Si aumenta </span><code>R</code><span> la intensidad disminuye pero si </span><code>R</code><span> es muy grande pierde el circuito la facultad de seleccionar tensiones y no habrá diferencias entre las corrientes que circulan a la frecuencia de resonancia y las que lo hacen a otras frecuencias. </span></p><p><span>Si </span><code>f</code><span> es baja el condensador se opone más, habrá un efecto de reactancia capacitiva. Si aumentamos la frecuencia llegan a igualarse la reactancia capacitiva y la inductiva, haciéndose la impedancia mínima; coincide entonces con la frecuencia de resonancia y el circuito resuena. La impedancia se reduce a </span><code>R</code><span> y entonces la intensidad es máxima.</span></p><p><span>Por encima de esta frecuencia la oposición al paso es de efecto inductivo ya que la bobina </span><code>L</code><span> presente siempre pegas al aumento de la frecuencia al contrario del condensador </span><code>C</code><span>. Al ejercer la bobina un efecto inductivo alto el circuito se comporta como capacitivo, discurre mayor corriente a toda ella por la capacidad o condensador.</span></p><p><span>En condiciones de resonancia se compensan los desfases entra </span><code>I</code><span> y </span><code>E</code><span>, el condensador adelanta a la intensidad y en la bobina en cambio se adelante la tensión </span><code>E</code><span>, ambas de 90°. La curva que representa la intensidad es exactamente opuesta a la curva que representaría la impedancia. </span></p><h5 id='resonante-paralelo'><span>Resonante paralelo</span></h5><p><img src="https://upload.wikimedia.org/wikipedia/commons/1/1d/Tuned_circuit_animation_3.gif" referrerpolicy="no-referrer"></p><p><span>La tensión de alimentación se origina fuera del circuito, no así en el resonante en serie. Toma el nombre de </span><a href='https://es.wikipedia.org/wiki/Circuito_LC'><span>circuito tanque</span></a><span> el que contiene una inducción </span><code>L</code><span> y una capacidad </span><code>C</code><span> sin fuente de alimentación por su facultad de almacenar energía perdiéndola y restituyéndola cíclicamente. </span></p><p><span>El circuito tanque ideal está formado por una combinación </span><code>LC</code><span> en paralelo con las reactancias </span><code>RL</code><span> y </span><code>RC</code><span> iguales. </span></p><p><span>La corriente de línea que entrega el generador es la intensidad en </span><code>L</code><span> menos la intensidad en </span><code>C</code><span>.</span></p><p><span>La impedancia </span><code>Z</code><span> es el producto de las reactancias en </span><code>L</code><span> y </span><code>C</code><span> dividido por su suma, como que son iguales y de signo contrario resulta que:</span></p><ul><li><span>El </span><a href='https://es.wikipedia.org/wiki/Fracci%C3%B3n'><span>denominador</span></a><span> se anula, por lo que Z tiende a infinito. </span></li><li><span>La corriente de línea en resonancia en este circuito se hace cero.</span></li></ul><p><span>En el interior del tanque la corriente es muy grande, aunque la de línea sea cero.</span></p><h4 id='221-características-de-los-circuitos-resonantes'><span>2.2.1 Características de los circuitos resonantes.</span></h4><p><img src="https://raw.githubusercontent.com/redeltaglio/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/XC12548.svg" referrerpolicy="no-referrer"></p><p><span>La anchura de banda </span><code>B</code><span>, banda de paso o </span><a href='https://es.wikipedia.org/wiki/Pasabanda'><span>pasabanda</span></a><span> de un circuito resonante es el número de ciclos a un lado y otro de la frecuencia de resonancia que prácticamente proporciona la misma corriente. Se define por convención como aquel margen en que la energía de la señal es igual o mayor a la mitad de energía máxima, esto es el margen comprendido entro los puntos donde el valor de la tensión o de la corriente está 6 </span><code>dB</code><span> por debajo del valor máximo.</span></p><p><span>Concepto de factor de calidad delos circuitos resonantes: dado que </span><code>L</code><span> y </span><code>C</code><span> se eligen para que el conjunto resuene a determinada frecuencia y que esa </span><a href='https://es.wikipedia.org/wiki/Frecuencia_de_resonancia'><span>frecuencia de resonancia</span></a><span> puede conseguirse con distintos conjuntos los cuales tendrán mayor o menos dispersión en la curva de selectividad.</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n235" cid="n235" mdtype="math_block" data-math-tag-before="0" data-math-labels="[]" data-math-tag-after="0"><div 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displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>Q</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><msub><mi>F</mi><mrow data-mjx-texclass="ORD"><mi>r</mi><mi>e</mi><mi>s</mi></mrow></msub><mi>B</mi></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p> </p><p><span>El </span><a href='https://es.wikipedia.org/wiki/Factor_de_calidad'><span>factor de calidad</span></a><span> </span><code>Q</code><span> es la relación que hay entre la frecuencia de resonancia y su ancho de banda. Para los circuitos en serie y paralelo se convierte en:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n241" cid="n241" mdtype="math_block" data-math-tag-before="0" data-math-labels="[]" data-math-tag-after="0"><div class="md-rawblock-container md-math-container" contenteditable="false" tabindex="-1"><mjx-container class="MathJax" jax="SVG" display="true" style="position: relative;"><svg xmlns="http://www.w3.org/2000/svg" width="12.139ex" height="10.962ex" role="img" focusable="false" viewBox="0 -2672.6 5365.6 4845.2" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -4.915ex;"><defs><path id="MJX-268-TEX-I-1D444" d="M399 -80Q399 -47 400 -30T402 -11V-7L387 -11Q341 -22 303 -22Q208 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435Q740 255 592 107Q529 47 461 16L444 8V3Q444 2 449 -24T470 -66T516 -82Q551 -82 583 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data-mml-node="mi" transform="translate(1620,0)"><use data-c="1D43F" xlink:href="#MJX-268-TEX-I-1D43F"></use></g></g><rect width="2501" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>Q</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mrow><mn>2</mn><mi>π</mi><mi>f</mi><mi>L</mi></mrow><msub><mi>R</mi><mi>s</mi></msub></mfrac></mtd></mtr><mtr><mtd><mi>Q</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><msub><mi>R</mi><mi>p</mi></msub><mrow><mn>2</mn><mi>π</mi><mi>f</mi><mi>L</mi></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><code>Q</code><span> es la facultad que tiene dicho circuito para seleccionar una frecuencia eliminando las demás. A mayor </span><code>Q</code><span> mayor agudeza en la curva de resonancia. La curva de un circuito de alta calidad, </span><code>Q</code><span> alto, será una curva muy estrecha; </span><code>Q</code><span> bajo corresponde a una cima más suave y baja, las variaciones de corriente serán más pequeñas y la curva será </span><a href='https://dle.rae.es/chato'><span>chata</span></a><span>. A mayor </span><code>R</code><span> menor factor de calidad </span><code>Q</code><span>.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/Radio%20Astor%20modelo%20PS.gif" referrerpolicy="no-referrer"></p><p><span>En los circuitos de radio y TV los circuitos serie son sistemas de resonancia con un factor </span><code>Q</code><span> de valores entra </span><code>50</code><span> y </span><code>200</code><span>. Hay diferencias entre de una bobina y el de un condensador, ambos tienen su </span><code>Q</code><span> propio; se eligen según la frecuencia a que deba resonar el conjunto, influyendo más </span><code>L</code><span>. </span><code>L</code><span> tiene un </span><code>Q</code><span> bajo y </span><code>C</code><span> alto; para altas frecuencias se requiere </span><code>Q</code><span> alto.</span></p><h4 id='23-comportamiento-de-resistencias-condensadores-y-bobinas-reales-en-altas-frecuencias'><span>2.3 Comportamiento de resistencias, condensadores y bobinas reales en altas frecuencias.</span></h4><p><span>Hay que tener en cuenta que </span><code>R</code><span>, </span><code>C</code><span> y </span><code>L</code><span> a altas frecuencias, mayor de </span><a href='https://es.wikipedia.org/wiki/Megahercio'><span>1 MHz</span></a><span>, no presentan un valor igual a su nominal, debido sobre todo a la aparición de capacidades e </span><a href='http://rubensm.com/el-inductancia-parasita-serie-de-un-condensador/'><span>inductancias parásitas</span></a><span>.</span></p><p><span>En la utilización de estos elementos en </span><a href='https://es.wikipedia.org/wiki/Filtro_paso_banda'><span>filtros</span></a><span> para supresión de interferencias hay que tener bien en cuenta su comportamiento real ya que se pueden hasta comportar de forma opuesta a la deseada, hecho de tener bien en cuenta en el diseño de los circuitos.</span></p><p><span>La resistencia en continua difiere de la resistencia en alterna, en esta última crece al aumentar la frecuencia debido al efecto pelicular.</span></p><p><span>Los condensadores no presentan solo una capacidad sino que tienen asociadas una resistencia e inductancia, debidas a los terminales y a la estructura del componente. Al aumentar la frecuencia disminuye la reactancia de un condensador y viceversa.</span></p><p><span>Las bobinas presentan, además de la inductancia, una resistencia en serie y una capacidad distribuida en el bobinado. Por ello a alta frecuencia la inductancia equivalente puede ser negativa es decir, el inductor se puede comportar como un condensador. Por lo tanto el factor de calidad real es siemrpe inferior al teórico.</span></p><h4 id='24-filtros'><span>2.4 Filtros.</span></h4><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/radio%20espa%C3%B1ola.jpg" referrerpolicy="no-referrer"></p><p><span>En los sistemas de comunicación necesitamos acoplar diferentes circuitos bien sea para transferir una señal o bien para eliminar otras. Dos circuitos están acoplados cuando una tensión o corriente en una red produce otra tensión corriente en la otra. Puede ser deseado o indeseado como consecuencia de un error de diseño.</span></p><p><span>Existen numerosas configuraciones para realizar el acoplamiento entre dos circuitos siendo desde le punto de vista de la radio afición las más interesantes los filtros y las llamadas redes en </span><a href='https://es.wikipedia.org/wiki/Red_R-2R'><span>escalera</span></a><span>.</span></p><p><span>Los filtros son redes que permiten o detienen el paso de una terminada frecuencia o grupo de frecuencias, banda de frecuencias. Un filtro es un circuito con al menos un elemento reactivo, </span><code>L</code><span> o </span><code>C</code><span>. Los que tienen solo un elemento toman el nombre de «filtro de primer orden» siguiendo así de par en par con el número de elementos. </span></p><p><span>La principal característica de un filtro es su frecuencia de corte, que delimita la banda de frecuencias que pasan o no por el filtro.</span></p><p><span>Además de que lo podemos clasificar en pasivos o activos:</span></p><ul><li><u><span>pasivos</span></u><span>: formados por combinaciones serie o paralelo de elementos pasivos </span><code>R</code><span>, </span><code>L</code><span> o </span><code>C</code><span>.</span></li><li><u><span>activos</span></u><span>: aquellos que emplean dispositivos activos como </span><a href='https://es.wikipedia.org/wiki/Transistor'><span>transistores</span></a><span> o </span><a href='https://es.wikipedia.org/wiki/Amplificador_operacional'><span>amplificadores operacionales</span></a><span> conjuntamente a </span><code>R</code><span>, </span><code>L</code><span> o </span><code>C</code><span>. </span></li></ul><p><span>Según su uso se pueden clasificar en:</span></p><ul><li><u><span>paso alto</span></u><span>.</span></li><li><u><span>paso bajo</span></u><span>.</span></li><li><u><span>paso de banda</span></u><span>.</span></li><li><u><span>supresión de banda</span></u><span>.</span></li></ul><h4 id='241-filtros-compuestos-de-elementos-pasivos-paso-alto-paso-bajo-paso-de-banda-supresión-de-banda-ancho-de-banda'><span>2.4.1 Filtros compuestos de elementos pasivos: paso alto, paso bajo, paso de banda, supresión de banda. Ancho de banda.</span></h4><p><img src="https://musiki.org.ar/images/2/2f/Captura_de_pantalla_2016-10-09_a_la%28s%29_10.16.52_a.m..png" referrerpolicy="no-referrer"></p><p><span>Paso alto el que permite paso de frecuencias desde una determinada hacia arriba; paso bajo es aquel que permite el paso de frecuencias bajas desde la frecuencia 0 o continua hasta una determinada.</span></p><p><span>Un filtro pasa banda o supresión de banda es el que permite o impide el paso de componentes de frecuencia dentro de un determinado rango, comprendido entre una frecuencia de corte superior y otra inferior. Es una combinación de paso alto y paso bajo. Si se modifican estas frecuencias de corte, se modifica el rango de frecuencias, ampliando o disminuyendo las frecuencias que pueden pasar por él.</span></p><p><span>Diremos pues que el ancho de banda de un filtro es la anchura, medida en hercios, del rango de frecuencias en el que se concentra la mayor parte de la potencia de la señal. Como veremos más adelante puede ser calculado a a partir de una señal temporal mediante el </span><a href='https://es.wikipedia.org/wiki/An%C3%A1lisis_de_Fourier'><span>análisis de Fourier</span></a><span>.</span></p><h4 id='242-redes-en-escalera-factor-de-calidad-de-un-circuito-sintonizado'><span>2.4.2 Redes en escalera. Factor de calidad de un circuito sintonizado.</span></h4><p><img src="https://raw.githubusercontent.com/redeltaglio/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/red_escalera.svg" referrerpolicy="no-referrer"></p><h2 ></h2><p><span>Las redes en escalera son redes formadas por combinaciones en serie y paralelo de inductancias y condensadores, en ocasiones hay también resistencias, además de las propias internas de los componentes. En caso no haya se dicen redes no disipativas, no consuman potencia.</span></p><p><span>El funcionamiento de un filtro se basa en la combinación de dos principios:</span></p><ul><li><span>Al aumentar f disminuye la reactancia de C y viceversa.</span></li><li><span>Al aumenta f aumenta la reactancia de L y viceversa.</span></li></ul><p><span>Recordemos que la reactancia capacitiva es negativa mientras que la inductiva es positiva. 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transform="translate(4759,0)"><use data-c="1D44E" xlink:href="#MJX-424-TEX-I-1D44E"></use></g><g data-mml-node="mi" transform="translate(5288,0)"><use data-c="1D45B" xlink:href="#MJX-424-TEX-I-1D45B"></use></g><g data-mml-node="mi" transform="translate(5888,0)"><use data-c="1D451" xlink:href="#MJX-424-TEX-I-1D451"></use></g><g data-mml-node="mi" transform="translate(6408,0)"><use data-c="1D44E" xlink:href="#MJX-424-TEX-I-1D44E"></use></g></g><rect width="11438" height="60" x="120" y="220"></rect></g></g></g></g></g></g></svg><mjx-assistive-mml unselectable="on" display="block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>Q</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mrow><mn>2</mn><mi>π</mi><mi>f</mi><mi>L</mi></mrow><msub><mi>R</mi><mi>s</mi></msub></mfrac><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><msub><mi>R</mi><mi>p</mi></msub><mrow><mn>2</mn><mi>π</mi><mi>f</mi><mi>L</mi></mrow></mfrac><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mrow><mi>f</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>u</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>i</mi><mi>a</mi><mtext> </mtext><mi>d</mi><mi>e</mi><mtext> </mtext><mi>r</mi><mi>e</mi><mi>s</mi><mi>o</mi><mi>n</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>i</mi><mi>a</mi></mrow><mrow><mi>A</mi><mi>n</mi><mi>c</mi><mi>h</mi><mi>o</mi><mtext> </mtext><mi>d</mi><mi>e</mi><mtext> </mtext><mi>b</mi><mi>a</mi><mi>n</mi><mi>d</mi><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>La caída de voltaje sobre la bobina o el condensador es </span><code>Q</code><span> veces el voltaje aplicado, el valor de </span><code>Q</code><span> para un circuito resonante serie tiene su mayor importancia cuando se consideran circuitos de equipos de radio aficionado, donde es necesario que se lo más alto posible, pues de ese factor dependerá la sobre tensión que pueda obtenerse.</span></p><h4 id='243-respuesta-en-frecuencia'><span>2.4.3 Respuesta en frecuencia.</span></h4><p><img src="http://www2.imse-cnm.csic.es/~rafael/SETI/escaRCact2.gif" referrerpolicy="no-referrer"></p><p><span>En cada filtro hay dos zonas principales llamadas </span><a href='https://github.com/redeltaglio/RNMnetwork/raw/master/es.telecomlobby.com/radio_aficion/SETI/tema2.pdf'><span>banda de paso y banda de atenuación</span></a><span>. En la banda de paso, es donde las frecuencias pasan con un máximo de su valor, o hasta un valor del </span><code>50%</code><span> con respecto a su original y con una atenuación de </span><code>6 dB</code><span>, a partir de aquí nos encontramos en la banda de atenuación.</span></p><h4 id='244-filtro-en-pi-y-filtro-en-t'><span>2.4.4 Filtro en PI y filtro en T.</span></h4><p><img src="https://raw.githubusercontent.com/noplacenoaddress/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/filtro_PI.svg" referrerpolicy="no-referrer"></p><p><span>Se llama </span><a href='https://es.wikipedia.org/wiki/Filtro_electr%C3%B3nico'><span>filtro en PI</span></a><span> a lo que tiene uno de sus brazos en serie y dos paralelos y cuya configuración se asemeja a la letra griega π.</span></p><p><span>Se llama filtro en T a lo que tiene uno de sus brazos en serie y otro en paralelo y cuya configuración se asemeja a la letra T.</span></p><p><img src="https://raw.githubusercontent.com/redeltaglio/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/filtro_T.svg" referrerpolicy="no-referrer"></p><p> </p><h2 id='bibliografía'><span>Bibliografía</span></h2><ul><li><span>Libro de examen de radioaficionado, Luis Alarcón Palencia </span><code>EA4DXP</code></li><li><a href='https://www.simbologia-electronica.com/'><span>Símbolos eléctricos & electrónicos</span></a><span>. </span></li><li><a href='http://opencircuitdesign.com/xcircuit/'><span>Xcircuit</span></a></li><li><span>Física práctica - </span><a href='https://www.fisicapractica.com/electricidad.php'><span>Electricidad</span></a><span>. </span></li><li><span>Proyecto 987 - </span><a href='http://www.proyecto987.es/corriente_alterna_0.html'><span>Corriente alterna</span></a><span>.</span></li><li><span>Tecnológico de Costa Rica, William Marin, «</span><a href='https://github.com/redeltaglio/RNMnetwork/raw/master/es.telecomlobby.com/radio_aficion/Documentos/conceptos_basicos_previos.pdf'><span>sistemas de comunicaciones - conceptos básicos</span></a><span>». </span></li><li><a href='http://opencircuitdesign.com/xcircuit/tutorial/'><span>Xcircuit tutorial</span></a><span>.</span></li><li><a href='http://rubensm.com/category/electronica/'><span>Rubén Sánchez - electrónica</span></a><span>.</span></li><li><a href='http://ngspice.sourceforge.net/'><span>ngspice</span></a><span> </span></li><li><span>ngspice - </span><a href='https://github.com/redeltaglio/RNMnetwork/raw/master/es.telecomlobby.com/radio_aficion/Documentos/ngspice-manual.pdf'><span>manual</span></a><span>. </span></li><li><a href='http://www2.imse-cnm.csic.es/~rafael/'><span>Rafael Domínguez Castro</span></a><span>, </span><a href='http://www2.imse-cnm.csic.es/~rafael/SETI/'><span>SETI</span></a><span>.</span></li></ul></div></div>
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