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f60c1fae31
RNMnetwork/es.telecomlobby.com/radio_aficion/URE_2.html
Riccardo Giuntoli ba4216b363
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2022-02-03 19:00:35 +01:00

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</style><title>URE_2</title>
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<body class='typora-export'><div class='typora-export-content'>
<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-499-TEX-I-1D44B" d="M42 0H40Q26 0 26 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rowspacing="3pt"><mtr><mtd><msub><mi>X</mi><mi>L</mi></msub><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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-500-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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</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. 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xlink:href="#MJX-501-TEX-I-1D457"></use></g><g data-mml-node="mi" transform="translate(4950,0)"><use data-c="1D44B" xlink:href="#MJX-501-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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mi>R</mi><mo>+</mo><mi>j</mi><mi>X</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p>&nbsp;</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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display="block"><mtable displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mi>f</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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-n84" cid="n84" mdtype="math_block" data-math-tag-before="0" data-math-tag-after="0" data-math-labels="[]"><div 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data-mml-node="mfrac" transform="translate(2624.6,0)"><g data-mml-node="msub" transform="translate(220,676)"><g data-mml-node="mi"><use data-c="1D439" xlink:href="#MJX-503-TEX-I-1D439"></use></g><g data-mml-node="TeXAtom" transform="translate(676,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45F" xlink:href="#MJX-503-TEX-I-1D45F"></use></g><g data-mml-node="mi" transform="translate(451,0)"><use data-c="1D452" xlink:href="#MJX-503-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(917,0)"><use data-c="1D460" xlink:href="#MJX-503-TEX-I-1D460"></use></g></g></g><g data-mml-node="mi" transform="translate(693.5,-686)"><use data-c="1D435" xlink:href="#MJX-503-TEX-I-1D435"></use></g><rect width="1906" 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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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><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-n86" cid="n86" 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="12.139ex" 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-504-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 -60T625 -3Q631 11 638 11Q647 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transform="translate(1620,0)"><use data-c="1D43F" xlink:href="#MJX-504-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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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><p><span>## </span></p><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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rowspacing="3pt"><mtr><mtd><mi>Q</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</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>&nbsp;</mtext><mi>d</mi><mi>e</mi><mtext>&nbsp;</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>&nbsp;</mtext><mi>d</mi><mi>e</mi><mtext>&nbsp;</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><h4 id='245-filtro-de-cristal-de-cuarzo'><span>2.4.5 filtro de cristal de cuarzo.</span></h4><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/cristales-de-cuarzo.jpg" referrerpolicy="no-referrer"></p><p><span>Basado en un circuito sintonizado, o resonante, de muy elevada selectividad que utiliza uno o más cristales de cuarzo.</span></p><p><span>El cuarzo es un mineral cristalino de sílice en el que se descubrieron hacia 1930 </span><a href='https://es.wikipedia.org/wiki/Piezoelectricidad'><span>propiedades piezoelectricas</span></a><span>, tales que el mineral cuando comprimido produce una separación de cargas eléctricas que genera a su vez una diferencia de potencial y reacciona mecánicamente cuando se somete a cun cierto voltaje.</span></p><p><span>El cristal de cuarzo se usa como componente de control de la frecuencia de circuitos osciladores convirtiendo las vibraciones mecánicas en voltajes eléctricos a una frecuencia específica, dado que presenta un comportamiento resonante. Así como un </span><a href='https://es.wikipedia.org/wiki/P%C3%A9ndulo'><span>péndulo</span></a><span> oscila a una frecuencia propia si, tras darle impulso, se le deja moverse libremente, un cristal de cuarzo sometido a un estímulo eléctrico puede continuar vibrando a una cierta frecuencia. Si se mantiene el estímulo de manera periódica y sincronizada, tendremos una </span><a href='https://es.wikipedia.org/wiki/Se%C3%B1al_el%C3%A9ctrica'><span>señal</span></a><span> a una frecuencia extraordinariamente precisa. Es la contrapartida electrónica de un reloj de péndulo. </span></p><p><img src="https://raw.githubusercontent.com/redeltaglio/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/equi_cristal.svg" referrerpolicy="no-referrer"></p><p><span>La gama de frecuencias de resonancia va desde las </span><a href='https://es.wikipedia.org/wiki/Espectro_audible'><span>frecuencias audibles</span></a><span> hasta varios centenares de MHz y tiene un bajo </span><a href='https://es.wikipedia.org/wiki/Coeficiente_de_dilataci%C3%B3n'><span>coeficiente de expansión</span></a><span> por temperatura lo que permite construir dispositivos electrónicos muy estables dentro de un amplio rango de temperaturas. Para aplicaciones que demandan una extremada estabilidad, se colocan en los llamados «hornos de cristal» que son receptáculos calentados mantenidos a una temperatura constante.</span></p><p><code>C0</code><span> representa la capacidad dentro los electrodos del cristal más la capacidad de la carcasa y sus terminales. R1, C1 y L1 conforman la rama principal del cristal y se conocen como componentes o parámetros «de movimiento», siendo:</span></p><ul><li><code>L1</code><span> la masa vibrante del cristal.</span></li><li><code>C1</code><span> la classicidad del cuarzo.</span></li><li><code>R1</code><span> las pérdidas producidas dentro del cristal.</span></li></ul><p><span>Los filtros de cristal de cuarzo tienen </span><code>Q</code><span> mucho más alto que los basados en </span><code>L</code><span>, </span><code>C</code><span> y </span><code>R</code><span>. Se construyen para ser utilizados como filtros de paso bajo, paso alto, paso banda o supresión de banda.</span></p><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/filtro_cristal.png" referrerpolicy="no-referrer"></p><h4 id='246-efectos-debidos-a-componentes-reales'><span>2.4.6 Efectos debidos a componentes reales</span></h4><p><span>Los componentes no siempre se comportan según el modelo ideal de diseño. Fundamentalmente la presencia de capacidades parásitas, las variaciones del valor y comportamiento de los distintos componentes y las pérdidas de inserción, nos obligan a la realización de pruebas para evaluar su comportamiento y efectuar las correcciones pertinentes con el fin de cumplir con las especificaciones de diseño.</span></p><h4 id='25-aplicación-y-uso-de-los-transformadores-transformador-ideal'><span>2.5 Aplicación y uso de los transformadores. 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xlink:href="#MJX-506-TEX-I-1D443"></use></g><g data-mml-node="TeXAtom" transform="translate(675,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D45D" xlink:href="#MJX-506-TEX-I-1D45D"></use></g><g data-mml-node="mi" transform="translate(503,0)"><use data-c="1D45F" xlink:href="#MJX-506-TEX-I-1D45F"></use></g><g data-mml-node="mi" transform="translate(954,0)"><use data-c="1D456" xlink:href="#MJX-506-TEX-I-1D456"></use></g><g data-mml-node="mi" transform="translate(1299,0)"><use data-c="1D45A" xlink:href="#MJX-506-TEX-I-1D45A"></use></g></g></g><g data-mml-node="mtext" transform="translate(2264.4,0)"><use data-c="A0" xlink:href="#MJX-506-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(2792.1,0)"><use data-c="3D" xlink:href="#MJX-506-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(3847.9,0)"><use data-c="A0" xlink:href="#MJX-506-TEX-N-A0"></use></g><g data-mml-node="msub" transform="translate(4097.9,0)"><g data-mml-node="mi"><use data-c="1D443" xlink:href="#MJX-506-TEX-I-1D443"></use></g><g data-mml-node="TeXAtom" transform="translate(675,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D460" xlink:href="#MJX-506-TEX-I-1D460"></use></g><g data-mml-node="mi" transform="translate(469,0)"><use data-c="1D452" xlink:href="#MJX-506-TEX-I-1D452"></use></g><g data-mml-node="mi" transform="translate(935,0)"><use data-c="1D450" xlink:href="#MJX-506-TEX-I-1D450"></use></g></g></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>P</mi><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></msub><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>e</mi><mi>c</mi></mrow></msub></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Es un dispositivos compuesto por al menos dos bobinas acopladas una conectada a una fuente de energía eléctrica denominada primario y otra que recibe la energía inducida denominada secundario.</span></p><p><span>Un transformador ideal es aquel que no tiene pérdidas.</span></p><p><span>Se emplean para transferir energía eléctrica entre dos circuitos independientes, desde uno a otro, mediante inducción y en esa trasferencia es posible cambiar la tensión existente en el primario en otra más alta igual o menos en el secundario. </span></p><p><span>Se emplea un núcleo de material magnetizable para que al aumentar la inductancia de las bobinas puedan tener un menor número de espiras. El secundario comunica la corriente a un circuito de utilización. el primario conectado a un fuente de alimentación alterna e recurrido pro una corriente produciendo en su núcleo un flujo alterno de igual frecuencia; así induce en el secundario una fem alterna de la misma frecuencia que la aplicada en el primario. La potencia aplicada en el primario es igual a la obtenida en el secundario salvo las pérdidas en los devanados y el núcleo. 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devanados deben estar bien aislados para evitar cortocircuitos.</span></p><h4 id='251-relación-entre-número-de-espiras-y-tensión'><span>2.5.1 Relación entre número de espiras y tensión.</span></h4><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n172" cid="n172" 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="38.278ex" height="4.731ex" role="img" focusable="false" viewBox="0 -1295.6 16918.9 2091.2" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.8ex;"><defs><path id="MJX-508-TEX-I-1D445" d="M230 637Q203 637 198 638T193 649Q193 676 204 682Q206 683 378 683Q550 682 564 680Q620 672 658 652T712 606T733 563T739 529Q739 484 710 445T643 385T576 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href='https://es.wikipedia.org/wiki/Dise%C3%B1o_de_transformadores#Relaci%C3%B3n_de_transformaci%C3%B3n'><span>relación de transformación</span></a><span> a la relación que hay entre el número de espiras del primario y el número de espiras del secundario. Si se trata del trasformador ideal, esta relación es la misma que hay entre las tensiones del primario y del secundario. O sea que las tensiones en cada devanado son proporcionales al número de espiras que lleva:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n174" cid="n174" 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="16.507ex" height="5.27ex" role="img" focusable="false" viewBox="0 -1414.6 7296.3 2329.2" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -2.069ex;"><defs><path id="MJX-509-TEX-I-1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path><path id="MJX-509-TEX-I-1D460" d="M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 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displaystyle="true" columnalign="right" columnspacing="" rowspacing="3pt"><mtr><mtd><mfrac><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>e</mi><mi>c</mi></mrow></msub><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></msub></mfrac><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mfrac><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>e</mi><mi>c</mi></mrow></msub><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></msub></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><h4 id='252-relación-entre-número-de-espiras-y-corriente'><span>2.5.2 Relación entre número de espiras y corriente.</span></h4><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n201" cid="n201" mdtype="math_block" data-math-tag-before="0" data-math-labels="[]" data-math-tag-after="0"><div 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data-mjx-texclass="ORD"><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></msub></mfrac></mtd></mtr><mtr><mtd><mi>N</mi><mrow data-mjx-texclass="ORD"><mo data-mjx-pseudoscript="true">²</mo></mrow><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mfrac><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>s</mi><mi>e</mi><mi>c</mi></mrow></msub><msub><mi>Z</mi><mrow data-mjx-texclass="ORD"><mi>p</mi><mi>r</mi><mi>i</mi><mi>m</mi></mrow></msub></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><h4 id='254-tipos-de-transformadores'><span>2.5.4 Tipos de transformadores.</span></h4><p><img src="https://upload.wikimedia.org/wikipedia/commons/3/33/Transformer3d_col3_es.svg" referrerpolicy="no-referrer"></p><p><span>Generalmente llevan núcleo de hierro cuando se usan en bajas frecuencias y núcleo de aire o de ferrita para las altas frecuencias.</span></p><p><span>Los transformadores de núcleo de hierro se componen de un núcleo de </span><a href='https://es.wikipedia.org/wiki/Hierro_forjado'><span>hierro dulce</span></a><span> laminado a cuyo alrededor hay dos o más devanados o bobinas independientes entre sí llamados primario y secundario. Los encontramos en </span><a href='https://es.wikipedia.org/wiki/Fuente_de_alimentaci%C3%B3n'><span>fuentes de alimentación</span></a><span> y pasos de audio de equipos antiguos. Caso particular aquellos que toman el nombre de </span><a href='https://es.wikipedia.org/wiki/Autotransformador'><span>autotransformadores</span></a><span> que tienen solo un devanado del que derivan las conexiones del primario y del secundario.</span></p><p><img src="https://raw.githubusercontent.com/redeltaglio/RNMnetwork/master/es.telecomlobby.com/radio_aficion/PCB/transformador_RF.svg" referrerpolicy="no-referrer"></p><p><span>Transformadores RF cuyas bobinas suelen estar devanadas sobre un soporte de </span><a href='https://es.wikipedia.org/wiki/Baquelita'><span>baquelita</span></a><span> o de cartón son de núcleo de aire o de ferrita para facilitar los ajustes entra etapas. En los acoplamientos por transformador el transformador hace variar la tensión manteniendo igual la potencia, adaptando además los valores de la corriente y tensión en cada circuito. Estos transformadores de acoplamiento deben calcularse para una frecuencia determinada de trabajo y ser ajustables para adaptar las impedancias, lo que se logra induciendo generalmente un núcleo de ferrita. </span></p><h4 id='26-formas-de-onda-no-sinusoidales'><span>2.6 Formas de onda no sinusoidales.</span></h4><p><span>Existen numerosos tipos de formas de onda eléctricas de CA que no son de forma sinusoidal:</span></p><ul><li><span>Ciertas señales de audio.</span></li><li><span>Las ondas cuadradas y rectangulares.</span></li><li><span>Las ondas triangulares y en diente de sierra.</span></li><li><span>Los pulsos y flancos o escalones.</span></li></ul><h4 id='261-señales-de-audio'><span>2.6.1 Señales de audio.</span></h4><p><img src="https://w3.ual.es/~vruiz/Docencia/Apuntes/Transduction/Audio/amplificacion.png" referrerpolicy="no-referrer"></p><p>&nbsp;</p><p><span>Una señal de audio es una señal electrónica que es una representación eléctrica exacta de una señal sonora. Está acotada dentro del rango de frecuencias audibles pro los seres humanos desde los 20 hasta los 20.000 hercios.</span></p><p><img src="https://upload.wikimedia.org/wikipedia/commons/9/9b/Ondes_compression_2d_20_petit.gif" referrerpolicy="no-referrer"></p><p><span>Dado que el sonido es una </span><a href='https://es.wikipedia.org/wiki/Onda_de_presi%C3%B3n'><span>onda de presión</span></a><span> se requiere un </span><a href='https://es.wikipedia.org/wiki/Transductor'><span>transductor</span></a><span> que convierte las ondas de presión de aire, </span><a href='https://es.wikipedia.org/wiki/Onda_sonora'><span>ondas sonoras</span></a><span>, en señales eléctricas analógicas. La conversión contraria se realiza mediante un altavoz.</span></p><p><span>Una señal de audio se caracteriza por su dinámica en cuanto a valor de pico, rango dinámico, potencia, </span><a href='https://es.wikipedia.org/wiki/Relaci%C3%B3n_se%C3%B1al/ruido'><span>relación señal-ruido</span></a><span> y por su espectro de potencia, ancho de banda, </span><a href='https://es.wikipedia.org/wiki/Frecuencia_fundamental'><span>frecuencia fundamental</span></a><span>, </span><a href='https://es.wikipedia.org/wiki/Arm%C3%B3nico'><span>armónicos</span></a><span>, </span><a href='https://es.wikipedia.org/wiki/Distorsi%C3%B3n_arm%C3%B3nica'><span>distorsión armónica</span></a><span>.</span></p><p><span>Por ejemplo una señal que representa voz humana, una señal vocal transformada de una </span><a href='https://es.wikipedia.org/wiki/Se%C3%B1al_de_voz'><span>señal de voz</span></a><span>, no suele tener información relevante más allá de los 10000 hercios y de hecho en telecomunicaciones se toman solo primeros 3500 hercios; con unos 2000 hercios basta para que la voz sea comprensible pero no para reconocer al hablante.</span></p><h4 id='262-ondas-cuadradas-y-rectangulares-presentación-gráfica-en-función-del-tiempo'><span>2.6.2 Ondas cuadradas y rectangulares. Presentación gráfica en función del tiempo.</span></h4><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/tipos-ondas-blog.png" referrerpolicy="no-referrer"></p><p><span>Las ondas cuadradas son las que pasan de un estado a otro de tensión, a intervalos regulares en un tiempo muy reducido. Son utilizadas usualmente para probar amplificadores debido a que este tipo de señales contienen en sí mismas todas las frecuencias. La televisión la radio y los ordenadores utilizan mucho este tipo de señales, fundamente como temporizadores.</span></p><p><span>Las rectangulares se diferencian de las cuadradas en no tener iguales los intervalos en los que la tensión permanece a nivel alto y bajo. Importantes para analizar circuitos digitales.</span></p><h4 id='263-ondas-triangulares-y-en-diente-de-sierra-pulsos-y-flancos-o-escalones'><span>2.6.3 Ondas triangulares y en diente de sierra. Pulsos y flancos o escalones.</span></h4><p><img src="https://upload.wikimedia.org/wikipedia/commons/8/82/Sawtooth-td_and_fd.png" referrerpolicy="no-referrer"></p><p><span>Generadas por una serie de circuitos diseñados para controlar voltajes linealmente, como puede ser el barrido horizontal de un osciloscopio analógico o el barrido tanto horizontal cuanto vertical de una televisión. Las transiciones entre nivel mínimo y máximo de la señal cambian a un ritmo constante, se denominan rampas.</span></p><p><span>La onda en </span><a href='https://es.wikipedia.org/wiki/Onda_de_sierra'><span>diente de sierra</span></a><span> es un caso especial de señal triangular con una rampa descendente de mucha más pendiente que la rampa ascendente. </span></p><p><span>Otras como los </span><a href='https://es.wikipedia.org/wiki/Flanco_(electr%C3%B3nica)'><span>flancos</span></a><span> o los pulsos se denominan señales </span><a href='https://es.wikipedia.org/wiki/R%C3%A9gimen_transitorio_(electr%C3%B3nica)'><span>transitorias</span></a><span>. Un flanco indica un cambio repentino en el voltaje, por ejemplo cuando se conecta un interruptor de alimentación, el pulso en este caso indicaría que se ha conectado el interruptor y un determinado tiempo se ha desconectado. Se encuentran en ordenadores, equipos de rayos X y comunicaciones.</span></p><h4 id='264-onda-fundamental-y-armónicos-superiores'><span>2.6.4 Onda fundamental y armónicos superiores.</span></h4><p><img src="https://github.com/redeltaglio/RNMnetwork/raw/master/Images/tumblr_inline_p9qoqj5U381t7xk4o_500.png" referrerpolicy="no-referrer"></p><p><span>Una función periódica no sinusoidal puede ser descompuesta en la suma de una función sinusoidal de la frecuencia fundamental y de otras funciones sinusoidales, cuyas frecuencias son múltiplos enteros de la frecuencia fundamental. Estas adicionales son conocidas como componentes armónicas o armónicos.</span></p><h4 id='265-ruido-térmico-del-receptor-de-banda-densidad-de-ruido-potencia-de-ruido-en-la-anchura-de-banda-del-receptor'><span>2.6.5 Ruido; térmico del receptor, de banda, densidad de ruido, potencia de ruido en la anchura de banda del receptor.</span></h4><p><img src="https://upload.wikimedia.org/wikipedia/commons/2/26/White_noise_image.png" referrerpolicy="no-referrer"></p><p><span>El término ruido en radiocomunicación se utiliza para denominar las señales no deseadas que aparecen, sobre las que no tenemos ninguna capacidad de control y que limitan su capacidad de recepción. Puede ser natural o artificial.</span></p><p><span>El ruido artificial aparece como consecuencia de actividades industriales; tracción de vehículos, transporte y distribución de energía eléctrica. El espectro del ruido artificial disminuye conforme aumenta la frecuencia. Un tipo de ruido artificial que existen en todas las bandas de frecuencia es el ruido impulsivo que se genera en fluorescentes, motores, pantallas de televisión y ordenador que se caracteriza por su elevada amplitud y corta duración.</span></p><p><span>Las fuentes naturales de ruido se modelan con una densidad espectral de potencia plana. Las fuentes naturales se clasifican en externas e internas al sistema.</span></p><p><span>Las externas se deben a la radiación producida por elementos naturales como la Tierra o el Sol y a los efectos del medio como lluvia, gases atmosféricos vegetación, sobre esta radiación.</span></p><p><span>Las internas se encuentran en los propios circuitos pasivos de conexión de la antena al receptor y en el propio receptor. </span></p><p><span>El </span><a href='https://es.wikipedia.org/wiki/Ruido_de_Johnson-Nyquist'><span>ruido térmico</span></a><span> es una perturbación de carácter aleatorio que aparece de forma natural en los conductores por agitación de los electrones; aumenta su potencia conforme aumenta la temperatura. Se puede considerar con </span><a href='https://es.wikipedia.org/wiki/Densidad_espectral'><span>densidad espectral</span></a><span> uniforme en una gama particular de frecuencias de trabajo. </span></p><p><span>El </span><a href='https://es.wikipedia.org/wiki/Ruido_blanco'><span>ruido de banda</span></a><span> es aquel cuya densidad espectral de potencia es constante y no depende de la frecuencia.</span></p><p><span>En un receptor, la señal, junto con el ruido suele pasar por filtros suficientemente selectivos para dejar pasar solo la señal. El tipo de filtro empleado suele ser un filtro de banda estrecha cuya frecuencia central es grande comparada con su ancho de banda. El ruido que puede aparecer después de este filtro se llama ruido de banda estrecha.</span></p><p><span>La potencia media de ruido es la que se entrega al receptor visto como una carga, y su valor máximo se puede obtener en condiciones de adaptación de impedancias. Su expresión es:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n552" cid="n552" 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="11.959ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 5285.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-512-TEX-I-1D443" d="M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 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490T848 631L654 322Q458 10 453 5Q451 4 449 3Q444 0 433 0Q418 0 415 7Q413 11 374 317L335 624L267 354Q200 88 200 79Q206 46 272 46H282Q288 41 289 37T286 19Q282 3 278 1Q274 0 267 0Q265 0 255 0T221 1T157 2Q127 2 95 1T58 0Q43 0 39 2T35 11Q35 13 38 25T43 40Q45 46 65 46Q135 46 154 86Q158 92 223 354T289 629Z"></path><path id="MJX-512-TEX-N-A0" d=""></path><path id="MJX-512-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-512-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></path><path id="MJX-512-TEX-I-1D447" d="M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 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xlink:href="#MJX-512-TEX-I-1D443"></use></g><g data-mml-node="mi" transform="translate(675,-150) scale(0.707)"><use data-c="1D440" xlink:href="#MJX-512-TEX-I-1D440"></use></g></g><g data-mml-node="mtext" transform="translate(1468.2,0)"><use data-c="A0" xlink:href="#MJX-512-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1995.9,0)"><use data-c="3D" xlink:href="#MJX-512-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(3051.7,0)"><use data-c="A0" xlink:href="#MJX-512-TEX-N-A0"></use></g><g data-mml-node="mi" transform="translate(3301.7,0)"><use data-c="1D458" xlink:href="#MJX-512-TEX-I-1D458"></use></g><g data-mml-node="mi" transform="translate(3822.7,0)"><use data-c="1D447" xlink:href="#MJX-512-TEX-I-1D447"></use></g><g data-mml-node="mi" transform="translate(4526.7,0)"><use data-c="1D435" xlink:href="#MJX-512-TEX-I-1D435"></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>P</mi><mi>M</mi></msub><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mi>k</mi><mi>T</mi><mi>B</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><code>k</code><span> es la </span><a href='https://es.wikipedia.org/wiki/Constante_de_Boltzmann'><span>constante de Boltzmann</span></a><span>, </span><code>T</code><span> la temperatura absoluta en </span><a href='https://es.wikipedia.org/wiki/Kelvin'><span>Kelvin</span></a><span> y </span><code>B</code><span> el ancho de banda en hercios.</span></p><h4 id='27-las-ondas-de-radio-como-ondas-electromagnéticas-velocidad-de-propagación-y-su-relación-con-la-frecuencia-y-la-longitud-de-onda-polarización'><span>2.7 Las ondas de radio como ondas electromagnéticas. Velocidad de propagación y su relación con la frecuencia y la longitud de onda. Polarización.</span></h4><p><img src="https://www.areatecnologia.com/imagenes/onda-electromagnetica.jpg" referrerpolicy="no-referrer"></p><p><span>Las ondas radio son una forma de radiación electromagnética y gracias a esta característica, debidamente utilizada, es posible transmitir información de un punto a otro. </span></p><p><span>No precisas de un medio material para desplazarse, pasan a través de los materiales aislantes, del aire y del vacío.</span></p><p><span>La velocidad de propagación de las ondas electromagnéticas en el vacío es la misma que la de la luz, es decir unos 300000 km/s. En otros medios es distinto.</span></p><p><span>Las ondas de radio, como cualquier otra radiación electromagnética, tienen dos campos, uno eléctrico y otro magnético que son variables y se encuentran siempre perpendiculares entre sí y con la dirección de propagación de la onda.</span></p><p><span>Si imaginamos los tres </span><a href='https://es.wikipedia.org/wiki/Coordenadas_cartesianas'><span>ejes de coordenadas</span></a><span> </span><code>X</code><span>, </span><code>Y</code><span> y </span><code>Z</code><span> que forman entre sí ángulos de 90°, si </span><code>X</code><span> es la dirección de propagación de la onda, el campo eléctrico seguirá el eje </span><code>Y</code><span> y el magnético </span><code>Z</code><span>.</span></p><p><span>Se denomina </span><a href='https://es.wikipedia.org/wiki/Longitud_de_onda'><span>longitud de onda</span></a><span> el espacio que recorre la onda durante un periodo o ciclo.</span></p><p><span>La relación entre longitud de onda, su velocidad de propagación en el vacío y su frecuencia viene dada por la conocida expresión:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n863" cid="n863" 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="13.25ex" height="5.052ex" role="img" focusable="false" viewBox="0 -1366.5 5856.6 2233" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -1.96ex;"><defs><path id="MJX-513-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-513-TEX-N-A0" d=""></path><path id="MJX-513-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-513-TEX-N-33" d="M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z"></path><path id="MJX-513-TEX-N-30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path><path id="MJX-513-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 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" transform="translate(0,24.5)"><g data-mml-node="mtd"><g data-mml-node="mi"><use data-c="1D706" xlink:href="#MJX-513-TEX-I-1D706"></use></g><g data-mml-node="mtext" transform="translate(583,0)"><use data-c="A0" xlink:href="#MJX-513-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1110.8,0)"><use data-c="3D" xlink:href="#MJX-513-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(2166.6,0)"><use data-c="A0" xlink:href="#MJX-513-TEX-N-A0"></use></g><g data-mml-node="mfrac" transform="translate(2416.6,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="33" xlink:href="#MJX-513-TEX-N-33"></use><use data-c="30" xlink:href="#MJX-513-TEX-N-30" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJX-513-TEX-N-30" transform="translate(1000,0)"></use><use data-c="30" xlink:href="#MJX-513-TEX-N-30" transform="translate(1500,0)"></use><use data-c="30" xlink:href="#MJX-513-TEX-N-30" transform="translate(2000,0)"></use><use data-c="30" xlink:href="#MJX-513-TEX-N-30" transform="translate(2500,0)"></use></g><g data-mml-node="mi" transform="translate(1445,-686)"><use data-c="1D453" xlink:href="#MJX-513-TEX-I-1D453"></use></g><rect width="3200" 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>λ</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mfrac><mn>300000</mn><mi>f</mi></mfrac></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>Para conocer la velocidad de propagación de una onda de una longitud determinada utilizaremos la expresión:</span></p><div contenteditable="false" spellcheck="false" class="mathjax-block md-end-block md-math-block md-rawblock" id="mathjax-n867" cid="n867" 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="8.988ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3972.6 1000" xmlns:xlink="http://www.w3.org/1999/xlink" aria-hidden="true" style="vertical-align: -0.566ex;"><defs><path id="MJX-560-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-560-TEX-N-A0" d=""></path><path id="MJX-560-TEX-N-3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path><path id="MJX-560-TEX-I-1D706" d="M166 673Q166 685 183 694H202Q292 691 316 644Q322 629 373 486T474 207T524 67Q531 47 537 34T546 15T551 6T555 2T556 -2T550 -11H482Q457 3 450 18T399 152L354 277L340 262Q327 246 293 207T236 141Q211 112 174 69Q123 9 111 -1T83 -12Q47 -12 47 20Q47 37 61 52T199 187Q229 216 266 252T321 306L338 322Q338 323 288 462T234 612Q214 657 183 657Q166 657 166 673Z"></path><path id="MJX-560-TEX-I-1D453" d="M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 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><path id="MJX-560-TEX-I-1D458" d="M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z"></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="1D463" xlink:href="#MJX-560-TEX-I-1D463"></use></g><g data-mml-node="mtext" transform="translate(485,0)"><use data-c="A0" xlink:href="#MJX-560-TEX-N-A0"></use></g><g data-mml-node="mo" transform="translate(1012.8,0)"><use data-c="3D" xlink:href="#MJX-560-TEX-N-3D"></use></g><g data-mml-node="mtext" transform="translate(2068.6,0)"><use data-c="A0" xlink:href="#MJX-560-TEX-N-A0"></use></g><g data-mml-node="mi" transform="translate(2318.6,0)"><use data-c="1D706" xlink:href="#MJX-560-TEX-I-1D706"></use></g><g data-mml-node="mi" transform="translate(2901.6,0)"><use data-c="1D453" xlink:href="#MJX-560-TEX-I-1D453"></use></g><g data-mml-node="mi" transform="translate(3451.6,0)"><use data-c="1D458" xlink:href="#MJX-560-TEX-I-1D458"></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>v</mi><mtext>&nbsp;</mtext><mo>=</mo><mtext>&nbsp;</mtext><mi>λ</mi><mi>f</mi><mi>k</mi></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></div></div><p><span>siendo </span><code>k</code><span> la constante dieléctrica del medio distinto al vacío. </span></p><p><span>Se llama </span><a href='https://es.wikipedia.org/wiki/Polarizaci%C3%B3n_electromagn%C3%A9tica'><span>polarización</span></a><span> de una onda a la posición que ocupa el campo eléctrico de la misma con respecto a la superficie de la Tierra.</span></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 &amp; 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><li><a href='http://www.ibiblio.org/kuphaldt/electricCircuits/'><span>Lessons in Electric Circuits</span></a></li><li><a href='https://vicente-gonzalez-ruiz.github.io/'><span>Vicente González Ruiz</span></a><span>, </span><a href='https://w3.ual.es/~vruiz/Docencia/Apuntes/Transduction/Audio/index.html'><span>Transducción de Señales de Audio</span></a></li></ul></div></div>
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