{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T14:59:13+00:00","modifiedTime":"2022-08-19T17:38:59+00:00","timestamp":"2022-09-14T18:19:56+00:00"},"data":{"breadcrumbs":[{"name":"Technology","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33512"},"slug":"technology","categoryId":33512},{"name":"Electronics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33543"},"slug":"electronics","categoryId":33543},{"name":"Circuitry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33549"},"slug":"circuitry","categoryId":33549}],"title":"Create Band-Pass and Band-Reject Filters with RLC Parallel Circuits","strippedTitle":"create band-pass and band-reject filters with rlc parallel circuits","slug":"create-band-pass-and-band-reject-filters-with-rlc-parallel-circuits","canonicalUrl":"","seo":{"metaDescription":"Learn about RLC circuits, how to get a transfer function, and how to create band-pass and band-reject filters.","noIndex":0,"noFollow":0},"content":"There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject filters. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel.\r\n\r\nYou can get a transfer function for a band-pass filter with a parallel RLC circuit, like the one shown here.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375230.image0.jpg\" alt=\"transfer function for a band-pass filter with a parallel RLC circuit\" width=\"535\" height=\"325\" />\r\n\r\nYou can use current division to find the current transfer function of the parallel RLC circuit. By measuring the current through the resistor <i>I</i><i><sub>R</sub></i><i>(s)</i>, you form a band-pass filter. Start with the current divider equation:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375231.image1.jpg\" alt=\"the current divider equation\" width=\"178\" height=\"50\" />\r\n\r\nA little algebraic manipulation gives you a current transfer function, <i>T(s) = I</i><i><sub>R</sub></i><i>(s)/I</i><i><sub>S</sub></i><i>(s)</i>, for the band-pass filter:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375232.image2.jpg\" alt=\"a current transfer function for the band-pass filter\" width=\"261\" height=\"53\" />\r\n\r\nPlug in <i>s = j</i><i>ω</i> to get the frequency response <i>T(j</i><i>ω</i><i>)</i>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375233.image3.jpg\" alt=\"the frequency response T(jω)\" width=\"312\" height=\"54\" />\r\n\r\nThis equation has the same form as the RLC series equations. For the rest of this problem, you follow the same process as for the RLC series circuit.\r\n\r\nThe transfer function is at a maximum when the denominator is minimized, which occurs when the real part of the denominator is set to 0. The cutoff frequencies are found when their gains |<i>T(jω</i><i><sub>C</sub></i><i>)</i>| = 0.707|<i>T(jω)</i>| or the –3 dB point. Therefore, <i>ω</i><i><sub>0</sub></i> is\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375234.image4.jpg\" alt=\"The cutoff frequencies for band-pass and band-reject filters.\" width=\"174\" height=\"44\" />\r\n\r\nThe center frequency, the cutoff frequencies, and the bandwidth have equations identical to the ones for the RLC series band-pass filter.\r\n\r\nYour cutoff frequencies are <i>ω</i><i><sub>C</sub></i><i><sub>1</sub></i> and <i>ω</i><i><sub>C</sub></i><i><sub>2</sub></i>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375235.image5.jpg\" alt=\"The cutoff frequencies for a band-pass filter.\" width=\"204\" height=\"109\" />\r\n\r\nThe bandwidth <i>BW</i> and quality factor <i>Q</i> are\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375236.image6.jpg\" alt=\"The bandwidth BW and quality factor Q\" width=\"142\" height=\"88\" />","description":"There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject filters. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel.\r\n\r\nYou can get a transfer function for a band-pass filter with a parallel RLC circuit, like the one shown here.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375230.image0.jpg\" alt=\"transfer function for a band-pass filter with a parallel RLC circuit\" width=\"535\" height=\"325\" />\r\n\r\nYou can use current division to find the current transfer function of the parallel RLC circuit. By measuring the current through the resistor <i>I</i><i><sub>R</sub></i><i>(s)</i>, you form a band-pass filter. Start with the current divider equation:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375231.image1.jpg\" alt=\"the current divider equation\" width=\"178\" height=\"50\" />\r\n\r\nA little algebraic manipulation gives you a current transfer function, <i>T(s) = I</i><i><sub>R</sub></i><i>(s)/I</i><i><sub>S</sub></i><i>(s)</i>, for the band-pass filter:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375232.image2.jpg\" alt=\"a current transfer function for the band-pass filter\" width=\"261\" height=\"53\" />\r\n\r\nPlug in <i>s = j</i><i>ω</i> to get the frequency response <i>T(j</i><i>ω</i><i>)</i>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375233.image3.jpg\" alt=\"the frequency response T(jω)\" width=\"312\" height=\"54\" />\r\n\r\nThis equation has the same form as the RLC series equations. For the rest of this problem, you follow the same process as for the RLC series circuit.\r\n\r\nThe transfer function is at a maximum when the denominator is minimized, which occurs when the real part of the denominator is set to 0. The cutoff frequencies are found when their gains |<i>T(jω</i><i><sub>C</sub></i><i>)</i>| = 0.707|<i>T(jω)</i>| or the –3 dB point. Therefore, <i>ω</i><i><sub>0</sub></i> is\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375234.image4.jpg\" alt=\"The cutoff frequencies for band-pass and band-reject filters.\" width=\"174\" height=\"44\" />\r\n\r\nThe center frequency, the cutoff frequencies, and the bandwidth have equations identical to the ones for the RLC series band-pass filter.\r\n\r\nYour cutoff frequencies are <i>ω</i><i><sub>C</sub></i><i><sub>1</sub></i> and <i>ω</i><i><sub>C</sub></i><i><sub>2</sub></i>:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375235.image5.jpg\" alt=\"The cutoff frequencies for a band-pass filter.\" width=\"204\" height=\"109\" />\r\n\r\nThe bandwidth <i>BW</i> and quality factor <i>Q</i> are\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/375236.image6.jpg\" alt=\"The bandwidth BW and quality factor Q\" width=\"142\" height=\"88\" />","blurb":"","authors":[{"authorId":9717,"name":"John Santiago","slug":"john-santiago","description":" <p><b>John M. Santiago Jr., PhD,</b> served in the United States Air Force (USAF) for 26 years. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. While assigned in Europe, he spearheaded more than 40 international scientific and engineering conferences/workshops. 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Create Band-Pass and Band-Reject Filters with RLC Parallel Circuits

By: John Santiago and

Updated: 08-19-2022

From The Book: Circuit Analysis For Dummies

Circuit Analysis For Dummies

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There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. You can use series and parallel RLC circuits to create band-pass and band-reject filters. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel.

You can get a transfer function for a band-pass filter with a parallel RLC circuit, like the one shown here.

transfer function for a band-pass filter with a parallel RLC circuit

You can use current division to find the current transfer function of the parallel RLC circuit. By measuring the current through the resistor I_R(s), you form a band-pass filter. Start with the current divider equation:

A little algebraic manipulation gives you a current transfer function, T(s) = I_R(s)/I_S(s), for the band-pass filter:

Plug in s = jω to get the frequency response T(jω):

This equation has the same form as the RLC series equations. For the rest of this problem, you follow the same process as for the RLC series circuit.

The transfer function is at a maximum when the denominator is minimized, which occurs when the real part of the denominator is set to 0. The cutoff frequencies are found when their gains |T(jω_C)| = 0.707|T(jω)| or the –3 dB point. Therefore, ω₀ is

The center frequency, the cutoff frequencies, and the bandwidth have equations identical to the ones for the RLC series band-pass filter.

Your cutoff frequencies are ω_C₁ and ω_C₂:

The cutoff frequencies for a band-pass filter.

The bandwidth BW and quality factor Q are

The bandwidth BW and quality factor Q

About This Article

This article is from the book:

Circuit Analysis For Dummies ,

About the book author:

John M. Santiago Jr., PhD, served in the United States Air Force (USAF) for 26 years. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. While assigned in Europe, he spearheaded more than 40 international scientific and engineering conferences/workshops.

This article can be found in the category:

Circuitry ,