Simulating normal modes and beats in a periodic inductor-capacitor circuit
This paper approaches a periodic inductor-capacitor circuit with N-coupled loops. Kirchhoff’s voltage and current laws are used in order to obtain N-coupled second-order differential equations. These equations are decoupled by using a standard discrete sine transformation. Then the voltages and curr...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Portuguese |
| Published: |
Sociedade Brasileira de Física
2024-03-01
|
| Series: | Revista Brasileira de Ensino de Física |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172024000100414&lng=en&tlng=en |
| _version_ | 1797265381939740672 |
|---|---|
| author | D.E. Almeida |
| author_facet | D.E. Almeida |
| author_sort | D.E. Almeida |
| collection | DOAJ |
| description | This paper approaches a periodic inductor-capacitor circuit with N-coupled loops. Kirchhoff’s voltage and current laws are used in order to obtain N-coupled second-order differential equations. These equations are decoupled by using a standard discrete sine transformation. Then the voltages and currents along the circuit are written as linear combinations of harmonic waves whose normal frequencies were determined. There are N of these frequencies that depend not only on the values of the capacitance and inductance but also, on how these elements are connected. Furthermore, one presents how each normal frequency can be synchronized using external batteries that initially charge the capacitors. Additionally, not only the analytical results are presented, but also, all circuits were simulated, using the free online platform Multisim, to corroborate the analytical calculations. Further, the simulations present a way of exploring the complex subject of coupled oscillations without dealing with all the analytical calculations. Moreover, one explores interferences that produce beats in the oscillating voltages in the circuit. Finally, a general interpretation of how the currents flow in the circuit is presented when a single normal mode is excited. |
| first_indexed | 2024-04-25T00:43:54Z |
| format | Article |
| id | doaj.art-2f98c187cfb0457d8813c87700f0eeb8 |
| institution | Directory Open Access Journal |
| issn | 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-04-25T00:43:54Z |
| publishDate | 2024-03-01 |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-2f98c187cfb0457d8813c87700f0eeb82024-03-12T07:39:24ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-91262024-03-014610.1590/1806-9126-rbef-2023-0326Simulating normal modes and beats in a periodic inductor-capacitor circuitD.E. Almeidahttps://orcid.org/0000-0002-0284-4288This paper approaches a periodic inductor-capacitor circuit with N-coupled loops. Kirchhoff’s voltage and current laws are used in order to obtain N-coupled second-order differential equations. These equations are decoupled by using a standard discrete sine transformation. Then the voltages and currents along the circuit are written as linear combinations of harmonic waves whose normal frequencies were determined. There are N of these frequencies that depend not only on the values of the capacitance and inductance but also, on how these elements are connected. Furthermore, one presents how each normal frequency can be synchronized using external batteries that initially charge the capacitors. Additionally, not only the analytical results are presented, but also, all circuits were simulated, using the free online platform Multisim, to corroborate the analytical calculations. Further, the simulations present a way of exploring the complex subject of coupled oscillations without dealing with all the analytical calculations. Moreover, one explores interferences that produce beats in the oscillating voltages in the circuit. Finally, a general interpretation of how the currents flow in the circuit is presented when a single normal mode is excited.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172024000100414&lng=en&tlng=enPeriodic inductor-capacitor structurescoupled oscillationsnormal modeselectrical circuit simulations |
| spellingShingle | D.E. Almeida Simulating normal modes and beats in a periodic inductor-capacitor circuit Revista Brasileira de Ensino de Física Periodic inductor-capacitor structures coupled oscillations normal modes electrical circuit simulations |
| title | Simulating normal modes and beats in a periodic inductor-capacitor circuit |
| title_full | Simulating normal modes and beats in a periodic inductor-capacitor circuit |
| title_fullStr | Simulating normal modes and beats in a periodic inductor-capacitor circuit |
| title_full_unstemmed | Simulating normal modes and beats in a periodic inductor-capacitor circuit |
| title_short | Simulating normal modes and beats in a periodic inductor-capacitor circuit |
| title_sort | simulating normal modes and beats in a periodic inductor capacitor circuit |
| topic | Periodic inductor-capacitor structures coupled oscillations normal modes electrical circuit simulations |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172024000100414&lng=en&tlng=en |
| work_keys_str_mv | AT dealmeida simulatingnormalmodesandbeatsinaperiodicinductorcapacitorcircuit |