The purpose of this paper is to define and develop a set of functions of an area in such a manner as to be analogous to the trigonometric and the hyperbolic functions.

Τα ασύρματα δίκτυα μικρής εμβέλειας (short-range wireless networks) γνωρίζουν σήμερα μεγάλη ανάπτυξη. Ένα βασικό δομικό στοιχείο των ασύρματων δικτύων είναι οι δέκτες (receivers), οι οποίοι περιλαμβάνουν μεταξύ των άλλων συστήματα για τον υποβιβασμό της συχνότητας του σήματος (down conversion) σε χαμηλότερες ενδιάμεσες συχνότητες (Intermediate Frequencies-IF). Κατά τη διαδικασία αυτή δημιουργείται το πρόβλημα της εμφάνισης ενός ειδώλου συχνότητας (image frequency), το οποίο συνυπάρχει με το σήμα προς επεξεργασία και θα πρέπει να απομακρυνθεί με χρήση κατάλληλων ηλεκτρονικών μιγαδικών φίλτρων (complex filters). Στόχος της Μεταπτυχιακής Διπλωματικής Εργασίας είναι η ανάπτυξη νέων δομών μιγαδικών φίλτρων τα οποία χρησιμοποιούνται σε δέκτες που λειτουργούν με τα πρότυπα Bluetooth/Zigbee. Κύρια πλεονεκτήματα αποτελούν η δυνατότητα λειτουργίας σε χαμηλή τάση τροφοδοσίας (1.2V), η ρύθμιση των χαρακτηριστικών τους με το ρεύμα πόλωσης, καθώς και η απουσία αντιστατών. Η εξομοίωση της λειτουργίας καθώς και η φυσική τους σχεδίαση έγιναν με χρήση του λογισμικού Cadence, σε τεχνολογία AMS 0.35μm. / Short-range wireless networks nowadays find great development. A basic structural component of wireless networks is the receivers, which include among others systems for down conversion of the signal into lower Intermediate Frequencies (IF). The problem of image frequency is created due to this procedure, which coexists with the under process signal and it should be removed through suitable electronic complex filters. The objective of this diploma Thesis is the development of new complex filters structures which are compatible with the Bluetooth/ZigBee standards. The main advantages are the operation availability in low-voltage supply (1.2V) environment, the adjustment of its characteristics through the dc bias current, and also the absence of resistors. The simulation of the filter and, also, the physical layout design were performed through the utilization of the Cadence with AMS BiCMOS 0.35um design kit.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-11-24T12:38:17Z No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-25T11:12:06Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) / Made available in DSpace on 2015-11-25T11:12:06Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3034727 bytes, checksum: 0259257effef3ff05f336dc98e4a1274 (MD5) Previous issue date: 2015-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we present a study about the Hyperbolic functions and their applications. We start with analysis of how these functions are approached in some di erential calculus books commonly used in graduate courses in exact sciences, noting that are made through its exponential setting. Then we exposed an approach using hyperbole as generating curve from the study of hyperbolic angles. The de nitions given it in parallel with the construction of the circular trigonometric functions, analyzing their similarities and di erences. Finally we present some of its applications, in particular and in more detail the catenary shape. / Neste trabalho apresentaremos um estudo das Funções Hiperbólicas e suas aplicações. Iniciamos com uma análise de como essas funções são abordadas em alguns livros de cálculo diferencial comumente usados nos cursos de graduação na área de exatas, constatando que são feitas através de sua defi nição exponencial. Em seguida expusemos uma abordagem utilizando-se da hipérbole como curva geratriz a partir do estudo de ângulos hiperbólicos. As de finições se deram paralelamente à construção das funções trigonométricas circulares, analisando suas semelhanças e diferenças. Por m apresentamos algumas de suas aplicações, em especial e de forma mais detalhada a catenária.

It is very unlikely to see at Czech high school in mathematics classes teaching the hyperbolic functions and their inverses. It's a pity, this could be a great opportunity to review and refresh the polynomial, rational, trigonometric and exponential function methods and skills. These functions even set an implicit connection between the exponential and gonio- metric functions, too. The aim of this thesis is to offer an alternative to the usual practice at the ordinary high schools and it is adopted to a limited schooling time available. Our approach has been successfully tested with a group of students at a small high school in the Czech borderland. The thesis also indicates the potential to expand this approach if more schooling time should have been available or more talented students should have been involved.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-29T15:12:58Z No. of bitstreams: 1 arquivototal.pdf: 1939955 bytes, checksum: f6ebf1c4db19321eabce5c175a32c2aa (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-08-29T15:43:41Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1939955 bytes, checksum: f6ebf1c4db19321eabce5c175a32c2aa (MD5) / Made available in DSpace on 2017-08-29T15:43:41Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1939955 bytes, checksum: f6ebf1c4db19321eabce5c175a32c2aa (MD5) Previous issue date: 2015-07-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work intends to show the hyperbolic functions, analyzing their similarities and contrasts with the circular trigonometric functions. To this, we start showing a short review about the circular trigonometry and hyperbole, describing their main elements and properties. Then, we made a study about hyperbolic functions, with the de nitions of sine, cosine and the other hyperbolic functions and their main properties. We nished this work with some applications of these functions on everyday. / Este trabalho tem como objetivo apresentar as funções hiperbólicas, analisando suas semelhanças e diferenças com as funções trigonométricas circulares. Para tanto, iniciamos apresentando uma breve revisão sobre a trigonometria circular e a hipérbole, descrevendo seus principais elementos e propriedades. Posteriormente, realizamos um estudo sobre as funções hiperbólicas, apresentando as de nições do seno, cosseno e das demais funções hiperbólicas e suas principais propriedades. Concluí- mos com algumas aplicações destas funções no cotidiano.