Comunicação serial, Conversor AD e Saídas PWM

(1)

❈♦♠✉♥✐❝❛çã♦ s❡r✐❛❧✱ ❈♦♥✈❡rs♦r ❆❉ ❡ ❙❛í❞❛s P❲▼

Pr♦❢✳▼❙❝✳❘♦❞r✐❣♦ ▼❛①✐♠✐❛♥♦ ❆♥t✉♥❡s ❞❡ ❆❧♠❡✐❞❛

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ■t❛❥✉❜á

(2)

(3)

❉✐s♣❧❛② ❞❡ ▲❈❉

❼ ❘♦t✐♥❛ ♣❛r❛ ❡♥✈✐♦ ❞❡ ❞❛❞♦s✴❝♦♠❛♥❞♦ ♣❛r❛ ♦ ▲❈❉

❼ P❛r❛ ❝♦♠❛♥❞♦ ❘❙ ❂ ✵❀ P❛r❛ ❞❛❞♦s ❘❙ ❂ ✶❀ ❼ ❍❛❜✐❧✐t❛r ❛ ❡s❝r✐t❛ ✭❘❲❂✶✮ ♦✉ ❧❡✐t✉r❛ ✭❘❲❂✵✮ ❼ ❆❝✐♦♥❛r t❡r♠✐♥❛❧ ❊◆ ✭❡♥❛❜❧❡✮

❼ ❉❡❧❛② ♣❛r❛ ♦ ▲❈❉ ❡♥t❡♥❞❡r ♦ ❝♦♠❛♥❞♦ ❼ ❉❡s❛❜✐❧✐t❛ ♦ t❡r♠✐♥❛❧ ❊◆

❼ ❘❡t♦r♥❛ ♦s t❡r♠✐♥❛✐s ♣❛r❛ ♥í✈❡❧ ❜❛✐①♦✶

✶_{P❛r❛ ♠❡❧❤♦r ✉s♦ é ✐♥t❡r❡ss❛♥t❡ r❡t♦r♥❛r ♦s t❡r♠✐♥❛✐s ♣❛r❛ ♦ ✈❛❧♦r q✉❡}

(4)

■♥str✉çã♦ ❘❙ ❘❲ ❉❛❞♦s ✭❜✐t✮_✼ _✻ _✺ _✹ _✸ _✷ _✶ _✵ ❚❡♠♣♦_{✭♠á①✳✮}

▲✐♠♣❛ ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✶ ✸✼ ✉s

❘❡s❡t ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✶ ✲ ✶✳✺♠s

❈♦♥✜❣✳ ✵ ✵ ✵ ✵ ✵ ✵ ✵ ✶ ■❉ ❙ ✸✼ ✉s

❈♦♥✜❣✳ ✵ ✵ ✵ ✵ ✵ ✵ ✶ ❉ ❈ ❇ ✸✼ ✉s

▼♦✈✐♠✳ ✵ ✵ ✵ ✵ ✵ ✶ ❙❈ ❘▲ ✲ ✲ ✸✼ ✉s

❈♦♥✜❣✳ ✵ ✵ ✵ ✵ ✶ ❉▲ ◆ ❋ ✲ ✲ ✸✼ ✉s

▼♦✈❡✭❧✱❝✮ ✵ ✵ ✶ ❳ ✵ ✵ ❈♦❧✉♥❛ ✸✼ ✉s

❖❝✉♣✳ ✵ ✶ ❇❋ ✲ ✲ ✲ ✲ ✲ ✲ ✲ ✶✵ ✉s

(5)

❉✐s♣❧❛② ❞❡ ▲❈❉

❼ ❉❡✜♥✐çõ❡s

❼ ■❉✿ ✶ ✕ ■♥❝r❡♠❡♥t❛✱ ✵ ✕ ❉❡❝r❡♠❡♥t❛

❼ ❙✿ ✶ ✕ ❖ ❞✐s♣❧❛② ❛❝♦♠♣❛♥❤❛ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❼ ❙❈✿ ✶ ✕ ❉❡s❧♦❝❛ ♦ ❞✐s♣❧❛②✱ ✵ ✕ ❉❡s❧♦❝❛ ♦ ❝✉rs♦r ❼ ❘▲✿ ✶ ✕ ▼♦✈❡ ♣❛r❛ ❞✐r❡✐t❛✱ ✵ ✕ ▼♦✈❡ ♣❛r❛ ❡sq✉❡r❞❛ ❼ ❉▲✿ ✶ ✕ ✽ ❜✐ts✱ ✵ ✕ ✹ ❜✐ts

❼ ◆✿ ✶ ✕ ✷ ❧✐♥❤❛s✱ ✵ ✕ ✶ ❧✐♥❤❛

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❼ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ❜✐❜❧✐♦t❡❝❛

❼ ❈r✐❛çã♦ ❞❡ r♦t✐♥❛s ❞❡ ❞❡❧❛② ✭✷♠s ❡ ✹✵✉s✮ ❼ ❋✉♥çã♦ ♣❛r❛ ❡♥✈✐❛r ❝♦♠❛♥❞♦s

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❉✐s♣❧❛② ❞❡ ▲❈❉

✶ ★✐♥❝❧✉❞❡ ✧❜❛s✐❝♦✳❤✧ ✷ ★✐♥❝❧✉❞❡ ✧❝♦♥❢✐❣✳❤✧ ✸ ★✐♥❝❧✉❞❡ ✧❧❝❞✳❤✧ ✹

✺ ✴✴✐♥✐❝✐♦ ❞♦ ♣r♦❣r❛♠❛ ✻ ✈♦✐❞ ♠❛✐♥✭✈♦✐❞✮ ✐♥t❡rr✉♣t ✵ ✼ ④

✽ ✉♥s✐❣♥❡❞ ✐♥t ✐✱❥❀

✾ ❝❤❛r ♠s❣❬❪ ❂ ✧❍❡❧❧♦ ❲♦r❧❞✦✧❀

✶✵ ■♥✐❝✐❛❧✐③❛▲❈❉✭✮❀ ✶✶ ❢♦r✭✐❂✵❀✐❁✶✶❀✐✰✰✮

✶✷ ④

✶✸ ❊♥✈✐❛❉❛❞♦s✭♠s❣❬✐❪✮❀ ✶✹ ❢♦r✭❥ ❂ ✵❀ ❥ ❁ ✻✺✵✵✵❀ ❥✰✰✮❀

✶✺ ⑥

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❈♦♠✉♥✐❝❛çã♦ ❙❡r✐❛❧

❼ ❱❛♥t❛❣❡♥s

❼ ❙✐♠♣❧✐✜❝❛çã♦ ❞♦ ❤❛r❞✇❛r❡

❼ ❆✉♠❡♥t♦ ❞❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❞❡✈✐❞♦ ❛ r❡❞✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ s✐♥❝r♦♥✐❛

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Pr♦t♦❝♦❧♦ ❚❛①❛ ✭▼❜✐t✴s✮ ❚❛①❛ ✭▼❜✴s✮

❆❚❆ ✸✸ ✭❯❧tr❛ ❉▼❆✮ ✷✻✹ ✸✸

❆❚❆ ✻✻ ✭❯❧tr❛ ❉▼❆✮ ✺✷✽ ✻✻

❆❚❆ ✶✵✵ ✭❯❧tr❛ ❉▼❆✮ ✽✵✵ ✶✵✵

❆❚❆ ✶✸✸ ✭❯❧tr❛ ❉▼❆✮ ✶✵✻✹ ✶✸✸

❙❡r✐❛❧ ❆❚❆ ✭❙❆❚❆✲✶✺✵✮ ✶✷✵✵ ✶✺✵

❙❡r✐❛❧ ❆❚❆ ✷ ✭❙❆❚❆✲✸✵✵✮ ✷✹✵✵ ✸✵✵

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❙❡r✐❛❧

Pr♦t♦❝♦❧♦ ❚■❆ ❘❙✷✸✷

✳

■♥t❡r❢❛❝❡ ❇❡t✇❡❡♥ ❉❛t❛ ❚❡r♠✐♥❛❧ ❊q✉✐♣♠❡♥t ❛♥❞ ❉❛t❛

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❼ ❈♦♠✉♥✐❝❛çã♦ s❡r✐❛❧ ✷✸✷

❼ ✶✾✻✷ ✲ ❘❡❝♦♠♠❡♥❞❡❞ ❙t❛♥❞❛r❞ ✷✸✷ ❼ ✶✾✻✾ ✲ ❘❡❝♦♠♠❡♥❞❡❞ ❙t❛♥❞❛r❞ ✷✸✷ r❡✈✳ ❈ ❼ ✶✾✽✻ ✲ ❊■❆ ✷✸✷ r❡✈ ❈

❼ ✶✾✾✼ ✲ ❚■❆ ✷✸✷ r❡✈ ❋

❼ Pr♦❝❡❞✐♠❡♥t♦ ❞❡ ❡♥✈✐♦

❼ ❯♠ ❜✐t ❞❡ ♠❛r❝❛çã♦ ❞❡ ✐♥✐❝✐♦ ❞❡ ♠❡♥s❛❣❡♠ ❼ ❖s ✽ ❜✐ts ❞❡ ❞❛❞♦s✷

❼ ❯♠ ❜✐t ❞❡ ♠❛❝❛çã♦ ❞❡ ✜♠ ❞❡ ♠❡♥s❛❣❡♠ ❼ ❯♠ ❜✐t ❞❡ ♣❛r✐❞❛❞❡ ✭♦♣❝✐♦♥❛❧✮

✷_{Pr✐♠❡✐r♦ ♦ ♠❡♥♦s s✐❣♥✐✜❝❛t✐✈♦✳ ❆❧❣✉♥s s✐st❡♠❛s ♠❛✐s ❛♥t✐❣♦s ♦♣❡r❛♠ ❝♦♠}

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❈♦♠✉♥✐❝❛çã♦ ❙❡r✐❛❧

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❼ P❛r❛ ❞♦✐s ❞✐s♣♦s✐t✐✈♦s s❡ ❝♦♠✉♥✐❝❛r❡♠ é ♥❡❝❡ssár✐♦ ❝♦♠♣❛t✐❜✐❧✐③❛r ♦ s✐st❡♠❛ ❢ís✐❝♦ ❡ ♦ s✐st❡♠❛ ❧ó❣✐❝♦✳

❼ ❋ís✐❝♦ ✭❍❛r❞✇❛r❡✮

❼ ❚✐♣♦ ❞❡ ❝♦♥❡❝t♦r ❼ P✐♥❛❣❡♠ ❞♦ ❝♦♥❡❝t♦r ❼ ◆í✈❡✐s ❞❡ t❡♥sã♦

❼ ▲ó❣✐❝♦ ✭❙♦❢t✇❛r❡✮

❼ ❈♦❞✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛ ❼ ❚❛♠❛♥❤♦ ❞❛ ♣❛❧❛✈r❛ ❼ ❚❛♠❛♥❤♦ ❞♦ st♦♣✴st❛rt ❜✐ts ❼ ❇✐t ❞❡ ♣❛r✐❞❛❞❡

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❈♦♠✉♥✐❝❛çã♦ ❙❡r✐❛❧

❼ ❆ ❝♦♥✜❣✉r❛çã♦ ❞❛ ❝♦♠✉♥✐❝❛çã♦ s❡r✐❛❧ é ❢❡✐t❛ ✸ _{❛tr❛✈és ❞❡ ✺}

r❡❣✐str♦s✳

❼ ❚❳❙❚❆ ❡ ❘❈❙❚❆ ✿ ❝♦♥✜❣✉r❛ ♦ ♠❡✐♦ ❞❡ tr❛♥s♠✐ssã♦ ❼ ❇❆❯❉❈❖◆ ✿ ❝♦♥tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡

❼ ❙P❇❘●❍ ❡ ❙P❇❘● ✿ ❝♦♥✜❣✉r❛çã♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡

✸_{P❛r❛ ♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r P■❈✶✽❋✹✺✺✵✳ ❖✉tr♦s ♠✐❝r♦❝♦♥tr♦❧❛❞♦r❡s ♣♦ss✉❡♠}

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❇✐ts ❞❡ ❈♦♥✜❣✉r❛çã♦ Pr❡❝✐sã♦ ❚❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❚①st❛✿✹ ❇❛✉❞❝♦♥✿✸ ❚①st❛✿✷

✵ ✵ ✵ ✽❜✐ts ❋✷✸✷= _[_✻✹ ❋❖❙❈

∗(♥+✶)]

✵ ✵ ✶ ✽❜✐ts _❋

✷✸✷ = _[_✶✻ ❋❖❙❈ ∗(♥+✶)]

✵ ✶ ✵ ✶✻❜✐ts

✵ ✶ ✶ ✶✻❜✐ts

❋✷✸✷= _[_✹ ❋❖❙❈ ∗(♥+✶)]

✶ ✵ ① ✽❜✐ts

✶ ✶ ① ✶✻❜✐ts

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❈♦♠✉♥✐❝❛çã♦ ❙❡r✐❛❧

❊①❡♠♣❧♦✿ ❈♦♥✜❣✉r❛r ♣❛r❛ ✉♠❛ t❛①❛ ❞❡ tr❛♥s♠✐ssã♦ ❞❡ ✺✼✱✻ ❦❜♣s✳ ❆ ❢r❡q✉ê♥❝✐❛ ❞❡ ♦s❝✐❧❛çã♦ é ✉♠ ❝r✐st❛❧ ❞❡ ✽▼❍③✳ ❯s❛♥❞♦ ❛s três ❢♦r♠✉❧❛s✿

❼ ♥✶ ❂ ✶❀ ❋✷✸✷ ❂ ✻✷✳✺✵✵✱ ❡rr ❂ ✲✼✱✻✹✪

❼ ♥✷ ❂ ✽✱ ❋✷✸✷ ❂ ✺✺✳✺✺✺✱ ❡rr ❂ ✸✱✻✸✪

❼ ♥✸ ❂ ✸✷✱ ❋✷✸✷ ❂ ✺✼✳✶✹✷✱ ❡rr ❂ ✵✱✼✾✪

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✶ ❇✐t❈❧r✭❇❆❯❉❈❖◆✱✵✮❀ ✴✴❉❡s❛❜✐❧✐t❛ ❛✉t♦ ❞❡t❡❝çã♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ✷ ❇✐t❙❡t✭❇❆❯❉❈❖◆✱✸✮❀ ✴✴❘❡❣✐str♦ ❞❡ ❣❡r❛çã♦ ❞❡ s✐♥❛❧ ❝♦♠ ✶✻ ❜✐ts ✸ ❇✐t❈❧r✭❇❆❯❉❈❖◆✱✻✮❀ ✴✴❖♣❡r❛çã♦ ❞❡ r❡❝❡♣çã♦ ❡st❛ ❛t✐✈❛

✹ ❇✐t❈❧r✭❘❈❙❚❆✱✶✮❀ ✴✴❉❡s❛❜✐❧✐t❛ ❜✐t ❞❡ ❡rr♦ ❞❡ ♦✈❡rr✉♥ ✺ ❇✐t❈❧r✭❘❈❙❚❆✱✷✮❀ ✴✴❉❡s❛❜✐❧✐t❛ ❜✐t ❡rr♦ ♥❛ ❝♦♠✉♥✐❝❛çã♦ ✻ ❇✐t❈❧r✭❘❈❙❚❆✱✹✮❀ ✴✴❍❛❜✐❧✐t❛ ❜✐t ❞❡ r❡❝❡♣çã♦

✼ ❇✐t❈❧r✭❘❈❙❚❆✱✻✮❀ ✴✴❙❡❧❡❝✐♦♥❛ ✽ ❜✐ts

✽ ❇✐t❙❡t✭❘❈❙❚❆✱✼✮❀ ✴✴❈♦♥❢✐❣✉r❛ ❘❳✴❚❳ ❝♦♠♦ ♣✐♥♦s ❞❡ ❝♦♠✉♥✐❝❛çã♦ ✾ ❇✐t❙❡t✭❚❳❙❚❆✱✷✮❀ ✴✴▼♦❞♦ ❞❡ ❛❧t❛ ✈❡❧♦❝✐❞❛❞❡ ❤❛❜✐❧✐t❛❞♦ ✶✵ ❇✐t❙❡t✭❚❳❙❚❆✱✸✮❀ ✴✴❊♥✈✐❛ ❜✐t ❞❡ ♣❛r❛❞❛ ✭❜r❡❛❦ ❝❤❛r❛❝t❡r ❜✐t✮ ✶✶ ❇✐t❈❧r✭❚❳❙❚❆✱✹✮❀ ✴✴▼♦❞♦ ❛ssí♥❝r♦♥♦

✶✷ ❇✐t❙❡t✭❚❳❙❚❆✱✺✮❀ ✴✴❍❛❜✐❧✐t❛ tr❛♥s♠✐ssã♦ ✶✸ ❇✐t❈❧r✭❚❳❙❚❆✱✻✮❀ ✴✴❙❡❧❡❝✐♦♥❛ ✽ ❜✐ts

(19)

❙❡r✐❛❧

(20)

✸ ✈♦✐❞ ❊♥✈✐❛❙❡r✐❛❧✭✉♥s✐❣♥❡❞ ❝❤❛r ❝✮ ④

✹ ✇❤✐❧❡✭✦❇✐t❚st✭P■❘✶✱✹✮✮❀ ✴✴❛❣✉❛r❞❛ ♦ r❡❣✐str♦ ❢✐❝❛r ❞✐s♣♦♥í✈❡❧ ✺ ❚❳❘❊●❂❝❀ ✴✴❝♦❧♦❝❛ ♦ ✈❛❧♦r ♣❛r❛ s❡r ❡♥✈✐❛❞♦ ✻ ⑥

✼ ✉♥s✐❣♥❡❞ ❝❤❛r❘❡❝❡❜❡❙❡r✐❛❧✭✈♦✐❞✮ ④

✽ ✐❢ ✭❇✐t❚st✭P■❘✶✱✺✮✮ ✴✴❱❡r✐❢✐❝❛ s❡ ❡①✐st❡ ❛❧❣✉♠ ✈❛❧♦r ❞✐s♣♦♥✐✈❡❧

✾ ④

✶✵ r❡t✉r♥ ❘❈❘❊●❀ ✴✴r❡t♦r♥❛ ♦ ✈❛❧♦r

✶✶ ⑥

✶✷ r❡t✉r♥ ✵❀ ✴✴❝♦♥❞✐çã♦ ❞❡ ❡rr♦ ✶✸ ⑥

✶✹ ✈♦✐❞ ■♥✐❝✐❛❧✐③❛❙❡r✐❛❧✭✈♦✐❞✮④

✶✺ ❚❳❙❚❆ ❂ ✵❜✵✵✶✵✶✶✵✵❀ ✴✴❝♦♥❢✐❣✉r❛ ❛ tr❛♥s♠✐ssã♦ ❞❡ ❞❛❞♦s ❞❛ s❡r✐❛❧ ✶✻ ❘❈❙❚❆ ❂ ✵❜✶✵✵✶✵✵✵✵❀ ✴✴❝♦♥❢✐❣✉r❛ ❛ r❡❝❡♣çã♦ ❞❡ ❞❛❞♦s ❞❛ s❡r✐❛❧ ✶✼ ❇❆❯❉❈❖◆ ❂ ✵❜✵✵✵✵✶✵✵✵❀ ✴✴❝♦♥❢✐❣✉r❛ s✐st❡♠❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞❛ s❡r✐❛❧ ✶✽ ❙P❇❘●❍ ❂ ✵❜✵✵✵✵✵✵✵✵❀ ✴✴❝♦♥❢✐❣✉r❛ ♣❛r❛ ✺✻❦

(21)

❙❡r✐❛❧

✶ ★✐❢♥❞❡❢ ❙❊❘■❆▲❴❍ ✷ ★❞❡❢✐♥❡ ❙❊❘■❆▲❴❍

(22)

✹ ✈♦✐❞ ♠❛✐♥✭✈♦✐❞✮ ✐♥t❡rr✉♣t ✵④ ✺ ✉♥s✐❣♥❡❞ ✐♥t ✐✱❥❂✵❀

✻ ❝❤❛r ♠s❣❬❪ ❂ ✧❍❡❧❧♦ ❲♦r❧❞✦✧❀ ✼ ✉♥s✐❣♥❡❞ ❝❤❛r r❡s♣❀

✽ ❚❘■❙❉ ❂ ✵①✵✵❀ ✴✴❛❝❡ss♦ ❛♦s ❧❡❞s

✾ ■♥✐❝✐❛❧✐③❛❙❡r✐❛❧✭✮❀ ✶✵ ❢♦r✭❀❀✮④

✶✶ ❢♦r✭✐ ❂ ✵❀ ✐ ❁ ✻✺✵✵✵❀ ✐✰✰✮❀ ✴✴❞❡❧❛② ✶✷ ❊♥✈✐❛❙❡r✐❛❧✭♠s❣❬❥❪✮❀ ✴✴❡♥✈✐❛ ❞❛❞♦s

✶✸ ❥✰✰❀

✶✹ ✐❢ ✭❥ ❃ ✶✶✮④ ✶✺ ❥❂✵❀

✶✻ ❊♥✈✐❛❙❡r✐❛❧✭✶✸✮❀ ✴✴❡♥✈✐❛ q✉❡❜r❛ ❞❡ ❧✐♥❤❛

✶✼ ⑥

✶✽ r❡s♣ ❂ ❘❡❝❡❜❡❙❡r✐❛❧✭✮❀ ✴✴r❡❝❡❜❡ ❞❛❞♦s ✶✾ ✐❢ ✭r❡s♣✦❂✵✮④

✷✵ P❖❘❚❉ ❂ r❡s♣❀

✷✶ ⑥

✷✷ ⑥

(23)

❈♦♥✈❡rs♦r ❆❉

(24)

P♦t❡♥❝✐ô♠❡tr♦ ❝♦♠♦ ❞✐✈✐s♦r ❞❡ t❡♥sã♦

❤tt♣✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴❋✐❧❡✿P♦t❡♥t✐♦♠❡t❡r❴✇✐t❤❴❧♦❛❞✳♣♥❣

❱❘▲ = _❘❱❙∗❘✷

✶+❘✷ =❱❙ ∗(

❘✷

(25)

❈♦♥✈❡rs♦r ❆❉

❙❡♥s♦r ❞❡ t❡♠♣❡r❛t✉r❛ ✭❛t✐✈♦✮

❈✐r❝✉✐t♦ ✐♥t❡❣r❛❞♦ ▲▼✸✺

❱❙ =❚ ∗✵.✺(

♠❱

(26)

❼ ❯t✐❧✐③❛çã♦ ❞❡ ❝♦♠♣❛r❛❞♦r❡s ❞❡ t❡♥sã♦

❼ ❉✐s❝r❡t✐③❛çã♦ ❞♦ s✐♥❛❧

❈♦♥✈❡rs♦r ❛♥❛❧ó❣✐❝♦ ❞✐❣✐t❛❧ ❞❡ ✷ ❜✐ts

(27)

❈♦♥✈❡rs♦r ❆❉

(28)

❚♦❞❛ ❝♦♥✈❡rsã♦ ❆❉ ❡①✐❣❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ t❡♠♣♦✳ P❛r❛ q✉❡ ♦ ♠✐❝r♦❝♦♥tr♦❧❛❞♦r r❡❛❧✐③❡ ❝♦rr❡t❛♠❡♥t❡ ❛ ❝♦♥✈❡rsã♦ é ♥❡❝❡ssár✐♦ s❡❣✉✐r ♦s s❡❣✉✐♥t❡s ♣❛ss♦s✿

✶ ❈♦♥✜❣✉r❛r ♦ ❝♦♥✈❡rs♦r

✷ ■♥✐❝✐❛r ❛ ❝♦♥✈❡rsã♦

✸ ▼♦♥✐t♦r❛r ♦ ✜♥❛❧ ❞❛ ❝♦♥✈❡rsã♦

(29)

❈♦♥✈❡rs♦r ❆❉

✶ ★✐♥❝❧✉❞❡ ✧❛❞❝✳❤✧ ✷ ★✐♥❝❧✉❞❡ ✧❜❛s✐❝♦✳❤✧ ✸ ✈♦✐❞ ■♥✐❝✐❛❧✐③❛❆❉✭✈♦✐❞✮

✹ ④

✺ ❇✐t❙❡t✭❚❘■❙❆✱✵✮❀ ✴✴s❡t❛ ♦ ❜✐t ✵ ❝♦♠♦ ❡♥tr❛❞❛ ✻ ❆❉❈❖◆✵ ❂ ✵❜✵✵✵✵✵✵✵✶❀ ✴✴s❡❧❡❝✐♦♥❛ ♦ ❝❛♥❛❧ ✵ ❡ ❧✐❣❛ ♦ ❆❉

✼ ❆❉❈❖◆✶ ❂ ✵❜✵✵✵✵✶✶✶✵❀ ✴✴só ❆◆✵ é ❛♥❛❧ó❣✐❝♦✱ r❡❢❡r❡♥❝✐❛ ❜❛s❡❛❞❛ ♥❛ ❢♦♥t❡ ✽ ❆❉❈❖◆✷ ❂ ✵❜✶✵✶✵✶✵✶✵❀ ✴✴❋❖❙❈✴✸✷✱ ❆❧✐♥❤❛♠❡♥t♦ à ❞✐r❡✐t❛ ❡ t❴❝♦♥✈ ❂ ✶✷ ❚❆❉ ✾ ⑥

✶✵

✶✶ ✐♥t ▲❡❱❛❧♦r❆❉✭✈♦✐❞✮ ✶✷ ④

✶✸ ✉♥s✐❣♥❡❞ ✐♥t ❆❉✈❛❧♦r❀

✶✹ ❇✐t❙❡t✭❆❉❈❖◆✵✱✶✮❀ ✴✴✐♥✐❝✐❛ ❝♦♥✈❡rsã♦

✶✺ ✇❤✐❧❡✭❇✐t❚st✭❆❉❈❖◆✵✱✶✮✮❀ ✴✴ ❡s♣❡r❛ t❡r♠✐♥❛r ❛ ❝♦♥✈❡rsã♦❀ ✶✻ ❆❉✈❛❧♦r ❂ ❆❉❘❊❙❍❀ ✴✴ ❧ê ♦ r❡s✉❧t❛❞♦

(30)

✶ ★✐❢♥❞❡❢ ❆❉❈❴❍ ✷ ★❞❡❢✐♥❡ ❆❉❈❴❍

(31)

❈♦♥✈❡rs♦r ❆❉

✶ ★✐♥❝❧✉❞❡ ✧❜❛s✐❝♦✳❤✧

✷ ★✐♥❝❧✉❞❡ ✧❝♦♥❢✐❣✳❤✧ ✸ ★✐♥❝❧✉❞❡ ✧❞✐s♣✼s❡❣✳❤✧

✹ ★✐♥❝❧✉❞❡ ✧❛❞❝✳❤✧

✺ ✈♦✐❞ ♠❛✐♥✭✈♦✐❞✮ ✐♥t❡rr✉♣t ✵ ④ ✻ ✉♥s✐❣♥❡❞ ✐♥t ✐❀

✼ ✐♥t t❡♠♣ ❂ ✵❀

✽ ■♥✐❝✐❛❧✐③❛❉✐s♣❧❛②s✭✮❀

✾ ■♥✐❝✐❛❧✐③❛❆❉✭✮❀ ✶✵ ❢♦r✭❀❀✮ ④

✶✶ t❡♠♣ ❂ ▲❡❱❛❧♦r❆❉✭✮❀ ✶✷ t❡♠♣ ✪❂ ✶✵✵✵✵❀

✶✸ ▼✉❞❛❉✐❣✐t♦✭t❡♠♣ ✴ ✶✵✵✵✱✸✮❀

✶✹ t❡♠♣ ✪❂ ✶✵✵✵❀

✶✺ ▼✉❞❛❉✐❣✐t♦✭t❡♠♣ ✴ ✶✵✵ ✱✷✮❀ ✶✻ t❡♠♣ ✪❂ ✶✵✵❀

✶✼ ▼✉❞❛❉✐❣✐t♦✭t❡♠♣ ✴ ✶✵ ✱✶✮❀ ✶✽ t❡♠♣ ✪❂ ✶✵❀

✶✾ ▼✉❞❛❉✐❣✐t♦✭t❡♠♣ ✱✵✮❀ ✷✵ ❆t✉❛❧✐③❛❉✐s♣❧❛②✭✮❀

✷✶ ❢♦r✭✐ ❂ ✵❀ ✐ ❁ ✶✵✵✵❀ ✐✰✰✮❀

✷✷ ⑥

(32)

(33)

❈♦♥✈❡rs♦r ❆❉

(34)

❼ ❱❛♥t❛❣❡♥s

❼ ▼❛✐s ❜❛r❛t♦ q✉❡ ✉♠❛ s❛í❞❛ ❛♥❛❧ó❣✐❝❛

❼ P♦❞❡ s❡r tr❛♥s❢♦r♠❛❞♦ ♥✉♠❛ s❛í❞❛ ❛♥❛❧ó❣✐❝❛ ❛tr❛✈és ❞❡ ✉♠ ✜❧tr♦ ♣❛ss❛ ❜❛✐①❛

❼ P❛r❛ ❛❧❣✉♠❛s s✐t✉❛çõ❡s ♦ ✜❧tr♦ ♥ã♦ é ♥❡❝❡ssár✐♦✹

❼ ❉❡s✈❛♥t❛❣❡♥s

❼ ◆ã♦ é ✉♠❛ s❛í❞❛ ❛♥❛❧ó❣✐❝❛

✹_{◗✉❛♥❞♦ ♦ ❞✐s♣♦s✐t✐✈♦ ❛ s❡r ❝♦♥tr♦❧❛❞♦ ❥á ♣♦ss✉✐ ✉♠ ✜❧tr♦ ♣❛ss❛ ❜❛✐①❛✱}

(35)

❈♦♥✈❡rs♦r ❆❉

❼ ❋r❡q✉ê♥❝✐❛ ❞♦ P❲▼

❼ ❉❡♣❡♥❞❡ ❞♦ ❝✐r❝✉✐t♦ q✉❡ ✐♠♣❧❡♠❡♥t❛ ♦ P❲▼

❼ ◗✉❛♥t♦ ♠❛✐s ❛❧t❛ ♠❡❧❤♦r ♣❛r❛ s✐♠✉❧❛r ✉♠❛ s❛í❞❛ ❛♥❛❧ó❣✐❝❛ ❼ P♦❞❡ s❡r ✉t✐❧✐③❛❞❛ ♣❛r❛ s✐♥❛❧✐③❛çã♦ s♦♥♦r❛

❼ ❈á❧❝✉❧♦✿

❋r❡q✉❡♥❝✐❛_P❲▼ = ❋❖❙❈

[(P❘✷) +✶]∗✹∗(❚▼❘✷Pr❡s❝❛❧❡r)

(36)

❼ Pr♦❜❧❡♠❛s ❝♦♠ ❢r❡q✉ê♥❝✐❛s ♠✉✐t♦ ❛❧t❛s✿ P❡r❞❛ ❞❡ r❡s♦❧✉çã♦

❘❡s♦❧✉çã♦P❲▼(♠❛①) =

❧♦❣(❋❖❙❈

❋P❲▼)

❧♦❣(✷) ❜✐ts

❼ P❛r❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ✷▼❍③ ✺ _{❛ r❡s♦❧✉çã♦ é ❞❡ ✷ ❜✐ts✱ ♦✉ s❡❥❛✱}

♣♦❞❡♠♦s ❝♦♥✜❣✉r❛r ♦ ❞✉t② ❝②❝❧❡ ❛♣❡♥❛s ♣❛r❛ ✶✷✳✺✪✱ ✸✼✳✺✪✱ ✻✷✳✺✪ ♦✉ ✽✼✳✺✪ ❞♦ ✈❛❧♦r✳

(37)

❈♦♥✈❡rs♦r ❆❉

❼ ❈♦♥❤❡❝❡♥❞♦ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❜✐ts ❞❡ r❡s♦❧✉çã♦ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ❛ ❢r❡q✉ê♥❝✐❛ ❡s❝♦❧❤✐❞❛ ♣♦❞❡♠♦s ❛❥✉st❛r ♦ ❞✉t②✲❝②❝❧❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❡①♣r❡ssã♦ ❛❜❛✐①♦✿

❉✉t②❈②❝❧❡_P❲▼ = [❈❈P❘①▲:❈❈P①❈❖◆(✺:✹)] (P❘✷ +✶)∗✹

❼ ❖ ✈❛❧♦r ❞❡✈❡ s❡r ❡♥t❡♥❞✐❞♦ ❝♦♠♦ ♣♦r❝❡♥t❛❣❡♠ ❞♦ t❡♠♣♦✱ ♦♥❞❡ ✶✵✷✹ ❂ ✶✵✵✪✻

✻_{◆❛ r❡❛❧✐❞❛❞❡ ✶✵✷✹❂✾✾✱✾✺✪✱ ❞❡✈✐❞♦ ❛♦s ❡❢❡✐t♦s ❞❡ ❞✐s❝r❡t✐③❛çã♦ ❞♦ ❝✐r❝✉✐t♦}

(38)

(39)

❈♦♥✈❡rs♦r ❆❉

P❛r❛ ❝♦♥✜❣✉r❛r ❛s s❛í❞❛s P❲▼ ❞❡✈❡♠♦s ❡s♣❡❝✐✜❝❛r✿

✶ ❋r❡q✉ê♥❝✐❛ ❞❡ tr❛❜❛❧❤♦ ❛tr❛✈és ❞❡ P❘✷✼ ❡ ❚❈❖◆✷

✷ ❉✉t② ❝②❝❧❡ ❡♠ ❈❈P❘✶▲ ❡ ❈❈P❘✷▲

✸ ❈♦♥✜❣✉r❛r ❝♦♠♦ s❛í❞❛ ❡♠ ❚❘■❙❈

✹ ❈♦♥✜❣✉r❛r ❛ s❛í❞❛ ❝♦♠♦ P❲▼ ❡♠ ❈❈P✶❈❖◆ ❡ ❈❈P✷❈❖◆

✼_{❖ ♣r❡s❝❛❧❡r ❢♦✐ ❝♦♥✜❣✉r❛❞♦ ♣❛r❛ ✶✻ ❜✐ts ❞❡ ♠♦❞♦ ❛ ♦❜t❡r ❛ ♠❛✐♦r ❢❛✐①❛ ❞❡}

(40)

✸

✹ ✈♦✐❞ ❙❡t❛P❲▼✶✭✉♥s✐❣♥❡❞ ❝❤❛r ♣♦r❝❡♥t♦✮④ ✺

✻ ✴✴❢♦r♠✉❧❛ ❞♦ ❞✉t② ❝②❝❧❡✿ ✼ ✴✴❉❈❴♣♦r❝❡♥t♦ ❂ ❱ ✴ ✭✭P❘✷✰✶✮✯✹❀

✽ ✴✴❱ ❂ ❉❈✴✶✵✵ ✯ ✭P❘✷✰✶✮ ✯ ✹ ❂ ❉❈ ✯ ✭P❘✷✰✶✮ ✴✷✺ ✾

✶✵ ✉♥s✐❣♥❡❞ ✐♥t ✈❛❧ ❂ ✭✭✉♥s✐❣♥❡❞ ✐♥t✮♣♦r❝❡♥t♦✮ ✯✭P❘✷✰✶✮❀ ✶✶ ✈❛❧ ❂ ✈❛❧ ✴ ✷✺❀

✶✷

✶✸ ✴✴❣❛r❛♥t❡ q✉❡ t❡♠ ❛♣❡♥❛s ✶✵ ❜✐ts ✶✹ ✈❛❧ ✫❂ ✵①✵✸❢❢❀

✶✺

✶✻ ✴✴♦s ✽ ♣r✐♠❡✐r♦s ❜✐ts sã♦ ❝♦❧♦❝❛❞♦s ♥♦ ❈❈P❘✶▲ ✶✼ ❈❈P❘✶▲ ❂ ✈❛❧ ❃❃ ✷❀

✶✽

✶✾ ✴✴♦s ú❧t✐♠♦s ❞♦✐s sã♦ ❝♦❧♦❝❛❞♦s ♥❛ ♣♦s✐çã♦ ✺ ❡ ✹ ❞♦ ❈❈P✶❈❖◆ ✷✵ ❈❈P✶❈❖◆ ⑤❂ ✭✈❛❧ ✫ ✵①✵✵✵✸✮ ❁❁ ✹❀

(41)

❈♦♥✈❡rs♦r ❆❉

✶ ✈♦✐❞ ❙❡t❛P❲▼✷✭✉♥s✐❣♥❡❞ ❝❤❛r ♣♦r❝❡♥t♦✮

✷ ④

✸ ✉♥s✐❣♥❡❞ ✐♥t ✈❛❧ ❂ ♣♦r❝❡♥t♦ ✯ P❘✷❀ ✹ ✈❛❧ ✴❂ ✷✺❀

✺ ✈❛❧ ✫❂ ✵①✵✸❢❢❀

✻ ❈❈P❘✷▲ ❂ ✈❛❧ ❃❃ ✷❀

✼ ❈❈P✷❈❖◆ ⑤❂ ✭✈❛❧ ✫ ✵①✵✵✵✸✮ ❁❁ ✹❀ ✽ ⑥

✾ ✈♦✐❞ ❙❡t❛❋r❡qP❲▼✭✉♥s✐❣♥❡❞ ✐♥t ❢r❡q✮ ✶✵ ④

✶✶ ✴✴P❘✷ ❂ ❢♦s❝✴✭❢♣✇♠✯✹✯♣r❡s❝❛❧❡r✮✲✶ ❂ ✭✽✵✵✵✵✵✵✴✭❢r❡q✯✹✯✶✻✮✮ ✲ ✶ ✶✷ P❘✷ ❂ ✭✶✷✺✵✵✵✴✭❢r❡q✮✮ ④⑥✲ ✶❀

✶✸ ⑥

✶✹ ✈♦✐❞ ■♥✐❝✐❛❧✐③❛P❲▼✭✈♦✐❞✮ ✶✺ ④

✶✻ ❇✐t❈❧r✭❚❘■❙❈✱✷✮❀ ✴✴❝♦♥❢✐❣✉r❛ ♦s ♣✐♥♦s ❝♦♠♦ s❛í❞❛s ✶✼ ❇✐t❈❧r✭❚❘■❙❈✱✸✮❀

✶✽ ❚✷❈❖◆ ⑤❂ ✵❜✵✵✵✵✵✵✶✶❀ ✴✴❝♦♥❢✐❣✉r❛ ♦ ♣r❡s❝❛❧❡ ❞♦ t✐♠❡r ✷ ♣❛r❛ ✶✿✶✻ ✶✾ ❇✐t❙❡t✭❚✷❈❖◆✱✷✮❀ ✴✴▲✐❣❛ ♦ t✐♠❡r ✷

(42)

✶ ★✐❢♥❞❡❢ P❲▼❴❍ ✷ ★❞❡❢✐♥❡ P❲▼❴❍

✸ ✈♦✐❞ ❙❡t❛P❲▼✶✭✉♥s✐❣♥❡❞ ❝❤❛r ♣♦r❝❡♥t♦✮❀ ✹ ✈♦✐❞ ❙❡t❛P❲▼✷✭✉♥s✐❣♥❡❞ ❝❤❛r ♣♦r❝❡♥t♦✮❀ ✺ ✈♦✐❞ ❙❡t❛❋r❡qP❲▼✭✉♥s✐❣♥❡❞ ✐♥t ❢r❡q✮❀ ✻ ✈♦✐❞ ■♥✐❝✐❛❧✐③❛P❲▼✭✈♦✐❞✮❀

(43)

❈♦♥✈❡rs♦r ❆❉

✶ ★✐♥❝❧✉❞❡ ✧❝♦♥❢✐❣✳❤✧

✷ ★✐♥❝❧✉❞❡ ✧❜❛s✐❝♦✳❤✧ ✸ ★✐♥❝❧✉❞❡ ✧♣✇♠✳❤✧ ✹ ★✐♥❝❧✉❞❡ ✧❛❞❝✳❤✧ ✺ ✴✴✐♥✐❝✐♦ ❞♦ ♣r♦❣r❛♠❛ ✻ ✈♦✐❞ ♠❛✐♥✭✈♦✐❞✮ ✐♥t❡rr✉♣t ✵ ✼ ④

✽ ✐♥t t❡♠♣❀ ✾ ■♥✐❝✐❛❧✐③❛P❲▼✭✮❀ ✶✵ ■♥✐❝✐❛❧✐③❛❆❉✭✮❀ ✶✶ ❢♦r✭❀❀✮ ④

✶✷ t❡♠♣ ❂ ▲❡❱❛❧♦r❆❉✭✮❀

✶✸ ✴✴❛❥✉st❛♥❞♦ ❛ ❢r❡q✉ê♥❝✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❡♥tr❛❞❛ ❛♥❛❧ó❣✐❝❛ ✶✹ ❙❡t❛❋r❡qP❲▼✭t❡♠♣✮❀

✶✺ ✴✴❛❥✉st❛♥❞♦ ♦ ❞✉t②✲❝②❝❧❡ ♣❛r❛ ✺✵✪ ✶✻ ❙❡t❛P❲▼✶✭✺✵✮❀

✶✼ ⑥