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❋❖❙❉❊▼ ✷✵✶✺ ❙♦❢t✇❛r❡ ❉❡✜♥❡❞ ❘❛❞✐♦ ❞❡✈r♦♦♠ ❆r✐t❤♠❡t✐❝ ❜❛s❡❞ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ♦❢ ❛ q✉❛❞r❛t✉r❡ ❋▼ ❉❡♠♦❞✉❧❛t♦r ❙❉❘ ✐♥ ●♥✉❘❛❞✐♦ ❉❡♥✐s ❇❡❞❡r♦✈ ✭❉▲✸❖❈❑✮

❖✈❡r✈✐❡✇ ❖✈❡r✇✐❡✇✿ ✶✳ ❇❛❝❦❣r♦✉♥❞ ♦❢ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ ✷✳ ❚r❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✸✳ ❆r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✹✳ Pr❡s❡♥t❛t✐♦♥ ♦❢ r❡s✉❧ts ✺✳ ❇✉❣ ✜①✐♥❣ ✐♥ ❢❛st ❛t❛♥ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✶

✶✳ ❇❛❝❦❣r♦✉♥❞ ♦❢ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ ●❡♥❡r❛❧❧ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ ✐♥ r❡❛❧ ✇♦r❧❞ ✭❘❋✮ ❢r❡q✉❡♥❝② ♦❢ ❝❛rr✐❡r✱ ♦♥ ✇❤✐❝❤ t❤❡ ♠♦❞✉❧❛t❡❞ s✐❣♥❛❧ ω c ✐s tr❛♥s♠✐t❡❞ ✐♥ t❤❡ r❡❛❧ ✇♦r❧❞ f ( t ) ∈ R ❧♦✇ ❢r❡q✉❡♥❝② ♠♦❞✉❧❛t✐♥❣ s✐❣♥❛❧ y ( t ) ∈ R r❡❛❧ s✐❣♥❛❧ tr❛♥s♠✐t❡❞ ❜② ω c ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✷

✶✳ ❇❛❝❦❣r♦✉♥❞ ♦❢ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ ❘❡❝❡✐✈✐♥❣ ♦❢ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ y T ( t ) ∈ C tr❛♥s♠✐t❡❞ s✐❣♥❛❧ ✐♥ ❧♦✇ ♣❛ss ❛r❡❛ y T ( t ) = y TR ( t ) + j · y TI ( t ) ✭✶✮ � �� � � �� � I Q ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✸

✶✳ ❇❛❝❦❣r♦✉♥❞ ♦❢ ❛♥❣❧❡ ♠♦❞✉❧❛t✐♦♥ ❋♦r♠❛❧ ❞❡✜♥✐t✐♦♥ ♦❢ ❆♥❣❧❡ ♠♦❞✉❧❛t✐♦♥   y ( t ) = A · cos  Φ( t ) ✭✷✮  PM : Φ( t ) = ϕ 0 + α · f ( t ) ✭✸✮ Ω( t ) = d Φ( t ) = ˙ FM : Φ = ω 0 + α · f ( t ) ✭✹✮ dt   t � y ( t ) = A · cos  ω 0 t + α · f ( τ ) dτ + ϕ 0 ✭✺✮  −∞ � � t � j ∆ ωt + α · f ( τ ) dτ + ϕ 0 y T ( t ) = A · e ✭✻✮ −∞ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✹

✷✳ ❚r❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛ tr❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■✮ ❇❛s✐❝ ✐❞❡❛ ✐s t❤❡ ♠✉❧t✐♣❧✐❝❛t✐♦♥ ♦❢ ❝✉rr❡♥t s❛♠♣❧❡ ✇✐t❤ ❝♦♥❥✉❣❛t❡ ❝♦♠✲ ♣❧❡① ✈❡rs✐♦♥ ♦❢ ♣r❡✈✐❡✇ s❛♠♣❧❡✳ y T ( nt s ) · y ∗ T (( n − 1) t s ) ✭✼✮ � � � � ( n − 1) ts nts � � ∆ ωt s n + α · f ( τ ) dτ + ϕ 0 ∆ ωt s ( n − 1)+ α · f ( τ ) dτ + ϕ 0 j − j = A · e −∞ A · e −∞ · � � nts � ∆ ωt s + α · f ( t ) dt j = A 2 · e ( n − 1) ts ✭✽✮ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✺

✷✳ ❚r❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛ tr❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■■✮ ❚❤❡ s♣❡❝✐✜❝ ✐♥t❡❣r❛❧ ❝❛♥ ❜❡ ❛♣♣r♦①✐♠❛t❡❞ ❜② s♠❛❧❧ ✈❛❧✉❡ ♦❢ t s ✐♥ ❢♦❧❧♦✇✐♥❣ ✇❛②✿ nt s � f ( t ) dt ≈ t s f ( nt s ) ( n − 1) t s ◆♦✇ ✇❡ ❝❛♥ s✐♠♣❧✐❢② ✭✽✮ � � � � ∆ ωt s + α · t s · f ( nt s ) 2 π ∆ ft s +2 π dev · t s · f ( nt s ) j j (8) = A 2 · e = A 2 · e ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✻

✷✳ ❚r❛❞✐t✐♦♥❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ◗✉❛❞r❛t✉r❡ ❋▼✲❉❡♠♦❞ ✐♥ ●♥✉❘❛❞✐♦ � � ( y T ( n ) · y ∗ out( n ) = Gain T ( n − 1) = ∆ f + dev · f ( nt s ) ✭✾✮ · arc � �� � 1 2 πts ✧❛r❝✧ ✐♠♣❧❡♠❡♥t❛t✐♦♥ ❝❛♥ ❜❡ ❜❛s❡❞ ♦♥ ❛r❝t❛♥✱ ❛r❝❝♦s✱ ❛r❝s✐♥ ❛♥❞ ♥❡❡❞s ♦❢t❡♥ ❤✐❣❤ ❝♦♠♣✉t❛t✐♦♥ ❡✛♦rt✳ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✼

✸✳ ❆r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛♥ ❛r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■✮ ❇❛s✐❝ ✐❞❡❛ ✐s t❤❡ ♠✉❧t✐♣❧✐❝❛t✐♦♥ ♦❢ ❞❡r✐✈❛t✐♦♥ s✐❣♥❛❧ ✇✐t❤ ✇✐t❤ ❝♦♥❥✉❣❛t❡ ❝♦♠♣❧❡① s✐❣♥❛❧✳ y T ( t ) · y ∗ ˙ T ( t ) ✭✶✵✮ � � t � � � ∆ ωt + α · f ( τ ) dτ + ϕ 0 j y T ( t ) = j · A · ˙ ∆ ω + α · f ( t ) · e −∞ � � t � ∆ ωt + α · f ( τ ) dτ + ϕ 0 − j y ∗ T ( t ) = A · e −∞ � � T ( t ) = j · A 2 y T ( t ) · y ∗ ˙ ∆ ω + α · f ( t ) ✭✶✶✮ ⇒ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✽

✸✳ ❆r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛♥ ❛r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■■✮ T ( t ) = ( i ′ + j · q ′ ) · ( i − j · q ) y T ( t ) · y ∗ ˙ � � + j · ( i · q ′ − i ′ · q ) ! = ( i ′ · i + q ′ · q ) = j · A 2 ∆ ω + α · f ( t ) � �� � =0 � � ( i · q ′ − i ′ · q ) = A 2 ∆ ω + α · f ( t ) ✭✶✷✮ ⇒ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✾

✸✳ ❆r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛♥ ❛r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■■■✮ ◆♦✇ ❧❡t ✉s ❛ss✉♠❡ t❤❛t i n := i ( nt s ) i n − 1 := i (( n − 1) t s ) q n := q ( nt s ) q n − 1 := q (( n − 1) t s ) ◆♦✇ ✇❡ ❝❛♥ ✇r✐t❡ t❤❡ ❧❡❢t s✐t❡ ♦❢ ✭✶✷✮ ❛s ❢♦❧❧♦✇ q n − q n − 1 − i n − i n − 1 i · q ′ − i ′ · q = i n q n t s t s 1 = ( i n q n − i n q n − 1 − i n q n + i n − 1 q n ) t s 1 = ( i n − 1 q n − i n q n − 1 ) ✭✶✸✮ t s ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✶✵

✸✳ ❆r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ▼❛t❤❡♠❛t✐❝❛❧ ❇❛❝❦❣r♦✉♥❞ ❢♦r ❛♥ ❛r✐t❤♠❡t✐❝❛❧ ❋▼✲❉❡♠♦❞✉❧❛t♦r ✭■❱✮ ◆♦✇ ✇❡ ♣✉t t❤❡ ✭✶✸✮ ✐♥t♦ ✭✶✷✮ ❛♥❞ ♦❜t❛✐♥✿ � � 1 ( i n − 1 q n − i n q n − 1 ) = A 2 ∆ ω + α · f ( nt s ) t s 1 ( i n − 1 q n − i n q n − 1 ) = ∆ f + dev · f ( nt s ) ✭✶✹✮ 2 πt s · ( i 2 n + q 2 n ) � �� � A 2 ◆♦✇ ✇❡ ❝❛♥ r❡✇r✐t❡ t❤✐s r❡s✉❧t s✐♠✐❧❛r ❧✐❦❡ ✭✾✮ · i n − 1 q n − i n q n − 1 out( n ) = Gain = ∆ f + dev · f ( nt s ) ✭✶✺✮ i 2 n + q 2 � �� � n 1 2 πts ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✶✶

✹✳ Pr❡s❡♥t❛t✐♦♥ ♦❢ r❡s✉❧ts ◆♦✇ ❜♦t❤ ❉❡♠♦❞✉❧❛t♦rs ✐♥ ❝❛rt❡s✐❛♥ ❢♦r♠ ✧❛r❝✧ ❜❛s❡❞ ❋▼✲❉❡♠♦❞✉❧❛t♦r✿ � � out( n ) = Gain ( i n i n − 1 + q n q n − 1 ) + j · ( q n i n − 1 − i n q n − 1 ) · arc � �� � 1 2 πts = ∆ f + dev · f ( nt s ) ✭✶✻✮ ✧❛r✐t❤♠❡t✐❝✧ ❜❛s❡❞ ❋▼✲❉❡♠♦❞✉❧❛t♦r✿ · i n − 1 q n − i n q n − 1 out( n ) = Gain = ∆ f + dev · f ( nt s ) ✭✶✼✮ i 2 n + q 2 � �� � n 1 2 πts ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✶✷

✹✳ Pr❡s❡♥t❛t✐♦♥ ♦❢ r❡s✉❧ts ❈♦♠♣❛r✐s♦♥ ♦♥ ❝♦♠♣✉t❛t✐♦♥ ♣❡r❢♦r♠❛♥❝❡ ✧❛r❝✧ ■♠♣❧❡♠❡♥t❛✐♦♥ ●❊◆❊❘■❈ ❙❙❊✸ ✶✶✱✷✽s ✾✱✾✵s ✧❛r✐t❤♠❡t✐❝✧ ■♠♣❧❡♠❡♥t❛t✐♦♥ ●❊◆❊❘■❈ ❙❙❊✸ ✶ t❤r❡❛❞ ✸✱✶✵s ✶✱✽✵s ✷ t❤r❡❛❞s ✶✱✻✺s ✶✱✵✹s ✸ t❤r❡❛❞s ✶✱✷✸s ✵✱✽✶s ✹ t❤r❡❛❞s ✵✱✾✽s ✵✱✻✺s ❚✐♠❡s ❛r❡ ♠❡❛s✉r❡❞ ❢♦r ❝♦♠♣✉t❛t✐♦♥ ♦❢ s♦♠❡ ♠✐❧❧✐♦♥s ♦❢ s❛♠♣❧❡s ♦♥ ❛ ✹ ❝♦r❡ ✐✼✲❈P❯✳ ❋❖❙❉❊▼ ✷✵✶✺✱ ✵✶✲❢❡❜✲✷✵✶✺ ♣❛❣❡ ✶✸