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Institutionen för Elektro- och informationsteknik Kretsteori, ellära och elektronik Daniel Sjöberg Mats Gustafsson Kretsteori, ellära och elektronik Daniel Sjöberg & Mats Gustafsson Tryckeriet i E-huset, Lund 2008

Kretsteori, ellära och elektronik

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Institutionen för Elektro- och informationsteknik

Kretsteori, ellära och elektronik

Daniel SjöbergMats Gustafsson

Kretsteo

ri, ellära

och

elektro

nik

Dan

iel Sjöberg &

Mats G

ustafsson

Tryckeriet i E-huset, Lund 2008

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� � � � � � � � � � � � � � � � � � � � � �# $ # % � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # ## $ � % � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # &# $ ' ( � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # )# $ & ( � � � � � * � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # +# $ , ( � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � �# $ ) � � � � � � � � � � - � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � '

� � � � � � � � � � � � � � � �� $ # � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � ,� $ � . � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � )� $ ' � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � +� $ & � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � �� $ , / � � � � � 0 � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � 1� $ ) 2 � 3 � " � � � � � � � / � � � � � " � " � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ' '� $ + ( � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ' ,� $ � % * � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ' +� $ 1 � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ' �

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� � � � � � � � � � � � � � � � � � � � �' $ # 4 � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ & ,' $ � 4 � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ & �' $ ' 4 � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ & 1' $ & ( � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , �' $ , 4 � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , �' $ ) % � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , �' $ + % * � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , &

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' $ � 2 � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , &

� � � � � � � � � � � � � � � � � � � � �& $ # � � 5 � � � � � � " � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ , 1& $ � ( � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ) �& $ ' ( � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ ) �& $ & . � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ ) 1& $ , ( � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ + #& $ ) ( � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ + �& $ + � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ + '& $ � ( � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ + +

� � � � � � � � � � � � � � � � � � ! �, $ # � � 6 � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ + 1, $ � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � &, $ ' � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ � +, $ & � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 1 #, $ , 7 � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 1 ', $ ) � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 1 ,, $ + � � * � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ 1 )

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* ' � � � � � � � � # � � � � � ) �) $ # 8 � � � � � � � � � " � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � ') $ � 8 � � � � � � � � � � " � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � ,) $ ' 8 � � � � � � � � � � � � � � � " � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � )) $ & 2 � � � � � � � � � � � � � � " � � � � � � � � � � � � � - � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � �) $ , 2 " � � � � � " � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # # �) $ ) � � � � 0 � � " � � � � � � � � � � � � � ! � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ # # #

! ' � � � � � � � � � � � � � � � � � � � !+ $ # 2 � � � � � � � � � � " � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # # �+ $ � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � �+ $ ' ( � � � � � � � � 0 � � � � � � " � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � #+ $ & 9 � � � � � � � � * � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � ,+ $ , % * � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � �

� � � � � �� � � ,

+ " � � � � � � � � � ( � � � �� $ # 7 " � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # ' #� $ � 9 � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # ' &� $ ' : � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # ' )� $ & 4 � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # & �� $ , 4 � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # & &

� ' � � � � � � � � � � � � � � � � � � � � �1 $ # 7 � � � � � � 5 � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # , #1 $ � 2 � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # , '1 $ ' 7 � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # , ,1 $ & ! � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � " � � � � � � � � $ $ $ $ $ $ $ $ # , )1 $ , 4 � ; � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # , �1 $ ) � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # , 1

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� ) . � � � � * �# � $ # � � � � � � � � " � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # ) ,# � $ � � � � � � � 0 � � � " � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + �# � $ ' � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + �# � $ & � � � 5 � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + ## � $ , ! � � � � � � � � � � � � � - � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + �# � $ ) / � � � � " � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + )

� � ' � � � � � � � � ! �# # $ # � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # + 1# # $ � 2 � � � � � � � � � � � � � - � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � ## # $ ' ! � � � � � � � � � � � � < � 7 � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � ,# # $ & � - � � � � � � � � � � � " � 7 � : % 2 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � �# # $ , : � � � � � � � � � � � � � � � � � � � 7 � : % 2 $ $ $ $ $ $ $ $ $ $ $ $ $ $ # � 1# # $ ) = � � � � " � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # 1 �

� � / � � � � � � � # � � � � � � � � � �# � $ # ( � � � � � � � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ # 1 )# � $ � ( � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # 1 +# � $ ' -� � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # 1 +# � $ & � � � � � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ # 1 1# � $ , � � " � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � �# � $ ) � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � #

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# � $ + � � � � � � � " � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � ## � $ � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � �# � $ 1 > � � � � � 0 � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � &

� � 0 � � � � � � � � � � � � � � � � � � � � � � � � ) !# ' $ # 2 � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � +# ' $ � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � 1# ' $ ' 7 � � � � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � # ## ' $ & 2 � � � 0 � � � � � � � � � " � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ � # '# ' $ , : � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � # )

1 2 � � � � � � � � � � � � � � �� $ # / � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � # 1� $ � % � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � �

� % � � � � � � � � � # � � � � � �

$ / � � � � � � � � 3 � � � � � � � � � � � � � � � � !< $ # � � � � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � +< $ � � � � � � � � � � � � � � � � � � � � � � � � � � 0 � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � � �< $ ' ! � � � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � ' �< $ & / � � � � � � � � � � � $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ � ' �

. � � � � � � � � � � � �

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