Information Transmission Appendix B, Circuit theory OVE EDFORS - PowerPoint PPT Presentation

Information Transmission Appendix B, Circuit theory OVE EDFORS ELECTRICAL AND INFORMATION TECHNOLOGY

L e a r n i n g o u t c o m e s A f t e r t h i s l e c t u r e t h e s t u d e n t s h o u l d – K n o w t h e p r o p e r t i e s o f , a n d b e a b l e t o p e r f o r m b a s i c c a l c u l a t i o n s w i t h , r e s i s t o r s , i n d u c t o r s a n d c a p a c i t o r s – K n o w h o w r e s i s t o r s , i n d u c t o r s , a n d c a p a c i t o r s , b e h a v e w h e n s i n u s o i d a l s i g n a l s a r e a p p l i e d . – K n o w K i r c h h o f f ' s v o l t a g e a n d c u r r e n t l a w s a n d u n d e r s t a n d h o w t h e y a r e a p p l i e d t o p e r f o r m b a s i c c a l c u l a t i o n s o n e l e c t r o n i c c i r c u i t s . – U n d e r s t a n d t h e i m p e d a n c e c o n c e p t a n d h o w t o c a c l c u l a t e t h e t o t a l i m p e d a n c e o f m u l t i p l e i m p e d a n c e s c o n n e c t e d i n s e r i a l o r p a r a l l e l O v e E d f o r s E I T A 3 0 - A p p e n d i x B 2

Wh e r e a r e w e i n t h e B I G P I C T U R E ? Electronics for analog input Models of transmission and Lecture relates to pages and output, including storage media. 281–293 in textbook. sampling and reconstruction. O v e E d f o r s E I T A 3 0 - A p p e n d i x B 3

R e s i s t o r s , I n d u c t o r s , C a p a c i t o r s O v e E d f o r s E I T A 3 0 - A p p e n d i x B 4

R e s i s t o r s Does not depend on frequency. O v e E d f o r s E I T A 3 0 - A p p e n d i x B 5

I n d u c t o r s Depends (increases) with frequency. O v e E d f o r s E I T A 3 0 - A p p e n d i x B 6

C a p a c i t o r s Depends on (decreases with) frequency. O v e E d f o r s E I T A 3 0 - A p p e n d i x B 7

I m p e d a n c e O v e E d f o r s E I T A 3 0 - A p p e n d i x B 8

I m p e d a n c e O v e E d f o r s E I T A 3 0 - A p p e n d i x B 9

K i r c h h o ff ’ s c u r r e n t l a w OR: O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 0

K i r c h h o ff ’ s v o l t a g e l a w O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 1

E x a m p l e 1 ( E x a m p l e B . 1 i n t e x t b o o k ) What is i 1 , i 2 , i 3 , v 1 , v 2 , v 3 ? Six unknowns – we need six equations! One of these are redundant, so we need one more. Ohms law: Kirchoff's voltage law: Kirchoff's current law: (loop 1) (resistor ) (loop 2) (node a) (resistor ) (outer loop) (resistor ) Solution: O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 2

S e r i a l i m p e d a n c e O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 3

E x a m p l e 2 ( E x a m p l e B . 2 i n t e x t b o o k ) What is v(t) ? Total (serial) impedance at frequency : Ohm's law gives: O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 4

P a r a l l e l i m p e d a n c e s What is the equivalent parallel impedance? O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 5

P a r a l l e l i m p e d a n c e s Often we have only two impedances in parallel and get O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 6

S p l i t o f v o l t a g e a n d c u r r e n t O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 7

S u m m a r y ● R e s i s t o r s , i n d u c t o r s & c a p a c i t o r s – We c a n a p p l y O h m ' s l a w , a l s o f o r i n d u c t o r s a n d c a p a c i t o r s , b y u s i n g a n d i n p l a c e o f ” r e s i s t a n c e ” . – I m p e d a n c e i s t h e r e l a t i o n b e t w e e n v o l t a g e a n d c u r r e n t ( o f t e n f r o m a c o m b i n a t i o n o f r e s i s t o r s , i n d u c t o r s a n d c a p a c i t o r s ) . ● K i r c h o f f ' s l a w s ( g e n e r a l ) – C u r r e n t l a w : A t a l l t i m e s , t h e s u m o f a l l c u r r e n t s i n t o a n o d e m o s t e q u a l t h e s u m o f c u r r e n t s l e a v i n g t h e n o d e . ( C h a r g e c a n ' t a c c u m u l a t e i n a n o d e . ) – V o l t a g e l a w : A t a l l t i m e s , t h e s u m o f v o l t a g e s a r o u n d a n y c l o s e d l o o p i n a c i r c u i t m u s t b e z e r o . ● T y p i c a l c i r c u i t s ( s p e c i a l c a s e s ) – S e r i a l a n d p a r a l l e l i m p e d a n c e – S p l i t o f v o l t a g e a n d c u r r e n t O v e E d f o r s E I T A 3 0 - A p p e n d i x B 1 8