MEMS 0031 Electric Circuits

Transcription

1 MEMS 0031 Elecric Circuis Chaper 1 Circui variables

2 Chaper/Lecure Learning Objecives A he end of his lecure and chaper, you should able o: Represen he curren and volage of an elecric circui elemen, paying paricular aenion o he reference direcion of he curren and o he reference direcion or polariy of he volage Calculae he power and energy supplied or received by a circui elemen Use he passive convenion o deermine wheher he produc of he curren and volage of a circui elemen is he power supplied by ha elemen or he power received by he elemen Use scienific noaion o represen elecrical quaniies wih a wide range of magniudes

3 Circui variables Circui elemen Circui A simple circui An elecric circui or elecric nework is an inerconnecion of elecrical elemens linked ogeher in a closed pah so ha an elecric curren may flow coninuously A general wo-erminal elecric circui elemen Resisor Swich capacior Inducor Sources o o Volage source Curren sources Transducer

4 Circui variables Charge: he quaniy of elecrically responsible for elecric phenomena Curren: ime rae of flow of he elecric charge pas a given poin i = dq d 18 1C = 6.24x10 elecron charge 1 e = x10 19 C i = i 1 2

5 Curren: Ne Posiive Charge Flow Q + L Q L Q + R Q R + + Q= ( Q Q ) ( Q Q ) R R L L Q = Ne + Q charge; iavg = Insananeous curren: dq i () = d Uni of Curren : Ampere (A); Uni of Charge: Coulomb (C); 1 A = 1 Coulomb per second

6 Circui variables A direc curren (DC) of magniude of I Time-varying curren i A Sinusoid, ω = angular frequency A Ramp, slope=m An exponenial, Deparmen I, of b= Mechanical consan Engineering

7 Circui variables If he charge is known, he curren can be find from i = dq d If he curren is known, he charge can be find by q = idτ = + 0 idτ q ( 0) q( 0) is he charge a =0 i i slope, M = i() = M + b

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9 Circui variables ( ) 2 i = 8 4 A 8 8 q id q d ( ) = τ + (0) = (8τ 4 τ) τ + 0 = τ 2τ = 2 C ( ) q = 4sin 3 C dq d i( ) = = 4sin 3 = 12cos3 A d d

10 Example: Charge is given, q(), find curren, i()

11 i = dq d Divide q() ino secions o ge q() expressions a each secion m = slope q() = m + b b= q ( = 0) = q ( ) m (1) < 1, q () = 0,() i = 0 (2)1s < 3, sq () = + 1,() i = 1 (3)3s< 5 sq, ( ) = , i ( ) = 1.5 (4)5s < 6, sq () = 1,() i = 0 (5)6s< 7, sq () = 7,() i = 1 (6)7 s q, ( ) = 0, i ( ) = 0

12 Example : From known curren, find charge q() The curren in a circui elemen is i() = 3 sin (5 + 30) when 0 and i() = 0 when < 0. Deermine he oal charge ha enered a circui elemen for 0 dq d i = q idτ = idτ + q ( 0 ) 0 0 = 0 ( ) q( ) = idτ = 3 sin (5 τ + 30) dτ + q = cos(5τ + 30) = cos(5 + 30) = cos(5 + 30)

13 Example : Find he charge and skech is waveform for he given curren enering a erminal of elemen as shown in P1.2-7

14 Circui variables Volage is he basic circui variable describing energy (w) required o cause charge (q) o flow. Volage across an elemen is he work (energy) required o move a uni posiive charge q from o + erminal of he elemen v = dw dq Energy is capaciy o perform work; Uni of volage is he vol (V). 1V = 1J/C v ab = v ba volage a b wr a Volage direcions = erminal polariies (-,+)

15 Circui variables Power Absorbed by elemen Power Supplied by he elemen

16 Circui variables

17 Power and Energy Power is ime rae of expending or absorbing energy (w) dw p = d For an elecric circui elemen, power absorbed or supplied by he elemen is: dw dq p=. = vi. dq d p= vi. = insananeous power

18 Power and Energy The energy absorbed by an elemen for a given power: dw = pd w = pd If he elemen only receives power for o, and Le o =0 w = 0 = 0 pd

19 Passive Convenion Power Absorbed by elemen Power Supplied by he elemen i () i () + v ab - Passive Convenion (Passive sign Convenion): - v ba + Curren eners erminal of higher volage, elemen absorbed power

20 Passive Convenion

21 Lumped Circui elemens Consider curren i() and v() of a circui elemen as shown: Passive Convenion Curren eners erminal of higher volage Elemen absorbed power

22 Example :

23 Example :

24 Example :

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