Microsoft PowerPoint - lec02_2005

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Microsoft PowerPoint - lec02_2005"

Transcription

1 회로이론의선형모델링 (a) (b) (a) (b) (a) An automobie ignition circuit. (b) Mode of the ignition circuit for starting a car. (a) An incandescent amp. (b) Votage-current reationship for an incandescent amp. The amp is inear within the range -i m < i< i m. - 선형소자는 superposition 과 homogeneity 를만족한다. Superposition : i 의응답 v, i 의응답 ν 이면 i + i 의응답은 v + v. Homogeneity : i 의응답 v 이면 ki 의응답은 kv. Lecture - 회로이론의가정 - 회로이론은전자기학의일부. - 가정을통해이론을단순화. - 회로이론을적용할때에는가정을만족하는지를따져야한다. 가정 () 전파 ( 傳播 ) 효과가무시될만큼계가작다. 즉, 계가순간적으로, 동시적으로변화한다 집중정수계. () 계에알짜전하는없다. (3) 계의구성부품간에자기적인결합은없다. Lecture -

2 - 가정 () 은외부에서인가하는물리량 ( 힘, 전류, 전압 ) 이동시에계의전부에작용한다는것을의미. F 집중정수계와분포정수계 단단한물체 ( 나무, 쇠 ) F 물렁물렁한물체 ( 두부, 젤리 ) - 물질에는파동의전파속도가있음. v p E ρ - 물체의반대편에신호가전파되는데걸리는시간 ( 지연시간 ) 은 t v () s 이다. - 왼쪽의단단한물체는전파속도가빠르므로계의모든부분이동시적으로외부물리량을느낀다. - 오른쪽의물렁물렁한물체는전파속도가느리므로계의모든부분이같은시간에같은물리량을갖지못한다. 따라서, 분포정수계의문제로다루어야한다. Lecture -3 - 지연시간의외부에서가해주는물리량의주기보다매우작아야한다. 이조건을만족시키면집중정수계로볼수있다. - 전자계에서전자파의진행속도는 c 이다. - 시스템의특성길이가이라하면지연시간은 t c 이되고, 60 Hz의상용전원에대해서생각해보면 8 따라서, 이웬만큼 ( 수천 km) 길지않으면집중정수계로보아도무방하다. - 만약, 주파수가 0 9 Hz이면어느정도의시스템까지집중정수계로볼것인가? 0.3 m 보다매우작아야한다. 집중정수계로판단하는기준 t / T << t / T /0 8 c ε µ 0 t / T / 60 0 << m/s Lecture -4

3 R : resistance Ω (Ohm) v R i 회로소자 -저항 + v - - 저항의중요특성 : 전압의부호에따라전류의부호가바뀜. i + - i - v + i - Inductor 나 Capacitor 는전압의부호에따라전류의부호가바뀌지않음. + + v i v i - - Lecture -5-9세기초 George Simon Ohm 이확립 r r J σe ( J r : 전류밀도, σ : 도전율, E r : 전계 ) 도체 ( 저항체 ) 전원을연결해서강제로전류를흘리면 m, q, v 도체 ( 저항체 ) 내부에전계가존재. t 0 일때전류를가하면도체내부의자유전하는전계에의해서가속되고, E 저항이방해하는힘이없다면전하는무한히가없는선속된다. 그러나, 도체내부에는무수히많은전 t0 하가있어서곧충돌하게되며가속운동운동방정식이방해받고일정한속도의움직임으로 r 된다. dν r r m qe mµ v dt Ohm s s Law (I) r ν : 속도, µ : 충돌빈도수 ( 실효충돌주파수 ) Lecture -6

4 Ohm s s Law (II) 회로의인덕턴스를무시하고, 전계를 step r function으로가정하자. d ν r q r E r + µ ν E dt m r q r µ t t ν ( t) ( e ) E mµ 전류는전하의단위시간당흐름이므로 r Nq r µ t J( t) N q v( t) ( e ) E mµ J r 인시정수 (N : 개수, q : 전하량, r µ ν(t) : 속도 ) r Nq t J r r E E mµ σ t Nq ( σ ( S mµ m ), 도전율 ) -t 0근처에서는 µ 인시정수로전류가증가하고, 충분한시간이흐른후결정. - 구리의경우, µ 0 4 Hz 이므로, 시정수는 0-4 초이다. - 따라서, 과도항 ( e µt ) 이무시되며, Ohm의법칙이성립. Lecture -7 저항율 300 K 에서의저항율 (Ωm) Conductors Auminum Carbon (amorphous) Copper God Nichrome Siver Tungsten Semiconductors Siicon (device grade) depends on impurity concentration Insuators Fused quartz Gass (typica) Tefon to > Lecture -8

5 Sheet Resistance Sheet resistance R s ρ/d (Ω) 그림과같은 thin fim resistor 의저항을구하라. 여기서, sheet resistance 은 00 Ω 이다. Thin fim resistor Boyestad 책 66 쪽그림 3. R ρ A ρ dw ρ d w R s w Lecture -9 Conductors Temperature Effects Therma energy increases the intensity of the random motion of the partices. Positive temperature coefficient. Semiconductors An increase in temperature resuts in an increase in the number of free carriers. Negative temperature coefficient. (a) Positive temperature coefficient-conductors; Insuators Positive temperature coefficient. (b) negative temperature coefficient-semiconductors. Boyestad 책 68 쪽그림 3.3 Lecture -0

6 Inferred Absoute Temperature Effect of temperature on the resistance of copper. Boyestad 책 69 쪽그림 3.4 Inferred absoute temperatures(t i ). Boyestad 책 69 쪽표 3.5 x y T T R R R R o C : inferred absoute temperature of copper. i + T Ti + T R R T Lecture - Temperature Coefficients of Resistance α 0 : temperature coefficient of resistance at a temperature of 0 o C R 0 α 0 ( Ω/ C/ Ω) C T i 0 [ + α ( 0 C) ] R0 0 T R 0 : resistance of the sampe at 0 o C. R : resistance at a temperature T. Temperature coefficient of resistance for various conductors at 0. Boyestad 책 70 쪽표 3.6 PPM/ o C R R nomina (PPM)( T ) 0 6 R nomina : resistance at room temperature. T : the change in temperature from the reference eve of 0 o C. Lecture -

7 Fixed Resistors Types of Resistors Fixed resistor 와 variabe resistor 가있다. Low-wattage. Moded carbon composition resistor. Fixed composition resistor. Boyestad 책 75 쪽그림 3.7 Fixed composition resistors of different wattage ratings. Boyestad 책 75 쪽그림 3.8 Curves showing percentage temporary resistance changes from +0 vaues. (Courtesy of Aen-Bradey Co.) Boyestad 책 75 쪽그림 3.9 Lecture -3 Fixed Resistors (I) Fixed resistors. [Parts (a) and (c) courtesy of Ohmite Manufacturing Co. Part (b) courtesy of Phiips Components Inc.] Boyestad 책 76 쪽그림 3.0 Lecture -4

8 Miniature Fixed Resistors Miniature fixed resistors. [Parts (a) courtesy of Ohmite Manufacturing Co. Parts (b) and (c) courtesy of Dae Eectronics, Inc.], Boyestad 책 76 쪽그림 3. Lecture -5 Variabe Resistors Rheostat 또는 potentiometer 로부른다. (a) The symbo (b) A mode for the potentiometer (a) A circuit containing a potentiometer (b)an equivaent circuit containing a mode of the potentiometer R R + R ac ab bc Potentiometer: (a) symbo; (b) and (c) rheostat connections; (d) rheostat symbo. Boyestad 책 77 쪽그림 3.3 Lecture -6

9 Potentiometers Potentiometers: (a) 4-mm( 5/3 )trimmer(courtesy of Bourns, Inc.); (b) conductive pastic and cermet eement (courtesy of Carostat Mfg. Co.). Boyestad 책 78쪽그림3.6 Moded composition-type potentiometer. (Courtesy of Aen-Bradey Co.) Boyestad 책 77 쪽그림 3.4 Lecture -7 Coor Coding 숫자를쓰기에작은저항에는색으로저항값을나타낸다. 색띠의위치는저항을옆으로놓고보면비대칭적이다. 저항의끝에서가까운쪽부터읽는다. 띠의의미 첫두개 : 두자리숫자. 세번째 : 0의승수 (power-of-ten) 네번째 : 제작자의허용오차 (manufacturer s toerance) 다섯번째 :,000시간사용시오동작할확률. Resistor coor coding. Boyestad 책 79 쪽표 3.7 Coor coding of fixed moded composition resistor. Boyestad 책 78 쪽그림 3.8 Lecture -8

10 Standard vaues of commerciay avaiabe resistors. Boyestad 책 80 쪽표 3.8 Standard Resistors (I) Standard vaues and their toerances. Boyestad 책 80 쪽표 씩증가하지않는이유? Lecture -9 Standard Resistors (II) Guaranteeing the fu range of resistor vaues for the given toerance: (a) 0 %; (b) 0 %. Boyestad 책 80 쪽그림 3.9 Lecture -0 0

11 Circuit Eements - Independent Sources - Votage and current sources Source : non-eectric energy를 eectric energy로변환. independent : 회로내의전류와전압에관계없이불변. dependent : 회로내의전류와전압에따라변화. - Idea independent votage source : 전압원내의전류값에관계없이지시된전압 v s 를유지. v s + - Idea independent current source : 전류원내의전압값에관계없이지시된전류 i s 를유지. i s Lecture - Circuit Eements - Dependent Sources - Idea dependent votage and current sources. 회로의다른곳의전압또는전류 (v x, i x ) 에의해서변화. + _ v s v s µv x ρi x i s i s αv x i s βi x R R i E R C 3 R E 트랜지스터증폭회로 +_ V CC b R R i E R C i B V β i b 0 + _ c 3 R E i CC V CC d 트랜지스터를 dependent source로치환한회로 a +_ Lecture -

12 Votmeters and Ammeters - The probes are coor coded. - Positive: red, negative: back. - Ammeters: series connection. - Votmeter: parae connection. - Votage-ohm-miiammeter (VOM) and digita mutimeter (DMM). - Idea ammeter: interna resistance 0. - Idea votmeter: interna resistance. Figure.7- (p. 39) (a) Idea ammeter. (b) Idea votmeter. Figure.7- (p. 38) (a) A direct-reading (anaog) meter. (b) A digita meter. Lecture -3 3 An Exampe Circuit - Idea ammeter: short circuits. - Idea votmeter: open circuits. - Ideay, adding the votmeter and ammeter does not disturb the circuit. - The reference direction is important. Figure.7-3 (p. 39) (a) An exampe circuit, (b) pus an open circuit and a short circuit. (c) The open circuit is repaced by a votmeter, and the short circuit is repaced by an ammeter. A resistances are in ohms. Lecture -4 4

13 Switches Switches have two distinct states : open and cosed. SPST : Singe-Poe, Singe-Throw Initiay open. Initiay cosed. SPDT : Singe-Poe, Doube-Throw 스위칭은아주짧은시간내에이루어지고, 회로의응답시간에비해아주빠르게스위칭한다. Lecture -5 5 Transducer - Temperature Sensor Transducer : Devices that convert physica quantities to eectrica quantities. Anaog Device 사의 AD590 은온도를전류로바꾸어서온도를측정하는소자이다. 소자는그림과같이표시한다. 이센서를적절히동작시키려면전압은 4 V 에서 30 V 사이에있어야한다. 이런조건에서전류는온도 K 의변화 에 µa 의전류가흐르게된다. i k T where k µa/ o K (a) The symbo and (b) a mode for the temperature sensor AD590 을이용하여수조의물온도를측정하는회로를설계하라. AD590, 전류계, 저항, 전압원 (0,, 5, 8, 4 V) 이사용가능하다. 300 K 이면전류는얼마가흐르는가? 이상적인전류계와실제적인전류계를사용했을때어떤변화가있는가? 여러전원중어떤전원을사용해야하는가? 그이유는? Lecture -6 6