An Introduction to Electrical and Electronic Engineering Electric Circuits. Dr. Cahit Karakuş, 2018

Transkript

1 An Introduction to Electrical and Electronic Engineering Electric Circuits Dr. Cahit Karakuş, 2018

2 Basic Electrical Concepts Voltages and Current Sources Electrical Circuits Kirchoff s Laws Seri ve Parelel Bağlama Thevenin s Equivalent Circuit Norton s Equivalent Circuit Course Contents

3 Basic Electrical Concepts

4 Basic concepts Electricity Charge Current Voltage Power and Energy

5 Basic Electronics What is electricity Voltage, Current, Resistance Ohm s Law Capacitors, Inductors Semiconductors Mechanical Components Digital Electronics

6 What is Electricity Everything is made of atoms There are 118 elements, an atom is a single part of an element Atom consists of electrons, protons, and neutrons

7 Electrons (- charge) are attracted to protons (+ charge), this holds the atom together Some materials have strong attraction and refuse to loss electrons, these are called insulators (air, glass, rubber, most plastics) Some materials have weak attractions and allow electrons to be lost, these are called conductors (copper, silver, gold, aluminum) Electrons can be made to move from one atom to another, this is called a current of electricity.

8 Surplus of electrons is called a negative charge (-). A shortage of electrons is called a positive charge (+). A battery provides a surplus of electrons by chemical reaction. By connecting a conductor from the positive terminal to negative terminal electrons will flow.

9 Voltage A battery positive terminal (+) and a negative terminal (-). The difference in charge between each terminal is the potential energy the battery can provide. This is labeled in units of volts. Water Analogy

10 Voltage Sources:

11 Voltage is like differential pressure, always measure between two points. Measure voltage between two points or across a component in a circuit. When measuring DC voltage make sure polarity of meter is correct, positive (+) red, negative (-) black.

12 ÖLÇÜMLER GERİLİM : Voltmetre akü veya alıcı uçlarına direkt bağlanır.bu tür bağlantıya PARELEL bağlama denir.

13 Ground

14 Exercise Measure DC voltage from power supply using multimeter Measure DC voltage from power supply using oscilloscope Measure DC voltage from battery using multimeter Measure AC voltage from wall outlet using a multimeter Measure AC voltage from wall outlet using an oscilloscope Effective or Root Mean Square Voltage (Measured with multimeter) E ERMS=0.707xEA

15 Akım I 1. DOĞRU AKIM (Simgesi: ) + - A I Zaman t İletken telin kesiti ve elektron hızı değişmezken serbest elektronlar hep aynı yöne doğru hareket ederlerse, bu bir doğru akımdır. Yani; birim zamanda yönü ve şiddeti değişmeyen akıma Doğru Akım denir. Şekildeki grafiğe göre doğru akım bütün bir zaman boyunca hep aynı düzeyde akmaktadır. Devrede görülen ampermetre ise hep aynı değeri göstermektedir. Kısacası, hep aynı yönde ve aynı şiddette akan elektrik akımı Doğru Akımdır.

16 Akım I 2. ALTERNATİF AKIM (Simgesi: ) G Bisiklet dinamosu A Zaman t Her iki yönde ve eşit mesafelerde serbest elektronlar hareket ederlerse bu bir alternatif akımdır. Şekilde alternatif akımın zamana göre grafiği görülmektedir. Buna göre alternatif akım zamana göre bir dalga hareketi yapmakta ve şiddetini değiştirmektedir. Sonuç olarak aynı şekil içinde görülen bisiklet dinamosu çevrilirse ampermetrenin ibresi sağa sola oynayacaktır. Kısacası, sürekli olarak yönünü ve şiddetini değiştiren elektrik akımı alternatif akımdır.

17 AKIM : Ampermetre elektrik devresinden geçen akımı ölçer.akımın geçtiği yol kesilip araya ampermetre bağlanır.bu tür bağlantıya SERİ bağlama denir

18 ELEKTRİKTE GÜÇ P = GÜÇ (Watt) GERİLİM, AKIM ARASINDAKİ İLİŞKİ GÜCÜ VERİR. Güç birim zamanda yapılan iş, elektrik devrelerinde harcanana güç birimi watttır. AKIM (Amper) U GERİLİM (Volt) P V R 2

19 Prototyping Board Example of how components are Inserted in the protoboard

20 ELEKTRİK Elektrik sözcüğü, Latince kehribar demek olan elektron kelimesinden türetilmiştir. Kehribar soyu tükenmiş bir soy ağacından oluşan reçinenin fosilleşmiş halidir. Sol elde oynandığında bedenin elektriğini toplar. Elektrik yükünü azalttığı için depresyona karşı da faydalıdır. 20

21 Elektrik Enerji Üretiminde Kullanılan Kaynaklar Elektrik enerjisinin elde edilmesinde tabiattaki enerji çeşitleri kullanılmaktadır. Bu kaynaklar değişik dönüşümler sonucu elektrik enerjisine çevrilir. Kaynakların bazıları ise direkt kullanılmaktadır. Şekil 1.1 de kullanılan kaynakların şeması görülmektedir. 21

22 İletken Tüm metaller iletkendir. İnsan vücudu iyi bir iletkendir. İyonlara sahip sıvılar iyi bir iletkendir ve bunlara elektrolit adı verilmektedir. Saf su yalıtkan, günlük hayatta kullandığımız içme suyu iletkendir. Toprak içinde su olduğu için iletkendir. Gazlar genelde yalıtkandır; fakat iyonlarına ayrılmış gazlar iletkenlik kazanırlar. Üzerinde serbestçe dolaşabilen yüklerin bulunduğu maddelere İletken Cisimler denir. Elektrik akımını ( elektron akımını ) ileten cisimler. 22

23 Yalıtkan Yalıtkan cisimlerde serbest elektronlar yok denecek kadar azdır. Cam, kauçuk, pamuk, yağ ve hava yalıtkan maddelere örnek olarak verilebilir. Üzerinde yüklerin serbestçe dolaşamadığı cisimlere Yalıtkan Cisimler denir. Yalıtkanlar yüklerin ( elektronların ) hareketini engeller. Elektrik akımını ( elektron akımını ) iletmeyen cisimler. 23

24 Elektrik Yükü Atomun yapısında bulunan proton ve elektronların elektriksel özellikleri birbirine zıttır. Protona (+) yüklü, elektrona (-) yüklü denmiştir. Nötronlar ise yüksüzdür. Elektrik yükü Q veya q ile gösterilir. Birimi coulomb tur. C ile gösterilir. Elemanlar Yük Kütle Elektron - 1, C 9, kg Proton +1, C 1, kg Nötron 0 1, kg 24

25 Bir atomda proton ve elektron sayıları birbirine eşitse bu atoma nötr atom denir. Atomların yüklenmesi atoma elektron verilmesi veya atomdan elektron alınması ile gerçekleşir. Bir atomda; proton sayısı elektron sayısından fazla ise (yani elektron kaybetmiş ise) böyle atomlara pozitif yüklü iyon ya da katyon denilir. +e ile gösterilir. Atomun içerisinde elektron sayısı fazla ise bu da dışarıdan elektron kazanmış ve negatif yüklü iyon diye adlandırılır ve -e ile gösterilir. Bunlara anyon da denmektedir. 25

26 Coulomb Kanunları Coulomb Kanunları - İki nokta yük arasındaki elektrik kuvvetin büyüklüğü yüklerin çarpımıyla doğru orantılı ve aralarındaki uzaklığın karesiyle ters orantılıdır. F k q q r r : iki yük arası uzaklık q 1,q 2 : yükler k : orantı sabiti - İki yükün birbirleri üzerinde oluşturdukları kuvvetlerin doğrultusu her zaman onları birleştiren doğru boyuncadır. - Yükler aynı işarete sahipse, kuvvetler iticidir. - Yükler zıt işarete sahipse, kuvvetler çekicidir. q 1 q 2 q 1 q F 2 on 1 r F 1 on 2 F 2 on 1 r F 1 on 2 q 1 q F 2 on 1 r F 1 on 2

27 Coulomb Kuvvetleri Coulomb Kuvvetleri ve Birimler F k q q r r : iki yük arasındaki uzaklık (m) q 1,q 2 : yükler (C) k : orantı sabiti k N m 2 / C 2 SI birimi N m 2 / C N m 2 / C 2 c k (10 N s 1 ; / C 2 8 m/s )c e (63) nC 10 C C C 2 /(N m Tanımdan elde edilen 2 ) Bir protonun yükü

28 I. Aynı cins elektrik yükleri ile yüklü cisimler birbirlerini İTERLER

29 II. Zıt yükler birbirlerini ÇEKER. +

30 Elektrik Alanı ve Alan Şiddeti Pozitif birim yüke (Q) etkiyen elektrostatik kuvvete (F) elektrik alanı denir. Elektrik alanı vektörel bir büyüklüktür ve kuvvet çizgileri ile gösterilir. Elektrik alan şiddeti (E) harfi ile gösterilir. Birimi volt metre dir. F E = -- formülü kullanılır. Q 30

31 Elektrik alan ve Elektrik kuvvetler Elektrik alan ve Elektrik kuvvetler A B A F q 0 + F 0 B maddesi çıkarıldığında P Yüklü A maddesinin varlığı uzayın niteliğini değiştirir ve bir elektrik alan oluşturur. Yüklü B maddesi çıkarıldığında, B maddesi üzerinde meydana gelen kuvvet gözden kaybolsa da, A maddesinin oluşturduğu elektrik alan kalır. Yüklü madde üzerindeki elektrik kuvvet, diğer yüklü maddelerin meydana getirdiği elektrik alan tarafından oluşturulur.

32 Elektrik alan ve Elektrik kuvvetler Elektrik alan ve Elektrik kuvvetler A A Deneme yükü P Test yükü yerleştiriliyor F q 0 F 0 Belirli bir noktada elektrik alanın olup olmadığını deneysel olarak bulmak için, noktaya yüklü küçük bir cisim(deneme yükü) yerleştiririz. F Elektrik alan şu şekilde ifade edilir: 0 E ( SI biriminde N/C ) q Bir q yükü üzerindeki kuvvet: 0 F qe

33 Elektrik Alan

34 Elektrik Akımı Elektrik Akımı: İletkenden birim zamanda geçen elektrik yükü (elektron) miktarına Akım denir. Birimi: Amper dir. Akım, elektronların hareketiyle ortaya çıkar ve artı (+) uçtan eksi (-) uca doğru akar.

35 1 amperlik akımın oluşabilmesi için İletkenin herhangi bir noktasından 1 saniyede 6,25x10 18 elektron geçmesi gerekir. Akım; doğru akım (DC) ve alternatif akım (AC) olmak üzere iki kısma ayrılır

36 Current and Charge Current is the rate of charge flow: 1 ampere = 1 coulomb/second (or 1 A = 1 C/s) 36

37 Current Current charge in motion. The flowing of charges through something. We typically think of charge flowing through a wire, but it can also flow through water, air and even vacuum. You can think of current as water flowing through the interior of a pipe, though current actually flows though the empty spaces between atoms in a wire. Current is represented by the mathematical symbol i. i = Q/t, or, current is equal to the number of electrons that flow past a point in a given amount of time. Current is measured in amperes, which is equal to coulombs/sec. Amperes is abbreviated with the letter A. Current is a through variable, meaning that in order to measure it, you need the current to go through something.

38 Electric current An ampere (A) is the number of electrons having a total charge of 1 C moving through a given cross section in 1 s. As defined, current flows in direction of positive charge flow

39 Voltage Can be thought of as the driving force behind the current (though it isn t really a force). Voltage is the energy per unit charge. Current flows through electrical elements when a voltage appears across the terminals of the element, similar to when water flows through a pipe when a pressure difference appears across the pipe. Voltage is an across variable. We talk about pressure differences and voltage differences. Voltage is related to potential energy. Voltage is defined as the electrical potential energy that a charge has by its position in space. If you pull two charges apart, you put potential energy into the system That potential energy can be converted into other forms of energy Energy can neither be created or destroyed, only transferred

40 Potansiyel ve Gerilim Elektrik alanı içindeki bir noktadaki elektrik yüklenmesi sonucu oluşan şarj olayına elektrik potansiyeli denir. U ile gösterilir, birimi Volt tur. Q yükünün alanı içerisindeki A noktasındaki elektrik potansiyeli 40

41 etmektedir: formülü kullanılır. Buradaki işaretler şunları ifade U A : A noktasının potansiyeli (volt) k : Yükün bulunduğu ortama ve kullanılan birim sistemine bağlı olan katsayı ( ) Q : Elektrik yükü (Culon) r A : A noktasının Q yüküne olan uzaklığı (metre) 41

42 Potansiyel fark Pozitif birim yükünü, elektrik alanının herhangi bir noktasından bir başka noktasına götürmek için elektriksel kuvvetlere karşı yapılan işe, bu iki noktanın potansiyel farkı denir. U AB = U B U A ( Q yükü A noktasından B noktasına gitmiş ise ) U AB = U A U B ( Q yükü B noktasından A noktasına gitmiş ise ) 42

43 Voltage and Batteries Batteries are voltage sources. Batteries can be thought of as charge pumps. They take a charge and though chemical reactions pump them up to a certain voltage, or potential energy level. As the charge flows through the circuit, this potential energy can be used by the circuit to do work. The charge loses energy as it goes through the loads. Heat up a filament Make a motor turn. Energy gained from the battery = energy lost by the loads. Law of conservation of energy

44 Battery as Voltage Source A voltage source is an idealization (no limit on current) and generalization (voltage can be time-varying) of a battery. A battery supplies a constant dc voltage V but in practice a battery has a maximum power. 44

45 Ground Reference voltage from which all other measurements are measured the potential of the Earth. Defined as having 0 V potential energy with respect to the rest of the circuit. In physics equations, ground level is used as the point of 0 potential energy when lifting a weight, another thing electrical systems have in common with mechanical systems. In wiring for houses, the ground is physically connected to the Earth a place of 0 potential energy when compared to the rest of the wiring. Ground provides a return path for the current back to the source because all the ground points are electrically the same point and provide a zero resistance path

46 Voltage Sources An ideal voltage source is a circuit element that will maintain the specified voltage v s across its terminals. The current will be determined by other circuit elements. 46

47 Current Sources An ideal current source is a circuit element that maintains the specified current flow i s through its terminals. The voltage is determined by other circuit elements. 47

48 Dependent Sources Dependent current sources (a) and (b) maintain a current specified by another circuit variable. Dependent voltage sources (c) and (d) maintain a voltage specified by another circuit variable. 48

49 Example: Dependent Sources Find the voltage v L in the circuit below. 49

50 Electrical sources An electrical source is a voltage or current generator capable of supplying energy to a circuit Examples: -AA batteries -12-Volt car battery -Wall plug

51 Ideal voltage source An ideal voltage source is a circuit element where the voltage across the source is independent of the current through it. Recall Ohm s Law: V=IR The internal resistance of an ideal voltage source is zero. If the current through an ideal voltage source is completely determined by the external circuit, it is considered an independent voltage source

52 Ideal current source An ideal current source is a circuit element where the current through the source is independent of the voltage across it. Recall Ohm s Law: I = V/R The internal resistance of an ideal current source is infinite. If the voltage across an ideal current source is completely determined by the external circuit, it is considered an independent current source

53 Dependent Sources A dependent or controlled source depends upon a different voltage or current in the circuit

54 Ohm s Law: Resistance A (linear) resistor is an element for which v=ir where the constant R is a resistance. The equation is known as Ohm s Law. The unit of resistance is ohm (Ω). 54

55 Resistors (a) typical resistors (b) power resistor (c) a 10 TΩ resistor (d) circuit symbol 55

56 Power Absorption Resistors absorb power: since v=ir p=vi = v 2 /R = i 2 R Positive power means the device is absorbing energy. Power is always positive for a resistor! 56

57 Example: Resistor Power A 560 Ω resistor is connected to a circuit which causes a current of 42.4 ma to flow through it. Calculate the voltage across the resistor and the power it is dissipating. v = ir = (0.0424)(560) = 23.7 V p = i 2 R = (0.0424) 2 (560) = W 57

58 Resistance of a Material R L A R is the resistance (in Ohms, Ω) is a property of the material called resistivity L is the length of the material (in cm) A is the cross-sectional area of the material (in cm 2 ) What are the units of? EGR

59

60 Direnç MADDENİN ELEKTRİKSEL DURUMLARI Yüksek İletken değil Lastik Porselen Plastik İzolasyon malz. Yarı iletken İndiyum arsenid Silikon Germanyum Galyum arsenidi Düşük İletken Altın Gümüş Bakır Demir

61 BİR İLETKENİN DİRENCİ 1. Sıcaklığına : Sıcaklık arttıkça direnci artar. 2. Uzunluğuna : Uzunluk arttıkça direnci artar. 3. Kesitine : Kesiti arttıkça direnci azalır. 4. Özdirencine : Özdirenci arttıkça direnci artar. Noise, Coupling, Repeaters, Crosstalk, Delay

62 Fuses and Circuit Breakers Excessive current flow in an electrical circuit may damage the circuit. Typical causes of increased circuit flow are low-resistance connections outside the normal path of current flow, called short circuits. Fuses and circuit breakers provide protection from excessive current flow.

63 Voltages and Current Sources

64 Voltage Sources in Series DC voltage sources in series can be combined and replaced with a single source. AC voltage sources in series can be combined and replaced with a single source only if the angular frequency of operation w are identical. DC and AC voltage sources can be added together when calculating a total voltage. AC voltage sources operating at different frequencies can be added together. The current flowing through one voltage source must be equal to the current flowing through the other voltage source.

65 Example 1

66 Or Example 2

67 Example 3 Or Or

68 Example 4 Or Or

69 DC and AC sources A 5V dc voltage source in series a 2V sin(10t) ac voltage source has a total combined voltage of 5V+2Vsin(10t). However, we do not have a symbol for a single voltage source that can replace the symbols for the dc and ac sources.

70 AC sources with Different w A 2V ac voltage source operating at 10 rad/s in series with a 2V ac voltage source operating at 10.5 rad/s has a total voltage of 2Vsin(10t)+2Vsin(10t). Again, there is not a symbol for a single ac voltage source that can replace the symbols for the two ac sources operating at different frequencies.

71 Voltage Sources in Parallel Since the voltage sources share common nodes, the only time two or more voltage sources are allowed in parallel is when they have exactly the same voltage, polarity, and frequency of operation (if ac sources). The multiple voltage sources can be replaced by a single source with the same voltage, polarity, and frequency of operation (if ac sources).

72 Example 5 Allowed Not Allowed

73 Example 6 Allowed Not Allowed

74 Current Sources in Parallel DC current sources in parallel can be combined and replaced with a single source. AC current sources in parallel can be combined and replaced with a single source only if the angular frequency of operation w are identical. DC and AC current sources in parallel can be added together when calculating a total current. AC current sources operating at different frequencies can be added together. The voltage drop across one current source must be equal to the voltage dropped across the other current sources in parallel.

75 Example 7

76 Example 8

77 Example 9 Or

78 DC and AC Current Sources A 5A dc current source in parallel a 2A sin(10t) ac current source means that they are contributing a total current of 5A+2Asin(10t) at that node. However, we do not have a symbol for a single current source that can replace the symbols for the dc and ac sources.

79 AC Sources with Different w A 2A ac current source operating at 10 rad/s in parallel with a 2V ac current operating at 10.5 rad/s means that they are contributing a total current of 2Asin(10t)+2Asin(10t) at that node. Again, there is not a symbol for a single ac current source that can replace the symbols for the two ac sources operating at different frequencies.

80 Current Sources in Series Since components in series must have the same current flowing through each component, the only time two or more currents sources are allowed in series is when they have exactly the same magnitude current, the current is flowing in the same direction, and frequency of operation (if ac sources). The multiple current sources in series can be replaced by a single source with the same magnitude, direction of current flow, and frequency of operation (if ac sources).

81 Example 10 Allowed Not Allowed

82 Summary Voltage sources in series can be added. Current sources in parallel can be added. Only in the case where the magnitude, polarity, and frequency of operation are identical can multiple voltage sources be in parallel. They can be replaced with a single voltage source of the same magnitude, polarity, and frequency of operation. Only in the case where the magnitude, direction of current flow, and frequency of operation are identical can multiple currents sources be in series. They can be replaced with a single current source of the same magnitude, direction of current flow, and frequency of operation.

83 Electrical Circuits

84 Ohm s Law I = V / R I V R = Current (Amperes) (amps) = Voltage (Volts) = Resistance (ohms) Georg Simon Ohm ( )

85 Mathematics for Electronics Students will understand the mathematical processes and applications that lead to solutions of electronic problems. P = Power (watts or volt-amps) I = Intensity (current in amps) E = Electromotive Force (Voltage) R = Resistance (Ohms)

86 Simple Circuits Series circuit All in a row 1 path for electricity 1 light goes out and the circuit is broken Parallel circuit Many paths for electricity 1 light goes out and the others stay on

87 Now that it is assembled, all that is left is to flip the switch from the open position to the closed position to make the entire circuit live with electrical energy.

88 Electric circuit An electric circuit is an interconnection of electrical elements linked together in a closed path so that electric current may flow continuously Circuit diagrams are the standard for electrical engineers

89 Rate of flow of charge form node a to node b Rate of flow of charge form node b to node a (i = current) A direct current (dc) is a current of constant magnitude An alternating current (ac) is a current of varying magnitude and direction

90 Voltage Driving force of electrical current between two points V ab V ba Voltage at terminal a with respect to terminal b Voltage at terminal b with respect to terminal a V ab = -V ba Note: In a circuit, voltage is often defined relative to ground

91 Voltage The voltage across an element is the work (energy) required to move a unit of positive charge from the - terminal to the + terminal A volt is the potential difference (voltage) between two points when 1 joule of energy is used to move 1 coulomb of charge from one point to the other

92 Power The rate at which energy is converted or work is performed A watt results when 1 joule of energy is converted or used in 1 second

93 Voltage, Current, and Power One Volt is a Joule per Coulomb (J/C) One Amp of current is one Coulomb per second (6.24 x10^18 electrons/second). If I have one volt (J/C) and one amp (C/s), then multiplying gives Joules per second (J/s) this is power: J/s = Watts So the formula for electrical power is just: P = VI: power = voltage current

94 Circuit schematic example

95 Circuit elements

96 Resistors Resistance (R) is the physical property of an element that impedes the flow of current. The units of resistance are Ohms (Ω) Resistivity (ρ) is the ability of a material to resist current flow. The units of resistivity are Ohm-meters (Ω-m) Example: Resistivity of copper Resistivity of glass Ω m to Ω m

97 Resistors

98 Resistors

99 Ohm s Law (remember, R is in Ω and ρ is in Ω-m)

100 Capacitors

101 Capacitors A capacitor consists of a pair of conductors separated by a dielectric (insulator). (ε indicates how penetrable a subtance is to an electric field) Electric charge is stored in the plates a capacitor can become charged When a voltage exists across the conductors, it provides the energy to move the charge from the positive plate to the other plate.

102 Capacitors Capacitance (C) is the ability of a material to store charge in the form of separated charge or an electric field. It is the ratio of charge stored to voltage difference between two plates. Capacitance is measured in Farads (F)

103 Capacitors The capacitor plate attached to the negative terminal accepts electrons from the battery. The capacitor plate attached to the positive terminal accepts protons from the battery. What happens when the light bulb is initially connected in the circuit? What happens if you replace the battery with a piece of wire?

104 Energy storage Work must be done by an external influence (e.g. a battery) to separate charge between the plates in a capacitor. The charge is stored in the capacitor until the external influence is removed and the separated charge is given a path to travel and dissipate. Work exerted to charge a capacitor is given by the equation:

105 Inductors An inductor is a two terminal element consisting of a winding of N turns capable of storing energy in the form of a magnetic field Inductance (L) is a measure of the ability of a device to store energy in the form of a magnetic field. It is measured in Henries (H)

106 Inductors Inductance in a cylindrical coil μ 0 = permeability of free space = 4π 10 7 H/m K = Nagaoka coefficient N = number of turns A = area of cross-section of the coil in m 2 l = length of coil in m

107 Inductors The magnetic field from an inductor can generate an induced voltage, which can be used to drive current While building the magnetic field, the inductor resists current flow

108 Inductors What happens to the light bulb when the switch is closed? What happens to the light bulb when the switch is then opened?

109

110 Energy storage Inductors can store energy in the form of a magnetic field when a current is passed through them. The work required to establish current through the coil, and therefore the magnetic field, is given by

111 Transformers and alternators Inductors are located in both transformers and alternators, allowing voltage conversion and current generation, respectively Transformer converts from one voltage to another Alternator produces AC current

112 Güvenlik Ekipmanları Şalterler Bakım ve servis için elektriği kesmeye yarar. Aşırı akım koruması Elektrik devresini aşırı akımdan korumaya yarar. Sigortalar Devre kesiciler

113 İnvertör - Özellikleri Görevi: Akülerde depolanan yada panellerden gelen DC elektrik akımını AC elektrik akımına dönüştürür.

114 Ne tür sistem dizayn ediyorsunuz? Ada sistemi - Off-Grid Şebeke Bağlantısız On Grid - Şebeke Bağlantılı Dikkat edilecek hususlar: AC Çıkış gücü (watt) Giriş Voltajı (FV modüllere bağlıdır) Çıkış Voltajı (monofaz 240V yada trifaz 380 V) Giriş Akımı (FV modüllere bağlıdır) Verim Muhafaza koruması (IP 65,67 etc.) Ölçüm ve izlenebilir olması İnvertör Seçimi

115 Topraklama Neden topraklama gerekli: Yıldırım Yüksek gerilim hattıyla istek dışı temas Yüksek gerilimi toprağa iletir. 2 çeşit topraklama mevcuttur: Cihaz topraklama : Her türlü FV cihazın dış muhafazasını iletken vasıtasıyla toprağa bağlamak. Sistem topraklama : Mevcut topraklama hattına sistemin topraklanması. Sistemin DC tarafı Negatif toprağa bağlanır. Sistemin AC tarafı Nötr toprağa bağlanır.

116 Kirchoff s Laws

117 Kirchoff s Laws Kirchhoff's current law (KCL): The sum of currents in a network of conductors meeting at a point is zero. Kirchhoff's voltage law (KVL): The voltage drop around a closed loop is 0.

118 Kirchhoff s Current Law Or KCL for short Based upon conservation of charge the algebraic sum of the charge within a system can not change. N n 1 i n 0 Where N is the total number of branches connected to a node. node i enter node i leave

119 Kirchhoff s Voltage Law Or KVL for short Based upon conservation of energy the algebraic sum of voltages dropped across components around M a loop is zero. m 1 v 0 Where M is the total number of branches in the loop. v drops v rises

120 Example 2 Suppose the current through R2 was entering the node and the current through R3 was leaving the node. Use KCL 3 ma ma + I are entering the node. 1.9 ma is leaving the node. I I 1.9mA 1.6mA V1 is dissipating power. 3mA 0.5mA I (3mA 1.9mA 0.5mA)

121 Voltage Divider +VDD = Use Ohm s Law, KCL, KVL! I 2 = 5 / (15K) = 0.33 ma I 1 = VDD / (R1 + R2) = 0.33 ma I 1 = 5 / (15K) = 0.33 ma Vout = [R1 / (R1 + R2)] * VDD Vout = 5/3 Volts

122 Electric Circuit Design Principles

123 Example: Resistors in series The resistors in a series circuit are 680 Ω, 1.5 kω, and 2.2 kω. What is the total resistance?

124 Series circuits A series circuit has only one current path Current through each component is the same In a series circuit, all elements must function for the circuit to be complete

125 Multiple elements in a series circuit

126 Example: Resistors in series The resistors in a series circuit are 680 Ω, 1.5 kω, and 2.2 kω. What is the total resistance? The current through each resistor?

127 Example: Voltage sources in series Find the total voltage of the sources shown What happens if you reverse a battery?

128 Example: Resistors in parallel The resistors in a parallel circuit are 680 Ω, 1.5 kω, and 2.2 kω. What is the total resistance?

129 Parallel circuits Voltage across each pathway is the same A parallel circuit has more than one current path branching from the energy source In a parallel circuit, separate current paths function independently of one another

130 Multiple elements in a parallel circuit For parallel voltage sources, the voltage is the same across all batteries, but the current supplied by each element is a fraction of the total current

131 Example: Resistors in parallel The resistors in a parallel circuit are 680 Ω, 1.5 kω, and 2.2 kω. What is the total resistance? Voltage across each resistor? Current through each resistor?

132 Seri ve Parelel Bağlama

133 Series and Parallel Combinations 133

134 DEVRE ÖRNEKLEME U tot = U 1 = U 2 = 12 V

135 DEVRE ÖRNEKLEME U tot = U 1 = U 2 = 12 V tot = tot = 4 A + 3 A = 7A

136 Resistors series combination parallel combination

137 Voltage Divider

138 Capacitors capacitance - [Farads]: Michael Faraday capacitor - two terminal device that stores energy in the form of an electric charge doğru gerilimin değeri zamanla değişmez. two conductors separated by a thin layer of dielectric capacitance ~ conductor surface area, thinness of dielectric two adjacent wires in a ribbon cable are subject to capacitive crosstalk (ground every other wire) big capacitors are polarized, terrible accuracy, temperature stability, leakage, and lifetime---a loud buzzing noise from electronics could be an electrolytic capacitor has died

139 RC Circuits

140 RC Circuits timing - RC is called the time constant,, of the circuit, voltage will fall to 37% of its initial value in RC seconds. smoothing - high frequency noise on top of a slowly varying signal can be rejected by observing the signal through a relatively large RC time constant

141 RC Differentiator choose R and C small so V out is small note - this can happen by accident, if a smooth signal is corrupted with noise, maybe it s capacitive coupling---perhaps a digital line is too close to an analog signal.

142 RC Integrator choose R and C large so V out is small

143 Inductors inductance - [Henries]: 1 volt across 1 Henry produces a current that increases at 1 amp per second an inductor is normally formed from a coil of wire that may be wound on a core of magnetic material. a voltage source across an inductor causes the current to rise as a ramp. stopping a current going through an inductor generates a high voltage.

144 Inductors series combination no mutual inductance parallel combination

145 Transformers primary secondary gearbox for AC voltage and current V ~ I ~ w constant power: VI ( w) V in step-down: less voltage V out more current V in step-up: V out more voltage less current 6 : 3 =6/3 3 : 6 =3/6 transformers are the main reason why AC power is used. often first stage for low voltage DC power

146 Çevre Akımları Bu yöntemde, devrenin her bir gözü için ( Herhangi bir çevrenin seçilmesinde de sakınca yoktur ) bir çevre akımı ve yönü seçilir Seçilen bu çevre akımlarından faydalanarak Kirşof un Gerilimler Kanunu her bir göze uygulanır ve göz adedi kadar denklem yazılır. Göz adedi kadar bilinmeyen çevre akımı olduğundan, elde edilen göz adedi kadar denklem çözülerek her bir gözün çevre akımı bulunur. Sonrada çevre akımları kullanılarak kol akımları kolaylıkla bulunabilir.

147 çözüm

148 Thevenin s Equivalent Circuit

149 Thevenin Teoremi Bu teoreme göre elektrik devreleri bir direnç ve ona seri bağlı olan bir üreteç eşdeğeri ile temsil edilebilir. Gerilim kaynakları kısa devre, akım kaynakları ise açık devre yapılarak Thevenin eşdeğer direnci bulunur. Thevenin en çok bağımlı kaynaklarının dönüşümünde işimize yarar. Bağımlı kaynağın etkisi devrede Thevenin eşdeğer direnci olarak kendini gösterir. Böylece devreyi bağımlı kaynaklardan arındırılmış bir şekilde çözebiliriz.*

150

151 Thevenin

152

153 Thevenin 2

154

155 Thevenin Örnek R6 daki Thevenin Eşdeğer devresini bulunuz

156 R3//(R4+R5) =RA=4Ω 1. Adım

157 2. Adım Vth I = V/R = (24-6) /12 = 1.5Amps RA üzerinden Akım akmaz V1 ve V2 birbirine ters olduğu için çıkarılır. R1 ve R2 birbirlerine Seridir. VT = I R2 = (1.5 x 8W) = 12 Volts

158 3. Adım Rth 1/R = 1/R1 + 1/R2 R = RA +R = 6.67 Ω Rth

159 4. Adım Eşdeğer Devre ile hesap R6 => I = VT/Reş = 12/( ) = 0.94 Amps

160 Linearity Characteristic 42V 6Ω RL I L + V RL - 4Ω 10V If R L change its value, how will it effect the current and voltage across it?

161 Thevenin s Theorem When we are interested in current and voltage across RL, we can simplify other parts in the circuit. 6Ω 4Ω 42V RL 10V Equivalent circuit R TH V TH RL

162 6Ω 4Ω 42V RL 10V I I SC Slope = 1/R R TH V TH RL V V OC Voc = Voltage open-circuit Isc = Current short-circuit R = R equivalent

163 Thevenin s Equivalent Circuit Thevenin s equivalent circuit V TH R TH RL VTH = Voc (by removing RL and find the voltage difference between 2 pins) RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

164 Why do we need equivalent circuit? To analyze a circuit with several values of RL For circuit simplification (source transformation) To find RL that gives maximum power (maximum power transfer theorem)

165 Procedure 1. Remove RL from the circuit 2. Find voltage difference of the 2 opened connections. Let it equal VTH. 3. From step 2 find RTH by 3.1 short-circuit voltage sources 3.2 open-circuit current sources 3.3 Look into the 2 opened connections. Find equivalent resistance.

166 Example Find Thevenin s equivalent circuit and find the current that passes through RL when RL = 1Ω 2Ω 10Ω 10V 3Ω RL 2Ω

167 Find VTH 10V 6V 6V 2Ω 10Ω 10V 3Ω 2Ω 0V 0V 0V 3 V TH 10 6V 2 3

168 Find RTH 2Ω 10Ω 10V 3Ω 2Ω R TH Short voltage source 2Ω 10Ω Ω RTH 2Ω

169 Thevenin s equivalent circuit 13.2Ω 6V RL If RL = 1Ω, the current is A

170 Example Find Thevenin s equivalent circuit 2Ω 10Ω 1A 3Ω RL 2Ω

171 Find VTH 5V 3V 3V 2Ω 10Ω 1A 3Ω 2Ω 0V 0V 0V V TH 1 3 3V

172 Find RTH 2Ω 10Ω 1A 3Ω 2Ω Open circuit current source 2Ω 10Ω R TH Ω RTH 2Ω

173 Thevenin s equivalent circuit 15Ω 3V RL

174 Example: Bridge circuit Find Thevenin s equivalent circuit R1=2K R3=4K 10V RL=1K + - R2=8K R4=2K

175 Find VTH 10V R1=2K R3=4K 10V 8V 2V R2=8K R4=1K 0V VTH = 8-2 = 6V

176 Find RTH R1=2K R3=4K RTH R2=8K R4=1K R1=2K R3=4K R1=2K R3=4K R2=8K R4=1K R2=8K R4=1K

177 R1=2K R3=4K R2=8K R4=1K R TH 2K 8K 4K 1K 1.6K 0.8K 2. 4K

178 Thevenin s equivalent circuit 2.4K 6V RL

179 Norton s Equivalent Circuit

180 Norton Teoremi Norton teoremi, elektrik devrelerinin çözümlenmesinin kolaylaştırılması için kullanılan teorem ve yöntemdir. Bu yöntem sayesinde karmaşık elektrik devreler oluşturulan basit eşdeğer devre üzerinden kolayca çözülebilir. Norton Teoremi, benzer bir yöntem olan Thevenin teoreminin uzantısıdır. Teorem 1926 yılında birbirinden bağımsız olarak; Siemens firmasından Hans Ferdinand Mayer ( ) ve Bell Laboratuvarları'dan Edward Lawry Norton ( ) tarafından geliştirilmiştir. Mayer konu ile ilgili çalışmasını yayımlamış, Norton'un çalışması ise firma içi teknik rapor olarak kalmıştır. Doğrusal bir devre, herhangi iki noktasına göre, bir akım kaynağı ve buna paralel bir direnç haline getirilebilir. Bunun için; Herhangi iki noktadan uçları kısa devre edildiğinde geçen akım kaynak akımıdır Gerilim kaynağı kısa devre edildiğinde, iki nokta arasındaki direnç eşdeğer dirençtir.

181

182 Norton Örnek Norton Eşdeğerini bulunuz?

183 Norton Akımı?

184 Norton Direnci =Rth

185 Ohm kanunu Norton Thevenin

186 Norton s Equivalent Circuit I N R N RL In= Isc from replacing RL with an electric wire (resistance = 0) and find the current Rn = RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

187 Example Find Norton s equivalent circuit and find the current that passes through RL when RL = 1Ω 2Ω 10Ω 10V 3Ω RL 2Ω

188 Find In 2Ω 10Ω 10V 3Ω Isc 2Ω Find R total Find I total Current divider (10 2) I V A R I SC A 3 12

189 Find Rn 2Ω 10Ω 10V 3Ω 2Ω R TH Short voltage source 2Ω 10Ω Ω RTH 2Ω

190 Norton s equivalent circuit RL If RL = 1Ω, the current is A

191 Relationship Between Thevenin s and Norton s Circuit I R V TH TH R I N N R TH I SC Slope = - 1/Rth V OC V

192 Thevenin s equivalent circuit Norton s equivalent circuit V RL RL Same R value R V TH TH I R N N R TH

193 Example Find Norton s equivalent circuit 2Ω 10Ω 1A 3Ω RL 2Ω

194 Find In 2Ω 10Ω 1A 3Ω Isc 2Ω Current divider 3 I SC A 3 12

195 Find RTH 2Ω 10Ω 1A 3Ω 2Ω Open circuit current source 2Ω 10Ω R TH Ω RTH 2Ω

196 Norton s equivalent circuit RL

197 Norton s equivalent circuit Thevenin s equivalent circuit RL 3V 15 RL 0.2 x 15 = 3

198 Equivalent Circuits with Dependent Sources We cannot find Rth in circuits with dependent sources using the total resistance method. But we can use R TH V I OC SC

199 Example 250 2K 1V 4K 80 + Vx Vx + RL - Find Thevenin and Norton s equivalent circuit

200 1V 4K 2K Vx Vx + - Find Voc I1 I ) ( I I I I I KVL loop ) ( ) ( I I I I Vx Vx I I I I KVL loop2

201 250 2K 1V I1 4K 80 + Vx I Vx + - Solve equations I1 = 3.697mA I2 = 3.678mA V OC 80I 2 100Vx 80I ( I1 80(3.678mA) ( ) 7.3V I 2)

202 1V 4K 2K Vx Vx Isc Find Isc I1 I2 I ) ( I I I I I KVL loop ) ( ) 2 80( ) ( I I I I I Vx Vx I I I I I KVL loop2 KVL loop ) 3 80( I I I Vx I I

203 Find Isc 250 2K 1V 80 + I1 4K Vx I2 I Vx Isc I1 = 0.632mA I2 = 0.421mA I3 = A Isc = I3 = A

204 R TH VOC I SC Thevenin s equivalent circuit Norton s equivalent circuit V RL RL

205 Kaynaklar Analog Electronics, Bilkent Unıversity Electric Circuits Ninth Edition, James W. Nilsson Professor Emeritus Iowa State University, Susan A. Riedel Marquette University, Prentice Hall, Lessons in Electric Circuits, By Tony R. Kuphaldt Fifth Edition, last update January 10, Fundamentals of Electrical Engineering, Don H. Johnson, Connexions, Rice University, Houston, Texas, Introduction to Electrical and Computer Engineering, Christopher Batten - Computer Systems Laboratory School of Electrical and Computer Engineering, Cornell University, ENGRG 1060 Explorations in Engineering Seminar, Summer Introduction to Electrical Engineering, Mulukutla S. Sarma, Oxford University Press, Basics of Electrical Electronics and Communication Engineering, K. A. NAVAS Asst.Professor in ECE, T. A. Suhail Lecturer in ECE, Rajath Publishers, İnternet ortamından sunum ve ders notları Atomların elektron yapısı, Yrd.Doç.Dr. İbrahim İsmet Öztürk, Namık Kemal Üniversitesi.