Network analysis lecture 1.pptx
- 1. Presented by C.S.Khandelwal Electronics and Telecommunication Department 5/16/2021 1
- 2. Electric Current Definition: rate of positive charge flow Symbol: i Units: Coulombs per second ≡ Amperes (A) i = dq/dt where q = charge (in Coulombs), t = time (in seconds) Note: Current has polarity. 5/16/2021 2
- 3. Electric Potential (Voltage) • Definition: energy per unit charge • Symbol: v • Units: Joules/Coulomb ≡ Volts (V) v = dw/dq where w = energy (in Joules), q = charge (in Coulombs) Note: Potential is always referenced to some point. 5/16/2021 3
- 4. Electric Power • Definition: transfer of energy per unit time • Symbol: p • Units: Joules per second ≡ Watts (W) p = dw/dt = (dw/dq)(dq/dt) = vi • Concept: As a positive charge q moves through a drop in voltage v, it loses energy energy change = qv rate is proportional to # charges/sec 5/16/2021 4
- 5. Basic Circuit Analysis Basic circuit elements are Resistor,Inductor and Capacitor Resistor: it opposes the flow of current It depends on following factors Directly proportional to its length Inversely proportional to the area of cross section of conductor Depends on the nature of the material Depends on the temperature of the conductor Rά l/A , R = ρl A 5/16/2021 5
- 6. Resistor • An element is said to have a resistance of 1 ohm, if it permits 1A of current to flow through it when 1V is impressed across its terminals. • Ohm’s law, which is related to voltage and current, v = Ri or R = v/ i where v is the potential across the resistive element, i the current through it, and R the resistance of the element. 5/16/2021 6
- 7. Resistor 5/16/2021 7 • The power absorbed by a resistor is given by • p = vi = v (v/ R)= v2/ R or • p = vi = (iR)i = i 2R • The equation for energy absorbed by or delivered to a resistor is t t • E= ∫ −∞ pdτ = ∫ −∞ i 2R dτ
- 8. Inductor Inductance: it opposes any change of current flowing through it It depends on the following factors Directly proportional to the square of the number of turns Directly proportional to the area of cross section Inversely proportional to the length Depends on the absolute permability of the magnetic material L ά N2A/l , L= μN2A/l 5/16/2021 8
- 9. Current –voltage relationship in an inductor V= L di/dt di=1/L Vdt Integrating both the sides i(t) t ∫ di = 1/L ∫ vdt i(0) 0 t i(t) = 1/L ∫ vdt 0 5/16/2021 9
- 10. Energy stored in an inductor 5/16/2021 10 V= L di/dt Energy supplied to the inductor during interval dt is given by dE= vi dt= L di/dt i dt = Li dt Total energy supplied to the inductor when current is increased from 0 to I ampere I I E = ∫ dE= ∫ Li dt =1/2 L I 2 0 0
- 11. Capacitor Capacitor: capacitor to store an electric charge when its plates at different potentials Capacitance of a capacitor depends on following factors Directly proportional to the area of the plates Inversely proportional to the distance between two plates It depends on absolute permitivity of medium between plates C ά A/d C=Є A/d Where d is the distance between two plates , A is cross sectional area of the plates , Є is absolute permitivity of the medium between the plates. 5/16/2021 11
- 12. Current –voltage relationship in a Capacitor Charge an a capacitor is given by q= cv Where q denotes charge and v is the potential difference across the plates i=dq/dt = d/dt cv = c dv/dt Expressing capacitor voltage as a function of current dv= 1/c idt Integrating both sides ∫dv =1/c ∫ idt V(t)= 1/c ∫ idt + v(0) v(0) is initial voltage 5/16/2021 12
- 13. Energy stored in a Capacitor Capacitor of capacitance C farads be charged from a source of v volts.The current I is given by i=c dv/dt Energy supplied to the capacitor during interval dt is given by d E= vi dt = vc dv/dt dt Total energy supplied by capacitor when potential difference is increased from 0 to v E= ∫ dEe= ∫cv dv=1/2 cv2 5/16/2021 13
- 14. Sources Independent sources: output characteristics of an independent are not dependent on any N/W 5/16/2021 14 V V(t)
- 15. Sources Dependent sources: If the voltage or current of a source depends in turn upon some other voltage or current . Four types of dependent source Voltage controlled voltage source: Voltage Vcd is propotional voltage Vab Vcd=μ Vab 5/16/2021 15 a b c d μ Vab Vab Vcd
- 16. Dependent Sources Voltage controlled Current source: Current icd in the branch is proportional to the voltage Vab icd= gm Vab (gm= tranconductance) 5/16/2021 16 a b Vab gm Vab c d icd
- 17. Dependent Sources Current controlled voltage source: voltage Vcd is proportional to the current iab Vcd= r iab ( r= transresistance) 5/16/2021 17 a b iab c d r iab Vcd
- 18. Dependent Sources • Current controlled current source: Current icd proportional to iab in branch of the network icd= β iab (β = dimensionless constant) 5/16/2021 18 a b iab icd c β iab
- 19. Network and Circuit Network means :The interconnect of two or more circuit elements (such as voltage source, resistor, inductor, capacitor) 5/16/2021 19
- 20. Network and Circuit If the network contains at least one closed path ,it is called an electric circuit 5/16/2021 20
- 21. Linear and Non linear Elements Linear element: If the resistance ,inductance or capacitance offered by an element does change linearly with change in applied voltage or current . Non linear element: in which current doesnot change linearly with change in applied voltage. ex. Semiconductor diode 5/16/2021 21
- 22. Active and Passive components Active components: An element which is a source of electrical signal or which is capable of increasing of level of signal energy is turned as an active elements Ex: Batteries, BJT, FET,OP-AMP Passive components: resistor, inductor , capacitor,VDR,LDR and thermistor are passive components 5/16/2021 22
- 23. Unilateral and Bilateral elements Unilateral:If the magnitude of current flowing through a circuit is affected when polarity of the applied voltage is changed Bilateral : when the voltage is applied ,current start flowing ,if we change the polarity of the applied voltage , direction of current is changed but its magnitude is not affected 5/16/2021 23
- 24. Active and passive networks 5/16/2021 24 Active networks:Network which contains at least one active elements Passive networks: Network which doesnot cotains any active elements
- 25. Time invariant and time variant networks Time invariant: if its input output relationship doesnot change with time Time variant: if its input output relationship does change with time 5/16/2021 25
- 26. Simplification of networks Series and parallel combinations of resistors R1,R2,R3,R4 be the resistors of three resistors connected in series across a dc voltage source v as shown in figure 5/16/2021 26
- 27. 5/16/2021 27 Consider a circuit with multiple resistors connected in series. Find their “equivalent resistance”. • KCL tells us that the same current (I) flows through every resistor • KVL tells us Equivalent resistance of resistors in series is the sum R2 R1 VSS I R3 R4 + Resistors in Series
- 28. 5/16/2021 28 I = VSS / (R1 + R2 + R3 + R4) Voltage Divider + – V1 + – V3 R2 R1 VSS I R3 R4 +
- 29. 5/16/2021 29 SS 4 3 2 1 2 2 V R R R R R V + + + = Correct, if nothing else is connected to nodes because R5 removes condition of resistors in series SS 4 3 2 1 2 2 V R R R R R V + + + ≠ When can the Voltage Divider Formula be Used? + – V2 R2 R1 VSS I R3 R4 + R2 R1 VSS I R3 R4 + R5 + – V2
- 30. 5/16/2021 30 • KVL tells us that the same voltage is dropped across each resistor Vx = I1 R1 = I2 R2 • KCL tells us R2 R1 ISS I2 I1 x Resistors in Parallel Consider a circuit with two resistors connected in parallel. Find their “equivalent resistance”.
- 31. 5/16/2021 31 What single resistance Req is equivalent to three resistors in parallel? + V I V + I R3 R2 R1 Req eq General Formula for Parallel Resistors Equivalent conductance of resistors in parallel is the sum
- 32. 5/16/2021 32 Vx = I1 R1 = ISS Req Current Divider R2 R1 ISS I2 I1 x
- 33. 5/16/2021 33 R2 R1 I I2 I1 I3 R3 + V + + = 3 2 1 R 1 R 1 R 1 I V + + = = 3 2 1 3 3 3 1/R 1/R 1/R 1/R I R V I Generalized Current Divider Formula Consider a current divider circuit with >2 resistors in parallel: