Lecture 2: Semiconductors PDF

Lecture #2, Oct 2020 © Sara A.Shehab  Lecture #2, Oct 2020 © Sara A.Shehab Ohm’s Law Kirchhoff’s Laws Series Resistors Parallel Resistors  Course Information Lecture #2, Oct 2020 © Sara A.Shehab In...

Lecture #2, Oct 2020 © Sara A.Shehab  Lecture #2, Oct 2020 © Sara A.Shehab Ohm’s Law Kirchhoff’s Laws Series Resistors Parallel Resistors  Course Information Lecture #2, Oct 2020 © Sara A.Shehab Instructor: Dr. Sara A.Shehab Email:[email protected]. edu.eg Lectures: Saturday, 11:00-01:00 (AI Program) Wednsday, 09:00-11:00 (CS Program) Office Hours: Saturday Wednsday T.A.: Eng. Amal el natat , Eng:Ahmed salem Reference: T. Floyd, Electronic devices - Conventional Current Version, 10th edition, Prentice Hall. 2  Ohm’s Law Lecture #2, Oct 2020 © Sara A.Shehab Georg Simon Ohm (1789 – 1854) German professor who publishes a book in 1827 that includes what is now known as Ohm's law. Ohm's Law: The voltage across a resistor is directly proportional to the currect flowing through it. 3  Ohm’s Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab Resistance   resistivity in Ohm-meters Resistance R  l A l = length 4 Good conductors (low ): Copper, Gold A Good insulators (high ): Glass, Paper 5  Ohm’s Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab v - + i R + - v v v  iR i R R i R i1 v  i1R (i  i1 ) 5 v - + Units of resistance, R, is Ohms (W) R = 0: short circuit R  : open circuit  Ohm’s Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab Conductance, G i G + - + v - 1 G Unit of G is siemens (S), R 1 S = 1 A/V 6 i i v i  Gv G G v  Ohm’s Law (Cont..) Power Lecture #2, Oct 2020 © Sara A.Shehab A resistor always dissipates energy; it transforms electrical energy, and dissipates it in the form of heat. Rate of energy dissipation is the instantaneous power 2 v (t ) p(t )  v(t )i (t )  Ri (t )  2 0 R 2 7 i (t ) p(t )  v(t )i (t )  Gv (t )  2 0 G  Ohm’s Law (Cont..) In the circuit, calculate the current i, the conductance G, Lecture #2, Oct 2020 © Sara A.Shehab and the power p. 8  Ohm’s Law (Cont..) 9 Lecture #2, Oct 2020 © Sara A.Shehab  Kirchhoff Law Lecture #2, Oct 2020 © Sara A.Shehab Gustav Robert Kirchhoff (1824 – 1887) Born in Prussia (now Russia), Kirchhoff developed his "laws" while a student in 1845. These laws allowed him to calculate the voltages and currents in multiple loop circuits. 10  Kirchhoff Law (Cont..) CIRCUIT TOPOLOGY Lecture #2, Oct 2020 © Sara A.Shehab Topology: How a circuit is laid out. A branch represents a single circuit (network) element; that is, any two terminal element. A node is the point of connection between two or more branches. A loop is any closed path in a circuit (network). A loop is said to be independent if it contains a 11 branch which is not in any other loop.  Kirchhoff Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab Fundamental Theorem of Network Topology For a network with b branches, n nodes and l independent loops: b  l  n 1 Example b 9 7W 1W 2W 6W 12 DC 3W 4W 5W 2A n 5 l 5  Kirchhoff Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab Elements in Series Two or more elements are connected in series if they carry the same current and are connected sequentially. I R1 R2 13 V0  Kirchhoff Law (Cont..) Lecture #2, Oct 2020 © Sara A.Shehab Elements in Parallel Two or more elements are connected in parallel if they are connected to the same two nodes & consequently have the same voltage across them. I I1 I2 R1 R2 14 V  Kirchoff’s Current Law (KCL) Lecture #2, Oct 2020 © Sara A.Shehab The algebraic sum of the currents entering a node (or a closed boundary) is zero. N i n 1 n 0 where N = the number of branches connected to the node and in = the nth current entering 15 (leaving) the node.  Kirchoff’s Current Law (KCL) Lecture #2, Oct 2020 © Sara A.Shehab Sign convention: Currents entering the node are positive, currents leaving the node are negative. N i n 1 n 0 i2 i1 i3 i5 i4 16 i1  i2  i3  i4  i5  0  Kirchoff’s Current Law (KCL) The algebraic sum of the currents entering Lecture #2, Oct 2020 © Sara A.Shehab (or leaving) a node is zero. i2 Entering: i1  i2  i3  i4  i5  0 i1 i3 i5 i4 Leaving: i1  i2  i3  i4  i5  0 The sum of the currents entering a node is equal to the sum of the currents leaving a node. 17 i1  i2  i4  i3  i5  Kirchoff’s Voltage Law (KVL) Lecture #2, Oct 2020 © Sara A.Shehab The algebraic sum of the voltages around any loop is zero. M v m 1 m 0 where M = the number of voltages in the loop and vm = the mth voltage in the loop. 18  Kirchoff’s Voltage Law (KVL) Sign convention: The sign of each voltage is the polarity of the Lecture #2, Oct 2020 © Sara A.Shehab terminal first encountered in traveling around the loop. I The direction of travel is arbitrary. + R1 V1 Clockwise: - A + V0  V1  V2  0 R2 V2 V0 Counter-clockwise: - 19 V2  V1  V0  0 V0  V1  V2  Kirchoff’s Examples 20 Lecture #2, Oct 2020 © Sara A.Shehab  Kirchoff’s Examples 21 Lecture #2, Oct 2020 © Sara A.Shehab  Kirchoff’s Examples 22 Lecture #2, Oct 2020 © Sara A.Shehab  Kirchoff’s Examples 23 Lecture #2, Oct 2020 © Sara A.Shehab Kirchoff’s Examples Find currents and voltages in the circuit Lecture #2, Oct 2020 © Sara A.Shehab 24  Series Resistors I Lecture #2, Oct 2020 © Sara A.Shehab + V0  V1  V2  IR1  IR2 R1 V1 -  I  R1  R2  A + R2 V2  IRs V0 - Rs  R1  R2 I Rs 25 V 26  Voltage Divider Lecture #2, Oct 2020 © Sara A.Shehab V0 V0 I I  Rs R1  R2 R1 V1 V0 V2  IR2  R2 A  R1  R2  R2 V2 V0 R2 V2  V0  R1  R2  R1 Also V1  V0  R1  R2  26  Parallel Resistors I Lecture #2, Oct 2020 © Sara A.Shehab V V I  I1  I 2   R1 R2 I1 I2 R1 R2 1 1  V V     R1 R2  V  1 1 1 Rp I   Rp R1 R2 Rp V R1 R2 Rp  27 R1  R2  Current Division Lecture #2, Oct 2020 © Sara A.Shehab i v(t ) R2 + i1 (t )   i (t ) i1 i2 R1 R1  R2 i(t) R1 R2 v(t) - v(t ) R1 i2 (t )   i (t ) R2 R1  R2 R1 R2 v(t )  R p i (t )  i (t ) R1  R2 28 Current divides in inverse proportion to the resistances  Current Division Lecture #2, Oct 2020 © Sara A.Shehab N resistors in parallel 1 1 1 1      v(t )  R p i (t ) Rp R1 R2 Rn v(t ) R p Current in jth branch is i j (t )   i (t ) Rj Rj 29  Parallel and Series Example 30 Lecture #2, Oct 2020 © Sara A.Shehab  Parallel and Series Example 31 Lecture #2, Oct 2020 © Sara A.Shehab  Parallel and Series Example 32 Lecture #2, Oct 2020 © Sara A.Shehab