* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download CSCI 2980: Introduction to Circuits, CAD, and Instrumentation
Power engineering wikipedia , lookup
Power inverter wikipedia , lookup
Electrical ballast wikipedia , lookup
History of electric power transmission wikipedia , lookup
Three-phase electric power wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Ground (electricity) wikipedia , lookup
Electronic engineering wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Topology (electrical circuits) wikipedia , lookup
Ground loop (electricity) wikipedia , lookup
Schmitt trigger wikipedia , lookup
Electrical substation wikipedia , lookup
Voltage optimisation wikipedia , lookup
Signal-flow graph wikipedia , lookup
Two-port network wikipedia , lookup
Stray voltage wikipedia , lookup
Earthing system wikipedia , lookup
Buck converter wikipedia , lookup
Current source wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Rectiverter wikipedia , lookup
Integrated circuit wikipedia , lookup
Mains electricity wikipedia , lookup
Electrical wiring in the United Kingdom wikipedia , lookup
Surge protector wikipedia , lookup
Current mirror wikipedia , lookup
Opto-isolator wikipedia , lookup
Flexible electronics wikipedia , lookup
EENG 2610: Circuits Analysis Class 2: Kirchhoff’s Laws, Single-Loop Circuits, SingleNode Pair Circuits Oluwayomi Adamo Department of Electrical Engineering College of Engineering, University of North Texas Some Important Concepts Lumped-Parameter Circuit Node A point of connection of two or more circuit elements. A node is one end of a circuit element together with all the perfect conductor that are attached to it. Loop Wires in circuits are assumed perfect conductor Interconnections in circuits have zero resistance Wire doesn’t consume energy; energy in circuits is lumped in each circuit element. A loop is any closed path through the circuit in which no node is encountered more than once. Branch A branch is a portion of a circuit containing only a single element and the nodes at each end of the element. Kirchhoff’s Current Law (KCL) KCL The algebraic sum of the currents ENTERING any node is zero: N i (t ) 0 j 1 j Our sign convention for KCL: - The algebraic sign of the current is ‘plus’ if the current is entering the node - The algebraic sign of the current is ‘minus’ if the current is leaving the node Example 2.5: Write all KCL equations Closed Surface as Super-Node Super-Node If some set of elements are completely contained within a surface that is interconnected, the surface is called super-node. Generalized KCL for Super-Node The algebraic sum of the currents entering any closed surface (or super-node) is zero. Write KCL equations for super-nodes Kirchhoff’s Voltage Law (KVL) KVL The algebraic sum of the voltages around any loop is zero: N v (t ) 0 j 1 j Voltage is defined as the difference in energy level of a unit positive charge located at each of the two points. KVL is based on the conservation of energy: the work required to move a unit charge around any loop is zero. Our Sign Convention for KVL As moving around a loop, the algebraic sign of voltage is positive in KVL equation if encounter the plus sign first, and the algebraic sign of voltage is negative in KVL equation if encounter the minus sign first. Example 2.9: Using KVL equation to find V R3 = 18 V = 12 V Convention for Voltage Notation Double-subscript notation Vab = Va – Vb a + and – notation Arrow notation Use an arrow between two points, pointing from negative node to positive node. KVL can be applied to a closed path even if part of the closed path is the arrow notation. Vab V = Vab b Example 2.11: Use KVL to find Vae and Vec Vae Vec Single-Loop Circuits Single-loop circuits Elements are connected in series. All elements carry same current. Voltage Divider Source v(t) is divided between two resistors in proportion to their resistance v(t ) vR1 vR2 0 vR1 i (t ) R1 vR2 i (t ) R2 i (t ) R1 v R1 R R v(t ) 1 2 v R2 v(t ) R2 R1 R2 v(t ) R1 R2 Multiple Voltage Sources in Single-Loop Circuit v3 v2 v4 Equivalent Transform + vR R vS _ + vR _ v1 v1 v2 v3 v4 vR 0 vS v1 v2 v3 v4 vS v R 0 R Multiple Resistors in Single-Loop Circuit i (t ) Equivalent Transform RS v (t ) v(t ) vR1 vR2 vR3 ... vRN 0 vR1 i (t ) R1 vR2 i (t ) R2 ... v i (t ) R N RN v R Ri i i Single-Node Pair Circuits Single-Node Pair Circuits Elements are connected in parallel Elements have the same voltage across them Current division v(t ) R1 R2 i (t ) R1 R2 Multiple Current Sources in Single-Node Pair Circuits Equivalent Transform i2 (t ) i5 (t ) Multiple Resistors in Single-Node Pair Circuits Equivalent Transform + v (t ) _ General current divider: io (t ) v(t ) RPiO (t ) Rp v(t ) iO (t ) iK (t ) ik (t ) R k Rk RP Example 2.19: Find the current IL Equivalent circuit