* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download EE 221 Review 1
Analog-to-digital converter wikipedia , lookup
Immunity-aware programming wikipedia , lookup
Regenerative circuit wikipedia , lookup
Radio transmitter design wikipedia , lookup
Topology (electrical circuits) wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Transistor–transistor logic wikipedia , lookup
Integrating ADC wikipedia , lookup
Valve audio amplifier technical specification wikipedia , lookup
Wilson current mirror wikipedia , lookup
Power electronics wikipedia , lookup
Voltage regulator wikipedia , lookup
Surge protector wikipedia , lookup
Negative-feedback amplifier wikipedia , lookup
Power MOSFET wikipedia , lookup
Schmitt trigger wikipedia , lookup
Two-port network wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Operational amplifier wikipedia , lookup
Current mirror wikipedia , lookup
Opto-isolator wikipedia , lookup
EE 221 Review 2 Nodal and Mesh Analysis Superposition Source transformation Thevenin and Norton equivalent Operational Amplifier Nodal Analysis - Approach 1. Redraw circuit to emphasize nodes. 2. Assign reference node and voltages. N nodes result in N-1 unknown voltages. 3. Use KCL to find N-1 equations. 4. Relate dependent sources to node voltages. 5. Form supernode to enclose voltage sources and apply KCL. Add voltage equations. Nodal analysis - Example KCL requires that all currents flowing into the region must sum to zero, or we would pile up or run out of electrons. At node 1: (KCL) v1 v2 v1 v3 83 3 4 At the “supernode:” (KCL) v2 v1 v3 v1 v3 v2 3 25 3 4 5 1 At the “supernode:” (KVL) 22 v3 v2 Nodal analysis - Example (I) (II) (III) variables Independent voltage source (supernode containing reference) v1 = -12 Mesh analysis - approach 1. Redraw planar circuit to emphasize meshes. 2. Assign clockwise mesh currents. M meshes result in M unknown currents. 3. Apply KVL around each mesh. 4. Relate dependent sources to mesh currents. 5. Use supermesh for current source shared between two meshes. Add current equation. Mesh analysis - Example Creating a “supermesh” from meshes 1 and 3: -7 + 1 ( i1 - i2 ) + 3 ( i3 - i2 ) + 1 i3 = 0 [1] Around mesh 2: 1 ( i2 - i1 ) + 2 i2 + 3 ( i2 - i3 ) = 0 [2] Finally, we relate the currents in meshes 1 and 3: i1 - i3 = 7 [3] Rearranging, i1 - 4 i2 + 4 i3 = 7 [1] -i1 + 6 i2 - 3 i3 = 0 [2] i1 [3] - i3 = 7 Solving, i1 = 9 A, i2 = 2.5 A, and i3 = 2 A. Circuit analysis (a) A voltage source set to zero acts like a short circuit. (b) A current source set to zero acts like an open circuit. Superposition (a) Linear circuits allow superposition. (b) Keep only one independent source at a time activate. (c) Always keep dependent sources. Source transformation A general practical voltage source connected to a load resistor RL. A general practical current source connected to a load resistor RL. • Convert between the two - Sources are related by: • RS = Rp, and • Vs = Rs Is = Rp Is • Useful when asked for: • Maximum terminal voltage (vs) and/or current (is) • (Maximum) power transferred (PL = vL iL when RL = Rs) Thevenin and Norton • "Dead" network to find equivalent source resistance RTH and RN • Open loop voltage to determine VTH (any method) • Short circuit current determines IN Thenenin - Example Source transformation is used here. • Open loop voltage to determine VTH and short circuit current determines IN • Find equivalent source resistance RTH and RN • use "Dead" network • use RTH = RN = VTH / IN (the only way in case of dependent sources) Operational Amplifier (a) Electrical symbol. Neglected: (1) Output voltage saturation. (b) “Minimum" op amp. Ideal: (1) No input current. (2) No voltage difference between input terminals. (2) Input/output resistance. (3) Limited open loop gain. (4) Input bias current. (5) Input offset voltage. Operational Amplifier - Circuits Op amp connected as an Inverting amplifier. Output characteristics. • 1st step: Determine voltage at input terminals • 2nd step: Determine current i Vout = - (Rf / R1) Vin • 3rd step: Find output voltage vout Operational Amplifier - Circuits (c) (a) An op amp used to construct a noninverting amplifier circuit. (b) Circuit with currents and voltages labeled. (c) Output characteristics. Vout = (1 + Rf / R1) Vin OpAmp - Example b Difference amplifier a c d • Your choice: Nodal analysis and/or superposition • vout = -Rb/Rc v1 + Rd(Ra+Rb) / (Ra(Rc+Rd)) v2