Useful Circuit Analysis Techniques Chapter 5: Useful Circuit Analysis Techniques 1 Dr. Amer Alsaraira

Objectives : Superposition Source transformation the Thevenin equivalent of any network the Norton equivalent of any network the load resistance that will result in maximum power transfer 2 Dr. Amer Alsaraira

Linearity and Superposition : Linear Elements and Linear Circuits a linear element is a passive element that has a linear voltage-current relationship. a linear dependent source is a dependent current or voltage source whose output current or voltage is proportional only to the first power of a specified current or voltage variable in the circuit (or to the sum of such quantities). a linear circuit is a circuit composed entirely of independent sources, linear dependent sources, and linear elements. 3 Dr. Amer Alsaraira

The principle of superposition : The response in a linear circuit having more than one independent source can be obtained by adding the responses caused by the separate independent sources acting alone. (a) A voltage source set to zero acts like a short circuit. (b) A current source set to zero acts like an open circuit. 4 Dr. Amer Alsaraira

Example 5.1: Use superposition to find the current ix. 5 Dr. Amer Alsaraira

Practice: 5.1 Use superposition to find the current Ix. 6 Dr. Amer Alsaraira

Example 5.3 : Use superposition to find the current Ix. 7 Dr. Amer Alsaraira

Example 5.3 : Use superposition to find the current Ix. 8 Dr. Amer Alsaraira

Practice: 5.2 Use superposition to obtain the voltage across each current source. 9 Dr. Amer Alsaraira

Source Transformation: (a) A general practical voltage source connected to a load resistor RL. (b) The terminal characteristics compared to an ideal source. (a) A general practical current source connected to a load resistor RL. (b) The terminal characteristics compared to an ideal source. 10 Dr. Amer Alsaraira

Equivalent Sources: 11 Dr. Amer Alsaraira

Equivalent Sources: 12 Dr. Amer Alsaraira

Example 5.4: Compute the current through the 4.7 k resistor after transforming the 9 mA source into an equivalent voltage source. 13 Dr. Amer Alsaraira

Practice: 5.3 compute the current ix after performing a source transformation on the voltage source 14 Dr. Amer Alsaraira

Example 5.5: Calculate the current through the 2Ω resistor 15 Dr. Amer Alsaraira

Practice: 5.4 Compute the voltage V 16 Dr. Amer Alsaraira

Thevenin and Norton Equivalent: A complex network including a load resistor RL. A Thévenin equivalent network connected to RL. A Norton equivalent network connected to RL. 17 Dr. Amer Alsaraira

Thevenin’s theorem: Given any linear circuit, rearrange it in the form of two networks A and B connected by two wires. Define a voltage voc as the open-circuit voltage which appears across the terminals of A when B is disconnected. Then all currents and voltages in B will remain unchanged if all independent voltage and current sources in A are “killed” or “zeroed out,” and an independent voltage source voc is connected, with proper polarity, in series with the dead (inactive) A network. 18 Dr. Amer Alsaraira

Example 5.6: Determine the Thevenin equivalent. 19 Dr. Amer Alsaraira

Example 5.7: Determine the Thevenin equivalent. (use Theory) 20 Dr. Amer Alsaraira

Practice: 5.5 Using repeated source transformations, determine the Thevenin equivalent of the highlighted network 21 Dr. Amer Alsaraira

Practice: 5.6 Use Thevenin’s theorem to find the current through the 2-c resistor 22 Dr. Amer Alsaraira

Example 5.8: Determine the Thevenin equivalent for the network faced by 1-kohm . 23 Dr. Amer Alsaraira

“killed” or “zeroed out,” and an independent current Norton’s theorem: Given any linear circuit, rearrange it in the form of two networks A and B connected by two wires. If either network contains a dependent source, its control variable must be in that same network. Define a current isc as the short circuit current that appears when B is disconnected and the terminals of A are short-circuited. Then all currents and voltages in B will remain unchanged if all independent voltage and current sources in A are “killed” or “zeroed out,” and an independent current source isc is connected, with proper polarity, in parallel with the dead (inactive) A network 24 Dr. Amer Alsaraira

Example: Determine the Norton equivalent for the network faced by 1-kohm . 25 Dr. Amer Alsaraira

Thevenin and Norton equivalents 26 Dr. Amer Alsaraira

Determine the Thevenin and Norton equivalents Practice: 5.7 Determine the Thevenin and Norton equivalents 27 Dr. Amer Alsaraira

Example 5.9: Determine the Thevenin equivalent. 28 Dr. Amer Alsaraira

Example 5.9: Determine the Thevenin equivalent. 29 Dr. Amer Alsaraira

Practice: 5.8 Determine the Thevenin equivalent 30 Dr. Amer Alsaraira

Example 5.10: Find the Thévenin equivalent of the circuit shown. 31 Dr. Amer Alsaraira

Practice: 5.9 Page 52 Determine the Thevenin equivalent 32 Dr. Amer Alsaraira

Example 5.9: Determine the Thevenin equivalent resistance (RTH). 33 Dr. Amer Alsaraira

Maximum Power Transfer: 34 Dr. Amer Alsaraira

Maximum Power Transfer: 35 Dr. Amer Alsaraira

Example: Select R1 so that maximum power is transferred from stage 1 to stage 2 and find the maximum power 36 Dr. Amer Alsaraira

Example 5.11: The circuit shown is a model for a common-emitter bipolar junction transistor amplifier. Choose a load resistance so that maximum power is transferred to it from the amplifier, and calculate the actual power absorbed. 37 Dr. Amer Alsaraira

Practice: 5.10 If Rout = 3kΩ, find the power delivered to it What is the maximum power that can be delivered to any Rout 38 Dr. Amer Alsaraira