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LAB_4 - Network Theorems and Devices

# LAB_4 - Network Theorems and Devices - Lab 4 Network...

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Lab 4 55 Network Theorems & Devices Educational Objectives In this lab, you will test the predictions of two important network theorems as well as experimen- tally verify: • Thévenin's Theorem • The Maximum Power Transfer Theorem Background Information 1. Thévenin's Theorem Any linear active one-port network can be replaced by a single voltage source, equal to the open- circuit voltage of the one-port, in series with the network in which all independent sources are set to zero. Proof : Consider the linear circuit represented in the top panel of Figure 1 (LAN: linear active network) which contains assorted sources and resistors, and has a single "port" by which it can be connected to the outside world. We attach a load resistor R L at the port as shown, and observe that R L draws load current i 1 and voltage v 1 from the network. Science is emphatically an important part of culture today, as scientific knowledge and its applications continue to transform the world, and condition every aspect of the relations between men and nations. - Vannevar Bush Figure 1: Development of Thévenin's Theorem

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Lab 4 56 In Figure 1b, a voltage source has been added in series with the load so as to oppose the current flow. We have increased the voltage of this source until the current i 2 is brought to zero. When zero cur- rent is flowing at a port, we say the port is "open-circuited". Therefore, in Figure 1b, the port voltage (not V 2 ) is the open-circuit voltage, V oc of the LAN. By Kirchoff’s Voltage Law, this is equal and opposite to the voltage of the external source we have applied. In Figure 1c, all independent sources inside the LAN have been turned to zero, creating a linear passive network or LPN. This means that voltage sources have been replaced by short circuits (zero volt- age) and current sources have been replaced by open-circuits (zero current). The only source now active is the external source of the center panel, V oc . Since this is the only active source, we now expect the cur- rent to flow in the direction shown as i 3 in the bottom panel. According to Thévenin's theorem, the load should receive the same current in the bottom panel 1c as it did in the top panel 1a. To prove that this is the case, apply the superposition principle. In the top panel, with the LAN sources active and the V oc source zero, current i 1 flows in the load. In the bottom panel, with the LAN sources all zero and the V oc source active, the load current is i 3 . Now, according to
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