ECE 201 Lecture 11 Borja Peleato Thevenin and Norton equivalents I 1 Review During the last few lectures we have studied different methods to simplify circuits or portions thereof Combine series or parallel resistors into a single one Combine series or parallel sources into a single one Transform a voltage source in series with a resistor into a current source in parallel with the same resistor Decompose the output a voltage or current of a circuit into multiple independent components one for each input independent source Today we will study the ultimate simplification tool Thevenin and Norton equivalents will allow us to transform ANY circuit with resistors sources dependent and independent and more into a single independent source and a resistor Not really but close 2 Thevenin equivalent Before you do anything remove the components that you do NOT want to replace We need to find two parameters RTH and VTH VTH measure the voltage between the two points without connecting anything at the output open circuit RTH Turn off all INDEPENDENT sources voltage becomes short circuit current becomes open circuit and measure the equivalent resistance of the remaining circuit If only passive elements eg resistors remain you can combine them using the usual formulas If there are dependent sources you will need to connect a source of arbitrary value and measure the ratio between V and I more on this later The whole circuit is equivalent to 3 Example Think of it as if you had a black box you knew it contains a voltage source in series with a resistor and you are trying to determine their values 4 Norton equivalent Same as Thevenin but with a current source instead Also resistance is in parallel If you find the Thevenin equivalent first and then do a source transformation you get the Norton equivalent and vice versa The Norton equivalent requires finding RN and IN First remove any unwanted element to avoid clutter IN Measure the current at the output when short circuited closed circuit RN Then disconnect independent sources and measure resistance exactly the same as in Thevenin hence RN RTH The whole circuit is equivalent to 5 Example Think of it as if you had a black box you knew it contains a current source in parallel with a resistor and you are trying to determine their values 6 Example cont 7 Comments The steps for finding RN RTH IN VTH are independent They can be performed in any order You do not need any of those quantities to compute the others Be careful with the signs The voltage current in the Thevenin Norton equivalent needs to have the same direction as the one that you measured Measuring the equivalent resistance of a circuit Equivalent resistance of a circuit or a black box for that matter is defined as the ratio between the voltage connected to it and the current that it draws If the circuit is linear this ratio will be constant Hence you can set whatever voltage or current you want measure the other and take the ratio 8 Example 9 Example cont 10
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