1• Thevenin and Norton equivalents (I)ECE 201: Lecture 11Borja PeleatoReview2• During the last few lectures we have studied different methods to simplifycircuits, 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 inparallel with the same resistor– Decompose the output (a voltage or current) of a circuit into multipleindependent components, one for each input (independent source)• Today we will study the ultimate simplification tool: Thevenin and Nortonequivalents will allow us to transform ANY* circuit, with resistors, sources(dependent and independent), and more into a single independent sourceand a resistor*: Not really… but closeThevenin equivalent• Before you do anything, remove the components that youdo NOT want to replace• We need to find two parameters: RTHand VTH– VTH: measure the voltage between the two points withoutconnecting anything at the output (open circuit)– RTH: Turn off all INDEPENDENT sources (voltage becomes shortcircuit, current becomes open circuit) and measure theequivalent resistance of the remaining circuit• If only passive elements (eg. resistors) remain, you can combine themusing the usual formulas• If there are dependent sources, you will need to connect a source (ofarbitrary value) and measure the ratio between V and I (more on thislater)• The whole circuit is equivalent to3Example• Think of it as if you had a black box, you knew itcontains a voltage source in series with a resistor andyou are trying to determine their values4Norton 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 asource transformation, you get the Norton equivalent,and vice versa• The Norton equivalent requires finding RNand 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 measureresistance (exactly the same as in Thevenin, hence RN=RTH)• The whole circuit is equivalent to:5Example• Think of it as if you had a black box, you knew itcontains a current source in parallel with a resistor andyou are trying to determine their values6Example (cont)7Comments• The steps for finding RN, RTH, IN, VTH areindependent. They can beperformed in any order. You do not need any of those quantities tocompute the others• Be careful with the signs. The voltage/current in theThevenin/Norton equivalent needs to have the same direction asthe one that you measured• Measuring the equivalent resistance of a circuit:– Equivalent resistance of a circuit (or a black box for that matter) isdefined as the ratio between the voltage connected to it and thecurrent that it draws.– If the circuit is linear, this ratio will be constant. Hence, you can setwhatever voltage or current you want, measure the other, and takethe ratio8Example9Example
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