Lecture notes, lecture 3 - Thevenin and Norton Equivalent Circuits PDF

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Summary

Thevenin and Norton Equivalent Circuits...

Description

Thevenin and Norton Equivalent Circuits Definition:

Any one-port network consisting only of sources and resistors can be replaced by a Thevenin or Norton equivalent circuit. RTH Isc

VTH

IN

RN

𝑉!" ! = ! 𝑉!" !&!𝐼! = −𝐼!" !&!𝑅! = 𝑅!" !!! Question – Calculate the Thevenin Equivalent circuit and Norton Equivalent circuit.

5600Ω

4V

6800Ω Iin Vin

8200Ω 4700Ω

• Calculate VOC, this will give you VTH.

5600Ω

4V

Calculations Use voltage divider formula: !"##

𝑉!" = !"##!!"## ×4 = 2.37𝑉

8200Ω

VOC=VTH

•

Calculate -ISC = IN, by putting a short across the terminals. Use any form of analysis to calculate ISC.

5600Ω

4V

6800Ω

-Isc=Iin

8200Ω 4700Ω

Calculations Using MESH 5600Ω

8200Ω

Ix

4V

6800Ω

-Isc=Iin

Iy 4700Ω

LOOP X

LOOP Y 8200𝐼! − 8200𝐼! + 6800𝐼! + 4700𝐼! = 0! −8200𝐼! + 19,700𝐼! = 0! 19,700𝐼! = 8200𝐼! ! 82 𝐼! = 𝐼 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(2) 197 !

5600𝐼! + 8200𝐼! − 8200𝐼! = 4! 13800𝐼! − 8200𝐼! = 4!!!!!!!!!!!!!!!!(1)

Substitute (2) into (1) 82 𝐼𝑋 = 4! 13800𝐼! − 8200 197 672400 13800𝐼! − 𝐼 = 4! 197 ! 4 𝐼! = ! 13800 − 672400 197 197 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!(3) 𝐼! = 511550

Substitute (3) into (2) 82 197 × = 160.3𝜇A! 197 511550 = −160.3𝜇A

𝐼! = 𝐼!"

•

Calculate RTH by using the following expression. 𝑅!" =

𝑉!" 2.37 = = 14828Ω −𝐼!" 160.3×10!!

Final Answer

14828Ω 2.377V

160.3µA

14828Ω

Summary

3 Calculate RTH using formula.

RTH = VTH/IN

14828Ω 2.377V

1

Calculate VTH

using some sort of analysis, mesh or nodal.

160.3µA

2 Calculate I SC again, using some sort of analysis,mesh or nodal.

14828Ω

Shorter Method An alternative shorter method is to calculate, VTH as above, and then work out RTH and finally ISC. •

Calculating RTH Rule 1. If there is a voltage source, replace with short circuit. Rule 2. If there is a current source, replace with an open circuit. 5600Ω

4V

6800Ω

8200Ω

5600Ω

6800Ω

8200Ω 4700Ω

“Short out source”

6800Ω

3327Ω 4700Ω

5600Ω // 8200Ω = 3327.536Ω

4700Ω

14828Ω...