100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Circuit Simplification $5.49   Add to cart

Class notes

Circuit Simplification

 4 views  0 purchase

Transform your understanding of Circuit simplification with this indispensable set of notes, crafted specifically for electrical and computer engineering students. Dive into key concepts like circuit analysis, Ohm’s Law, Kirchhoff’s Laws, Thevenin’s and Norton’s theorems, and AC/DC circuit ...

[Show more]

Preview 2 out of 13  pages

  • November 10, 2024
  • 13
  • 2012/2013
  • Class notes
  • Smr10
  • All classes
All documents for this subject (8)
avatar-seller
derrickwesonga
Chapter 4 Circuit Simplification


4.1 Thevenin’s Equivalent Circuit IL
Rsrc
 For a voltage divider supplying a load, the v-i
relation at the load terminals is given by +
Equation 2.7.5, which may be expressed as: V +
SRCoc VL Load
VL = VSRCoc – RsrcIL (4.1.1) –

where VSRCoc is the open-circuit voltage of an
equivalent source and Rsrc is the effective
Figure 4.1.1
source resistance (Figure 4.1.1).
 This circuit is in fact Thevenin’s equivalent circuit of the voltage divider as seen from
the load terminals and applies quite generally.

Concept In an LTI resistive circuit, the v-i characteristic at any specified
pair of terminals is that of an ideal voltage source in series with a source
resistance.
 To justify this, we consider
VSRC2
the representative, 10 
generalized three-mesh – +
circuit of Figure 3.6.1,
redrawn in Figure 4.1.2 10  I2 20 
with the 10  resistance in
mesh 3 considered as a 30 
VSRC1 + IL
I1
load resistance RL –
connected to terminals ab a +
IL
of the circuit, and I3 20  VL
RL
designated as IL. VSRC3 –
 The mesh current + – b
equations are:
Figure 4.1.2
40I1 – 10I2 – 20IL =
VSRC1
-10I1 + 60I2 – 30IL = VSRC2
-20I1 – 30I2 + 50IL = VSRC3 – VL (4.1.2)
where VL is considered as a voltage drop in mesh 3 and is included on the RHS of



4-1/13

, the equation for this mesh.
 Solving for IL and rearranging:

V L= [ 15 V SRC 1 +14 V SRC 2
23
+V SRC 3 − ]
430
23 L
I
(4.1.3)
 Equation 4.1.3 is of the form of Eq 4.1.1, where VSRCoc equals the bracketed terms,
and Rsrc = 430/23. Since the circuit of Figure 4.1.2 is quite arbitrary, it is concluded
that the v-i relation for any given circuit at specified terminals ab is the same, in
general, as that of an ideal voltage source VSRCoc in series with a resistance Rsrc.
 The VSRCoc-Rsrc circuit is the TEC of the given circuit at terminals ab and is the
simplest possible equivalent circuit, since it consists of just an ideal source and a
resistor. It is customary to refer to VSRCoc as the Thevenin voltage VTh, and to Rsrc as
the Thevenin resistance RTh.
 VTh is determined as the open-circuit voltage at specified pair of terminals. If
terminals ab in Figure 4.1.2 are open circuited, IL = 0 and the mesh current equations
for the circuit become:
40I1 – 10I2 = VSRC1
-10I1 + 60I2 = VSRC2 (4.1.4)
0 .6 V SRC 1 +0 .1 V SRC 2 0 .1 V SRC 1 +0. 4 V SRC 2
I1= I2=
 Solving for I1 and I2, 23 and 23 . From KVL,
VL = 30I2 + 20I1 + VSRC3. This gives: a
15 14
V Th = V SRC 1 + V SRC 2 +V SRC 3
23 23 (4.1.5) RTh
+
which is the open-circuit voltage determined above. VTh ISC

 RTh can be determined in one of two ways. The first
follows from TEC (Figure 4.1.3a) when terminals ab
(a) b
V Th
RTh = RTh IT
are short circuited, which gives: I SC . a

 In the above example, if terminals ab are short
circuited, VL = 0 and IL = ISC = +
VT
15 V SRC 1 +14 V SRC 2 +23 V SRC 3 –
=
430 . This gives

(b) b
430 Figure 4.1.3
RTh =
23 , as above.


4-2/13

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller derrickwesonga. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $5.49. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

67163 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$5.49
  • (0)
  Add to cart