PAPER 2E7: ELECTRICAL ENGINEERING
Dr Anil Kokaram
Electronic and Electrical Engineering Dept.
anil.kokaram@tcd.ie www.mee.tcd.ie/∼ack
EQUIVALENT CIRCUITS
• You now know enough to start summarising circuits i.e. simplifying them
to focus on important components
• Need to formalise a generalisation of circuit design
+
Source
(obeys some I-V
characteristic)
Linear
Network
v
(obeys some I-V
characteristic)
-
2E7 Introduction to EE
1
www.mee.tcd.ie/∼sigmedia
1 OPEN AND SHORT CIRCUITS
1
Open and Short Circuits
2E7 Introduction to EE
2
www.mee.tcd.ie/∼sigmedia
2 THEVENIN AND NORTON
2
Thevenin and Norton Equivalent Ccts
Section 3.5, Page 90, 3rd Ed.
THEVENIN’S THEOREM
From the perspective of any load, a linear electric
circuit may be represented by an ideal voltage
source VT H in series with an output impedance
or resistance RT H .
+
Source
v
Load
Load
-
NORTON’S THEOREM
From the perspective of any load, a linear electric circuit may be represented by an ideal current source iT H in parallel with an output
impedance or resistance RN .
+
Source
v
Load
Load
-
Remembering this is always a bit tricky since both theorems involve
an equivalent resistance .. try this ... there is a V in “Thevenin” so
its the one with the voltage source in the equivalent circuit.
2E7 Introduction to EE
3
www.mee.tcd.ie/∼sigmedia
2.1 Computing Equivalent Resistance
2.1
2 THEVENIN AND NORTON
Computing Equivalent Resistance
• Idea is to identify the load resistance in the cct, remove that
(replace with an open cct), remove all voltage and current sources
and then
• Estimate the resistance that the load would ‘see’ when looking at
the rest of the network
• Alternatively ... if the load resistance is replaced with a current
source of 1 Amp .. the Equivalent Resistance is the net resistance
that the current would encounter as it traverses the rest of the
circuit.
• The method for computing equivalent resistance is the same whether
you are generating a Thevenin or Norton equivalent cct.
Method:
1. Remove the load
2. Zero all independent voltage and current sources
3. Compute the total resistance between the load terminals with the
load removed.
2E7 Introduction to EE
4
www.mee.tcd.ie/∼sigmedia
2.1 Computing Equivalent Resistance
2 THEVENIN AND NORTON
−→
←−
2E7 Introduction to EE
5
www.mee.tcd.ie/∼sigmedia
2.2 Thevenin Voltage
2.2
2 THEVENIN AND NORTON
Thevenin Voltage
Aim: To estimate the Thevenin Equivalent Voltage for an arbitrary
linear electric cct
Method:
1. Remove the load, leaving the load terminals OPEN circuited
2. Define the open-circuit voltage Voc
3. Use any method (e.g. nodal or mesh analysis) for calculating Voc
4. That voltage is the Thevenin equivalent voltage VT H = Voc
2E7 Introduction to EE
6
www.mee.tcd.ie/∼sigmedia
2.2 Thevenin Voltage
2E7 Introduction to EE
2 THEVENIN AND NORTON
7
www.mee.tcd.ie/∼sigmedia
2.3 Thevenin Example
2.3
2 THEVENIN AND NORTON
Thevenin Example
A
50V
1.5A
B
2E7 Introduction to EE
8
www.mee.tcd.ie/∼sigmedia
2.4 Norton Current
2.4
2 THEVENIN AND NORTON
Norton Current
Aim: To estimate the Norton Equivalent Current for an arbitrary
linear electric cct
The NEC is the equivalent current that would flow were the load
replaced by a short circuit
Method:
1. Replace the load with a short circuit
2. Define the short circuit current as isc
3. Use any method (e.g. nodal or mesh analysis) for calculating isc
4. That current is the Norton equivalent current iN = isc
2E7 Introduction to EE
9
www.mee.tcd.ie/∼sigmedia
2.4 Norton Current
2 THEVENIN AND NORTON
6V
2A
2
6
3
2
6
3
6V
2A
6
2E7 Introduction to EE
2
3
10
www.mee.tcd.ie/∼sigmedia
3 EQIV BY EXP
3
Experimental Determination of Eq ccts
• Possible to determine equivalent ccts by measurement.
• Idea is to model the network as the required equivalent cct then
take measurements of voltage and current across the relevant output terminals.
• Measuring the Thevenin Equivalent voltage VT H is easy: just
place a voltmeter across the relevant terminals.
• Measuring the equivalent resistance is a bit more tricky. Measure the current through the short cct load and then set up a
relationship . . .
2E7 Introduction to EE
11
www.mee.tcd.ie/∼sigmedia
3.1 Example
3.1
3 EQIV BY EXP
Example
Measurements are made across the load terminals of some unknown
electrical network. The short cct current was 3.75mA and the open
circuit voltage was 6.5 Volts. The internal resistance of the ammeter
used was 15Ω while the voltmeter can be assumed to have infinite
input impedance. Derive the Thevenin and Norton equivalent of the
network.
2E7 Introduction to EE
12
www.mee.tcd.ie/∼sigmedia