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Thevenin + Norton Eq. circuits
Low distortion audio power amplifier

TO MATCH SPEAKERS AND
AMPLIFIER ONE SHOULD ANALYZE
THIS CIRCUIT

From PreAmp
(voltage )

To speakers

RTH
TO MATCH SPEAKERS AND AMPLIFIER
IT IS MUCH EASIER TO CONSIDER THIS
EQUIVALENT CIRCUIT!

VTH

+
-

REPLACE AMPLIFIER
BY SIMPLER
“EQUIVALENT”
Independent Sources (Thevenin)
RTh

Voc

Circuit with independent
sources

+
–

Thevenin equivalent circuit
Thevenin's Theorem states that it is possible to simplify any
linear circuit, no matter how complex, to an equivalent circuit
with just a single voltage source and series resistance connected
to a load.
Thevenin Theorem
Example Application
To create the Thevenin Equivalent Circuit we need:
1. Value of the Thevenin Voltage Source

2. Value of the Thevenin Resistance
Determination
of the Thevenin
Voltage

EThevenin = Open circuit voltage with load removed
Determination
of the Thevenin
Voltage

EThevenin = Open circuit voltage with load removed

EThevenin = 11.2
Determination
of the Thevenin
Resistance

RThevenin = Net resistance in network with sources set to zero

RThevenin = 0.8 ohms
Thevenin Theorem
Summary

EThevenin = 11.2 volts
RThevenin = 0.8 ohms
The Maximum Power Transfer Theorem simply states, the
maximum amount of power will be dissipated by a load
resistance when that load resistance is equal to the
Thevenin/Norton resistance of the network supplying the
power.
5k

6V

VO

1k
(6V ) 1[V ]
1k 5k
THEVENIN & NORTON
THEVENIN’S THEOREM: Example
Find VX by first finding VTH and RTH to the left of A-B.

4

12

A

+

_
30 V +

6

VX

2

_
B

First remove everything to the right of A-B.
THEVENIN & NORTON
THEVENIN’S THEOREM: Example
4

12

_
30 V +

A

6

B

VAB

(30)(6)
6 12

10V

Notice that there is no current flowing in the 4 resistor
(A-B) is open. Thus there can be no voltage across the
resistor.
THEVENIN & NORTON
THEVENIN’S THEOREM: Example
We now deactivate the sources to the left of A-B and find
the resistance seen looking in these terminals.

4

12

A

RTH

6

B

We see,
RTH = 12||6 + 4 = 8
THEVENIN & NORTON
THEVENIN’S THEOREM: Example
After having found the Thevenin circuit, we connect this
to the load in order to find VX.

RTH

A

8
VTH

+
_

10 V

+
2

VX
_

B

VX

(10)( 2)
2 8

2V
EXAMPLE: SOLVE BY SOURCE TRANSFORMATION

In between the terminals we connect a voltage
source in series with the resistor
The equivalent current source will have the
value 12V/3k
The 3k and the 6k resistors now are in parallel
and can be combined

In between the terminals we connect a current
source and a resistance in parallel
The equivalent source has value 4mA*2k
The 2k and the 2k resistor become connected
in series and can be combined

After the transformation the sources can be combined
The equivalent current source has value 8V/4k
and the combined current source has value 4mA
Options at this point
1. Do another source transformation and get
a single loop circuit
2. Use current divider to compute I_0 and then
compute V_0 using Ohm’s law
LEARNING EXAMPLE

COMPUTE Vo USING THEVENIN
In the region shown, one could use source
transformation twice and reduce that part to
a single source with a resistor.
... Or we can apply Thevenin Equivalence
to that part (viewed as “Part A”)

RTH
The original circuit becomes...

VTH

6
3 6

4k

12[V ] 8[V ]

For the open loop voltage
the part outside the region
is eliminated

And one can apply Thevenin one more time!
For open loop voltage use KVL
1
VTH

1
TH

R

1
VTH

4k

...and we have a simple voltage divider!!

V0

8
8 8

16[V ] 8V

4k * 2mA 8V

16V
PROBLEM Compute V_0 using source transformation

EQUIVALENT CIRCUITS

I0

Or one more source transformation

R eq

Veq

+
-

3 current sources in parallel and
three resistors in parallel

R3

RTH
VTH
Veq Req I eq

R4

V0

Veq

Req I eq

V0

R4

R4
Veq
R3 Req

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Thev norton eq

  • 1. Thevenin + Norton Eq. circuits
  • 2. Low distortion audio power amplifier TO MATCH SPEAKERS AND AMPLIFIER ONE SHOULD ANALYZE THIS CIRCUIT From PreAmp (voltage ) To speakers RTH TO MATCH SPEAKERS AND AMPLIFIER IT IS MUCH EASIER TO CONSIDER THIS EQUIVALENT CIRCUIT! VTH + - REPLACE AMPLIFIER BY SIMPLER “EQUIVALENT”
  • 3. Independent Sources (Thevenin) RTh Voc Circuit with independent sources + – Thevenin equivalent circuit
  • 4. Thevenin's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
  • 6. To create the Thevenin Equivalent Circuit we need: 1. Value of the Thevenin Voltage Source 2. Value of the Thevenin Resistance
  • 7. Determination of the Thevenin Voltage EThevenin = Open circuit voltage with load removed
  • 8. Determination of the Thevenin Voltage EThevenin = Open circuit voltage with load removed EThevenin = 11.2
  • 9. Determination of the Thevenin Resistance RThevenin = Net resistance in network with sources set to zero RThevenin = 0.8 ohms
  • 10. Thevenin Theorem Summary EThevenin = 11.2 volts RThevenin = 0.8 ohms
  • 11.
  • 12. The Maximum Power Transfer Theorem simply states, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power.
  • 14. THEVENIN & NORTON THEVENIN’S THEOREM: Example Find VX by first finding VTH and RTH to the left of A-B. 4 12 A + _ 30 V + 6 VX 2 _ B First remove everything to the right of A-B.
  • 15. THEVENIN & NORTON THEVENIN’S THEOREM: Example 4 12 _ 30 V + A 6 B VAB (30)(6) 6 12 10V Notice that there is no current flowing in the 4 resistor (A-B) is open. Thus there can be no voltage across the resistor.
  • 16. THEVENIN & NORTON THEVENIN’S THEOREM: Example We now deactivate the sources to the left of A-B and find the resistance seen looking in these terminals. 4 12 A RTH 6 B We see, RTH = 12||6 + 4 = 8
  • 17. THEVENIN & NORTON THEVENIN’S THEOREM: Example After having found the Thevenin circuit, we connect this to the load in order to find VX. RTH A 8 VTH + _ 10 V + 2 VX _ B VX (10)( 2) 2 8 2V
  • 18. EXAMPLE: SOLVE BY SOURCE TRANSFORMATION In between the terminals we connect a voltage source in series with the resistor The equivalent current source will have the value 12V/3k The 3k and the 6k resistors now are in parallel and can be combined In between the terminals we connect a current source and a resistance in parallel The equivalent source has value 4mA*2k The 2k and the 2k resistor become connected in series and can be combined After the transformation the sources can be combined The equivalent current source has value 8V/4k and the combined current source has value 4mA Options at this point 1. Do another source transformation and get a single loop circuit 2. Use current divider to compute I_0 and then compute V_0 using Ohm’s law
  • 19. LEARNING EXAMPLE COMPUTE Vo USING THEVENIN In the region shown, one could use source transformation twice and reduce that part to a single source with a resistor. ... Or we can apply Thevenin Equivalence to that part (viewed as “Part A”) RTH The original circuit becomes... VTH 6 3 6 4k 12[V ] 8[V ] For the open loop voltage the part outside the region is eliminated And one can apply Thevenin one more time! For open loop voltage use KVL 1 VTH 1 TH R 1 VTH 4k ...and we have a simple voltage divider!! V0 8 8 8 16[V ] 8V 4k * 2mA 8V 16V
  • 20. PROBLEM Compute V_0 using source transformation EQUIVALENT CIRCUITS I0 Or one more source transformation R eq Veq + - 3 current sources in parallel and three resistors in parallel R3 RTH VTH Veq Req I eq R4 V0 Veq Req I eq V0 R4 R4 Veq R3 Req