Thevenin Equivalent Circuits

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Thevenin Equivalent Circuits
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Review Independent Source(s)
Circuit with one or more independent sources
Thevenin equivalent circuit
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Review No Independent Sources
RTh
Circuit without independent sources
Thevenin equivalent circuit
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Finding the Thevenin Equivalent

• I-V characteristics are straight lines (a
  consequence of the linearity of resistor models).
• Circuits with independent sources
• Intercepts are voc(t) and isc(t)
• Circuits w/o independent sources
• Slope is RTh

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No Independent Sources
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Finding RTh

• With no independent sources, Voc and Isc are both
  zero.
• To find the slope, we apply a test source with a
  given voltage (or current) and measure the
  current (voltage) produced by the source.
• This gives the slope of the I-V line.

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Example CE Amplifier
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Small Signal Equivalent
Ib

2kW
1kW
50W

Vin
Vo
100Ib
-
-
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Thevenin Equivalent _at_ Input
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Apply a Test Current Source
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Solve for Vx

• Use Nodal Analysis

Ib
Vx
V1
2kW
50W
1mA
100Ib
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Solve for Vx
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Compute RTh
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Apply a Test Voltage Source
V1
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Solve for Ib
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Compute RTh
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AC Steady State

• Thevenins theorem also applies to AC steady
  state analysis.
• An arbitrary linear circuit can be replaced by an
  equivalent source and impedance.
• The determination of source and impedance values
  is essentially the same as for resistor circuits.

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Independent Source(s)

Voc
-
Circuit with one or more independent sources
Thevenin equivalent circuit
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No Independent Sources
ZTh
Circuit without independent sources
Thevenin equivalent circuit
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Example IC Interconnects

• Find the Thevenin equivalent circuit

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Find Impedances, then Voc and Isc

• w 1010

500W
15W
15W
15W

Vs
-j1.43kW
-
-j1.43kW
-j1.43kW
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Source Transformations
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Source Transformations Cont.
15W
15W
455W-j164W

-
-j1.43kW
-j1.43kW
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Source Transformations Cont.
15W
-j1.43kW
470W-j164W
-j1.43kW
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Source Transformations Cont.

15W
348W-j250W

Voc
-
-j1.43kW
-
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Source Transformations Cont.
363W-j250W

Voc
-j1.43kW
-
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Source Transformations Cont.
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Voc

• Voc (0.446-j0.503) Vs

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Isc

• Isc (0.00184-j0.00005) Vs

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ZTh