Circuit Analysis with Dependent Sources PDF

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Teacher: Jones
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EET 300 || Chapter 2(F) Lesson Notes

Dependent Sources

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9/6/2011

Circuit Analysis with Dependent Sources Independent Source: Specifies that the magnitude of the source is independent of the network to which it is applied (i.e., the source value is not affected by a varying load) and that the source displays its terminal characteristics even if completely isolated. Dependent Source: A dependent or controlled source is one whose magnitude is determined (or controlled) by a current or voltage of the system in which it appears. The controlling function will be either the voltage across or current thru some other device in the network. A Dependent source is signified by a diamond vice a circle around the source type symbol.

+ V + k1V -

Controlled Voltage Source

k2I

Controlled Current Source

I

EET 300 || Chapter 2(F) Lesson Notes

Dependent Sources

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9/6/2011

Differences in methods when analyzing a circuit with dependent sources. Source conversions: It is allowed to perform a source conversion on a dependent source, as long as the controlling variable (V or I) is not determined by the portion of the circuit to which the conversion is to be applied.

Mesh Analysis: When performing the KVL’s necessary in MESH analysis, the designer must treat dependent VOLTAGE sources like independent VOLTAGE sources. However, once the equation is written, a substitution of the equation for the controlling quantity must be made to ensure that the unknowns are limited solely to the chosen mesh currents. If the source is a CURRENT source, see the following paragraph. The dependent current source must be defined in terms of a MESH current, not a branch current. Therefore, if the function is a branch current, the branch current must have the mesh current(s) substituted in the controlling equation. For example, suppose that i1 is equal to mesh equation I1-I2. If i1 is part of a dependent source’s control equation (k1i1), then the new control equation would be:

K1  I1  I2  NODAL analysis: For Nodal analysis of networks which contain dependent sources, take the above discussions and substitute voltage for current and current for voltage in the discussion.

EET 300 || Chapter 2(F) Lesson Notes

Dependent Sources

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9/6/2011

MESH Example:

Solve for the current thru R1 in the circuit below by MESH.

R1 4 

3IR1

+ -

12v

R2 6 

The dependent current source needs to be converted to a voltage source but R1 can’t be used since it is part of the control expression for the dependent source. So, use R2. Along with the source conversion, the IR1 term in the control expression will have to be expressed in terms of the mesh currents i1 and i2.

18(i1  i2 )

3IR1 * 6   18IR1 18I R1  18( i1  i2 )

For i1

0  -18  i1 - i2   6i1  4(i1  i2 )

0   14  i1 - i2   6i1

0   14i1  14i2  6i1 0   8i1  14i2 For i2

0  12v  4  i2 - i1

12  -4i1  4i2  0    8 14  i1           1 i 2 4 4        2 IR1  i1  i2  7A  4A

 7A    4A  3A

EET 300 || Chapter 2(F) Lesson Notes

Dependent Sources

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Use Multisim to simulate the original and final circuits. Demonstrate that the current thru R1 . The Current Controlled Current Source (ICIS) is in the Sources Group under the subheading: ‘Controlled_Current_Sources’. Note that it looks a lot different from the one in the lecture notes. Care must be taken to hook-up the control section of the source in the correct direction.

3IR1

R1 4 

+ 12v -

R2 6 

The Current Controlled Voltage Source (ICIS) is found in the Sources Group under the subheading: ‘Controlled_Voltage_Sources’. Even more care must be taken here to connect up the controlling current in the correct direction. Since the controlling equation is written with i1 first, it assumes that the controlling current thru R1 is going from downward. So that is how it must be wired.

18(i1  i2 )...