Circuit Theory/Example70

< Circuit Theory

original circuit

The series components can be lumped together .. which simplifies the circuit a bit.

Node AnalysisEdit

 

File:Example70mupad.png
mupad and matlab code for all the work below
 
 

Mesh AnalysisEdit

 

 
 
 

Solving

 

Which is the same as the voltage through the 1 ohm resistor.

Thevenin voltageEdit

 

Make ground the negative side of  , then:

 
 
 

Solving

 

Norton CurrentEdit

 
 

Thevenin/Norton ImpedanceEdit

 

short voltage sources, open current sources, remove load and find impedance where the load was attached

 

check

 

yes! they match

Evaluate Thevenin Equivalent CircuitEdit

 

Going to find current through the resistor and compare with mesh current

 

yes! they match

Find Load value for maximum power transferEdit

 

Find average power transfer with Load that maximizesEdit

 
 

SimulationEdit

 

The circuit was simulated. A way was found to enter equations into the voltage supply parameters which improves accuracy:

To compare with the results above, need to translate the current and voltage through the resistor into the time domain.

PeriodEdit

Period looks right about 6 seconds ... should be:

 

CurrentEdit

Current through 1 ohm resistor, once moved into the time domain (from the above numbers) is:

 

From the mesh analysis, the current's through both sources were computed:

 

The magnitudes are accurate, they are almost π out of phase which is can be seen on the simulation.

VoltageEdit

The voltage is the same as the current through a 1 ohm resistor:

 

The voltage of the first (left) source is:

 

The magnitudes match. The voltage through the source peaks before the current because the first source sees the inductor.

The voltage through the resistor should peak about 171 - 45 = 126° before the source ... which it appears to do.