8.4 The Natural Response of a Series/Parallel RLC Circuit

More documents

Recommendations

Info

8.6 State EquationStep1. Pick a tree which contains all the capacitors andnone of inductors.Step2. Use the tree-branch capacitor voltages and thelink inductor currents as unknown (i.e. , state)variables.Note: (a) Nodal AnalysisEvery unknown of the circuit can becalculated from nodal voltages.(b) Mesh AnalysisEvery unknown of the circuit can becalculated from mesh currents.C.T. Pan558.6 State Equation(c) State Equation• The chosen variables include bothvoltage and current unknown. It belongsto mixed type.• Every unknown of the circuit can becalculated from the state variables byreplacing each inductor with a currentsource and each capacitor with a voltagesource and then solving the resultingresistive circuit.C.T. Pan56
8.6 State EquationStep3. Write a fundamental cutset equation (i.e. KCLequation) for each capacitor.Note that in these cutsetequations, all branchcurrents must be expressed in terms of x and u.Step4. Write a fundamental loop equation (i.e. KVLequation) for each inductor.Note that in these loop equations, all branchvoltages must be expressed in terms of x and u.Step5. Rearrange the above equations into standard formand find the solution for the given initial condition.C.T. Pan57•Example 18.6 State EquationStep1treeC.T. Pan58
Page 2 and 3: 8.1 Linear Second Order Circuits•
Page 5: 8.3 Finding Initial ValuesUnder tra
Page 8 and 9: 8.3 Finding Initial Values• Examp
Page 14 and 15: 8.4 The Natural Response of a Serie
Page 20 and 21: 8.5 The Step Response of a Series/P
Page 30 and 31: 8.6 State EquationStep2 choose i an
Page 32 and 33: • Example 3 : Find v R48.6 State
Page 34 and 35: 8.6 State EquationR∴v = e - ( i +
Page 36: Summary• Objective 1 : Be able to

8.4 The Natural Response of a Series/Parallel RLC Circuit

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?