| Methods of AC Analysis |
| Voltages and currents of independent sources | ||
| Not dependent upon any voltage or current elsewhere in the circuit | ||
| In some circuits | ||
| Operation of certain devices replaces device with an equivalent model | ||
| Models are dependent upon an internal voltage or current elsewhere in the circuit |
| Have a magnitude and phase angle determined by voltage or current at some other circuit element multiplied by a constant k | |
| Magnitude of k is determined by parameters within particular model | |
| Units of constant correspond to required quantities in the equation |
| A voltage source E in series with an impedance Z | ||
| Equivalent to a current source I having the same impedance Z in parallel | ||
| I = E/Z | ||
| E = IZ | ||
| Voltages and currents at terminals will be the same | ||
| Internal voltages and currents will differ | ||
| A dependent source may be converted by the same method | ||
| Controlling element external to circuit | ||
| If controlling element is in the same circuit as the dependent source | ||
| Procedure cannot be used | ||
| Method exactly the same as for dc | ||
| Convert all sinusoidal expressions into phasor notation | ||
| Convert current sources to voltage sources | ||
| Redraw circuit, simplifying the given impedances | ||
| Assign clockwise loop currents to each interior closed loop | |
| Show polarities of all impedances |
| Apply KVL to each loop and write resulting equations | ||
| Voltages that are voltage rises in the direction of the assumed current are positive | ||
| Voltages that drop are negative | ||
| Solve the resulting simultaneous linear equations or matrix equations |
| Method is exactly the same as for dc | |
| Nodal analysis will calculate all nodal voltages with respect to ground | |
| Convert all sinusoidal expressions into equivalent phasor notation |
| Convert all voltage sources to current sources | ||
| Redraw the circuit | ||
| Simplifying given impedances and expressing impedances as admittances | ||
| Assign subscripted voltages to nodes | ||
| Select an appropriate reference node | ||
| Assign assumed current directions through all branches | ||
| Apply KCL to each node | ||
| Solve resulting equations for node voltages | ||
| Impedance in any arm of a Y circuit | ||
| Determined by taking the product of two adjacent D impedances at this arm | ||
| Divide by the summation of the D impedances | ||
| Any impedance in a D | ||
| Determined by summing all possible two-impedance product combinations of the Y | ||
| Divide by impedance found in opposite branch of the Y | ||
| Bridge circuits are used to measure the values of unknown components | |
| Any bridge circuit is balanced when the current through branch between two arms is zero |
| The condition of a balanced bridge occurs when |
| When a balanced bridge occurs in a circuit | ||
| Equivalent impedance of bridge is found by removing central Z and replacing it by a short or open circuit | ||
| Resulting Z is then found by solving series-parallel circuit | ||
| For an unbalanced bridge | ||
| Z can be determined by D-to-Y conversion or mesh analysis | ||
| Used to determine the L and R of an inductor having a large series resistance | |
| L = R2R3C R = R2R3/R1 |
| Used to measure the L and R of an inductor having a small series resistance |
| Used to determine an unknown capacitance |