7.1 PHASORS

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Phasors are used for the analysis of sinusoidal, steady state conditions.

Sinusoidal means that if we measure the voltage (or current) at any point `i' in the circuit it will have the general form,

Steady state means that the transients have all stopped. This can be crudely though of as the circuit has `charged-up' or `warmed-up'.

Consider the example below,

Steady state is another important concept, it means that we are not concerned with the initial effects when we start a circuit (these effects are known as the transients). The typical causes of transient effects are inductors and capacitors.

We typically deal with these problems using phasor analysis. In the example before we had a voltage represented in the time domain,

Basically to do this type of analysis we represent all components voltages and currents in complex form, and then do calculations as normal.

Consider the simple example below,

7.1.1 RMS Values

When dealing with alternating currents we are faced with the problem of how we represent the signal magnitude. One easy way is to use the peak values for the wave.

Another common method is to use the effective value. This is also known as the Root Mean Squared value.

7.1.2 LR Circuits

One common combination of components is an inductor and resistor.

7.1.3 RC Circuits

Capacitors are often teamed up with resistors to be used as filters,

7.1.4 LRC Circuits

These circuits tend to weigh off capacitors and inductors to have a preferred frequency.

7.1.5 LC Circuits

Inductor capacitor combinations can be useful when attempting to filter certain frequencies,