1.1 PHASORS

• 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,

1.1.1 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.

 

 

 

1.1.2 LR Circuits

 

• One common combination of components is an inductor and resistor.

 

 

 

1.1.3 RC Circuits

 

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

 

 

 

1.1.4 LRC Circuits

 

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

 

 

 

1.1.5 LC Circuits

 

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