December 2017

Response Under Load

When a transformer is loaded, a current flows through its secondary coil. This current attenuates the magnetic field by producing an opposing magnetic field according to Lenz's law. As a result, part of the field is shifted out of the iron core so that the two coils are not subjected to the full magnetic field any more. The displaced field lines are termed stray field lines.

Electrical Transformer Design

Transformers are electrical compnents which convert alternating current or three-phase supplies to higher or lower voltages. Apart from this this voltage conversion that plays a key part in high-voltage energy transmission, transformers can also fulfil the role of converters in instrumentation applications or as repeaters for transmission of low-current signals. Transformers operate on the principle of electromagnetic induction.

Parallel Resonant Circuits

Connecting an inductor coil and capacitor in parallel results in a parallel resonant circuit as illustrated below. 

Electric Resonant Circuits !

Bandwidth

As already mentioned, a series resonant circuit can be used to filter out certain signal frequencies. This type of circuit is also termed a notch filter or more usually a band-stop filter. The diagram below shows a filter circuit with an input voltage Ue and output voltage Ua.

Resonance

Because both inductive and capacitive reactance are frequency-dependent, so is the impedance Z of an oscillating circuit. The current I in the circuit is at a maximum when the impedance is at a minimum. This happens when the inductive and capacitive reactances are equal, i.e. XL = XC. The second added component under the root sign becomes zero, leaving the impedance as:

Series Resonant Circuits

So far, we have merely considered AC circuits containing reactances of a single kind (capacitor or coil). Combining both these types of reactance results in an oscillating circuit. Due to their selective frequency properties they are usually called resonant circuits.

Equivalent Circuit Diagram for a Coil

In addition to its inductive reactance, every real coil also possesses an active resistance (due to the wire it is made of) that is dependent on the material used for the wire and its length (i.e. the number of coil windings). Consequently, a real coil can be represented by the following equivalent circuit diagram in the form of an ideal coil of inductance L connected in series with an active resistance RV.

Power Factor

The ratio of the actual electrical power dissipated by an AC circuit to the product of the r.m.s. values of current and voltage. The difference between the two is caused by reactance in the circuit and represents power that does no useful work.

Active, Reactive and Apparent Power in AC Circuits

Active power:

If an active resistance (e.g. a heating element) is connected to an AC circuit, the resulting voltage and current are in phase (blue and red curves in the diagram below). Multiplying associated pairs of instantaneous voltage and current values provides the instantaneous power (green curve). 

Band-Pass Filters

Combining a low-pass element and a high-pass element by connecting them in series results in a band-pass filter circuit. As its name suggests, this type of circuit allows passage of a particular band of frequencies while attenuating frequencies outside this band. The band-pass circuit shown in the example below comprises a series-connected LR low-pass element (green background) and CR high-pass element (blue background).

RL High-Pass Filters

Like an RC element, an RL element is also a frequency-dependent voltage divider. In this case, however, the inductive reactance XL increases with the frequency f. Consequently, the element's output voltage UL also increases with the frequency. In other words, an RL element allows high frequencies to pass while progressively blocking low frequencies. An RL element is accordingly termed a high-pass filter.

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