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# What is the Electrical Length?

Discuss Certain Phenomenon Where Circuit Theory Fails. Electrical length is one of the important concepts for understanding the electromagnetics. It has no unit and it is represents the length of a wire or a device at a certain frequency. It is measured as the ratio of the length of physical wire (L) to the ratio of wavelength (λ) of a certain frequency signal. The formula is given as:

**Electrical Length= L/λ**

## Example:

Consider the length of an antenna is 1m long. At the frequency of 1KHz the electrical length can be computed as:

**λ=c/f **

**c=3× 10 ^{8}**

so,

**λ=c/f=3× 10 ^{8}/1000**

**=3×10 ^{5}**

**=1/3×10 ^{5}**

**=3.3×10 ^{-6}**

We can simply interpret it like 1 meter antenna is **3.3×10 ^{-6 }**

**λ**long at the frequency of 1KHz. At this frequency this antenna is said to be electrically short antenna.

But if the frequency is 100MHz, then the electrical length is computed as:

**λ=c/f=3× 10 ^{8}/100×10^{6}**

**=3**

**=1/3**

**=0.3**

so this antenna is considered as electrically long antenna. Generally we can say that any device whose length is less than about 1/20 is electrically short. But this is not true in case of the wires that have large impedance mismatching or considerable losses. Electrically short circuits can be generally described by the basic circuit theory. They do not need to be explained using the concepts of electromagnetics.

While circuits that are electrically long need the understanding of RF techniques and electromagnetics. So we can say that when the wavelength is much longer that the length of wires, then basic electronic techniques can be applied and there will be no need of electromagnetics.

## Finite Speed of Light

You can look through the other perspective that the period of the wave is much larger as compared to the delay through the wires. While designing the low frequency circuits, we can easily ignore the fact that electrical signals are carried by waves and they must travel at the speed of light.

So there is always certain delay present when you turn ON the light switch and bulb receives the power. This delay is very small for human perception but still it is present. This delay is ignored whenever you approximate a wire as an deal short circuit.

While designing RF or high speed circuits, the speed of light delay plays a vital role and it plays an important role.

### RF Techniques

Basic circuit theory causes problem at higher frequencies. If the wires are electrically long then we can face the transmission lines effects. Here at this point we can not apply basic circuit theory because the reflected wave along the wires can cause problems.

These reflected waves can cause constructive or destructive interference which may result in breakdown of circuit theory. In fact when a transmission line has length equal to one quarter wavelength of signal, a short placed at the end will appear as open circuit at the other end. Obviously we can not ignore these types of effects.

Also circuits at higher frequencies radiate energy more readily so they can be considered like antennas. Other parameters like parasitic capacitance and inductance can also cause problem. Because no components is practically ideal. The small inductance of components and wires can cause huge voltage drop at higher frequencies.

Similarly, stray capacitance between the leads of the component packages can effect the operation of circuit at high frequencies.

### How to define the high frequency regime?

There is not specific limit or order but when wavelength of signals is similar in size or smaller than the wire length, it becomes important to consider the effects of high frequency. Or you can say when a wire or circuit element becomes electrically long, you are dealing with high frequency regime.

We can also say that when a signal period is comparable in magnitude or smaller than the delay through the interconnecting wires, high frequency effects become important.

### Why we need to study electromagnetic field theory?

### Voltages Induced in Secondary of Transformer

Now it becomes quite easier to understand and answer this question why we need to study the electromagnetic field theory. Let us consider a case when we connect an ac source at the primary side of a transformer. The changing current produces the changing magnetic filed. When the secondary coil is brought into this field, the emf or voltages are induced in it but of of opposite polarity. Although there is no electric connection between source and secondary coil but still there are voltages induced in secondary. This can be explained by the Faraday’s law of electromagnetic induction.

### Radiating Antenna

As we always believe in the fact that the conduction takes place in the closed path. But what about the communicating devices like mobile phones that receive and transmit the data. The transmission takes place via antenna present where they actually radiate the electric current.

**Engineering Electromagnetics by William Hyatt-8th Edition**

**Electromagnetic Field Theory Assignment 1 **

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