relation between "resonant frequency" and "resonant length"

[alexbugo]

Hi.
what is exact relation between "resonant frequency" and "resonant length" in a antenna?
in a reference,I saw:
electrical length = L / λ
where L is physical length of an antenna and λ is wavelength in operating frequency.
while, in antenna textbooks, I saw :
electrical length is a multiple of the wavelength (for example, in a dipole antenna electrical length is 0.5λ approximately)
finally, electrical length is proportional to λ or inversely?
please clarify me...

 

[biff44]

you are thinking much too simplistically. There is no such equation.

 

[reidintransit]

λ, Lamda is the wavelength or the length of a 360 degree (or 2*pi) cycle. Electrical length is a length in relation to a full cycle. Wavelength is inversely proportional to the frequency, where higher frequencies have shorter wavelengths. Might be easier to understand with units. L is physical length like meters or inches. λ is physical length of 360 degrees (2*pi) or length/360 degrees. This changes depending on frequency and material. Electrical length is degrees or radians. electrical length = L / λ is correct. For the antenna example using electrical length is a way to discuss phenomenon that are based on multiple of wavelength whatever the frequency or material. Electrical length is proportional to wavelength.
Let's say you have a material and frequency that makes λ = 1 meter/360 degrees, the 360 degrees is implied, so poeple will just say λ = 1 meter. How long would an antenna need to be? The electrical length is λ/2 or 180 degrees. The physical length would be 1/2 meter.

 

[alexbugo]

Re: relation between "resonant frequency" and "resonant length"

you are thinking much too simplistically. There is no such equation.

thank you.But please don't confuse me again.
why there is no equation?So how should relate resonant frequency of an antenna to electrical length?

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electrical length = L / λ is correct.
Electrical length is proportional to wavelength.

So,electrical length is proportional to wavelength or is inverse with it?
if "electrical length = L / λ is correct",So why you say that "Electrical length is proportional to wavelength" again?
please don't confuse me!

 

[reidintransit]

Sorry for confusion.
Electrical length = L / λ relates length, wavelength and electrical length. With those assumptions if we keep the physical length constant and change the frequency to twice the original frequency then the wavelength is 1/2 as long. The same physical length in that case would now have twice as much electrical length at the new frequency.
using numbers assume electrical length = 180º, Length = 1 meter, λ is 2 meters then if we change frequency λ = 1 meter, length = 1meter, electrical length = 360º.
This is an inversely proportional relationship.
"while, in antenna textbooks, I saw: electrical length is a multiple of the wavelength (for example, in a dipole antenna electrical length is 0.5λ approximately)"
this is not an equation, just a value for the electrical length of an antenna regardless of wavelength. It is stating that you would keep electrical length constant at 180º and solve for L if given λ or solve for λ if given L . Still an inversely proportional relationship between Electrical length and λ.
Part of the confusion is that we sometimes state the electrical length in terms of wavelengths rather than degrees or radians as given in antenna book.

 

[alexbugo]

thank you for your reply.
So,you say that electrical length in transmission line theory and antenna theory differ.
in fact:
in transmission line theory we use from "Electrical length = L / λ". while in antenna theory we use from : "electrical length = a multiple of the wavelength".
is it true?
in antenna theory,how electrical length is inversely proportional to wavelength?while it is a multiple of wavelength.

 

[reidintransit]

No, Electrical length is same in both if you are going to tie them to a physical length.
The difference is how we are defining units of wavelength. Is it 360 degrees? or is it a physical length? In some discussions we don't care what the frequency or the material or physical length are, so it is simpler to talk about electrical length relative to the wavelength. This is not a quantitative equation but a qualititative observation.

 

[alexbugo]

Now,I have a question.
suppose we have an antenna that covered by a loss-less dielectric.now thickness of the dielectric layer increased.
in this case,resonant frequency and electrical length of the antenna decreases or increases?

 

[jiripolivka]

An elmag wave propagation in vacuum is the longest case. If it propagates in a dielectric medium with a permittivity k, the wave length will be shorter by 1/(sqrt k).
If an antenna is immersed in a dielectric, to resonate, it must be shortened by the same coefficient.

 

[alexbugo]

So,if physical length of the antenna be constant,resonant frequency will be decreased?

 

[jiripolivka]

So,if physical length of the antenna be constant,resonant frequency will be decreased?

The basic equation for any wave is : c = f x lambda. If the c, velocity of propagation, changes, the wavelength changes, too. The frequency is assumed to be constant.

 

[alexbugo]

I know that in antenna design,resonant frequency is important and we want to be constant.
But,I've done a simulation,where physical length is constant.then I increased radius of the antenna element and saw smaller resonant frequency.
my result is true?
Now,if I put a loss-less dielectric layer around the same antenna,do I have to expect a reduced resonant frequency?

 

[biff44]

In a purely theoretical sense, a monopole will be resonant when it is quarterwave, 3/4 wave, 5/4 wave...
a dipole will be resonant when it is half wave, full wave, 3/2 wavelength.

But in reality, there are feedpoint issues, fringing capacitance issues, non-infinite ground plane issues, nearby objects causing effects (like a human body). So, one almost always ends up with lengths that are significantly far from what any equation predicts after the electronic tuning is done.

Equations can only give a "starting point"

 

[jiripolivka]

I know that in antenna design,resonant frequency is important and we want to be constant.
But,I've done a simulation,where physical length is constant.then I increased radius of the antenna element and saw smaller resonant frequency.
my result is true?
Now,if I put a loss-less dielectric layer around the same antenna,do I have to expect a reduced resonant frequency?

I do not know about simulation but the answer to the second question is yes. The antenna immersed in a dielectric becomes "longer" by 1(sqrt k), therefore the resonance frequency decreases. This can be seen in implanted antennas due to tissue permittivity.

Antenna radius (if you mean dipole element diameter) affects the impedance and bandwidth, I do not see why the resonance frequency should change.

 

[alexbugo]

Antenna radius (if you mean dipole element diameter) affects the impedance and bandwidth, I do not see why the resonance frequency should change.

1.Yes,I know that increasing the radius,increase Bandwidth.But what is it's effect on the impedance(decrease or increase)?
2. what do you mean from " do not see why the resonance frequency should change"?
when radius increase,because of added capacitance,resonant frequency reduces.

 

[jiripolivka]

1. I do not know, I usually try to measure the result. Antenna experts may know, also antenna type decides.
2. Antenna resonance is a function of its length, not element width. Element width does not affect any capacitance. A butterfly dipole resonates at the same frequency defined by its length but the width only affects bandwidth of impedance matching.

 

[alexbugo]

2. Antenna resonance is a function of its length, not element width. Element width does not affect any capacitance. A butterfly dipole resonates at the same frequency defined by its length but the width only affects bandwidth of impedance matching.

Antenna resonance is a function of both its length and diameter.when diameter increases,fringing capacitance increases.So if we look at the antenna as a "resonator",then resonant frequency is inversely proportional to capacitance.Therefore resonant frequency reduces (assuming length of the antenna is constant) .

 

[Terminator3]

alexbugo, for microstrip resonator, it's resonant length is a little smaller than calculated wave-length, because of end-effect. For example: microstrip ring resonator lenght is almost the same as calculated from electrical length. So it is equal to lambda in dielectric. for microstrip resonator with half-wavelen patches, their length is a little smaller, than lamba/2 in dielectric. So it is some lambda/2-delta length. If we try to make ring resonator from two half-wave resonators, then we get (lambda-2*delta), wich would be wrong. Resonant length for ring resonator is not affected by end-effect. if we cut ring in two places, there would be "ends", that exted somehow in space beyond microstrip conductor. Proffessionals correct me if i am wrong.
Google some on end-effect.