how calculate and plot antenna efficiency versus frequency?

Hi.
I want to plot antenna efficiency using numerical methods(such as finite difference)
what is meaning of "frequency" in antenna efficiency calculation?
I know that:
η(f) = radiated power(f) / input power(f)

and I know that " f " in radiated power calculation is "far field frequency" , such that in radiated power formula f is according with k0 = 2*pi*f/3e8.

but I don't know meaning of "f" in input power.what is it's mean?
I know that input power is :
Pin = 0.5*Real[V(w)*I(w)] , where V and I are voltage and current inputs to antenna.

Now,I want to plot antenna efficiency relation versus frequencies (for example VHF band:f=(30-300) MHz).
I have got antenna radiated power values versus frequency.BUT,I don't know that what is meaning of frequency in antenna input power.
I think that input power doesn't any relation to far field frequency.SO,how calculate and plot antenna efficiency formula?

thanks
ghasem

I'm unable to read a sense into the term "far field frequency" related to this question (and to RF technique in general). Where did you pick it up?

Antenna measurements will be usually performed with a single frequency (sine CW) generator signal. The frequency is swept during the measurement and the parameters like gain, input impedance, "efficiency" are recorded with the frequency as independent parameter. Respective diagrams are mostly plotted versus frequency with the exception of Smith charts. You can e.g. feed a constant power to the antenna, so radiated power is directly proportional to efficiency.

thanks for your attention
I mean from far field frequency is the frequency that in it we observe antenna pattern.
suppose we have a monopole antenna.so resonant frequency is f=3e8/lambda where lambda = 4*L and L is antenna length.
So in receiver antenna I want to observe another frequencies,aslo.for example suppose resonant frequency is 120 MHz.now I want to plot antenna efficiency versus frequency in VHF range (30-330) MHz.
How can I do it?
also, "far field frequency" term is not new.for example,when in HFSS you see antenna pattern in several frequencise,in fact those are far field frequency.

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I have another question.
(I created a topic for it,but I don't receive any answer there in RF and analog design forum.)

I have a structure.I want to apply two siganl to it,SIMULTANEOUSLY.
Now I want to simulate S11,S22,S12 and S21 in this two excitation port with HFSS.but HFSS in multiple port problems,simualte only with a excitation port,while another are matched load.
How can I simulate S parameters in this structure?
thanks...

How can I do it?

Click to expand...

As sketched in previous post. Sweep a signal generator over the intended frequency range, measure input and radiated power, calculate the ratio for each frequency, plot the result.

I have another question...

Click to expand...

Several misunderstandings of S-parameters seems to be involved.
- S parameters can be applied for arbitrary load and source impedances, not only matched situation. They allow to calculate forward and reverse in- and output waves.
- S parameters are describing linear systems, thus superposition theorem applies. Multiple sources can be activated seperately and the results superimposed. Of course you need to know both source impedances. Superposition is a simple linear equation system with complex values.

To avoid confusion:

Radiaton efficiency = radiated power / input power = η (frequently expressed in a percentage, so always less then 100%).

Some references may call this also "antenna efficiency", this can be confusing.

Input power = Forward power - reflected power = power that is actually delivered to the antenna. = Pforward*(1-|S11|^2)

Antenna efficiency = radiated power / forward power = total Antenna efficiency

(total) Antenna efficiency takes into account the loss due to ohmic heating and impedance mismatch.

Directivity (D) is gain in fieldstrength with respect to isotropic antenna due to the shape of the radiation pattern. Heat loss and mismatch loss is not included. Directivity is always 1 or more (so it cannot be below 0 dBi) for at least one direction. In real world an antenna will always have a direction where D> 0 dBi. Every electrically short straight wire has D=1.76 dBi (perpendicular to the wire).

Gain (G) is gain in fieldstrength with respect toan isotropic antenna based on the actual input power (Pinput = Pforward - Prefl). Heat loss is included, but mismatch loss is not included.

Realized gain (Gr) is gain over isotropic antenna based on the forward power (incident power). Realized gain includes heat loss and mismatch loss.

In the EMC world Realized Gain is mostly called just "Gain" (so this can be confusing).

Of course gain can be referenced to a half wave dipole (dBd), but Directivity is always referenced to a perfect isotropical antenna (no heat loss, perfectly matched).

Generally, all parameters can be plotted or tabulated versus excitation frequency.

I know these difinitions.
in IEEE which definition is used for input power?I don't use from matching network in feeding,so do I have to include reflected power?namely,Do I have to use from input power = Pforward*(1-|S11|^2) only?or do I can't leave S11 effect on efficiency plotting?
in reference paper,the author used from :
input power = 0.5*Real{V(w)*conjucate[I(w)]}.
So it seems that he don't include s11 effect on efficiency calculation.

To avoid confusion:

Radiaton efficiency = radiated power / input power = η (frequently expressed in a percentage, so always less then 100%).

Some references may call this also "antenna efficiency", this can be confusing.

Input power = Forward power - reflected power = power that is actually delivered to the antenna. = Pforward*(1-|S11|^2)

Antenna efficiency = radiated power / forward power = total Antenna efficiency

(total) Antenna efficiency takes into account the loss due to ohmic heating and impedance mismatch.

Click to expand...

Thanks for clarification. I overlooked the reference to input instead of forward power in the original post. I was thinking about technical antenna measurements that are usually perfomed with known generator respectively forward power. Also a source port in simulation has known forward power.

The other point is that "internal" (ohmic and dielectric dissipation) losses of technical antennas are mostly low compared to mismatch losses.

In simulation, it's quite easy to "measure" exact input respectively reflected power, determine different internal loss elements and so on.

I don't know what is important for you, but In IEEE

input power = Pforward*(1-|S11|^2) = (1/T)*integral( v(t)*i(t)*dt ) = 0.5*Re(V*conjugate(I) ).

All V and I should be taken at the input terminals of the antenna.

You are right, if the author uses the input power, he doesn't include mismatch (S11) in his definition for antenna efficiency and in fact he calculates the "radiation efficiency". Due to some mismatch, antenna efficiency is below radiation efficiency.

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@FvM : I'm involved in EMC related issues and as far as I know, gain is always based on forward power (as you mentioned), without adding the word "realized". When discussing gain, I always refer to forward power (without mentioning it, so this caused confusion several times in the past).

When it is based on input power (as in IEEE), you need to measure both forward and reflected power. In case of reception (measurement) you need too know both |S11| and Gain. So Gain based on forward power is the most usefull parameter for practical antenna/EMC measurements.

@Gashem: make sure for yourself what is important for you: definitions based on input power or forward power.

thank you very much for your attentions...
I think I understand.in fact I want to plot "radiation efficiency".So I don't need to include reflected power and I have to consider forward power only.did I just say?
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now I have another problem.can you help me?
I have a copper monopole,such that I have to apply two signal to it.my configuration is as following.
in fact,I have two signal (signal 1 with center frequency = 500 MHz & signal 2 with center frequency = 100 MHz) and my frequency range is (30-300)MHz in HFSS. " I have to apply two signal,simultaneously" to monopole.
my purpose is measuring of s12 and s21.how implement this structure in HFSS and find s12 and s21?

I'm confused a little.in above picture,where is input terminal of antenna?in left side of inner probe of coaxial feed or in meeting point of inner probe to monopole bar?
thanks...

As shown, the structure is a three-port and must be described a 3x3 S-parameter matrix, e.g. port 1 and 2 being the conducted and port 3 the radiated port.

The forward power feed to port 1 will be partly reflected back, partly transmitted to port 2 and radiated to port 3, and partly dissipated internally. It's not obvious which effciency definition should be used in this case.

I am not familiar with HFSS, but I assume it has a single function to plot radiation efficiency versus frequency.

@FvM: though you can see it as a 3-port as you described, HFSS or other simulator will handle this as a 2-port circuit as he has to create two signal ports.

If you want radiation efficiency, you need to find: (radiated power) / (input power) for your list of frequencies. Note that input power is now the sum of input power from port 1 and port 2. If you drive port 1 only, some power will go to port 2 and counts as negative. I don't know whether HFSS can do this automatically for you. Best is to check this with a simulation that you know. Your antenna structure should have a radiation efficiency of > 90% over your 30..300 MHz band, as it is just thick metal.

I am not sure whether I understand what you want to know from simulating this structure. As I am not familiar with HFSS, I can't help you with how to model your structure. Maybe you can start a new thread on your second question.

thank you very much...
in fact in "second question" I want to find only S12 and S21 parameters.I don't want antenna efficiency here.
Som,antenna length is not important.I want to find this two port effect on each other.
why power is transmitted to port 2 from port 1?why power is not transmitted to port 2?
how and in which software,I can to find S parameters in this two port structure?

though you can see it as a 3-port as you described, HFSS or other simulator will handle this as a 2-port circuit as he has to create two signal ports.

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I wasn't referring to simulation setups, just to the fact that the structure has three ports and you can expect some power sent to each port in the general case. In simulation, it would be most simple to treat both sources separately and terminate the unused port with the signal source impedance.

I don't assume that the structure itself has any properties that suppress unwanted leakage into the other signal port, so band filters might be reasonable.

I also think that radiation efficiency is a purely theoretical quantity without considering an impedance matching means that minimizes reflected power.

@ghasem: You can use whatever EM software (ADS, HFSS, Ansoft, IE3D) to determine the S-parameters of your circuit. Use that package that you know, or that some other people around you know how to use. This will save you lots of time. Very likely S12=S21 (reciprocal circuit)?

@FvM: Sorry to say, I only see two ports. That part of metal on top of it is just part of the circuit (I see it as a lossy transmission line resonator, where the loss is in the form of radiation).

Regarding radiation efficiency, I agree with you. In the end it is the Gain (whoops: IEEE Realized Gain) that matters, as this includes mismatch loss and heat loss.

Sorry to say, I only see two ports. That part of metal on top of it is just part of the circuit (I see it as a lossy transmission line resonator, where the loss is in the form of radiation).

Click to expand...

Just a matter of viewpoint. I think, I made clear that I wanted to analyze the over-the-air connection as a port, which would e.g. simplify to distinguish radiated and internally dissipated power. But if you don't like the idea, see it as a two-port with different loss elements.

@FvM: I understand your viewpoint, but defining a third port in a descent simulator will complicate the matter. If I had to put his problem into an EM simulator ( for example IE3D (now Hyperlynx) ), I would model it as a two-port (as shown on his image). The simulator will give me the S-parameters, heat loss, radiation loss, radiation pattern, etc.

@Ghasem: You should draw your circuit in the simulator as it looks like in reallity. There are wires (red colored in your graph) between your inputs (I assume coaxial connectors) and the vertical structure (the vertical bar with connection to ground) . When that is the real situation, you need to draw that wires and very likely you need to use a localized port at the location of connectors.

When you need to draw round wires and ratio (distance to other metallic structure)/Dwire > 2...3, you can use a metallic strip in simulation with D = 2*Dwire. Same is valid for the vertical bar. It saves you lots of drawing and simulation time compared to drawing square, hexagonal or octagonal approximations for round wires. Once you are close to what you want you can draw your problem using a better wire approximation (for example square cross section wires) to do the final tweaking.

thank you very much fo your attention WimRFP
but I have a problem.
suppose,I have to calculate "radiation efficiency" of my antenna (my attachment).I can to calculate "radiated power".

now my problem is that WHERE I have to place input port to calculate "input power" to antenna:

1- do I have to calculate "input power" in left hand side of inner probe (namely in connector Location)?
2- or do I have to calculate "input power" in right hand side of inner probe (namely in connection Location of inner probe to vertical bar(my monopole))?

this point confused me...