### Author Topic: Antenna impedance and circuit model from receiver perspective  (Read 1788 times)

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#### highvoltageboogie

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##### Antenna impedance and circuit model from receiver perspective
« on: May 14, 2024, 05:53:01 pm »
Hi all,

a question that has made me confused lately:

From transmitting point of view an antenna looks like an impedance - it has a reactive part and a resistive part, and the resistive part is divided into ohmic resistance (converts power to heat) and radiation resistance (radiates power as EM waves).

When we have a transmitter with certain properties and a transmission line with given impedance, we can select an antenna or add a matching circuit to a given antenna to optimize power that is transfered to antenna (and make sure that the transmitter is not damaged).

But how does an antenna look like from receiving point of view? This is not really addressed in many antenna related materials.

I found one source on the internet saying that it could be modeled as a voltage source with the aforementioned impedance in series.  But that was not a very professional source.

If that is correct, we can say that the antenna impedance is the same as in the transmitting case, the radiation resistance scatters power back to the environment and the ohmic resistance and reactance work in the same way as in the transmitting case - is this correct?

With a receiver with given impedance, if we have an antenna that is a voltage source in series with an impedance, it would be useful to minimize the resistive part of the antenna impedance to increase the power that is transfered to the receiver. If there is reactance in series with the receiver, canceling it with opposite reactance would be beneficial.

But what happens if we choose an antenna with much smaller radiation resistance compared to a matching antenna? Less power scattered vs absorbed by the receiver... And let's neglect ohmic resistance now, let's think that the antenna is a superconductor.

Can we still say that it's always the best idea to match the antenna to the receiver? Or are there cases in which we could have an antenna with more suitable impedance and it would transfer more power to the receiver? Let's neglect antenna directivity too.

Or does it always hold that choosing an antenna with lower radiation resistance will either change its reactance in a non-optimal way, or decrease the voltage that is induced by the EM field, and thus it will provide less power to the load compared to a matching antenna? Even if we neglect ohmic resistance?

Writing a general equation for antenna radiation resistance does not work since it depends on the antenna type and shape (thus the resulting EM field distributions).

Writing an equation for the induced voltage is also more or less a case-by-case problem.

And thus we cannot write a general equation in closed form that would give us the voltage of the voltage source when we input the EM field strength, antenna impedances, frequency?

But can we generalize this matter?

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #1 on: May 14, 2024, 07:27:51 pm »
If that is correct, we can say that the antenna impedance is the same as in the transmitting case, the radiation resistance scatters power back to the environment and the ohmic resistance and reactance work in the same way as in the transmitting case - is this correct?

Yes, but for receiver its less critical because it's more easy to add high gain amplifier in order to compensate losses due to bad tuned antenna. For tansmitter it is more critical, because it's more complicated and expensive to push much more power into antenna. For example if receiver needs additional amplification from 1 uW V to 10 uW that's not a big deal, the only limit here is noise figure, but if transmitter needs additional amplification from 100W to 1000W, that's serious issue. In addition it will requires more powerful cable.

With a receiver with given impedance, if we have an antenna that is a voltage source in series with an impedance, it would be useful to minimize the resistive part of the antenna impedance to increase the power that is transfered to the receiver.

That's incorrect. The power is transferred with max efficiency when source impedance is equals to load impedance. If you decrease antenna impedance it will reduce signal power which enters into feeder. The same, if you increase antenna impedance it will reduce signal power which enters into feeder.

You can achieve the best receiver sensitivity when antenna impedance equals to coax cable impedance. Since it may be different it may require matching circuit.

But what happens if we choose an antenna with much smaller radiation resistance compared to a matching antenna? Less power scattered vs absorbed by the receiver... And let's neglect ohmic resistance now, let's think that the antenna is a superconductor.

If you're using antenna with smaller radiation resistance it will lead to less EM wave power captured by such antenna. As result more weak signal on it's output.

Writing a general equation for antenna radiation resistance does not work since it depends on the antenna type and shape (thus the resulting EM field distributions).

I can give you impedance equation for half wavelength dipole. It is very complex, but what is the reason for that. It is already known that half wavelength dipole has about 73 Ω. The same for other types of antennas, you can just get it's impedance from book.

Antenna is just a kind of transformer between EM waves in a free space and your feeder. So, it works exactly the same for receive and for transmit. The same as step down transformer can work as step up transformer.
« Last Edit: May 14, 2024, 07:49:58 pm by radiolistener »

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#### tautech

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #2 on: June 02, 2024, 03:59:16 am »
Antenna is just a kind of transformer between EM waves in a free space and your feeder. So, it works exactly the same for receive and for transmit. The same as step down transformer can work as step up transformer.
This ^^

It need be mentioned in closing that antenna transmission and reception properties are equal therefore designing for optimum transmission also results in optimum reception properties.
This is known as antenna reciprocity and the fundamental reason why an antenna is proven by its transmission properties.

https://www.eevblog.com/forum/rf-microwave/antenna-project-log/
Avid Rabid Hobbyist.

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #3 on: June 02, 2024, 06:23:31 pm »
It need be mentioned in closing that antenna transmission and reception properties are equal therefore designing for optimum transmission also results in optimum reception properties.
This is known as antenna reciprocity and the fundamental reason why an antenna is proven by its transmission properties.

https://www.eevblog.com/forum/rf-microwave/antenna-project-log/

yes, but it needs to be taken into account, that some component of antenna may not support high power, for example if it uses impedance match network with inductor on a core, it's core may enter into saturated state and don't work as expected in transmission mode due to high power changes it's core properties. Another example is a capacitor on magnetic loop antenna, it can work ok in receive mode but in transmission mode the air gap can be broken by high voltage because capacitor is not rated to work with high voltage, but in receive mode it can work with no issue because voltage is very low.
« Last Edit: June 02, 2024, 06:28:24 pm by radiolistener »

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#### uer166

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #4 on: June 02, 2024, 07:12:28 pm »

If that is correct, we can say that the antenna impedance is the same as in the transmitting case, the radiation resistance scatters power back to the environment and the ohmic resistance and reactance work in the same way as in the transmitting case - is this correct?

Kind of? In a perfectly matched antenna setup with a 100% efficient antenna, 50% of the energy is scattered back into environment with the antenna radiation pattern, and 50% ends up in the termination resistance. I'm not sure the assertion that the "radiation resistance" is responsible for this however. You can only go downhill from here when you mismatch the impedance of termination vs. antenna impedance itself (whether it goes up or down is irrelevant).

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#### uer166

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #5 on: June 02, 2024, 07:15:34 pm »
Can we still say that it's always the best idea to match the antenna to the receiver?

There are cases where you want maximum mismatch instead! An example is an antenna that you want to re-radiate instead of absorb field into termination resistance. E.g. director elements in a Yagi antenna are just dipoles shorted out with 0-Ohm termination resistance for maximum mismatch, allowing them to scatter (i.e. re-radiate) 100% of energy in the ideal case.
« Last Edit: June 02, 2024, 07:18:50 pm by uer166 »

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#### highvoltageboogie

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #6 on: June 09, 2024, 10:07:22 am »

Yes it's logical that the circuit properties are equal in receiving and transmitting case (excluding non-linearities such as saturation and breakdown now). And I've read this from antenna theory books too, I think.

It also "makes sense" that impedance matching provides the best reception too.

But what originally made me confused is this:

(trying to attach image here)

Let's say we just have a voltage source, a battery for example, or mains socket, and we have a load resistor (Rrec) with fixed value which we can't choose.

Let's say X = 0 and Rphys = 0 now. How to choose Rrad in this circuit to maximize power in Rrec?

Now let's say that there's an antenna which gets some voltage (Vant) from incoming EM field and it has radiation resistance (Rrad), material resistance (Rphys) and reactance (X). It's connected to a receiver with purely resistive impedance (Rrec). We could add a transmission line with Z0 = Rrec here but we can also leave it out.

Let's say Rrec = 73 ohm, and the antenna is a classic half-wave dipole so Rrad = 73 ohm, X = 0, Rphys ~~ 0, Rphys << Rrad. This should provide the optimal reception (let's exclude directivity now and only consider low-directivity antennas).

From that circuit point of view, it would be logical to make changes to the dipole to bring Rrad down to increase power that is delivered to Rrec. But this doesn't work so one or both of the following must always happen:

1) Vant gets smaller if we make such changes to the dipole dimensions and thus power to Rrec doesn't increase but decreases

2) X gets so much higher that power to Rrec doesn't increase but decreases

How to generalize this? Can we write one rule or formula that does it for any antenna type?

#### mag_therm

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #7 on: June 09, 2024, 12:09:36 pm »

#### A.Z.

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #8 on: June 09, 2024, 03:30:50 pm »

#### highvoltageboogie

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #9 on: June 09, 2024, 08:07:18 pm »
Jacobi's Law
https://en.wikipedia.org/wiki/Maximum_power_transfer_theorem

I know that law, yes. But it is about matching a load to a given source, not the other way around.

Again, let's say we have the following components connected in series:

A 12-volt battery
A variable resistor which we can freely choose
A fixed resistor of 12 ohms

How should we choose the variable resistor resistance to get maximum power to the fixed resistor? The answer is not 12 ohms and the problem I presented here is similar.

Clearly, an antenna with very small radiation resistance does not provide the best reception, so one or both of the two things must happen: voltage from the EM field strongly decreases, or antenna reactance strongly increases, if we start from a matched antenna and change it to reduce its radiation resistance. But can we write some kind of a rule for this?

Or, is it actually wrong to model a receiving antenna as a series connected set of a voltage source, ohmic resistance, radiation resistance and reactance? I haven't seen any other models in use.
« Last Edit: June 09, 2024, 08:11:57 pm by highvoltageboogie »

#### mag_therm

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #10 on: June 09, 2024, 09:37:38 pm »
But read in the Wiki the section "Maximizing power transfer versus power efficiency"
I think it covers the case you are concerned with which seems to be (1)  maximizing power Transfer to a Load  rather than (2) maximizing  Transfer Efficiency for an unavoidable, existing  source impedance
The Rs=Rr rule maximizes transfer efficiency in (2)  and also minimises reflections on the transmission line.
And read further that Jacobi caused a controversy, I think in similar way to your concern.

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##### Re: Antenna impedance and circuit model from receiver perspective
« Reply #11 on: June 10, 2024, 12:06:23 am »
Or, is it actually wrong to model a receiving antenna as a series connected set of a voltage source, ohmic resistance, radiation resistance and reactance? I haven't seen any other models in use.

You can model antenna with feeder as a transformer one coil of which is loaded to a free space which impedance is constant 377 Ω. Since feeder impedance is 50 Ω, transformer impedance ratio is 377/50=7.54 or voltage ratio sqrt(7.54) = 2.75.

As you can see transformer efficiency don't depends on power flow direction. Exactly the same thing with antenna+feeder, because it works as transformer between feeder input and a free space.

In other words, antenna+feeder is just a kind of impedance match circuit between feeder input port and a free space 377 Ω environment
« Last Edit: June 10, 2024, 12:28:22 am by radiolistener »

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