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In an ideal world, if the transmitter is outputting 30dBm to an antenna with 100% efficiency with 10dBi of gain. The receiver has an antenna with 0dBi of gain (100% efficiency as well) and is sitting right next to the transmitting antenna. Based upon the link budget analysis, the receiver is getting 40dBm of power.

Since the antenna is a passive device, how can this be true?

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  • \$\begingroup\$ I'm confused by the question. "Since the antenna is a passive device, how can this be true?" What exactly are you referring to when you say "this can't be true?" the 10 dBi gain of the antenna? \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 18:25
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    \$\begingroup\$ @jason, if the TX power is 30dBm and the RX power is 40 dBm, then power has been created out of thin air. It would be a violation of conservation of energy. OP knows that it is impossible for passive devices to act as power amplifiers. Hence the question. \$\endgroup\$
    – user57037
    Commented Mar 19, 2021 at 18:55
  • \$\begingroup\$ @mkeith that makes much more sense. Thanks for clarifying. \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 19:08

2 Answers 2

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We both agree your link budget analysis is wrong.

You forget that antenna factors only apply to far field! You can't have two antennas sitting "right next to each other" , i.e. closer than the Fraunhofer distance, which is \$2d^2/\lambda\$, with d being the dimension of the antenna defining the directivity of emission (typically, it's simply the largest dimension of your antenna). A 10 dBi antenna will be rather large, so that quadratic part really says "can't claim 10 dBi gain and 'right next to each other' at the same time".

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  • \$\begingroup\$ Don't fret, by the way: engineering is full of simplifications, and it often takes experience or a complete lack of it to not do them when they're not appropriate. Learning is the process of understanding concepts, and it seems you're doing fine. \$\endgroup\$
    – mmmm
    Commented Mar 19, 2021 at 0:34
  • \$\begingroup\$ Practically, all of this is true. But link budgets don't care about this. I don't think this answers: "since the antenna is a passive device, how can this be true?" \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 18:39
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    \$\begingroup\$ I think it does answer the question. If you actually do the experiment with antennas right next to each other you will find that the RX power is not higher than the TX power. It is known that antenna properties are specified for the far field. Near field properties are different because there are evanescent fields which do not propagate. \$\endgroup\$
    – user57037
    Commented Mar 19, 2021 at 18:57
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    \$\begingroup\$ @mkeith You're right. I follow the question now. \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 19:11
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I'm not sure I entirely follow your question but I think you might be asking how a passive device can have 10 dBi (i.e. positive gain)?

An isotropic antenna has 0 dB of gain (unity) in all directions (isotropic is the 'i' in 'dBi').

When we say "10 dBi" of antenna gain (e.g. directivity) we mean that in a particular direction the signal gain is 10 dBi. However, in other directions the signal gain will be much, much lower. So instead of radiating equally in all directions we can "direct" energy in a particular direction to get more gain at the expense of reducing energy radiating in other directions.

Edit: as others have pointed out it seems you were focused on the energy conservation and as the other answer pointed out: 10 dBi only applies in the farfield. Even in a vacuum, free space loss cannot be 0 dB. So for the equation to not violate conservation of energy you must include free space loss at a minimum. So in your link budget we know that free space loss must be at least -10 dB.

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    \$\begingroup\$ The OP seems to be asking how you can receive 10W when the transmitter outputs 1W. It's a conservation of energy question. If this were possible, you'd be getting something for nothing. \$\endgroup\$
    – Phil Freedenberg
    Commented Mar 19, 2021 at 18:58
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    \$\begingroup\$ If we could do it with microwaves, we could take a 1mW transmitter, cascade several stages of 10dBi gain antennas, then boil liters of water in seconds with the output at the final stage. \$\endgroup\$
    – user57037
    Commented Mar 19, 2021 at 19:06
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    \$\begingroup\$ Thanks! This phrasing makes much more sense. I was focused on the antenna question. \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 19:09
  • \$\begingroup\$ I added an edit but I agree that @mmmm answer is correct. \$\endgroup\$
    – Jason
    Commented Mar 19, 2021 at 19:17

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