Mengapa 50 Ω sering dipilih sebagai impedansi input antena, sedangkan impedansi ruang bebas adalah 377 Ω?

Agar dapat mengalirkan daya secara efisien ke bagian sirkuit yang berbeda tanpa refleksi, impedansi semua elemen rangkaian harus dicocokkan. Ruang bebas dapat dianggap sebagai elemen lebih lanjut, karena antena pengirim pada akhirnya harus memancarkan semua daya dari saluran transmisi ke dalamnya.

Sekarang, jika impedansi pada saluran transmisi dan antena dicocokkan pada 50 Ω, tetapi impedansi ruang bebas adalah 377 Ω, tidak akankah ada ketidakcocokan impedansi dan akibatnya radiasi yang kurang optimal dari antena?

EDIT:

Sejauh yang saya kumpulkan dari jawaban, literatur, dan diskusi online, antena bertindak sebagai transformator impedansi antara garis umpan dan ruang bebas. Argumennya: tidak ada daya dari feed line yang dipantulkan dan harus masuk ke antena. Antena dapat dianggap resonansi dan karena itu memancarkan semua kekuatannya ke ruang bebas (mengabaikan kehilangan panas dll). Ini berarti bahwa tidak ada daya yang dipantulkan antara antena dan ruang bebas, dan oleh karena itu transisi antara antena dan ruang bebas cocok.

Hal yang sama harus benar dalam arah sebaliknya untuk antena penerima (Prinsip Timbal Balik): gelombang di ruang bebas ( $Z_0$ ) menimpa antena, dan daya yang diterima dimasukkan ke dalam saluran transmisi (sekali lagi melalui transformasi impedansi). Setidaknya dalam satu kertas (Devi et al., Desain pita lebar 377 Ω antena patch berbentuk E untuk pemanenan energi RF, Microwave dan Optical Letters (2012) Vol. 54, No. 3, 10.1002 / mop.26607) menyebutkan bahwa antena 377 with dengan sirkuit terpisah yang cocok dengan 50 50 digunakan untuk "mencapai lebar pita impedansi" dengan tingkat daya yang tinggi. Jika antena biasanya sudah menjadi transformator impedansi, untuk apa rangkaian yang cocok untuk itu? Atau sebagai alternatif, dalam keadaan apa antena bukan juga transformator impedansi?

Beberapa sumber dan diskusi bermanfaat yang saya temukan:

• Klaus Kark, Antenne und Strahlungsfelder (dalam bahasa Jerman)
• Pencocokan Impedansi ( http://www.phys.ufl.edu/~majewski/nqr/reference2015/nqr_detection_edukasi/Impedance_matching_networks.pdf )
• Forum diskusi yang menyebutkan transformasi impedansi untuk antena F-terbalik ( http://www.antenna-theory.com/phpbb2/viewtopic.php?t=776&sid=dede0d4127170d16cc3a583ab0929f3e )
• Beberapa catatan umum tentang antena 8http: //fab.cba.mit.edu/classes/862.16/notes/antennas.pdf)

Impedansi input perangkat / sirkuit (transformator) tertentu tidak perlu mencocokkan impedans outputnya.

Pertimbangkan antena 50Ω (atau impedansi apa pun) sebagai transformator yang mengubah 50Ω (sisi kawat) menjadi 377Ω (sisi ruang).

Impedansi antena tidak (hanya) diberikan oleh impedansi ruang bebas tetapi (juga) dengan cara dibangunnya.

Jadi antena tidak cocok dengan impedansi ruang bebas (di satu sisi); dan idealnya juga impedansi sirkuit (di sisi lain).
Karena impedansi sisi ruang selalu sama (untuk semua jenis antena yang dioperasikan dalam ruang hampa atau udara), itu tidak perlu disebutkan.
Hanya sisi kawat yang Anda butuhkan dan dapat Anda pedulikan.

Alasan 50Ω atau 75Ω atau 300Ω atau ... dipilih sebagai impedansi antena adalah karena alasan praktis untuk membangun antena / saluran transmisi / amplifier tertentu dengan impedansi itu.

Ansatz yang mungkin untuk menghitung resistansi radiasi $R$ antena adalah:

Temukan jawaban untuk pertanyaan: "Berapa besar daya $P$ (rata-rata lebih dari satu periode) yang dipancarkan jika sinyal sinusoidal dari tegangan (atau arus) amplitudo $V_0$ (atau $I_0$ ) diterapkan pada antena?"

Maka Anda mendapatkan $R = \frac{V_0^2}{2P}$ (atau$=\frac{2P}{I_0^2}$ )

Anda mendapatkan daya radiasi $P$ dengan mengintegrasikan vektor Poynting $\mathbf{S}$ (= daya radiasi per area) di atas bola yang melingkupi antena.

Vektor Poynting adalah $\mathbf{S} = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B}$di mana$\mathbf{E}$dan$\mathbf{B}$adalah bidang listrik / magnet yang disebabkan oleh tegangan dan arus di antena Anda.

Anda dapat menemukan contoh perhitungan seperti itu di Wikipedia Wikipedia tentang "antena Dipole", dalam paragraf Short Dipole .

Semua jawaban menyebutkan beberapa poin yang valid, tetapi mereka gagal untuk benar-benar menjawab pertanyaan yang ingin saya ulangi untuk kejelasan:

Why is 50 Ω often chosen as the input impedance of antennas, whereas the free space impedance is 377 Ω?

Jawaban Singkat & Sederhana

Kedua impedansi ini tidak memiliki hubungan sama sekali. Mereka menggambarkan fenomena fisik yang berbeda: impedansi input antena tidak terkait dengan impedansi ruang bebas 377 Ω. Hanya kebetulan bahwa unit kedua istilah itu sama (i, e., Ohms). Selanjutnya, 50 Ω hanyalah nilai umum untuk impedansi karakteristik saluran transmisi dll., Lihat jawaban lainnya.

Pada dasarnya, impedansi input antena, resistansi atau reaktansi lainnya, dan impedansi karakteristik adalah deskripsi level-sirkuit untuk menangani voltase dan arus, sedangkan impedansi gelombang ruang bebas adalah untuk menggambarkan medan listrik dan magnet. Secara khusus, impedansi input 50 Ω yang bernilai berarti jika Anda menerapkan tegangan 50 V pada umpan antena, 1 Arus akan mengalir melalui titik umpan antena. Impedansi ruang bebas tidak ada hubungannya dengan antena atau konfigurasi material apa pun. Ini menggambarkan rasio medan listrik dan magnet dalam gelombang bidang propagasi, yang diperkirakan diperoleh dalam jarak tak terbatas ke antena yang memancar.

Jawaban yang Lebih Panjang

Impedansi pertama yang disebutkan dalam pertanyaan adalah impedansi input antena, yang merupakan jumlah dari ketahanan radiasi, ketahanan kehilangan dan komponen reaktif yang digambarkan sebagai bagian imajiner. Hal ini terkait dengan arus $I$ dan tegangan $V$ pada feed feeding pada level rangkaian-deskripsi, yaitu,

$$R = \frac{V}{I}\,.$$ Mengubah titik makan antena, nilai resistansi radiasi ini mungkin berubah (fakta ini digunakan misalnya untuk pencocokan antena tambalan patch antena mircostrip). Namun, bidang yang diradiasi tetap sama.

Impedansi $R$ dari resistansi radiasi ini sama dengan resistor atau impedansi karakteristik saluran transmisi dari garis koaksial atau jalur mikrostrip, karena ini juga ditentukan melalui tegangan dan arus.

Resistansi radiasi bukan resistensi nyata, itu hanya model untuk kasus radiasi (yaitu, operasi antena untuk mengirimkan daya), di mana daya hilang dari sudut pandang sirkuit karena dipancarkan.

Impedansi kedua adalah impedansi gelombang bidang, yang menggambarkan rasio medan listrik ( $E$ ) dan magnet ( $H$ ). The-ruang bebas impedansi, misalnya diberikan sebagai

$$Z_{0,\mathrm{free\,space}} = \frac{E}{H} = \pi 119,9169832\,\Omega\approx377\,\Omega\,.$$ Kita dapat segera melihat bahwa medan dan tegangan memiliki hubungan yang mungkin berubah dengan geometri dll, atau mungkin tidak ada definisi tegangan yang unik (misalnya, dalam pandu gelombang berlubang).

Untuk membuat kurangnya hubungan dari jenis-jenis impedansi ini menjadi lebih jelas, sebuah contoh dapat membantu. Dalam kasus yang sangat sederhana dari gelombang TEM di dalam kabel koaksial, kita tahu bagaimana menghitung karakteristik impedansi kabel koaksial berdasarkan geometri sebagai

$$Z_{0,\mathrm{coax}}=\frac{1}{2\pi}\sqrt{\frac{\mu_0}{\epsilon_0}}\ln\frac{r_{\mathrm{outer}}}{r_{\mathrm{inner}}}\,,$$ jika kita berasumsi bahwa bahan pengisi vakum. Ini adalah impedansi karakteristik (dari saluran transmisi) untuk arus dan voltase saluran ini, dan ini adalah jenis impedansi yang harus disesuaikan dengan impedansi input antena.

Namun, setelah melihat bidang di dalam kabel, kami menemukan bahwa medan listrik hanya memiliki komponen radial (nilai yang tepat tidak relevan dalam konteks ini)

$$E_r \propto \frac{1}{r \ln(r_{\mathrm{inner}}/r_{\mathrm{outer}})} \,.$$ Lebih menarik,bidang$B$ hanya memilikikomponen$\phi$ yang merupakan versi skala dari bidang radial listrik $$B_\phi = \frac{k}{\omega}E_r=\frac{1}{c}E_r\,,$$ mana$c$ adalah kecepatan cahaya, yang berasal dari ruang bebas (!) karena media di dalamnya adalah ruang bebas. Dengan menggunakan $$B = \mu H\,,$$ kita akhirnya tahu komponen phi dari medan magnet sebagai $$H_\phi =\frac{\sqrt{\epsilon}}{\sqrt{\mu}}E_r=Z_{0,\mathrm{free\,space}}E_r\,,$$ Oleh karena itu, rasio medan listrik dan magnet konstan dan hanya bergantung pada medium; Namun, itu tidak tergantung pada geometri kabel.

Untuk ruang bebas di dalam kabel koaksial, impedansi gelombang selalu sekitar 377 Ω, sedangkan impedansi karakteristiknya bergantung pada geometri dan dapat mengambil nilai yang mungkin dari hampir nol hingga nilai yang sangat besar.

Kesimpulan & Keterangan Akhir

Jika kita melihat kembali contoh kabel koaksial dan membiarkannya terbuka di ujungnya, mencapai impedansi karakteristik ~ 377 Ω tidak berhubungan dengan apa pun tentang bidang. Setiap kabel koaksial yang diisi dengan udara memiliki impedansi gelombang ~ 377 Ω, tetapi ini sama sekali tidak membantu untuk membuat bagian terbuka kabel koaksial menjadi antena yang baik. Oleh karena itu, definisi antena yang baik tidak berhubungan sama sekali dengan impedansi, tetapi berbunyi

An antenna is a transducer from a guided wave to an unguided wave.

50 ohm adalah sebuah konvensi. Jauh lebih nyaman jika ruangan yang penuh dengan peralatan semuanya menggunakan impedansi yang sama.

Why is it the convention? Because coax is popular, and because 50 ohms is a good value for coax impedance, and it's a nice round number.

Mengapa itu nilai yang baik untuk membujuk? Impedansi coax adalah fungsi dari rasio diameter perisai dan konduktor tengah, dan bahan dielektrik yang digunakan:

$$Z_0 = {138 \over \sqrt{\epsilon}} \log_{10}\left(D\over d\right)$$

Atau disusun ulang secara aljabar:

$${D \over d} = 10^{\sqrt{\epsilon} Z_0 / 138}$$

where:

• $Z_0$ is the characteristic impedance of the coax
• $\epsilon$ is the dielectric constant (air is 1, PTFE is 2.1)
• $D$ is the diameter of the inside surface of the shield
• $d$ is the diameter of the outside surface of the center conductor

As the characteristic impedance increases, the center conductor must become smaller if the shield geometry and dielectric material remain constant. For $Z_0 = 377\:\Omega$, and PFTE dielectric:

$${D \over d} = 10^{\sqrt{2.1}\ 377 / 138} = 9097$$

So for a coax cable with an outside diameter of 10 mm (RG-8, LMR-400, etc are approximately this size), the center conductor would have to be 10 mm / 9097 = 1.10 micrometers. That's impossibly fine: if it could even be manufactured with copper it would be extremely fragile. Additionally loss would be very high due to the high resistance.

On the other hand, the same calculation with $Z_0 = 50\:\Omega$ yields an inner conductor of approximately 3 mm, or 9 gauge wire. Easily manufactured, mechanically robust, and with sufficient surface area to result in acceptably low loss.

OK, so 50 ohms is a convention because it works for coax. But what about free space, which we can't change? Is that a problem?

Not really. Antennas are impedance transformers. A resonant wire dipole is a very easy to construct antenna, and it has a feedpoint impedance of 70 ohms, not 377.

It's not such a foreign concept. Air and other materials also have an acoustic impedance, which is the ratio of pressure to volume flow. It's analogous to electrical impedance which is the ratio of voltage to current. Somewhere in your house you probably have a speaker (perhaps a subwoofer) with a horn on it: that horn is there to take the very low acoustic impedance of air and transform it to something higher to better match the driver.

An antenna serves the same function, but for electric waves. The free space into which the antenna radiates has a fixed 377 ohm impedance, but the impedance at the other end depends on the geometry of the antenna. Previously mentioned, a resonant dipole has an impedance of 70 ohms. But bending that dipole so it forms a "V" instead of a straight line will decrease that impedance. A monopole antenna has half the impedance of the antenna: 35 ohms. A folded dipole has four times the impedance of the simple dipole: 280 ohms.

More complex antenna geometries can result in any feedpoint impedance you like, so while it would be technically possible to design an antenna with a feedpoint impedance of 377 ohms, but you wouldn't want to use it with coax for the reasons above. But perhaps twin-lead would work, though there wouldn't be any particular advantage to 377 ohm twin-lead.

At the end of the day, the antenna's job by definition is to convert a wave in one medium (free space) into a wave in another medium (a feedline). The two don't usually have the same characteristic impedance and so an antenna must be an impedance transformer to do the job efficiently. Most antennas transform to 50 ohms because most people want to use 50 ohm coax feedlines.

I'm doing my first steps in antenna and RF field. I was learning about Antenna Impedance when I found this question and I will try to answer it. Hopefully I have understood the question! Sorry if the answer looks stupid, I'm just a "BEGINNER" :)

You said "Why is 50 Ω often chosen as the input impedance of antennas, whereas the free space impedance is 377 Ω?", I think the answer is already included in the question. Yes, it's the word "INPUT". The 50 Ohm is chosen as an input not as an output impedance, if we want to transmit or receive the maximum power between the coaxial line and the antenna we have to match their impedance.(in this case is 50 Ohm because of the standards) If you chose 377 Ohm as the input impedance of the antenna to match it to the air impedance you will lose the power transmission between the coaxial line and the antenna.
If we consider the antenna as an element of the circuit that has an input and an "output impedance" it will look as follows:

^{simulate this circuit – Schematic created using CircuitLab}

The radiation resistance, $\small R_r$, of a half-wave dipole is $\small 73\Omega$. This relates directly to the feedpoint impedance, i.e. this is the impedance presented to the transmission line by the antenna at the design frequency.

$\small R_r$ is related to the impedance of free space (i.e. the impedance seen by an E-M wave travelling in free-space), but is not equal to it.

This question is a good example of over interpreting electrical engineering rules that were devised to make the physics more manageable in practical contexts. Impedance simply isn't that important.

The energy of a radio wave is embodied in the electric and magnetic fields distributed in a spatial volume. Maxwell's equations establish requirements for the relationships among those fields, and the homogenous equations imply that a disturbance from equilibrium will propagate. The latter is evident from the fact that the wave equation is easily derived from the fundamental equations.

In the wave equation there is an implied velocity of propagation that is the reciprocal of the square root of the product of the magnetic permeability and electric permittivity of the medium of propagation.

The square root of the quotient of those two quantities has units of impedance, and when the medium in question is a vacuum or air, it is called the 'radiation impedance of free space'.

This phrase refers to the ease (or difficulty) of establishing a non-equilibrium electro-magnetic disturbance. Loosely, it is a measure of the capacity of a volume of the medium to store energy in electro-magnetic form. More energy requires more volume or you risk non-linear breakdown. Very loosely, we are quantifying how hard it is to push energy into the system.

In a transmission line, say an old fashioned twin lead, we have a similar situation with different boundary conditions. The energy in the line is stored (transiently) in the oscillating electric field between conductors and the oscillating magnetic field about the conductors. This energy can propagate in two directions. If you have equal amounts of energy propagating in both directions, you have resonance or a standing wave. If you have matched terminations, energy leaves the line when it gets to the end and does not reflect or propagate back. It is important to understand that the power is transmitted in the insulator, not the conductors. The conductors are present only to provide boundary conditions, and the charge carriers in the conductors oscillate essentially in place, providing terminals for electric fields, and coupling the electric and magnetic fields. These ideas apply equally well to coaxial lines, but it is easier to visualize in a twin lead.

Like free space, a transmission line has a characteristic impedance that is a measure of its capacity to temporarily store energy distributed along its length. This impedance is dependent upon the geometry of the conductors (boundary conditions) and the relative permeability and permittivity of the materials from which the line is fabricated. Likewise, there is a characteristic propagation velocity that is typically a substantial fraction of the velocity of light in a vacuum.

The requirement for 'matching' impedances arises from the physics of wave reflection. Obviously any reflected energy is not propagated out of the system. A match eliminates reflected energy. It is important to realize that broadband matches are difficult. Matches are typically tuned to the specific design frequency of the system, and out of band signals may exhibit significant reflections.

In a resonant feed line, this fact is exploited by driving the line at its resonant frequency. At resonance, the line impedance is purely resistive. The difficulty is, you need to control the feed line length precisely, and it is only useful at its resonant frequency.

A more practical compromise is to match impedance. Then the feed line may be any reasonable length, and the signal may be a composition of many frequencies, or many independent signals, within the limitations of the bandwidth of the match.

A simple antenna like a dipole is operated at resonance. It is a resonant feedline. It therefore presents a purely resistive characteristic impedance (dependent on geometry and physics) at its design frequency. A line matched to that impedance will deliver all of its energy to the antenna. The antenna, being a resonant feedline, in turn delivers all of its energy to the next system, which is typically free space. It does this because at its design frequency, there is no reactive impedance. If you need to push more energy, you need to drive the antenna harder, which raises the peak voltages and currents in the antenna, which increases the amount of energy pushed out into free space during a given cycle. Obviously there are limitations imposed by non-linear breakdown.

A broadband antenna is really just a lossy feedline. Within its design bandwidth, all energy is radiated by the time an oscillation reaches the end of the feedline. Such antennas typically embody conical geometry in some form, with the low frequency limit set by the base of the cone and the high frequency limit set by practal limits on the pointiness of the cone.

All this is good in theory but what works in practice is a different story. I have been a communications engineer for the better part of 50 years. What we have to keep in mind here is we are attempting to explain a device called an antenna and why it does or does not work, or how well it does or does not do its job. Yes a new student can usually make a functional device from all these calculations, however that is not always true. I have built some very exacting antennas from theory that simply performed very poorly if at all. A good example is the J pole the performance is often not at all what one would expect even if when hooked up to very fancy antenna test equipment i.e. VNA's, it looks like it should be a great radiator and receptor when in fact it was more of a dummy load. Practice and theory often don't intersect. 50 ohms has been mentioned, yes it is a great compromise between the worlds of 37.5 and 73 ohms and it works well for that, in fact 50 was chosen because it worked in practice and it was easy to build from existing materials. In particular 1/2 inch water pipe inserting insulators and a center conductor for use on US Navy ships for WWII. Isolation had to be had for the feedlines to go from the antennas on deck to the equipment located within the safety of the ship. Before WWII there were literally Shacks "Radio Shacks" and I don't mean the defunct electronics stores, built right out on the main deck so as to be able to conduct the antennas to the radios. Even in the newer (at the time) ships the radio room was built on the main deck on an outside wall. Now for obvious safety reasons in a war ship the radio room should never be on deck or easily exposed to enemy fire, equipment and personal safety was a must so coax was born. Yes there were theoretical applications before that but not in general practice, there was shielded wire in use but it was not coaxial nor did it need to be, but to conduct signals from above deck to below deck and vice versa a different feedline than twinlead or ladder line was needed, both to protect the signals coming and going but also to protect the personnel and other things like gunpowder from the RF. Antennas are much the same. I often see mention of 1/4 wave antennas mentioned, truth is there really is no such thing. Nearly all practical antennas are some sort of 1/2 wave dipole. In the case of the 1/4 wave the other half of the antennas is usually the car or some other ground plane. As for 377 ohms to 50 or any other impedance it is all about feed point and or literal angle of the antenna, such as the "V" antenna mentioned earlier. Take for example a 1/2 wave end fed antenna it needs somewhere between a 9:1 to a 12:1 Balun Transformer to make it match and work. As does the Off Center Fed Dipole. Now there is that magical and sometimes nasty word BalUn! It is very simply nothing bad or magical it is simply a matching transformer. Often used to go from a balanced feedline or antenna to a unbalanced feedline or antenna! Does the transformer know balanced from unbalanced, NO it does not. In fact it does not even know what the impedance is, it only knows ratios i.e. 1 to 1, 4 to 1 or 9 to 1. Again I point out practice is not THEORY, thousands upon thousands of 4:1 Baluns are in use all over the world matching 50 ohm devices (Radios) and feedlines usually coax to 300 400 and even 600 ohm antennas. Do they work, fantastically they do, are they text book correct, not on your life, but then again all this would be moot if it did not work in practice! So quit worrying about the numbers being correct they are at best guidelines, what works, WORKS! Besides 377 ohms is theoretical freespace and just like isotropic Virginia It Simply Does Not Exist!

"...In order to efficiently deliver power to a different part of a circuit without reflection, the impedances of all circuit elements need to be matched...."

This is your assumption. And it is correct, but not in the case of antennas.

Because in antennas, we have "reflection". Power applied to the feed point (in a dipole, for example) travels down to the end of the wire, and is reflected back to the feed point, where (if resonant) it will meet a voltage or current 180 degrees out of phase, thus canceling, and represented by the (so-called) standing wave.

So, the applied power bounces back and forth in the antenna wire until all is radiated or lost as heat. So it does not matter if the antenna impedance is different than free space. What really matters, practically speaking, if the energy is reflected back into the transmitter and warms the final amp device, thus wasting the power/energy appliled. This happens when the impedance of the final amp does not match the antenna system (transmission line plus antenna). But once the antenna system is matched to the transmitter, almost all the energy will be transmitted to free space (except for resistance in the wire, which is usually negligible. Or so I am told.

And to comment on the answer by Laurin Cavender WB4IVG: In theory, there is no difference between theory and practice.