Theory of cone antennas BowTie

Foreword

The issue of cone antennas (Butterfly, BowTie) is very poorly lit in the literature, although it is the most popular type of TV antennas in the world, along with Uda-Yagi.

Therefore, in the article we describe the principles of their work and design: the wave properties of a single butterfly vibrator, the influence of reflectors and directors on the directivity pattern and antenna gain, the principles of connecting butterfly vibrators into common-mode arrays.

In addition, we will present the reader with 7 CAD-optimized practical designs of television antennas based on a butterfly vibrator from the simplest (including non-reflex) to a very high-performance antenna with an average gain of 16.3 dBi for long-range reception.

At the base of all antennas, an active element (vibrator, radiator) is necessarily present, to which the voltage is applied during transmission operation, or the voltage is removed during reception operation.
In most types of antennas, the vibrator is a half-wave dipole and its variations (split dipole, loopback, double loop, quarter-wave pin, a set of dipoles with a log-periodic geometry, etc.).
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The design of parasitic elements and the coordination of the antenna come from the properties of the vibrator. The properties of a half-wave dipole are well known and widely described. The radiation resistance is 73Ω at the center frequency, the radiation pattern is almost circular, with a small gain of 2.15 dBi perpendicular to the axis.

The dipole axis passes through the E-plane, i.e. the polarization of the radiation coincides with the axis of the dipole.

The radiation resistance decreases rapidly with decreasing frequency and increases with increasing frequency.
A dipole centered at 600 MHz with a CWS = 1 per line 73Ω will have a CWS = 2 already at frequencies 560 and 650 MHz, i.e. retains an acceptable CWS in the range of -7% ... + 8%.

The dipole is ideal for narrowband applications, and you can make it broadband only by compromise ways - add parasitic elements (reflectors, directors), selecting their geometry so as to equalize the characteristic impedance in different parts of the range. With this geometry selection, the gain of a multi-element antenna will be significantly lower than with the same number of parasitic elements optimized for a narrow range. Antenna gain is very uneven in range, and the CWS goes beyond the bounds of decency at the edges of the range.

Part I. Cone Vibrator (BowTie radiator)

There are also other designs of vibrators, the so-called VSS, frequency-independent. Their radiation resistance is significantly less dependent on frequency; they can operate in a relatively wide frequency range with high efficiency and acceptable SWR.

One of these designs is the biconical antenna:



Its properties are preserved if instead of volume cones to apply their projections - flat triangles in the form of a bow tie (eng. - BowTie).

If the triangles are infinite - the antenna will work at all frequencies:


If you create triangles of finite size - they can work in some large frequency range.


Moreover, the triangle does not have to be solid.


Its properties are preserved even when only two beams are left from the plane, although with jumpers, the triangle radiates a little better.


Next, we will consider only the version of the two whiskers (eng. - Whiskers) - the most simple and common.

The center frequency for the BowTie is such a wavelength when each of the 4 whiskers has a length of ~ 0.47λ (with a technological gap in the center of 1 "= 2.5 cm).

This means that the BowTie vibrator is about 2 times larger than a half-wave dipole. The full width of the dipole is ~ 0.5λ, and the full width of the BowTie is ~ 1λ.

Such dimensions make it unacceptably large at frequencies below 200 MHz, so it does not apply on TV channels 1-5 and does not apply in the FM radio.

For frequencies 200 ... 800 MHz, its dimensions are quite acceptable, which, in combination with broadband, ensured mass, and dominance in the antenna segment 10+ dBi.


The radiation impedance at the center frequency (all examples will be for 600 MHz) is about 545Ω (for a conductor diameter of 2.8 mm) and smoothly drops to 200Ω at frequencies of 350 and 800 MHz.

Matching the 545Ω to the 75Ω coaxial line is very non-standard (albeit implemented if necessary), but for working in a wide frequency band it is unnecessary and even undesirable. Acceptable for television CWS will be if you use power from 300 to 600Ω. The minimum averaged in the range of 470 ... 790 MHz CWS is obtained by supplying ~ 400Ω.

Here is the SWR (eng. - SWR) in the frequency band 400..800 MHz with 400Ω power supply, and a comparison with the SWR of the half-wave dipole to the 73Ω line.


The graph shows options with a mustache opening angle from 20 to 60 degrees. The angle does not greatly affect, the optimum angle is about 33 degrees. If the classical dipole allows you to keep SWR <2 in the 560 ... 650 MHz band, then the BowTie vibrator has a CWS <2 in the 470 ... 690 MHz band, i.e. covers the entire TV band of UHF (in the future, channels 49 and above will be sold for the needs of LTE-700 after SECAM ceases broadcasting), and in the frequency band up to 790 MHz it has a CWS <3, which is also acceptable.

The radiation pattern of the BowTie differs slightly from the dipole. Up / down BowTie emits 3-4 dB weaker than forward / backward. The side suppresses radiation much stronger than the classical dipole. Due to this, the forward / backward gain at the center frequency of about 4.8 dBi (versus 2.15 dBi dipole), and in the 400 ... 800 MHz frequency band smoothly increases from 3.6 dBi to 6.7 dBi.


For matching a 75Ω cable with a single BowTie, a 6: 1 balun (Bal-Un, Balanced-Unbalanced transformer) will be optimal, which can be made from a 4: 1 balun or by running on a 2-hole ring:


A standard 300Ω 4: 1 balun will also work, but the CWS will be> 2.

Part Ia Cone Vibrator - All Wave?

Cone antenna refers in part to the PNA (frequency-independent antenna) and to UWB (Ultra-Wide Band) antenna type.

The maximum radiation resistance of the cone vibrator has a whisker length of 0.47λ (about 545Ω), with a deviation of length in any direction - the resistance drops to a minimum of 84Ω (at 0.31λ).

Further shortening of the wave leads again to an increase in resistance to 545Ω with the length of the whiskers of a multiple of 0.47λ (600, 1200, 1800, 2400 MHz), and to a cyclic fall to 84Ω with the length of the whiskers of a multiple of 0.47λ, but with a fixed shift of 0.24λ (900, 1500, 2100, 2700 MHz).


Thus, if we have the possibility of matching the impedance in the range of 84-545Ω, the antenna can be used in a very wide frequency range, unlike a dipole whose resistance will increase indefinitely or fall at low frequencies to zero.

The practical benefit of this property of cone antennas can only be extracted with an active matching device installed directly next to the antenna, which will convert 84-545Ω to 50 or 75Ω resistance of the radio receiver and / or transmitter transmission lines.

With passive matching via a fixed transformer, it is practically impossible to benefit from such broadband properties. An acceptable VSWR is maintained in a relatively narrow frequency range, although it is wider than that of a conventional dipole. If by SWR = 2 the matching range is + -8% for a dipole, then for a tapered vibrator it is + -18%.

What is the frequency for a butterfly vibrator resonant? To answer this question, let us return first to the definitions.

Here is a model of any abstract antenna:



The total (complex) radiation resistance is equal to the sum of the real part (blue) and the imaginary part (red).

The imaginary part consists of two reactive components: inductive (with a + sign) and capacitive (with a - sign).

When the inductive and capacitive reactivity are equal, the imaginary part is zero. The antenna impedance is equal to the actual radiation resistance. This frequency is called the resonant frequency of the antenna. For a half-wave dipole, the resonance length of the dipole is 0.5λ (taking into account the end capacitance in thick conductors - about 0.47λ, the exact value depends on the L / D ratio), the actual resistance at the resonant frequency is 73Ω.

For a butterfly vibrator, there are two resonances when the inductive component is zero: these are the points of both the maximum resistance and the minimum. Those. for a 600 MHz vibrator, the frequencies 600, 1200, 1800 and 900, 1500, 2100, etc. will be resonant. With a resonant length of each bore multiple of 0.47λ (with a 33-degree opening angle and a conductor diameter of 2.8 mm), the resistance of the vibrator is maximum possible (around 600Ω), and with a multiple of 0.47λ * K + 0.24λ (a quarter-wavelength shift) possible (around 85Ω).

The exact value of the real resistance R is very sensitive to the diameter of the conductors of which the whiskers are made. With a very thin conductor D = 0.1 mm, the resistance R at the resonant frequency reaches 1444 Ω, and with a 10-mm-diameter mustache it reaches only 345 Ω. The resonant frequency is also shifted.

Here is a table of dependences Rmax (at the resonant frequency), Rmin (at frequencies with a shift of 1/4 from the first resonant frequency) and the corresponding whisker lengths corresponding to these frequencies, depending on the diameter of the conductor.


For a conventional dipole, the diameter of the conductor has almost no effect on the resonant resistance, and the thick dipole reduces the reactive component — makes the impedance curve more gentle, and the dipole itself becomes more broadband.

For a butterfly vibrator, the diameter of the conductor has a very strong influence on both the resonant and reactive, and hence on the impedance.

Let's compare the curves of the full (complex) resistance Z for a vibrator with a 4x223 mm mustache, with a diameter of 1, 3 and 6 mm.



As you can see, the diameter significantly affects Rmax, and almost does not affect Rmin. In addition, increasing the diameter of the whiskers reduces the resonant frequency (i.e. the whiskers can be made shorter).

In a thicker vibrator, the slope of the slopes is less and the resistance drop in the frequency range is less. This makes it easy to calculate matching for a wide frequency range.

Part Ib Cone Vibrator - DN in Frequency Band

As we know, the DN of a normal dipole is the same in the entire frequency band and does not depend on the distance from the resonant frequency. Is that true for a butterfly vibrator?


As we see, with increasing frequency, the diagram first narrows, and starting from about 0.62λ, side lobes begin to grow, the intensity of which at the frequency near the second resonance reaches the intensity of the main lobe, and as the frequency grows further, the main lobe almost disappears. With the passage of each of the next resonant frequency, the petals split into two and the radiation lobes appear upwards.

Conclusion: although the butterfly vibrator is formally all-wave, the shape of the radiation pattern begins to split apart after more than 1 wavelength is placed in the total length of the vibrator (both whiskers). Although the vibrator will emit, the direction of this radiation is unsuitable for practical applications.

The practicable range from above is limited by the pattern of the whisker length 0.6λ.

From below it is limited by the fall of the radiation resistance and the growth of the CWS. With a mustache length shorter than 0.19λ, the R falls below 25Ω, and the CWS rises to 4+ even with 50 / 75Ω power.

Suitable for practical use (when deciding the issue of impedance matching) is the wavelength range from 0.2-0.6λ, i.e. +28% ..- 57% of the resonant frequency 0.47λ

Part II / Parasites

Parasitic elements are conductors that lie in the E-plane, i.e. parallel to the vibrator and lie in the polarization of the radiation of the vibrator and electrically isolated from the vibrator.

Metallic connection is allowed only for points with zero potential and is only constructive.

Parasites significantly affect the dipole, and the effect depends on whether the parasite is longer or shorter than the vibrator. If the parasite is shorter, then it has capacitive reactivity and increases the radiation towards itself, and if the parasite is longer, it has inductive reactivity and “pushes” the radiation away from itself. Short parasites are called directors, while long ones are called reflectors. The more parasites and the closer they are to a dipole, the lower its radiation resistance.

Already 1 reflector greatly reduces radiation back and forth and down and adds forward. Radiation forward increases from 2.15 dBi + 4.7 dB = 6.9 dBi.

If the reflector has a length of the vibrator, then it reduces the radiation only up / down, and the forward / backward radiation is equivalent.

By reducing the length of the reflector below the length of the vibrator, it turns into a director, the radiation backwards exceeds the radiation forward. The gain of 1V1D can reach up to 6.2 dBi (slightly less than 1V1R).

The directors differ from the reflector in that the further addition of the number of directors leads to a further narrowing of the DN and, accordingly, an increase in the gain. The second reflector behind the first has almost no effect on the radiation of the antenna.

With a conical antenna, parasites behave differently. The parasite begins to show any properties from a length of about 0.2λ. Its optimum distance is 0.15λ from the vibrator.

From 0.3 to 0.47λ, the parasite works as a director, with a gain peak at 0.448λ = 8.91 dBi. At 0.47λ, the parasite is neutral (suppresses only up / down), and from 0.48λ and above (to infinity) behaves as a reflector, with a gain peak of 0.49λ = 8.52 dBi (+3.71 dB against the bare cone)

0.0λ - 4.81 dBi (without parasite)
0.1λ - 4.83 dBi
0.2λ - 4.94 dBi
0.3λ - 5.32 dBi (works as a director)
0.4λ - 6.89 dBi (works as a director)
0.449λ - 8.92 dBi (works as a director)
0.47λ - 7.57 dBi (front / back orientation is the same)
0.49λ - 8.52 dBi (works as a reflector)
0.5λ - 8.45 dBi (works as a reflector)
0.6λ - 7.18 dBi (and further works as a reflector)
0.7λ - 6.77 dBi
0.8λ - 6.63 dBi
0.9λ - 6.57 dBi
1.0λ - 6.55 dBi
1.2λ - 6.55 dBi
1.3λ - 6.60 dBi
1.4λ - 7.04 dBi
1.5λ - 7.7 dBi
1.6λ - 7.14 dBi
2.0λ - 6.87 dBi


The radiation resistance increases strongly (the dipole slightly decreased). So a 0.49λ reflector raises resistance from 545 to 1150Ω. In addition, in a wide band, the properties of the parasite change dramatically with the passage of the point 0.47λ. The parasite turns from a reflector into a director and the signal is attenuated in the right direction (but the radiation of the rear hemisphere increases). Therefore, this design does not make sense for any practical purposes.

In order for the reflector to behave in a wide frequency band as a reflector, it is necessary to take at least 1.0λ at ​​the center frequency. But the characteristics of such an antenna are very mediocre - the PDC on the front / back is very weak (zero at some frequencies), the SWR exceeds 2.6 at the edges of the range.

Conclusion : parasites with the aim of creating an antenna directivity (gain gain and KZD) are very impractical and therefore not used in practice. Parasites can be carefully used to correct the frequency response in the upper part of the range and to create a blockage of frequencies along the upper edge. For example, if for a broadband antenna (like Polish ASP-8) for a band of 50 ... 800 MHz add a director who at a frequency of 800 MHz will have a length of <0.45λ, then at high frequencies, where its effective length is> 0.3λ it will begin to influence:

- will raise the radiation resistance (and as we already know, it falls as we move away from the center frequency)
- will raise the gain due to the focus forward
- when the length begins to approach 0.47λ, the resistance will increase sharply (and the CWS) and the director will turn into a reflector and reduce the gain forward. The director will work as a notch filter, with a cut-off frequency F = 300 / L / 0.47 = 141 / L of its length.

In the lower frequencies, the length of such a director will have <0.3λ and almost will not affect the operation of the antenna.

Part III / Reflector Screens

The screen reflector is a flat reflector. It can be made both from a solid conductor (metal sheet, foil) or from a grid of horizontal conductors (if the position of the vibrator whiskers is horizontal). Vertical conductors do not affect the properties of the screen. They can only be used for design reasons to give strength to the structure.

Like a single parasite, the properties of the screen depend on its width. If the screen has a width of less than 0.47λ, it works as a director: the radiation grows in the direction of such a screen. If the screen has a width of more than 0.47λ, it works as a reflector.

The distance to the reflector can be any from 0.1λ to 0.5λ. With a reflector 1λ wide and 0.5λ high (± 0.25λ from the radiation axis) with a grid step of 0.025λ, the radiation resistance and the gain of a single BowTie will be:

0.10λ - 1700Ω - 9.83 dBi
0.15λ - 871Ω - 9.63 dBi
0.20λ - 603Ω - 9.35 dBi
0.25λ - 496Ω - 8.94 dBi
0.30λ - 442Ω - 8.35 dBi
0.35λ - 414Ω - 7.48 dBi
0.40λ - 404Ω - 6.15 dBi
0.45λ - 412Ω - 4.04 dBi
0.50λ - 443Ω - 0.67 dBi

A reflector offset from 0.15λ to 0.35λ is practically useful. As the screen approaches <0.15λ, resistance increases very rapidly to impractical values. When removing> 0.35λ, the directivity decreases rapidly and at 0.42λ it is the same as that of a bare vibrator.

For operation at the center frequency, the optimal distance is 0.2λ - the resistance is very convenient 600Ω, and the directivity reaches 9.35 dBi. For operation in a wide frequency band, it is possible to select the optimal position in the interval 0.15 ... 0.25λ, improving the matching / gain in those parts of the range where a dip is observed.

Consider the influence of the width of the reflector, with Offset = 0.2λ:

0.50λ - 890Ω - 08.95 dBi - 05.86 F / B
0.75λ - 657Ω - 09.11 dBi - 10.57 F / B
1.00λ - 603Ω - 09.35 dBi - 12.37 F / B
1.25λ - 574Ω - 09.90 dBi - 14.46 F / B
1.50λ - 583Ω - 10.18 dBi - 19.33 F / B
1.75λ - 586Ω - 10.04 dBi - 19.77 F / B
2.00λ - 585Ω - 09.96 dBi - 19.48 F / B

With a width of less than 0.47λ, the screen behaves like a director and concentrates the radiation in its direction.

With a length of> 0.47λ, the screen behaves like a reflector-reflector, with 0.59λ the ratio Front / Back reaches 8 dB.

At 1λ, the antenna already has decent parameters - a convenient impedance of 600Ω, a gain of> 9 dBi and a PDA of> 12 dBi.

With a further increase in the width of the screen, the gain almost does not grow, but the CDD rises to 18..20 dB.

Peak gain and KZD at 1.5λ, a further increase does not give any increase. In the frequency range of 470 ... 690 MHz, the CWS grows too much at the edges of the range with 0.20λ offset. If work is required on any of the channels 21..49, then it is necessary to increase the offset to 0.25λ, then the antenna will have the following parameters for a load of 600Ω:


The antenna can work with baluns 4: 1, 6: 1 and 8: 1. The CWS will be different in a wide frequency band:


Consider whether it is possible to add a parasite director to such an antenna. As the analysis showed in the previous part, the director length should not be close to 0.47λ in the entire band of the antenna.

Suppose we need to design the antenna under the range of 470 ... 700 MHz. Take a director with a length of 0.41λ at a frequency of 700 MHz, at the center frequency of the previous antenna (600 MHz), its length will be 0.35λ. Step-by-step optimizer showed that the optimal distance to the vibrator is 0.20λ.


The second director 0.34λ at 0.16λ from the first one can give another ~ 0.5 dB gain in the range of 550 ... 690 MHz, at the cost of worsening of the CWS by 0.1.

The two-story first director (the optimum height is about 0.13λ) gives more growth than the second director.

Part IV / Reflector with sides

When the width of the main screen canvas reaches 1-1.2λ, a further increase in the width of the screen no longer gives a significant increase. Further increase in the width of the screen at an angle, i.e. creating bent sides is often more beneficial than rectilinear widening of the width. Optimal for 1λ screen bumpers are ~ 0.2-0.25λ at an angle of 30 degrees to the canvas.

The radiation pattern varies slightly in the horizontal plane - a slight increase (up to 1 dB) of radiation ahead, a very significant suppression of radiation back, but its redistribution is not forward, but in the rear hemisphere. The ratio of the front and rear hemispheres even slightly deteriorates, but since radiation strictly backward prevailed in the rear hemisphere - even reducing it by redistribution in the same hemisphere is very beneficial in terms of improving the antenna's protective effect.


The combination of the screen with side walls and a 2-story director is practically a ceiling that can be pulled out of a single BowTie vibrator. Here is his set of parameters:



This is how the electric field strength changes in the plane of such an antenna and how far-field radiation is generated from near-field oscillations.

Part V / Single-Screen Common Mode

As you can see, the capabilities of a single vibrator are exhausted by the screen-reflector. If it is required to create an antenna with a narrower radiation pattern and increased gain, it remains only to use several antennas, connecting them in phase into a single array of an increased aperture. For any type of antenna, doubling the number of antennas in the common-mode array can produce up to 3 dB gain gain due to narrowing of the radiation pattern. The radiation pattern narrows in the plane where we add new antennas. When increasing the number of floors of the lattice - the diagram narrows in a vertical plane (becomes pressed to the horizon), when adding new floors to the right or left - in the horizontal plane (narrowing the beam in azimuth).

The main obstacle to creating in-phase gratings is technological difficulties. The complexity of calculation and design increases dramatically, because you must first align each antenna with the transmission line, then add the signals from each pair of lines to the tee, the summing signal is again matched with the wave impedance of the feeder.

The collection and transmission of a signal from each antenna (each antenna array vibrator) can be performed:

* asymmetric (coaxial) line
* symmetric (two-wire) line

Each type of line has its advantages and disadvantages.

Coaxial line:

+ can pass near metal elements and in holes through them
— (50 75Ω, 100 150Ω, )
— Bal-Un (Balanced-Unbalanced)
—
— , ( )

:

+
+
+
+
+ , ,
— ,
— , . , . , , , , , .


() .


Using two short (usually shorter than the wavelength) segments of identical length, two signals of equal strength and phase are added, the output is a signal that is 2 times (+3 dB) more powerful than a signal in a single vibrator.

For ideal operation, the impedance of the summing line should be the same as that of the vibrator (at this frequency). The output impedance of such a grid will be equal to half the impedance of each vibrator and line.

In a wide frequency range, the vibrator's own impedance varies widely from 85 to 545Ω. The impedance of symmetrical lines does not depend on the frequency, but only on the diameter of the conductors and the distance between them. Therefore, in a wide frequency band such a line will always be inconsistent. Short unmatched lines (a length commensurate with a wavelength or less) act as a transformer of resistances. This property of such lines is often used for its intended purpose if it is necessary to transform the characteristic impedance of the lines.

The calculation of the wave resistance of the line produced by the formula or using the finished utility .

So, two conductors with a diameter of 2 mm at a distance of 25 mm with an air gap have a resistance of 386Ω


Take, for example, a short line of 0.3λ (looking ahead to say that it will be half the optimal distance of the spacing of floors, that is, it will be the length of the line from one of the floors to the tee addition to the feeder) and see how it transforms the vibrator's own radiation resistance in frequencies.

One line is 25/2 mm (386Ω), the second is 25/1 mm (469Ω) and the third is twice as long as 25/2 mm (386Ω) for comparison:



Blue (Direct) indicates the intrinsic resistance of a BowTie taper vibrator when the feeder is directly connected.

As you can see, the collecting line has a very strong influence on the resulting impedance. Moreover, the transformation ratio to a lesser extent depends on the resistance of the transformer, and more on its length (relative to the wavelength). Since for different frequencies, the same transformer section is a very different length.

To calculate this resistance, there is a formula



When ZA = Z0, then Zin = Z0. The line matched to the source does not change the resulting impedance.
In other cases, Z0 is multiplied by a coefficient that depends on f * L (ie, on the wavelength) and depends on ZA and ZO

The length of the collecting lines in the in-phase grating can theoretically be any (just to be equal, so that the signals come in-phase and fold), but from technological motives rationally perform them the shortest way, connecting the floors in a straight line. With this approach, the line length will be set based on the optimal distance between the floors, and it is necessary to improve the matching only by varying the line resistance: by changing the diameter of the conductors or the distance between them.

When constructing 3 or more floors, it is technologically very impractical to carry out independent lines from each next floor to the adder. Fortunately, the signal from the adjacent floors can be added directly to the terminals of the neighbor. Since Since floors are placed approximately at a length of 1 / 2λ between each other, then when passing along a collecting line 1 / 2λ long, the phase of the signal is reversed by 180 degrees. In order for such signals to be summed up and not mutually destroyed, it is necessary to connect the conductors in antiphase. All floors are connected to each other only in antiphase, overlapped lines. An exception is the power point of the grid (feeder, balun), because it is at an equal distance from the floors (not necessarily the shortest path), then the signal on it will be in-phase when connected, not overlap, but straight.

The shape of the radiation pattern (NAM) of an in-phase antenna array is determined by the DN of the antennas that make up the array, and the configuration of the array itself (number of rows, number of floors and the distance between them).

With two omnidirectional antennas placed side by side on 1 / 2λ (between the axes of the antennas), the DN in the horizontal plane looks like a figure eight, and there is no reception from side directions perpendicular to the main one. If you increase the distance between the antennas, the width of the main lobe of the radiation pattern decreases, but side lobes appear with maxima in directions perpendicular to the principal.

At a distance of 0.6λ, the level of side lobes is 0.31 of the level of the main lobe, and the width of the DN at half power decreases by 1.2 times relative to the array with a distance between antennas of 2/2.

At a distance of 0.75λ, the level of side lobes increases to 0.71 of the main level, and the width of the DN decreases by 1.5 times. At a distance of 1λ, the level of side lobes reaches the level of the main lobe, but the width of the radiation pattern decreases by a factor of 2 compared with the distance between antennas in half-waves.

This example shows that it is more expedient to choose the distances between the antennas equal to the wavelength. This provides the greatest narrowing of the main lobe of the radiation pattern. There is no need to fear the presence of side lobes, since when using directional antennas in the array, they are not receiving signals from directions perpendicular to the main one.

These are general guidelines for any type of antenna. Antennas are usually mounted this way when they are added through a coaxial cable. Sections of flexible cable of arbitrary (if only the same) length fit arbitrarily. Changing the distance between the antennas does not violate the alignment and summation, so you can choose any distance from 0.5 to 1λ.

Consider a particular bottom grille of 2 BowTie vibrators with a reflector depending on the separation between the floors.


As you can see, as the separation increases, the gain increases from 11 dBi@0.4λ to 12.6@0.6λ
With a separation of more than 0.6λ, the amplification of the main lobe does not grow, but it itself becomes narrower in the vertical, and due to this, two parasitic lobes grow up and down. Although formally the antenna gain of 0.6-1λ is the same, but a narrower lobe requires a more vain orientation of the antenna to the subscriber (usually the horizon)

For a 2-storey grid of conical antennas, you can choose any distance from 0.4 to 1λ. But with an increase in the separation above 0.6λ, the screen size and the length of the carrier beam also increase, i.e. material consumption, weight increase and strength deteriorates, without increasing parameters.

In addition, as we have already seen, an increase in the length of an uncoordinated collecting line significantly affects its transformation ratio. Therefore, for practical reasons, 2-storeyed lattices are designed with a minimum separation of 0.5-0.6λ.

For 3 or more floors it is not rational to collect signals from individual lines (they should be between the vibrator and the reflector, away from metal objects) from each floor to the tee, and it is structurally easier to sum up the neighboring floors directly to the vibrator. If the distance is not a multiple of 0.5λ, then the delay of the signal in the line will not be a multiple of 180 degrees and the signals will not stack in phase. Therefore, for a direct connection along the shortest path, a spacing of only 0.5 or 1λ is suitable. At 0.5λ, the lines should overlap (to rotate the phase by 180 degrees), at 1λ directly (without phase rotation). For the practical reasons described for the 2-storey grid, the spacing of 1λ is not used.

Part VI / Matching with a transformer of resistances

Three types of structures are used to convert the antenna impedance into the feeder impedance:
1) Broadband transformers with a fixed conversion factor. They are usually performed on ferrite cores or printed on micro-patch lines. The transformation ratio is determined by the configuration of the straps and the ratio of the number of turns in them.
2) A wide variety of shunt circuits with L and C elements.
3) Transformers using wave line segments

The disadvantage of broadband transformers is the cost of their manufacture and the difficulty of obtaining non-multiple (arbitrary) transformation ratios. Low cost can be obtained only in mass production, and therefore on a limited range. In fact, only 4: 1 baluns can be called affordable. The need to produce a balun for another coefficient (6: 1, 8: 1) puts an end to both mass production and homemade homemade products.

The disadvantage of shunt circuits is the complexity of manufacturing (as with non-standard baluns), narrowband and the need to adjust the sample on the instruments.

Segments of wave lines do not greatly complicate the design of the vibrator (can be its constructive continuation), simplify the technological installation of the box with the balun (or the combined Balun + LNA board) due to the removal of the box beyond the break of the vibrator. Can be calculated and made to convert almost any resistance to any selection of the length of the segment and its own resistance.

Let us consider in more detail the fundamental formula for the transformation of resistance, given in the previous section.


From this formula follow a series of observations:

• With a line length of 0 or a multiple of 1 / 2λ, the resulting resistance is equal to the source resistance, the line does not make a change in the impedance, because the tangent of the multiples of 180 is zero
• When the length of the line with a shift of 1 / 4λ from multiples of 1 / 2λ - the resulting resistance changes as much as possible, because the tangent of angles 90 and 270 tends to infinity
• A line with a resistance equal to the source resistance (consistent) does not make a change in the resultant coincidence at any line length
• A line of fixed geometric length will behave differently in a wide frequency band when changing the wavelength. If the line length in lambda approaches 0 or a multiple of 1 / 2λ with a change in frequency, the line contribution decreases, if the length approaches 1 / 4λ - the line contribution increases sharply. This property can potentially be used to equalize the vibrator’s own impedance.

Create Excel to work with this formula: goo.gl/w8z9U2 (Google Docs)

Suppose our BowTie vibrator has Z = 750 + j0 at the frequency of the first resistance resonance.
To convert 750 Ohms to 300 (for connection to a 4: 1 balun), you can use a symmetric waveguide of only 0.1λ (5 cm for a frequency of 600 MHz) with a resistance of 231 Ohms.
Using the above coax_calc calculator, you can choose a combination of wire diameter and distance between them to get 231 Ohms.

Part VII / Case Studies

The scope of use of cone antennas is very limited. At frequencies below 300 MHz, such antennas have unacceptably large dimensions compared to a half-wave dipole, which has a span of 0.5λ versus 1λ.

At frequencies above 800 MHz there are almost no radio technologies where high directional antennas are needed. CDMA, GSM, GPS, LTE, WiFi are needed, or omnidirectional antennas at the subscriber, or sector antennas with a clearly predictable sector shape on the operator’s side.
A small demand for highly directional antennas exists among fixed cellular subscribers. Using BowTie radiators, it is theoretically possible to manufacture LTE-700, CDMA2000 / LTE 800 Mhz antennas, GSM / UMTS / LTE-900 and CDMA2000 / LTE 450 Mhz antennas. The industry of such antennas did not produce, and in Part VIII we will try to construct such an antenna, at the same time checking how efficient and competitive such a design is.

At frequencies above 2 GHz, cone antennas can be made only by printing (microstrip), there are no advantages in parameters or simplicity of design and manufacture compared to patch antennas at such frequencies.

In the range between 300 and 800 MHz, only television broadcasting works: PAL / SECAM / NTSC (analog) or DVB-T / T2 / T2 HD (digital).

It is the market of subscriber antennas of TV broadcasting that brought unbelievable popularity to conical antennas.

In the 1960s, such antennas acquired most of the market in geographically large countries: Canada and the USA. Large areas, predominantly flat, led to a lower density of television towers compared to Europe. For large radii of coverage, high gain antennas were required by 10 ... 16 dB. To achieve such a gain from single antennas, the wave channel is very problematic, and it is difficult and expensive to use common-mode arrays of 2-4 antennas compared to the simplicity of a multi-level cone antenna with a reflector.

The widest distribution of such antennas in Eastern Europe was facilitated by the emergence of a large number of low-power TV channels in the UHF range (1-5 kW compared to 20-25 kW for the three central television channels), which require antennas with a gain of 10+ dB, as well as broadband with the capture (albeit low-gain) sections of the MV range, which eliminated the need to contain an additional antenna of the MV range, additional cables, amplifiers, adders, etc.

We present the reader 7 antenna designs, carefully optimized (using Python scripts using NEC-engine for modeling) to maximize the average gain in the range of 470-700 MHz (21-50 UHF channels) and minimize the average SWR. For 2017, such antennas are relevant only for DVB-T / T2 reception.

Without reflector:

1) 2-Bay: 50x55 cm, whiskers 8x279 mm
2) 3-Bay: 60x50 cm, whiskers 12x241 mm
3) 3-Bay (1 small): 80x65 cm, whiskers 4x276, 4x302 and 4x190 mm

With reflector / screen:

4) 1-Bay: 25x72 cm (50 + 2x12.5 cm sides), whiskers 4x222 mm (from the example in the article)
5) 2-Bay: 86x57 cm, whiskers 4x254 mm
6) 4-Bay: 102x86 cm
7) 6-Bay: 152x84 cm



The antenna gain averaged over the 470-700 MHz band is 7 to 42 times, or 8.5 to 16.3 dBi.
The third column shows the area of ​​the frontal projection in m2, and in the last - the specific gain, in times per 1 m2 of the frontal area.

For comparison, the antenna wave channel (Uda-Yagi), specially optimized for the same range, has an average gain of 10 dBi (from 8.1 to 12.1) in the 1R-5D configuration (1 reflector, 5 directors, loop vibrator, 624x293x45 mm) and 12.7 dBi in 2R-15D configuration (2 reflectors, 15 directors, loop vibrator, L = 1621 mm)

Conclusions: when designing antennas with medium amplification up to 10 dBi, traditional dipole antennas wave channel is simpler, smaller, lighter, easier to manufacture (both artisanal and industrial) and more durable. If gain> 10 dBi is required, then adding directors to Uda-Yagi adds very little directivity (1R5D = 10 dBi, 2R10D = 11.5 dBi, 2R15D = 12.7 dBi), whereas even a 2-story cone antenna with a reflector gives an average gain of 13.1 dBi .

When an average gain of 15-16 dBi is required, there are no alternatives to 4 and 6-storey conical antennas. In the antenna segment with a gain of 10-13 dB, a 2-storey conical antenna is smaller and simpler than long wave channels for 10 or more directors).

Here is a general view and a DN of seven antennas, in the order numbered above:


All 7 models in the * .NEC format can be downloaded here and see the detailed dimensions (including creating executive drawings) using the free program 4NEC2 .

Disclaimer : The 6 UHF-TV antennas presented were developed by DigitalHome Canada forum participants under the guidance of holl_ands and mclapp users .

Part VIII / Industrial Antenna Analysis

4-storey ASP-8 type antennas have gained wide popularity in the CIS.
These antennas have many modifications, which differ slightly from each other (in trifles).
Older antennas had longer upper-floor whiskers (and were labeled 47-860 MHz antennas).
The new antennas (which are sold in 2017) have the upper floor a little shorter than the old ones, probably for better performance in the UHF, where DVB-T / DVB-T2 are now working.

For the analysis, the sizes from such a sample cost $ 3.6 were taken (for the price - as a 3-element room Yagi Wave-1)



The antenna has the following elements:
1) Screen-reflector 75x50 cm, 36 cm width of the central part, side sides 2x8 cm bent forward 4.5 cm.
The screen consists of 2x6 horizontal conductors with a diameter of 2.1 mm, each of the two groups has a height of 33 cm, and between them (in the central part of the antenna) a gap of 9 cm.
Offset screen from vibrators - 85 mm

2) The gap between the mustache vibrators on all 4 floors 34 mm (along the centers of the waveguide lines)

3) Upper vibrator 4x254 mm mustache with a diameter of 5 mm, with an opening angle of 45 degrees

4) Three lower floors - vibrators 4x140 mm mustache with a diameter of 4 mm, with an opening angle of 50 degrees

5) The collecting two-wire line of steel conductors with a diameter of 2.1 mm, the distance between the conductors of 34 mm at the entry points to the mount of the vibrator. At the entrance to the power box 30 mm from the bottom and up to 72 mm from the top.

6) Distance between floors (1st - upper): 1-2 = 183 mm, 2-3 = 192 mm, 3-4 = 178 mm

7) Length of connecting lines: 200 mm between 1-2 and 3-4. 84 + 132 = 223 mm between floors 2-3. The terminals of the power box are located 84 mm from the top and 132 mm from the bottom floor.

8) On each floor there is a traverse with 5 short directors.

9) Carrier Ridge Antenna - 12x6 mm aluminum hollow profile 28 mm behind the waveguides

At once, we say that the traverse with 5 directors has no influence whatsoever on the antenna at frequencies up to 900 MHz. At frequencies above 800 MHz, they add only +0.1 dB to the directivity.
Their function is extremely decorative - to destroy the antenna with additional mechanical loads and attract birds to destroy the antenna.

Imagine the main components of the geometry of the antenna in wavelengths, in different parts of the declared range of work


The dimensions of all the elements of this antenna are extremely strange: the length of the whiskers, the separation between the floors, the width of the reflector, the deliberate displacement (dephasing) of the power supply point.

Consider the properties of individual vibrators (taking into account the influence of the screen).
Bay-1 : The top long vibrator has a resonant frequency of 490 MHz and an impedance of 850Ω. The second resonance is at 780 MHz and the resistance is 31Ω. At frequencies below 300-320 MHz, the radiation resistance R is negligible, it can be considered that 320 MHz is the lower operating frequency. The gain of this floor alone reaches 10 dBi, but the radiation pattern is slightly (1 dB) shifted down by 30 degrees, like a hanging belly

Bay-2 : The second on top vibrator has a resonant frequency of 780 MHz and a resistance of 515Ω. The second resonance is above 1000 MHz. At frequencies below 460 MHz, the radiation resistance R is negligible, we can assume that 460 MHz is the lower operating frequency. The gain of this floor alone reaches 11 dBi, but the directivity pattern is STRONGLY shifted down by 35 degrees. Amplification forward is only 6 dBi, and down by 35 degrees - up to 11.1 dBi

Bay-3 : The third vibrator on top has a resonant frequency of 790 MHz and a resistance of 620Ω. The second resonance is above 1000 MHz. At frequencies below 440 MHz, the radiation resistance R is negligible; we can assume that 440 MHz is the lower operating frequency.The gain of this single floor reaches 10.6 dBi, the shape of the DN is not distorted, but looks forward

Bay-4 : The lower vibrator has a resonant frequency of 810 MHz and a resistance of 570Ω. The second resonance is above 1000 MHz. At frequencies below 440 MHz, the radiation resistance R is negligible; we can assume that 440 MHz is the lower operating frequency. The gain of this floor reaches 9.6 dBi, the shape of the pattern is distorted upwards by 20 degrees (2-3 dB stronger than forward). The second directional bubble is directed downward by 30 degrees.

The manufacturer made a very strange choice of the length of 3 whiskers on 3 floors - with a resonance near 800 MHz, and not in the middle of the UHF range (in the interval of 600 .... 700 MHz).
It is also a very strange choice of spacing floors and lengths of the collecting lines. The length of the waveguides that go overlap - centered at 750 MHz. At a frequency of 470 MHz, the phase delay in such a line is 112 instead of 180 degrees.


, . <2 (), =2...3.2 ( , ), 21- (470 ) =3.6
. 565 (+30/-40 ) — , 5 dBi

+ 47-860 .
. 220 .
As we learned from the theory, when the parasite is less than 0.47λ in length, it turns from a reflector into a director, since NAM shifts towards this “reflector”, i.e. in the opposite direction from the TV tower. In the direction of the TV tower, the signal is attenuated by 10–16 times compared to a half-wave dipole.


In addition to this free-antenna, let's analyze the ChannelMaster 4251 antenna, which is popular in North America, from 2 floors.
Its dimensions are much smaller: 38x35 cm (against 75x50 cm)


Gain grows smoothly from 8 to 10 dBi, the shape of the bottom is perfectly smooth, the CWS is moderate. There are no resonance anomalies between 400 and 900 MHz.
CM4251 with a frontal projection is 2.8 times smaller than that of the ASP-8, it works about the same, but without abnormal frequency response sections and without SWR drops.

Both antennas are significantly inferior to a 2-story antenna from an article optimized using CAD.
The optimal dimensions for 2 floors - 86x57 cm (86 - width), this screen is slightly larger than the “Polish dryer”, but turned to the side.
Attempts to fit 4 floors on such an area are very unsuccessful and are only of a marketing nature.
The American version, though not having an outstanding gain, but small-sized.

Part XIX / Calculation of highly directional transceiver antenna

A conical radiator with a reflector allows theoretically to produce antennas with a gain of about 10 dBi for 1 floor, 12-13 dBi for 2 floors, 14-16 dBi for 4 floors, 16-18 dBi for 6 floors.
When working with horizontal polarization, the in-phase array will have a vertical layout. With 2 floors, the radiation pattern will be the same both vertically and horizontally: attenuation 3 dB at angles of ± 25 in any direction from the main beam.
At 4th and 6th floors, the azimuth selectivity does not change, and the beam becomes very narrow in the vertical direction, so at 16 dBi the attenuation is 3 dB already at ± 8 degrees vertically.

A distinctive feature of transceiver antennas from pure receiving (television) are:
- feeder resistance 50Ω
- increased requirements for low VSWR

( ) ( .. ) (LNA) .

( SNR) .



Nf (effective) = Nf (nominal) + 10*log((2+SWR+1/SWR)/4)

=2 =3 LNA 0.5 1.25 dB .

<2, <1.5

, 2- 50Ω.

821-894 (858 ±37 ), CDMA2000/EV-DO.

, .. 1 .

® , , 400-1000Ω :
— ( , R)
— ( , R )
— ( )

Such an order of magnitude of R is very far from 50Ω, therefore the use of a transformer of resistances is inevitable.
Even if R = 50Ω, you still need to use Bal-Un 1: 1, since BowTie vibrator is symmetrical, and coaxial power cable is asymmetrical.
The easiest way to use the combined BalUn-transformer.
When using a 4: 1 transformer, it is necessary to calculate the antenna with an output of 200 Ω, when using a 6: 1 transformer - by 300 Ω.

When adding a signal from 2 floors to a tee, the output resistance of the grid is 2 times less than the resistance of the floors. Those.It is necessary to calculate a single vibrator at 400Ω or 600Ω.
Collective lines should have the same resistance as a single vibrator, i.e. 400Ω or 600Ω, otherwise they will work as transformers with an unpredictable effect.

Using the coax_calc program, we try to simulate a symmetric waveguide at 400Ω and 600Ω.
To get 600Ω, even with a thin conductor d = 1 mm, 74-75 mm spacing is needed. This is a sufficiently large separation (relative to the total width of the vibrator of the order of 25-30 cm), and quite thin (non-rigid) conductor. For such a large spacing also increases the protective zone, where there should be no metal objects.

400Ω : 35 , d=2.5 ( 5 2)


400Ω , 4:1 , 6:1 .

1λ (349 858 )

R 400Ω , . 6 ( « »). 13-15 . 10 .

, :
— 11λ ( 21 , 2 , , 0.05λ)
— 35
— 6 , 0.6λ (±0.3λ )
— 33

, (858 ) R=400Ω, , X=0Ω ( 0, .. )

2-3 0.4442λ (138.5 ), 0.2455λ (86 )

(R, Z), ( , 400Ω).



, : <1.5 730...1020 , 290 ±18%
821-894 , ≤1.11
, 11.8 12.4 dBi

, BiQuad () 11λ ( ), 10.6-10.8 dBi 1.52 1.86 .