Small Antennas for High Frequencies

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Iulian Rosu, YO3DAC / VA3IUL

http://www.qsl.net/va3iul/

This is about Small Antenna types and their properties which can help choosing proper antenna for high-frequency wireless communications as: two-way radio, microwave short links, repeaters, radio beacons or wireless telemetry.

Basic Antenna Theory

• Every structure carrying RF current generates an electromagnetic field and can radiate RF power to some extent.

• A transmitting antenna transforms the Radio Frequency (RF) energy produced by a radio transmitter into an electromagnetic field that is radiated through space.

• A receiving antenna it transforms the electromagnetic field into RF energy that is delivered to a radio receiver.

Most practical antennas are divided in two basic classifications:

• MARCONI Antennas (quarter-wave, which is the Monopole and derivates).

• HERTZ Antennas (half-wave, which is the Dipole and derivates).

Forming a radio wave

• When an alternating electric current flows through a conductor (wire), Electric-E and Magnetic-H fields are created around the conductor.

• If the length of the conductor is very short compared to a wavelength (<< λ/4), the electric and magnetic fields will decrease dramatically within a distance of one or two wavelengths.

• There is impossible to make a small antenna to radiate like a big antenna.

• However, as the conductor is lengthened, the intensity of the fields enlarges and part of the energy escapes into the space. When the length of the conductor approaches a quarter of a wavelength (λ/4) at the frequency of the applied alternating current, most of the energy will escape in the form of electromagnetic radiation.

Radiation

A conductor once connected to a transmitter source, it begins to oscillate electrically, causing the wave to convert the transmitter power into an electromagnetic radio wave.

The electromagnetic energy is created by the alternating flow of electrons impressed at the feeding end of the conductor. The electrons travel upward on the conductor to the top, where they have no place to go and are bounced back toward the feeding end. As the electrons reach the feeding end in phase, the energy of their motion is strongly reinforced as they bounce back upward along the conductor. This regenerative process sustains the oscillation. The conductor is resonant at the frequency at which the source of energy is alternating.

• The energy stored at any location along the conductor is equal to the product of the Voltage (V) and the Current (I) at that point.

• Radiation Resistance (Rr) is defined as the value of a hypothetical resistor which dissipates a power equal to the power radiated by the antenna when fed by the same Current (I).

Radiated Fields

When RF power is delivered to an antenna, two fields evolve. One is an Induction field (or Near-Field), which is associated with the stored energy; the other is the Radiated field. At the antenna, the intensities of these fields are large and are proportional to the amount of RF power delivered to the antenna.

The Radiated Field is divided in three distinctive regions:

• Reactive Near-Field is the region close to the antenna where the Electric-E and Magnetic-H fields are not orthogonal and anything within     this region which couple with the antenna will distort the radiated pattern. Antenna Gain is not a meaningful parameter here.

• Radiating Near-Field (transition region or Fresnel region) is the region between near and far field. In this region the antenna pattern is      taking shape but is not fully formed. Antenna Gain will vary with distance.

• Far-Field (Fraunhofer region) region is defined as that region of the field where the angular field distribution is essentially independent of the distance from the antenna. Antenna Gain is constant with distance.

 where  and  

Radiation Patterns

The radio signals radiated by an antenna form an electromagnetic field with a definite pattern, depending on the type of antenna used. This radiation pattern shows the antenna’s directional characteristics.

The pattern is usually distorted by nearby obstructions.

• The Directivity of an antenna is a measure of the antenna’s ability to focus the energy in one or more specific directions.

For example a vertical monopole antenna radiates energy equally in all azimuth directions (omnidirectional) and a horizontal dipole antenna is mainly bidirectional.

• The ratio between the amounts of energy propagated in particular directions and the energy that would be propagated if the antenna were not directional is known as Antenna Gain.

• The Gain of an antenna is constant whether the antenna is used for transmitting or receiving.

• Ground losses affect radiation patterns and cause high signal losses for some frequencies. Such losses can be greatly reduced if a good conducting ground is provided in the vicinity of the antenna.

Polarization

• A radiated wave polarization is determined by the direction of the lines of making up the Electric-E field.

• If the lines of Electric-E field are at the right angles to the Earth’s surface, the wave is vertically polarized.

• If the lines of Electric-E field are parallel to the Earth’s surface, the wave is horizontally polarized.

• A vertical antenna receives vertically polarized waves, and a horizontal antenna receives horizontally polarized waves.

• If the field rotates as the waves travel through space, both horizontal and vertical components of the field exist, and the wave is elliptically polarized.

• Circular polarization describes a wave whose plane of polarization rotates through 360° as it progresses forward. The rotation can be clockwise or counter-clockwise. Circular polarization occurs when equal magnitudes of vertically and horizontally polarized waves are combined with a phase difference of 90°. Rotation in one direction or the other depends on the phase relationship.

• "Hand rules" are used to describe the sense of circular polarization. The sense is defined by which hand would be used in order to point that thumb in the direction of propagation and point the fingers of the same hand in the direction of rotation of the Electric-E field vector.

For example, if your thumb is pointed in the direction of propagation and the rotation is counterclockwise looking in the direction of travel, then you have Left Hand Circular Polarization (LHCP).

If the rotation is clockwise then you have Right Hand Circular Polarization (RHCP).

Wave propagation between two identical antennas is analogous to being able to thread a nut from one bolt to an identical opposite facing bolt.

à    RHCP

• Axial ratio is a parameter of Circular Polarization that describes the shape of the polarization ellipse (or how perfect the circle is).

The Axial Ratio is the amplitude ratio of the major axis to minor axis of polarization, and always is ≥ 1 (0dB)

• Polarization Loss occurs between linear antennas that are misaligned in orientation, between circular antennas that are not truly circular or use different polarization sense, or between linear and circular polarized antennas.

The actual Polarization loss between a circularly polarized antenna and a linearly polarized antenna will vary depending upon the Axial ratio of the circularly polarized antenna.

• In the real world there is no perfect Linear or Circular polarized antenna (all are more or less Elliptical)

Resonance and Impedance

Antennas can be classified as either resonant or non-resonant, depending on their design.

• In a Resonant Antenna, almost the entire radio signal fed to the antenna is radiated.

• If the antenna is fed with a frequency other than the one for which it is resonant, much of the fed signal will be lost and will not be radiated.

• A resonant antenna will effectively radiate a radio signal for frequencies close to its design frequency.

• Antenna Input Impedance Zin is defined as the impedance presented by the antenna at its terminals, or the ratio of the Voltage (V) to Current (I) at a pair of terminals, or the ratio of the appropriate components of the Electric-E to Magnetic-H fields at a point.

Zin = Res + jXa

Resistance (Res) tells us how much power is radiated and Reactance (jXa) tells us how much power is reflected, or how much the Voltage (V) and Current (I) are out of phase.

The reactance, jXa models the energy stored in the antenna near-field, just as in an ordinary Inductor or Capacitor.

• The difference between resonators and antennas is that a good resonator has a High-Q, whereas a good antenna has a Low-Q.

• Every antenna will present a certain amount of impedance to its source, impedance that may be a function of frequency.

• For minimum Power Loss, the transmitter output impedance should be matched to the antenna impedance.

Sometimes to achieve match, loading coils or matching networks are used.

Usually the lumped matching networks are narrow band, and in this case the frequency range where the antenna can be used will be narrow also.

• The various properties of an antenna apply equally, regardless of whether the antenna is used for transmitting or receiving. For example, the more efficient a certain antenna is for transmitting, the more efficient it will be for receiving the same frequency. The directive properties of a given antenna will be the same whether it is used for transmission or reception.

• A large Impedance Mismatch at the antenna/transmission-line interface of a radio receiving system can cause a significant increase in the system internal Noise Factor. In the absence of a matching network, the limiting noise of the system is generated within the system (by the transmission line and receiver) and can be more than 20 dB larger than the external man-made noise or atmospheric noise. With a matching network, the limiting noise of the system is the external noise.

• At antenna resonance, the waves travel back and forth in the antenna, reinforcing each other, and are transmitted into the space at maximum radiation.

• When the antenna is not at resonance, the waves tend to cancel each other and energy is lost in the form of heat.

• Since the antenna must always be in resonance with the applied frequency, you must either lengthen it or shorten it to produce the required resonance.

Changing the antenna dimensions physically is impractical, but changing them electrically is relatively simple.

To change the electrical length of an antenna, you can insert in series with the antenna either an inductor (if the antenna is too short for the wavelength), or a capacitor (if is too long).

• The radiation characteristics of a linear antenna will be modified whenever the antenna is mounted on, or placed in proximity to a ground-plane. Therefore, either by proper design of the ground-plane where feasible (in terms of its size, shape and conductivity), or by choosing an appropriate location on the ground-plane, the radiation patterns with certain desirable properties can be achieved.

When the antenna is located at a height that is small compared to the skin depth of the conducting ground, the input resistance may be greater than its free space values. This leads to antennas with low efficiency and improvements can be obtained by placing radial wires or metallic disks on the ground.

Small Antenna Types

Monopole Antennas

• A Monopole Antenna is a λ/4 whip placed over a ground-plane.

• The Ground-plane of this antenna can be the metal case of a radio, the body of a vehicle, the metallic roof of a house, or λ/4 radials.

• The pattern of this antenna corresponds to that of a λ/2 vertical dipole as a result of the image element posed by the ground-plane.

• Its input impedance is only half of the dipole (36.5 ohms).

• Since half of the radiating plane is cut-off by the ground-plane, the radiated power (and hence the radiation resistance) of a monopole is only half compared to the dipole with the same current; however, the directivity of a monopole antenna is doubled (3 dB larger) compared to a λ/2-dipole since the power is confined only above the ground-plane.

For a finite-sized ground-plane of radius r, the pattern will tilt upward (from the ground-plane) and this tilt would vary inversely with r/λ ratio. So the antenna need less ground dimensions for higher frequencies.

• Monopole elements with perfect ideal ground-planes have a radiation pattern that has its peak on the horizon and is omnidirectional in azimuth. The current on the exterior of the element feed cable is zero. For this case, the interference of the element and the image fields is totally constructive in the direction of the horizon, the feed cable is completely shielded from the element fields, and the current on the bottom surface of the ground plane is zero.

• For imperfect ground-planes, the direction of peak directivity are at an angle above the horizon, and the current on the exterior of the element feed cable is nonzero because the feed cable is not completely shielded from the element fields. The current on the bottom surface of the ground plane at the feed cable is also nonzero.

A λ/4-stub with an outer conductor shaped in the form of a conical skirt, constitutes a typical ground-plane modified antenna. When the cone or skirt part of this antenna is degenerated into a sleeve (cylinder), the resulting radiator is popularly known as a sleeve antenna.

    Usually, the sleeve is made of a centre conductor of a coaxial cable connected to an element whose length is λ/4, and the outer conductor of the coaxial cable is connected to a cylindrical skirt (whose length is again equal to λ/4). The coaxial (cylindrical) skirt behaves like a λ/4-choke and prevents the RF current leaking into the outer surface of the coaxial feeder line.

As a result, this structure exhibits almost the same radiation characteristics of a vertical λ/2 Hertzian Dipole.

Since this antenna has suppressed “ground-plane effects” by means of the RF-choke deployed, any related gain degradation and/or pattern distortion are minimal.

The feeder is simple and is compatible with coaxial lines and standard connectors; this antenna is suitable for frequencies between 400MHz and 2.5GHz.

5λ/8 monopole

• By increasing the height of the monopole from λ/4 to 5λ/8, the directivity of the antenna will increase facilitating a high-gain structure.

• The antenna focuses more energy towards the horizon, thus not wasting any energy towards unwanted areas like the sky.

• Compared to a λ/4 ground-plane antenna 5λ/8 has 3dB of gain.

Because of the non-resonant length involved, a series inductor is used for impedance-matching purposes.

The pattern of the antenna with increased length will have some minor lobes. The main beam becomes narrower (yielding a higher directive gain), but the excess energy will spill out as side lobes. As long as such side lobes do not significantly influence the signal integrity (along the main beam), such minor lobes can be tolerated, in the context of higher directivity achieved along the major lobe.

Dipole Antennas

• A Half-wave Dipole antenna is a wire or conducting element whose length is half the transmitting wavelength and is fed at the center.

• In free-space a thin dipole at resonance presents an input impedance of approximately 73 ohms.

• This impedance is not difficult to match to 50 ohms transmission lines, and a number of convenient matching circuits have been designed to make the transition from various coaxial and other   transmission lines. For example the mismatch of 50 ohm cable feeding a 75 ohm antenna is minimal with a resultant SWR of 1.5:1  This corresponds to roughly a 5% waste of power.

• A balun (BALanced to Unbalanced) allows the direct connection of a coax line to the dipole.

             Folded Balun 1:1             Sleeve Balun 1:1                        Half-wavelength Balun 4:1

• The antenna pattern of a horizontal dipole over the ground resembles a figure eight (8).

• The radiation pattern of a thin, vertical half-wave dipole in free-space has the characteristic of a doughnut shaped pattern.

• The input impedance of a vertical dipole over a conductive ground changes compared to the impedance of a horizontal dipole placed to the same height from the ground.

The distance between the dipole antenna and the conductive ground should be never lower than λ/4, and for best performance should be greater than 2λ.

         L << λ/2                                     L = λ/2                                        L = λ                                  L = 3λ/2           

                           Current (I) distribution for various lengths of center-fed Dipole

             L < λ/2                           L = λ/2                                     L = λ                                       L = 5λ/4                 

                                    Antenna Patterns for various Dipole lengths

    The antenna pattern of a 5λ/4 Dipole will have the same behavior as a 5λ/8 Monopole, in terms of narrower beam-width and side lobes.

At http://www.amanogawa.com/archive/DipoleAnt/DipoleAnt.html you can find a Java Applet that shows the Dipole Pattern variation vs Length.

To reduce the size of the dipole, several options exist:

• Replacing some of the wire length with loading coils

• Bending the dipole ends back on the dipole

• Folding the dipole into a meander pattern

• Hairpin or coil loading of the center

• Capacitive loading of the dipole ends

The Folded Dipole

The folded dipole consists of two parallel dipoles connected at the ends forming a narrow loop with dimension d much smaller than Length (L) and much smaller than wavelength. The folded dipole has an impedance transforming feature that multiplies the antenna impedance by a number related to the diameter and spacing of the wires in the folded dipole.

• The input impedance of a half-wave folded dipole at resonance is four times of an ordinary dipole (~280 ohms)

Wideband Dipoles – Fan Dipoles

Due to the shape of the antenna arms these types of dipole antennas provides a broad impedance bandwidth.

A bowtie antenna is a type for a fan dipole antenna. By using triangular elements instead of rods, the bandwidth is greatly increased. The bowtie antenna has also a broad pattern with low gain similar to the pattern of a dipole. The gain could be increased by arraying several elements together and adding the reflecting screen.

Loop Antennas

The Loop Antenna refers to a radiating element made of a coil of one or more turns.

• The dissipative resistance in the loop, ignoring dielectric loss, is depended by the Loop Perimeter, the conductor Width/Thickness, the Magnetic Permeability µ, the Conductivity σ, and by the Frequency.

• The loop's inductance is determined by the Circumference, the Enclosed Area, the conductor Width/Thickness, and the Magnetic Permeability.

Loop antennas can be divided in three groups:

• Full-wave Loop antenna

• Half-wave Loop antenna

• Series-loaded, Small-loop antenna

• The Full-wave Loop is approximately one (λ) wavelength in circumference. Resonance is obtained when the loop is slightly longer than one (λ) wavelength. The full wave loop can be thought of as two end-connected dipoles. Like any other loop, the shape of the full wave loop is not critical, but efficiency is determined mainly by the enclosed area. The feed impedance is somewhat higher (approximately 120 Ohms) than the half-wave loop.

The main advantage of the full wave loop is it does not have the air gap in the loop, which is very sensitive to load and PCB capacitance spread.

• The Half-wave Loop consists of a loop approximately λ/2 wavelength in circumference with a gap cut in the ring. It is very similar to a half-wave dipole that has been folded into a ring and most of the information about the dipole applies to the half-wave loop. Because the ends are very close together, there exists some capacitive loading, and resonance is obtained at a somewhat smaller circumference than expected. The feed-point impedance is also somewhat lower than the usual dipole, but all the usual feeding techniques can be applied to the half-wave loop.

The half-wave loop is popular at lower frequencies but at higher frequencies, the tuning capacitance across the gap becomes very small and critical.

• The circumference of a Small-Loop antenna is smaller than λ/2. The radiation resistance of the Small-Loop antenna is extremely small. In addition, the resistance arising from the dissipative losses can be more than ten times the radiation resistance. The radiation resistance of a small-loop can be increased increasing the number of turns, or inserting within its circumference a ferrite core with high permeability.

Typically, a small loop may be able to radiate only a few percent of the power that comes from the transmitter.

The radiation pattern of a small loop antenna is identical with that of a small dipole. In the near-field the loop stores most of its energy in a Magnetic-H field and the short dipole stores its near-field energy in an Electric-E field, but the waves radiated by each have the same E/H; they are equally electric and magnetic.

 

For matching a Small-loop antenna, it is important to remember that its equivalent series impedance is an inductance with a tiny series resistance, which consists predominantly of loss resistance and an even smaller radiation resistance. The small-loop antenna's equivalent parallel impedance is an inductance with a large parallel resistance (5k to 50k). For matching network can be used “two split capacitors” or a PI network.

Patch Antennas

• A rectangular Patch antenna is defined by its Length L and Width W.

• For a simple microstrip line, the Width is much smaller than the wavelength.

• For the patch antenna, the Width is comparable to the wavelength to enhance the radiation from the edges.

• The length L should be slightly less than λ/2, where λ is the wavelength in the dielectric medium. Here, λ is equal to λo / √Eeff , where λo is the free-space wavelength and Eeff is the effective dielectric constant of the patch.

• The value of Eeff is slightly less than Er, because the fringing fields around the periphery of the patch are not confined in the dielectric substrate but are also spread in the air.

• The electric field is zero at the center of the patch, maximum (positive) at one side, and minimum (negative) on the opposite side.

• The far-field radiation pattern is orientated orthogonal to the surface conductor.

• The surface conductor does not form the radiating element as it does in a dipole. Instead, radiation occurs from along edges L and W, and which edge depends upon the electromagnetic mode of radiation the antenna is operating in.

Effect of Feed-Point Location:

• With an increase in frequency, the input impedance moves to the clockwise direction in the Smith chart.

The width W of the patch antenna has significant effect on the Input impedance, Bandwidth, and Gain of the antenna.

• With an increase in W, the input impedance decreases, so the feed point is shifted toward the edge to obtain input resistance Rin in the range of 50 ohms to 65ohms.

Effect of the height h (substrate thickness):

• With the increase in h, the fringing fields from the edges increase, this increases the extension in effective length L, however decreasing the resonance frequency.

• The input impedance plot moves clockwise (i.e., an inductive shift occurs) due to the increase in the probe inductance of the coaxial feed.

• The Bandwidth of patch antenna increases with height.

• The directivity of the antenna increases marginally with increasing height because the effective aperture area is increased marginally due to increase in ΔL.

• Generally, the antenna efficiency increases with an increase in the substrate thickness initially due to the increase in the radiated power, but thereafter, it starts decreasing because of the higher cross-polar level and excitation of the surface wave.

• The surface waves get excited and travel along the dielectric substrate (i.e., between the ground plane and the dielectric-to air interface due to total internal reflection). When these waves reach the edges of the substrate, they are reflected, scattered, and diffracted causing a reduction in gain and an increase in end-fire radiation and cross-polar levels.

• The excitation of surface waves is a function of Er and h. The power loss in the surface waves increases with an increase in the normalized thickness h/λo of the substrate.

Effect of Er:

• Decreasing the substrate Dielectric Constant Er the Bandwidth of the patch antenna increases.

Effect of Finite Ground Plane:

• In practice, the size of the patch ground plane is finite.

• When the size of the ground plane is greater than the patch dimensions by approximately six times the substrate thickness all around the periphery, the results are similar to that of the infinite ground plane.

• If the loss in the dielectric material increases the input impedance Zin of the patch antenna decreases.

    Modified feeding structures can enhance the impedance performance of Patch antennas.

For instance, the coaxial probe excites the planar radiator via a U-shaped or inverted E-shaped transition which forms an impedance transformer for broadband impedance matching

    The radiator can theoretically be of any shape. Figure below shows a variety of shapes which have been used in planar antenna design. Among these, elliptical planar antennas are of importance to planar antenna design due to their broadband and high-pass impedance performance. The slots or apertures in annular and slotted planar antennas are often employed to improve the impedance bandwidth by changing the current distributions on the radiators.

    The impedance-matching networks can be used to increase the BW of the Patch Antenna. Some examples that provide about 10% BW are the rectangular patch antenna with a coplanar microstrip impedance-matching network and an electromagnetically coupled patch with single-stub matching.

Matching networks for Patch Antenna

Circular polarized Patch Antennas

Slot Antennas

The basic slot antenna is a λ/2 wave slot cut in a conducting sheet of metal. The feed point is across the center of the slot and it is balanced. The feed impedance is high, typically several hundred ohms.

                                                                                                        λ/2 slot antenna                              complementary λ/2 dipole

Even if mechanically the slot antenna is the opposite of a dipole because is a non-conducting slot in a sheet of metal (compared to a wire in a free space), the slot antenna has a lot of similarities to a dipole.

However, it does exhibit some differences as follows:

• The feed point is across the center instead of in series, so the feed point impedance is high instead of low.

• E and H fields are switched so that the polarity is opposite.

• When energy is applied to the slot antenna, currents flow in the metal sheet. These currents are not confined to the edges of the slot but rather spread out over the sheet. Radiation then takes place from both sides of the sheet. In the case of the complementary dipole, however, the currents are more confined; so a much greater magnitude of current is required to produce a given power output using the dipole antenna.

• A horizontal slot is equivalent to a vertical dipole.

• The slot antenna may be of interest if the RF unit must be placed in a metal enclosure where the slot antenna could be made in the enclosure itself.

• If the slot antenna is cut in the center, a λ/4 wave slot antenna is created which is equivalent to the monopole.

• Impedance matching is accomplished by tapping across the slot close to the shorted end.

• The slot antenna can be used if a metal enclosure is required or if considerable board area is available.

• If a slot antenna is implemented in a PCB made with FR4 material, considerable dielectric loading occurs which causes the physical length to be shorter than expected.

Helical Antenna

A conducting wire wound in the form of a screw thread can form a Helix antenna.

Usually the Helix uses a ground plane with different forms.

The diameter of the ground plane should be greater than 3λ/4.

In general the Helix is connected to the center conductor of a coaxial transmission line and the outer conductor of the line is attached to the ground plane.

• The parameters which characterize a Helix antenna are:

• N = the number of turns,

• D = the diameter of the Helix,

• S = the spacing between each turn,

• L = total Length of the antenna

• α = the Pitch angle which is the angle formed by the line tangent to the helix wire and a plane perpendicular to the helix axis.

When α = 0˚, then the winding is flattened and the helix reduces to a loop antenna of N turns.

When α = 90˚, then the helix reduces to a linear wire.

When 0˚ < α < 90˚, then a true helix is formed.

• The radiation characteristics of the antenna can be varied by controlling the size of its geometrical properties compared to the wavelength.

• The input impedance is critically dependent upon pitch angle and the size of the conducting wire, especially near the feed point.

• The main modes of operation of the Helix antenna are Normal mode (broadside) and the Axial mode (endfire).

Normal mode

• In the Normal mode of operation the field radiated by the Helix is maximum in a perpendicular plane to the Helix axis.

• To achieve the Normal mode of operation the dimensions of Helix are usually small compared to wavelength (D<<λ and L<<λ).

• In the Normal mode it can be thought that the Helix consists of N small loops and N short dipoles connected together in series.

• Since in the Normal mode the Helix dimensions are small, the current through its length can be assumed to be constant and its relative far-field pattern to be independent of the number of loops and short dipoles.

• In Normal mode the bandwidth is narrow and the radiation efficiency is small.

• In Normal mode to get circular polarization in all directions the Helix antenna shall satisfy following conditions:

            - Diameter: D = (√2*S* λ) / Π   

            - Pitch angle: tan α = (Π*D) / (2* λ)

Axial mode

• The Axial mode is practical because can achieve circular polarization over wider bandwidth and is more efficient.

In this mode of operation there is only one major lobe and its maximum radiation intensity is along the axis of the Helix.

To achieve circular polarization in Axial mode the following parameters of the Helix must be in the range:

• Diameter: 3/4 < [(Π*D) / λ] < 4/3   or D = λ / Π for optimum performance

• Spacing between turns: S = λ/4 or S = 0.25* Π*D

• Pitch angle: 12˚ ≤ α ≤ 14˚

• The dimension of the Helix antenna in Axial mode is not as critical, this resulting in wider bandwidth.

• The terminal impedance in the Axial mode is nearly resistive with values between 100 and 200 ohms.

     50 ohms impedance can be obtained by properly designing the feed.

• The Helix input impedance (purely resistive) can be approximate by:

Z_helix (ohms) = 140*[(Π*D) / λ]

• For matching the resulting Helix antenna impedance to the feeding cable usually 50 ohms, can be used a λ/4 stub having the impedance:

 Zs = SQRT (Z_helix * 50)

• Another simple way to match the input impedance of a Helix from nearly 150 ohms down to 50 ohms is increasing the thickness of the conductor near the feed-point. The wire of the first ¼ turn should be flat in the form of a copper strip (triangle shape) and the transition into a helix should be very gradual.

There is a formula to calculate the width of the triangle strip at the feeding point, which includes the dielectric constant Er, but probably the best way to find it is tuning experimentally using a Network Analyzer or a SWR meter.

References:

1. Antenna Theory – C. Balanis

2. Antenna Theory and Design – R. Elliott

3. Handbook of Antennas – L. Godara

4. Antenna Theory and Design – W. Stutzman

5. Antennas – J. Kraus

6. Antennas and Radio Wave Propagation – R. Collin

7. Field Antenna Handbook – MCRP-6-22D

8. Monopole Antennas – M. Weiner

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