Antenna input impedance

Antenna input impedance(or antenna input impedance) - the main characteristic of the transmitting and receiving antenna, which is defined as the ratio of high-frequency voltage and supply current

Antenna input impedance is defined as the sum of the radiation resistance and the antenna loss impedance.

The loss resistance, in turn, is made up of ohmic losses in the elements and wires of the antenna, insulation losses (due to leaks), resistance to losses in the ground and heat losses in surrounding objects lying in the near zone of the antenna.

To increase the efficiency of the antenna, it is necessary to strive to match the input impedance of the antenna with the characteristic impedance of the line, that is, to fulfill their equality, as well as to reduce the losses in the antenna.

see also

Literature

• Antenna // Physical encyclopedic dictionary / Ch. ed. A.M. Prokhorov - M .: Sov. encyclopedia, 1983. - 928s., pp. 24-28
• Drabkin A. L., Zuzenko V. L., Kislov A. L. Antenna-feeder devices. 2nd edition, rev., Add. and revised M .: "Sov. radio ", 1974, S. 536, p. 11
• Rothamel, Karl Antenna, 11th Edition, revised and updated by engineer Alois Krishke, 2005, pp.

Links

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The design, manufacture and use of antennas for long (LW), medium (MW), and short (KB) wavelengths are significantly less problematic than antennas for VHF, especially television. The fact is that in the LW, MW, KB bands, transmitters, as a rule, have a high power, the propagation of radio waves in these bands is associated with high values ​​of diffraction and refraction in the atmosphere, and the receiving devices are highly sensitive.

When transmitting and receiving a signal in the VHF range and, in particular, a television signal, ensuring the necessary values ​​of these parameters causes a number of difficulties, namely: the achievement of the power of television transmitters, such as broadcasting ones, has not yet been possible; the phenomena of diffraction and refraction in the VHF range are insignificant; the sensitivity of a television receiver is limited by its own noise level and is, due to the need to receive a broadband signal, about 5 μV. Therefore, to obtain a high level of image on the TV screen, the input signal level must be at least 100 µV. However, due to the low power of the transmitter and the worst conditions for the propagation of radio waves, the strength of the electromagnetic field at the receiving point is low. Hence, one of the main requirements for a television antenna arises: for a given field strength at the receiving point, the antenna must provide the necessary signal voltage for the normal operation of the television receiver.

The receiving antenna is a single wire or a system of wires designed to convert the energy of electromagnetic waves into energy of high frequency currents. The parameters of the antennas during operation for reception and transmission are identical, therefore, the principle of reciprocity of antenna devices can be applied, which makes it possible to determine some characteristics and parameters of the antennas in the transmission mode, and others in the reception mode.

Radio waves, falling on surrounding objects, induce high-frequency electric currents in them. The latter create an electromagnetic field, and the electromagnetic wave is reflected. The antenna receives both direct and reflected radio waves, which distort the image on the TV screen.

Experimental studies have shown that when using vertical polarization, significantly more reflected waves arrive at the receiving site than when using horizontal polarization. This is due to the fact that in the surrounding space, especially in cities, there are many vertical, well-reflecting obstacles (buildings, poles, pipes, magnets). When choosing the type of polarization, the properties of the antennas are also taken into account. Structurally, horizontal antennas are simpler than vertical ones. Almost all of them have directionality in the horizontal plane, which weakens the reception of interference and reflected waves due to spatial selectivity.

Receiving television antennas must meet the following basic requirements:

Have a simple and easy-to-use design;

High spatial selectivity;

Pass a wide frequency band;

Provide a high ratio of the signal level to the level of interference during reception;

Have a weak dependence of the input impedance and gain on frequency.

An antenna is a signal source that is characterized by an electromotive force (EMF) and an internal resistance called the antenna input impedance. The input impedance is determined by the ratio of the direction at the antenna terminals to the current at the feeder input. The value of the antenna input impedance must be known in order to correctly match the antenna with the cable and the TV: only under this condition the highest power is supplied to the TV input. With proper matching, the input impedance of the antenna should be equal to the input impedance of the cable, which, in turn, should be equal to the input impedance of the TV.

Antenna input impedance has active and reactive components. The input impedance of the tuned antenna is purely active. It depends on the type of antenna and its design features. For example, the input impedance of a linear half-wave vibrator is 75 ohms, and that of a loop vibrator is about 300 ohms.

Antenna-to-cable matching is characterized by traveling wave ratio (TWR). In the absence of a perfect match between the antenna and the cable, the incident wave (input voltage) is reflected, for example, from the end of the cable or another point where its property changes dramatically. In this case, the incident and reflected waves propagate along the cable in opposite directions. At those points where the phases of both waves coincide, the total voltage is maximum (antinode), and at the points where the phases are opposite, it is minimal (node).

The traveling wave coefficient is determined by the ratio:

In the ideal case, KBV = 1 (when there is a traveling wave mode, that is, a signal of the maximum possible power is transmitted to the input of the TV, since there are no reflected waves in the cable). This is possible by matching the input impedances of the antenna, cable and TV. In the worst case (when U min = 0) KBV = 0 (there is a standing wave mode, that is, the amplitudes of the incident and reflected waves are equal, and the energy is not transmitted along the cable).

The standing wave ratio is determined by the ratio:

The receiving omnidirectional antenna receives signals from all directions. The directional receiving antenna has spatial selectivity. This is important, because with a low level of field directivity at the receiving site, such an antenna increases the received signal level and attenuates external interference coming from other directions.

The directional gain of a receiving antenna is a number indicating how many times the power supplied to the TV input when receiving on a directional antenna is greater than the power that can be obtained when receiving on an omnidirectional antenna (at the same field strength).

Antenna's directivity properties are characterized by a directivity pattern. The directional diagram of the receiving antenna is a graphical representation of the dependence of the signal voltage at the input of the TV on the angle of rotation of the antenna in the corresponding plane. This diagram characterizes the dependence of the EMF induced in the antenna by the electromagnetic field on the direction of arrival of the signal. It is built in a polar or rectangular coordinate system. On rice. 12 the antenna radiation patterns of the "wave channel" type are presented.

Rice. 1. The radiation pattern of the antenna in the polar coordinate system

Antenna radiation patterns are most often multi-lobe. The petal corresponding to the direction of arrival of the wave at which the maximum EMF is induced in the antenna is called the main one. In most cases, the radiation pattern also has reverse (rear) and side lobes. For the convenience of comparing different antennas with each other, their directional patterns are normalized, that is, they are plotted in relative values, taking the largest EMF as one (or one hundred percent).

The main parameters of the radiation pattern are the width (opening angle) of the main lobe in the horizontal and vertical planes. The width of the main lobe is used to judge the directional properties of the antenna. The smaller this width, the greater the directivity.

Rice. 2. Antenna radiation pattern in a rectangular coordinate system

The level of the side and back lobes characterizes the noise immunity of the antenna. It is determined using the antenna protection factor (SPC), which is understood as the ratio of the power emitted by the antenna at the matched load when receiving from the rear or lateral direction to the power at the same load when receiving from the main direction.

The coefficient of protective action is often expressed in logarithmic units - decibels:

The directional properties of the antenna are also characterized by the directional action coefficient (DIR) - a number that shows how many times the signal power entering the input of the TV when received at a given directional antenna is greater than the power that could be obtained when receiving on an omnidirectional or directional reference antenna. A half-wave dipole (dipole) is most often used as a reference antenna, the directivity of which with respect to a hypothetical omnidirectional antenna is 1.64 (or 2.15 dB). The LPC characterizes the maximum possible power gain that an antenna can give due to its directional properties, assuming that there are no losses in it at all. In fact, any antenna has losses and the power gain it gives is always less than the maximum possible. The real gain of the antenna in terms of power relative to a hypothetical isotropic radiator or half-wave vibrator is characterized by the power gain K p, which is related to the LPC by the ratio:

where η - coefficient of performance (efficiency) of antennas.

Antenna efficiency characterizes the power loss in the antenna and is the ratio of the radiation power to the sum of the radiation powers and losses, that is, to the total power supplied to the antenna from the transmitter:

where P u- radiation power, P n- power losses.

The bandwidth of a receiving television antenna is a frequency spectrum within which all the main values ​​of its electrical characteristics are maintained. The frequency response of a tuned antenna is similar to the resonance curve of an oscillatory circuit. Therefore, by analogy with the loop bandwidth, the antenna bandwidth can also be determined.

At the resonant (fixed) frequency, the antenna has a certain value of the input impedance, which is consistent with the load impedance. This frequency is usually taken to be the average frequency of a television channel, at which the antenna reactance is zero. At frequencies below the resonant, it is capacitive, and at frequencies above the resonant, it is inductive.

Thus, a change in frequency leads both to a change in the active component and to the appearance of a reactive component of the input resistance. As a result, the power supplied to the load is reduced.

This is especially noticeable at the extreme frequencies farthest from the resonant frequency. The power can be reduced by no more than two times. Based on this bandwidth 2Af such a frequency spectrum near the resonant frequency is considered, within which the power supplied to the load will decrease by no more than two times.

To ensure good reception quality, the antenna must pass the entire frequency spectrum of the television signal, which for one channel is 8 MHz. The image quality is still good enough if the antenna has a bandwidth of at least 6 MHz. Further narrowing the frequency band leads to a deterioration in the quality of the image and to the loss of its clarity. The most effective method of bandwidth expansion is to reduce the vibrator's equivalent wave impedance by increasing its lateral dimensions. In this way, the linear capacitance increases and the linear inductance of the vibrator decreases. Among other things, the antenna bandwidth is limited by the bandwidth of the drop feeder.

antenna input impedance. It is believed that it is a series-connected reactance and resistance. But there is no real resistor, capacitor or inductor in the antenna or feeder. All this is only the result of calculating the equivalent resistances of the antenna circuit. Let a certain "black box" be used as a load, the input connector of which is supplied with RF voltage. On this connector, you can actually measure the instantaneous voltage u 'and the current i', as well as the phase difference between them j. The input resistance is the calculated active and reactance, connecting to which the given HF voltage we get exactly the same u ’, i’ and j.
It is known that such an equivalent can have both serial (serial, Zs = Rs + jXs) and parallel (parallel, Zp = Rp || + jXp) connection of active and reactance resistances. Each series connection of active (Rs) and reactive (Xs) resistances corresponds to a parallel connection of active (Rp) and reactance (Xp) resistances. In general, Rs # Rp and Xs # Xp. Here are the formulas by which you can recalculate the numerical values ​​from one compound to another.

For example, let's convert the serial connection Zs = 40 + j30W to parallel Zp.

More often, the equivalent of series connection is used, but the equivalent of parallel connection has the same practical significance. Zs is called series impedance, R is resistance, X is reactance, and Zp is parallel impedance. In parallel connection, administration is often used, but this is conductivity, and visibility when using it is greatly reduced. Usually the term "impedance" indicates that we are talking about a series connection of equivalent resistance and reactance.

88) The powers supplied to the antenna and radiated by the antenna.

The power is divided into two parts:

1) emitted

2) losses on active resistance (in the ground, in the surrounding metal conductors, guys, buildings, etc.)

- the radiated power, as for any linear circuit, is proportional to the square of the effective value of the current in the antenna.

- coefficient of proportionality.

Radiation resistance can be defined as the coefficient that connects antennas with at a given antenna point.

(antenna shape, geometric dimensions, l)

- useful power

Power loss:

- Equivalent loss resistance related to current I

- full power (supplied to the antenna)

where - active resistance of the antenna at the feed point

To assess the efficiency of the antenna, the concept of antenna efficiency is introduced , to increase it is necessary to decrease.

89) Symmetrical electric vibrator in free space.

Approximate laws of distribution of current and charge over the vibrator.

Rice. 15. Symmetrical vibrator

Symmetrical vibrato - two arms of the same size and shape, between which the generator is switched on.

Before the development of a rigorous theory of a symmetrical vibrator (late 30s - early 40s), an approximate method was used to calculate the vibrator field. It is based on the assumption of a sinusoidal current distribution over the vibrator (the law of standing waves) associated with some external analogy between a symmetrical vibrator and a 2-wire line open at the end.

After a series of experiments with helical antennas, a graph was plotted

input impedance of dipole and vertical helical antennas depending on the shortening factor (Fig. 6.9) in the range of 7 ... 28 MHz. The antennas were made on a dielectric frame with a diameter of 10 mm to 10 cm, the spiral winding was uniform, and a wire with a diameter of more than 0.5 mm was used.

Experiments have shown that for shortened spiral antennas with K = 2 ... 10, a change in the diameter of their frame within 1 ... 10 cm does not significantly affect the input resistance. However, for highly shortened spiral antennas with K> 10, my results showed that the input impedance largely depends on the diameter of their dielectric frame and on the frequency at which the spiral antenna has resonance, therefore, for them, such a simple graph as in Fig. 6.9 failed to get.

As can be seen from this graph, a coaxial cable with a characteristic impedance of 50 Ohm, an electrical length that is a multiple of half the wavelength of the antenna, is suitable for powering dipole and vertical spiral antennas with K> 3. In some cases, vertical antennas initially had an input impedance significantly higher than in Fig. 6.9, but tuning the "ground" of the antenna to resonance allowed it to be lowered. Connecting a coaxial cable to a vertical antenna usually slightly changes its input impedance at the end of the cable connection to the transceiver, in this case, changing the input impedance

occurs in the direction of decreasing. Dipole helical antenna

in comparison with the vertical, it usually has an input impedance closer to that shown in the graph. However, connecting a coaxial cable to a dipole spiral antenna can lead to the fact that the antenna resistance will differ significantly from that indicated in the graph, both in the direction of increase and in the direction of decrease. At least 10 ferrite beads installed at the ends of the coaxial cable reduce its effect

on the input impedance, but not completely eliminated. If the elongation factor of the spiral antenna exceeds 5, it is advisable to install a high-frequency choke not from ferrite rings at the end of the coaxial cable supplying the antenna, but in the form of 5–20 turns of a coaxial cable with a diameter of 10 ... 20 cm.

Changing the diameter of the coil and the diameter of the wire used to wind a real shortened antenna does not significantly affect the input impedance of the antenna. This happens because with an increase in the diameter of the spiral, the antenna radiates more efficiently, therefore, the radiation resistance of the antenna increases, and its input impedance increases. With a decrease in the diameter of the spiral, the radiation efficiency of the antenna of electromagnetic waves decreases, therefore the radiation resistance decreases, but the dielectric losses in the spiral frame increase. An increase in dielectric losses leads to an increase in the input impedance of the helical antenna. Obviously, in order to increase the efficiency of the spiral antenna, it is necessary to use a wire of the largest possible diameter to make its spiral, and the diameter of the spiral turns must be the maximum possible for the practical implementation of the antenna. The frame on which the antenna spiral is made must have low dielectric losses. In the design of a helical antenna, it is desirable to use a uniform spiral winding.

What is Antenna Input Impedance?

Everyone knows that the input impedance (impedance) of an antenna is rarely equal to the characteristic impedance of the feed line. Here I will try to show how to match the load with the feeder using effective methods.
Further, all examples will be given for a coaxial cable with a characteristic impedance of 50 ohms, but the principle of calculation is valid for other both single-ended and balanced transmission lines.

Antenna input impedance

First, let's find out what the antenna input impedance is. It is believed that it is a series-connected reactance and resistance. But there is no real resistor, capacitor or inductor in the antenna or feeder. All this is only the result of calculating the equivalent resistances of the antenna circuit.

Let a certain "black box" be used as a load, the input connector of which is supplied with RF voltage. On this connector, you can actually measure the instantaneous voltage u 'and current i', as well as the phase difference between them j ... The input resistance is the calculated active and reactance, connecting to which this HF voltage we get exactly the same u '', i '' and j.

It is known that such an equivalent can have both serial (serial, Zs = Rs + jXs) and parallel (parallel, Zp = Rp || + jXp) connection of active and reactance resistances. Each series connection of active (Rs) and reactive (Xs) resistances corresponds to a parallel connection of active (Rp) and reactance (Xp) resistances. In general, Rs No. Rp and Xs No. Xp. Here are the formulas by which you can recalculate the numerical values ​​from one compound to another.

For example, recalculate the serial connection Zs = 40 + j30 W to parallel Zp.

More often, the equivalent of series connection is used, but the equivalent of parallel connection has the same practical significance. Zs is called series impedance, R is resistance, X is reactance, and Zp is parallel impedance.

In parallel connection, administration is often used, but this is conductivity, and visibility when using it is greatly reduced. Usually the term "impedance" indicates that we are talking about a series connection of equivalent resistance and reactance.

However, recalculation of the series connection of resistances into parallel connection is quite often needed to compensate for the reactive component. It should only be borne in mind that with serial and parallel compensation, we get different active components of the resistance.

For converting Zs to Zp and vice versa, the NETCALK program is very suitable.
The question arises of how to measure the parameters of the complex load. Unfortunately, a simple VSWR meter is of little use here. For this I use a VA1 vector analyzer, which shows all the necessary digital values ​​on the display. You can also use the AA-330.

Reactive compensation

It is useful to compensate for the reactive component of the resistance (impedance). This reduces the SWR. The essence of compensation is phase alignment of voltage and current. You can change the phase angle between voltage and current by connecting a reactive element in series or in parallel.

In order for the difference in the phase angles to become zero, it is necessary to connect such a reactance that is present in the equivalent load circuit, only with the opposite sign. It is known that the reactance of the capacitor has a negative sign, the inductance - positive.

In the case of serial compensation, an additional equivalent reactive element with the opposite sign is connected in series and a serial circuit is obtained, and in the case of parallel compensation, in parallel, a parallel circuit is obtained. In the case of a series connection of resistances, they simply add up

And in the case of a parallel connection

If the load is fully compensated, these circuits are in resonance, with Xs = 0 or Xp =Ґ ... For example, we have a load Zs = 50 + j30 W (Zp = 68 || + j113 W), SWR = 2.

If in series with the load we turn on the capacity with Xc = -30 W, we get Z = 50 W and SWR = 1. If parallel to the load we connect a capacitance with Xc = -113 W, we get Z = 68 W and SWR = 1.36. In the case of serial compensation, an additional element with an equivalent corresponds to a serial circuit, in the case of a parallel one - to a parallel one.

Resistance matching

As I already wrote, connecting the compensating element in different ways, in the general case, we get a different Z, thereby also the VSWR. Let's see how you can compensate (match) the load Zs = 22 + j25 W (Zp = 50.4 || + j44 W), SWR = 2.94.

By connecting a capacitor in series with Xc = -25 W we get Z = 22 W (SWR = 2.27). If in parallel to the load we connect a capacitor with Xc = -44 W, we get Z = 50.4 W and SWR = 1.01. As you can see, in this case, parallel compensation is undoubtedly better. If such a load is connected to a transmitter that operates at a frequency of 14 MHz, then a capacitor with a capacity of

If the transmitter has an output P-circuit, then this capacitance must be added to the output (cold) capacitor. This can be done with an output capacitor if it is increased by the required amount. In this case, we get a good match of the transmitter, designed for 50 W , with load (at the point of connection of the feeder with the transmitter, r = 0), although the VSWR in the cable will remain 2.94. W , then parallel to the capacitor of the P-circuit it is necessary to connect an inductance of 0.5mH (Xl = 44 W ) or, if there is such a possibility, reduce the capacity of the "cold" capacitor of the P-circuit by 258pF (Xs = -44 W ). Partially because of this, by tuning the P-circuit to the real load, we get an unequal capacity of the "cold" capacitor compared to 50 W equivalent.

Partly because, by varying the capacitance of the P-circuit capacitors, it is possible, within certain limits, to tune the transmitter to a load that is not equal to that calculated during the design of the transmitter. If the transmitter does not have a P-loop or tuner, then this uncompensated reactance will upset the transmitter output filter, the reflectance r > 0 and the transmitter is not capable of delivering the calculated power to the feeder.

I want to note that neither the P-circuit, nor the tuner in the transceiver or near it, does not change the SWR in the feeder. These devices are only capable of matching the output impedance of the transmitter with the input impedance of the feeder at the point of its connection to the transmitter (not to be confused with the characteristic impedance of the feeder), i.e. improve the reflection coefficient r ... To improve the VSWR in the cable, it is necessary to match the load with the characteristic impedance of the feeder at the point of their connection.
Serial and parallel compensation can be applied simultaneously. It depends on the specific case. Here's a real example. Antenna impedance at 1.9MHz has an impedance of Zs = 26 + j44 W (Zp = 100 || + j59 W), SWR = 3.7.

If a capacitor with Xc = -59 is connected in parallel with the load W, we get Z = 100 W , SWR = 2, if we connect in series a capacitor with Xc = -44 W , we get Z = 26, SWR = 1.92. The latter is better, but still bad. Now, without changing Rs, select Xs such that Rp becomes 50 W ... This option corresponds to Zs = 26 + j25 W ... Connect the reactivity in series with the load Xs = (26 + j25) - (26 + j44) = - j19 W (4.4nF capacitor). Received Zs = 26 + j25 W recalculate in Zp = 50 || + j52 W.

Now we connect in parallel the reactivity Xp = -j52 W (capacitor 1.6nF) and we get Z = 50 W and SWR = 1. That's it, antenna with 50 W feeder agreed!
All this can be easily calculated using the MMANA program. I wrote all this in order to understand the configuration mechanism and what affects what.

You can agree in another way. It is known that if a load is connected to the feeder, the resistance of which is not equal to the characteristic impedance of the feeder, then the feeder will transform the load impedance.

The numerical value of the resistance at the input of the feeder will depend on the load resistance, characteristic impedance and the length of the feeder. Using the APAK-EL program, we find that if the load Zs = 26 + j44 W connect feeder 50 W length 4.76 m., then at a frequency of 1.9 MHz at its input we get Zs = 50 + j69 W.

If in this place we turn on in series a capacity with Xc = -69 W (capacitor 1.2nF), then we get Z = 50 W and SWR = 1. From this place you can connect 50 W feeder of any length.

Other variants of agreement are also possible. It depends on understanding the essence and fantasy.
Now let's try to match an antenna at 14 MHz, the impedance of which is Zs = 150-j260 W (Zp = 600 || -j346 W ). As you can see, we cannot do with one compensating element.

We need to get 50 W, not 150 W or 600 W ... Enter the data into APAK-EL and find the point closest to the load, where Rtr = 50 W.

As you can see, the length of the additional cable will be only 30cm. In this place we will have Zs = 50-j161 W ... If in this place we connect in series the inductance with Xl = 161 W , then we get full agreement (Z = 50 W , SWR = 1).
All this can be coordinated at the point where the load is connected to the feeder. Example with MMANA

As you can see, you can agree by connecting an inductance of 1.35 m H parallel to the load, and apply the signal to the load through a 68.5pF capacitor.

Loops

Loops are short-circuited or open sections of the feeder. In an ideal feeder (feeder without losses), the resistance of such sections is purely reactive, there is no active part.

Such sections of the feeder can be used to compensate for the reactive component. This is useful when parallel compensation is used. Sections up to a quarter wavelength are often used. They can be longer, but real feeders have losses and the longer the line, the greater.

Closed loop of electrical length up to 1/4 l has an inductive reactance at the end, open - capacitive. Such sections of the feeder can simulate both inductance and capacitance. But we must not forget that the inductance or capacitance of the loop depends on the frequency.

In the given example, we see that it is necessary to connect an inductance of 1.352 m H. With the help of MMANA, we find that such an inductance at 14 MHz has a loop from the RG58 / U cable with a length of 2.62 m shorted at the end.

Using the same example, let's try to reconcile the same with MMANA in a different way, using only a loop.

Thus, if the short-circuited loop is 67.5 cm long. connect parallel to the feeder at a distance of 2.57m. from the load, then we will also fully match the feeder with the load. Alternatively, you can connect an open loop with a length of 2.84m in parallel. at a distance from the load of 3.82 m.
Other variants of agreement are also possible. But it should be remembered that the losses in low-impedance (coaxial) feeders at high VSWR values ​​are significant, so it is advisable to choose a matching method that produces the shortest lengths of the feeder with a large VSWR and use thick high-quality cables.
As you can see, practically everything can be coordinated in different ways.
Only for this you need a measuring device, and, of course, a computer. The complex impedance of the antenna can not be measured with either a tester or a VSWR meter. Without this data, reconciliation becomes time consuming and often leads to unsatisfactory results.

In this article, I have described several reconciliation methods. I tried to describe the essence of the issue as simply as possible, but it does not work out very simply in such a question.
This article was written by me several years ago in Lithuanian and has now been translated into Russian. Other versions of APAK-EL and MMANA are currently available, examples are given using older versions.
APAK-EL has a utility that can also be used to calculate compensating reactivities. However, the very principle of coordination does not change from this.
I hope this article will be useful to some people.

Vytas (LY3BG), ly3bgtakas.lt