2.3.1 Rectangular waveguide horn in open space

Let us consider a rectangular waveguide horn situated in open space, as described by ..\Antennas\Horns\horn1.pro. In Fig. 2.3.1-1 we can see the horn in various 2D and 3D Windows of QW‑Editor. The horn has been drawn using a standard object horn1.udo from the library antennas.

Fig. 2.3.1-1 QW-Editor display of horn1.pro.

The user can easily invoke its header and modify the dimensions by pressing (Select Object ) and double-clicking horn1.udo on the list.

Note that the horn is situated vertically, which is optimal from the point of view of the number of elements used by the QW-Editor to record its geometry. A look at the list of elements (displayed upon pressing Select Element button) reveals that the horn shape is described by only two Combined Elements. It is, of course, possible to situate the same horn horizontally, for example by applying another standard object named horn1h.udo and available in the antennas library. However, in such a case its geometry description would involve slices of the horn walls. As a consequence, the Select Element list would be very long, and the corresponding UDO script - significantly more complicated.

We will now discuss the analysis of radiating horns with reference to horn1.pro as an example. We assume that the reader is already familiar with Waveguide-to-coax transition of this manual and therefore we will not be paying much attention to the problems of S-parameter extraction and field distribution displays. We shall concentrate on the software features specific to the radiation problems.

Fig. 2.3.1-2 Edit Transmission Line Port dialogue in the example horn1.pro.

Let us take a closer look at the project. The horn has its external walls marked red and the inner walls marked blue. We can also see that the horn is surrounded by a green box. This is the surface of the near-to-far transformation (called in brief NTF box ), whereat the near fields directly produced by the FDTD simulation are transformed into the far field radiation patterns. Furthermore, the computing domain is surrounded by six absorbing walls. These walls are marked blue with a triangular pattern suggesting their similarity to unechoic chamber walls. Each of the absorbing walls is treated by the software as a port. That is why upon invoking I/O Ports Parameters dialogue (which can be alternatively use for configurting e.g. transmission line ports, point ports, etc.) we can see that the number of ports is equal to 7. However, six of these ports have NR:0, which indicates that they will not participate in the S-parameter extraction. Only one port – the waveguide input named inp appears with NR: 1. Thus we will be extracting S-parameters of a one-port device.

Let us now invoke S-Parameters and Near To Far dialogues. We obtain the dialogues of Fig. 2.3.1-3 and can see that S-Parameters and Near To Far post-processings have been activated for this project. The choice made in S-Parameters dialogue will result in the calculation of the horn return loss from 18 to 30 GHz with the frequency step of 0.05 GHz. The choice made in Near To Far dialogue will result in the preparation of data for the radiation pattern calculations at 20 GHz and 25 GHz.

Fig. 2.3.1-3 S-Parameters and Near To Far dialogues in the example horn1.pro.

Fig. 2.3.1-4 Results of S-parameters calculation in the example horn1.pro.

Let us now start the project simulation by pressing . When QW-Simulator starts the 3D analysis, we invoke Results window (by pressing button in Results tab of QW-Simulator) to monitor the evolution of the return loss. After about 1000 iterations we notice that the curve of |S11| versus frequency has reached a stable form as presented in Fig. 2.3.1‑4, and does not change with an increasing number of iterations.

The radiation patterns of the antenna are obtained by invoking the Results window for 2D radiation pattern results. This can be done by pressing button in 2D Radiation Pattern section of Results tab of QW-Simulator. We obtain the Radiation Patterns dialogue of Fig. 2.3.1-5. Its settings indicate that we wish to calculate the radiation patterns versus angle Theta (q ) varying between 0 and 180 degrees with a step of 2 degrees. They will be calculated with a constant angle Phi (f) equal to 0 degrees. The definition of the angles is explained in the lower right part of the window. Note that this definition depends on the choice of the reference axis. The angle Theta is always counted from the reference axis (Z in the considered example). The angle Phi is always counted around it.

The reference axis can be set to X, Y or Z by clicking respective radio buttons in the Axis column of the dialogue. There is also an option to define an arbitrary reference axis. For an example of application of this option, please refer to the Two dipoles in free space excited in phase.

We can set the reference point or in other words the origin of the coordinate system for the NTF transformation. The position of the reference point does not influence the absolute values of the radiation patterns (in lossless NTF background medium) but it does influence their phase characteristics. Moving the reference point can be helpful in a search for the antenna electrical centre. The reference point position is expressed in the same coordinates and units as those used in the project and defined in QW-Editor. To recall what units have been used, we can just take a look at the title bar of the window. In the considered example we see Units: mm.

Fig. 2.3.1-5 Radiation Patterns dialogue with parameters used in the example horn1.pro.

QW-Simulator offers a choice of Gain References. With the choice of Directive as in Fig. 2.3.1-5, the radiation patterns calculated by QW-3D are expressed as (unitless) directive gain with respect to an isotropic antenna radiating the same total power. Thus the software needs to calculate the total power radiated by the antenna as a reference value. Two methods of doing this are available in QW‑3D. They correspond to the chosen characteristic Type. The detailed discussion regarding the two methods of radiated power calculation is given in Radiated Power. In this case radiated power is calculated based on integration of the Poynting vector over the NTF box (NTF fields option).

Take a look at the radiation patterns presented in Fig. 2.3.1-6. They show two curves corresponding to the two polarisations. Polarisation definition is based of the direction of the E-field with respect to the angular components Phi and Theta. In our case the E-field of the wave exciting the horn was in Y-direction. The radiation pattern presented in Fig. 2.3.1-6 has been calculated with Z reference axis and Phi=0, which means in ZX plane. Since the dominant E-field is perpendicular to this plane, the software detects E_phi polarisation as the dominant one. It gives a maximum directive gain of 11.79 dB and the back radiation at a level lower by about 26 dB. The E_theta polarisation, which can be considered here as a cross-polarisation, is 110 dB below the main lobe of E_phi. Calculation of the patterns for Phi=90 (in ZY plane) would show a dominant role of E_theta.

The parameters for radiation pattern calculation can be viewed in Radiation Patterns dialogue (Fig. 2.3.1-5) invoked by pressing button in Results window. We may modify the settings and re-calculate the characteristics. For example, the lower picture in Fig. 2.3.1-6 shows the results in linear scale, with Fields at 1m scaling option. This means we are considering the electric field intensity in the far zone, scaled to 1m distance from the reference point, and divided by a square root of the NTF background medium impedance (which is vacuum in this case). This has the physical significance of a square root of the radiated power density.

In the status bar of the window we can read some additional important information. The software indicates there:

· Fr - radiation frequency, at which the characteristics have been calculated,

· Pr - time-maximum power radiated at this frequency (this information is important when considering relations between radiated power and field amplitudes in the investigated structure),

· Ef - antenna efficiency defined as the ratio of the radiated power (Pr) to the power injected into the antenna by the source (Pi),

· Rr - radiation resistance of the antenna defined as the ratio of the radiated power (Pr) to square of the current injected into the antenna by a lumped source (|I|^2); since horn1.pro is not fed by lumped source, radiation resistance is not calculated here,

· Pi - time-maximum power injected into the antenna by the source; its value close to zero indicates that calculations of antenna effciency may be ill-conditioned,

· |I|^2 - square of the amplitude of current injected into the antenna by a lumped source; since horn1.pro is not fed by lumped source, the injected current is not calculated here.

Fig. 2.3.1-6 Radiation patterns calculated for the example horn1.pro at 20 GHz, scaled in directive gain and shown in manual decibel scale (upper) and scaled as Fields at 1m and shown in linear scale (lower).

It should be noted that the above information is not shown in the status line when we choose (via Config option) to have a common display of several radiation patterns calculated at different frequencies. In such a case (see Fig. 2.3.1-7) we can read it in the cursor pane (right part of the window) together with the numerical values of the radiation patterns at the angles indicated by the cursors.

Note that the values related to the input power (Ef, Rr) are not displayed when the considered NTF frequency is not one of the frequencies at which S-parameters have been calculated. The reason is that in such a case the software does not have enough information to calculate the actual power injected by the source.

Fig. 2.3.1-7 Radiation patterns calculated for the example horn1.pro at 20 GHz and 25 GHz displayed in one window.

The discussed displays of radiation patterns were in one plane, versus either Phi or Theta angle. In some cases, the users may wish to see a 3D radiation pattern, with both Phi and Theta varying in steps. Such a pattern for the horn1 example is presented in Fig. 2.3.1-8 right. It is obtained in 3D Radiation Pattern window, which is opened via button from Results tab of QW-Simulator. It invokes the 3D Radiation Patterns dialogue shown on the left of Fig. 2.3.1-8. It allows setting the reference axis and steps for angles Phi and Theta, defined with respect to that axis in the same way as for the 2D radiation pattern case. A single frequency is also selected. Note that the calculations of 3D radiation pattern may be quite time consuming.

Fig. 2.3.1-8 The 3D Radiation Patterns dialogue and 3D Radiation Pattern window with 3D radiation pattern calculated for the example horn1.pro at 20 GHz.