**Golden ****Engineering**

**Top-loaded short antenna for AM (Amplitude Modulation) transmissions**

The antenna is composed of four vertical monopoles over ground. Each monopole is fed at its base by a voltage source of the same amplitude and phase as the others.

The top-load is used to tune the antenna. The total radiation resistance is the sum of the real parts of the four input impedances.

**Broadside antenna**

Broadside antenna array composed of four parallel half-wave dipoles. The array is fed at its base by a bi-filar transmission line.

The separation between the vertical dipoles determines the number of radiation lobes obtained.

**Car with roof antenna**

Simulation of a car above ground having a dipole antenna on its roof. The distorsion of the dipole radiation pattern can be seen due to the electromagnetic interaction with the car and ground.

**Coil inductor**

Simulation of a coil using a helical wire at 1 MHz. Coil size is just 0.0001 of wavelength. A Method of Moments segment in the coil equals only one turn, so this is an extreme example of the curvature that the AN-SOF segments can support.

The imaginary part of the input impedance at the position of the voltage source is practically the same as the theoretical reactance that is obtained using the coil formulas in terms of the coil diameter and number of turns. The space relative permeability can also be changed to model the presence of a magnetic core inside the coil.

Simulation of this example is not possible using NEC-based softwares due to the very small structure size in wavelenghts and the straight segment approximation used in NEC code.

**Cylindrical antenna**

Frequency sweep simulation of a cylindrical dipole antenna. The results show how the current distribution along the wire approachs a sine function. More radiation pattern lobes appears as the frequency increases because the dipole length also increases if it is measured in wavelengths.

The input impedance can be plotted as a function of frequency in order to show the resonance frequency (imaginary part goes to zero).

**Reflector-type directional antenna**

Directional antenna consisting of a parabolic reflector and a Yagi-like array at the location of the parabola's focus.

Only a reflector having linear wires parallel to the dipoles at the focus are needed since the Yagi-like antenna is horizontally polarized.

**Folded dipole**

Simulation of a folded dipole using curved wires at the dipole ends. The curved part is modeled exactly using conformal segments. AN-SOF applies the Conformal Method of Moments (CMoM) instead of the traditional MoM, which uses a straight wire approximation to curved wires.

The standard donut shaped radiation pattern is obtained with a small distorsion. Folded dipoles are used to increase the radiation resistance of a standard half-wave dipole (about 75 Ohm). The input impedance of the folded dipole shows a real part near to 300 Ohm.

**Half-wave dipole antenna**

Center-fed half-wave dipole antenna at 300 MHz.

The wavelength is close to 1 meter, so the dipole length equals 0.5 meters.

The standard donut-shaped radiation pattern is obtained having a maximum dimensionless gain of 1.65, which is very close to the theoretical value of 1.64, which is the gain of an infinitely thin wire half-wavelength long.

The effect of the finite wire radius can also be seen in the input impedance. The obtained radiation resistance (real part of input impedance) equals 91 Ohm, which is greater than the theoretical value of 73 Ohm for the infinitely thin dipole.

**Directional helix antenna backed by a perfect ground plane**** **

Directional helix antenna backed by a perfect ground plane.

A directional radiation pattern is obtained pointing towards the helix axis as can be expected since the helix size (diameter and number of turns) was set according to the theoretical helix formula.

The input impedance shows that the helix is practically a resonant antenna having 300 Ohm as radiation resistance (input reactance is almost zero).

**Directional helix antenna backed by circular plate**** **

Frequency sweep simulation of a directional helix antenna backed by a ground plane of finite size.

The ground plane is modeled using a circular grid of thin wires.

A directional radiation pattern is obtained pointing towards the helix axis as can be expected since the helix size (diameter and number of turns) was set according to the theoretical helix formula. The radiation pattern and gain are almost constants within the frequency range.

**Horn antenna**** **

Simulation of a horn antenna fed by a rectangular waveguide.

The holes size of the wire structure is about one-tenth of the wavelength (0.1 lambda), so this is enough to model a continuous metallic surface in this case.

The radiation pattern shows a main lobe pointing towards the horn axis (y-axis) as it is expected. The near-field modes of transmission can be seen by plotting the E- and H-field as color maps near the horn mouth.

**Log-periodic antenna**** **

Frequency sweep simulation of a log-periodic array of linear elements.

The antenna is fed by a voltage source at its end and the excitation is distributed between the antenna elements by means of a transmission line oriented along the antenna axis (y-axis).

The radiation pattern changes slowly as a function of frequency, so the broadband behavior of the log-periodic array is confirmed.

**Loop in receiving mode**** **

Frequency sweep simulation of a receiving circular loop antenna.

The loop is modeled using conformal segments, which exactly follow the contour of the antenna geometry. This is far better than using straight segments as in NEC-based softwares. AN-SOF is the only commercial simulation software that implements the Conformal Method of Moments (CMoM).

The antenna is in receiving mode, so it is excited by an external incoming plane wave. As the frequency increases, more sine function semi-cycles are obtained as a current distribution along the loop.

The radiation pattern shows the re-radiated power and a plot of the RCS (Radar Cross Section) can be obtained in this case.

**Magic-tee (hybrid tee) waveguide combiner**

A thin-wire approximation is used to model the metallic surface of the waveguide structure where the holes size is about one-tenth of the wavelength (0.1 lambda), which is enough in this case to model its electromagnetic behavior.

The near E-field can be plotted as a function of position along the y-axis to show a sine function profile. The magic-tee can be used as a power combiner or divider.

**Microstrip antenna array**

Microstrip array of four rectangular patches over a dielectric substrate and backed by a perfect ground plane.

The array is fed by a vertical bias between the ground plane and the plane above the substrate. The excitation is distributed between the patches by means of microstrip dividers.

A directional radiation pattern is obtained pointing towards the axis perpendicular to the plane of the antenna (z-axis).

**Microstrip patch dipole**

Microstrip patch dipole antenna over a dielectric substrate and backed by a perfect ground plane.

The rectangular patch is fed by a vertical bias between the ground plane and the plane above the substrate. A microstrip transmission line is used to transmit power from the vertical bias to the patch.

A directional radiation pattern is obtained with a main lobe pointing towards the axis perpendicular to the plane of the antenna (z-axis).

**Two-ports microstrip filter**

The filter can be excited at each port by using a voltage source in a vertical bias between the ground plane and the plane above the dielectric substrate. The filter response can be analized by plotting the current distribution as a color map on the metallic traces.

**Microstrip patch antenna**

Microstrip patch antenna over a dielectric substrate and backed by a perfect ground plane.

The patch is fed by a vertical bias between the ground plane and the plane above the substrate. A microstrip 1/4-wave transmission line is used to transmit power from the vertical bias to the patch.

A directional radiation pattern is obtained with a main lobe pointing towards the axis perpendicular to the plane of the antenna (z-axis).

**Microstrip spirals**

Microstrip patch antenna over a dielectric substrate and backed by a perfect ground plane.

The antenna is made of two spirals in order to obtain circular polarization in the radiation pattern.

The spiral strips are fed by a vertical bias between the ground plane and the plane above the substrate.

The spiral sizes must be ajusted if a main radiation lobe is needed, since two main lobes are obtained.

The modeling of spirals requires the implementation of the Conformal Method of Moments (CMoM), which uses curved segments instead of the traditional straight segment approximation.

**Monopole antenna above a real ground plane**

The monopole is used for AM (Amplitude Modulation) radio transmissions. The far-field radiation pattern in the Fraunhofer zone is distorted due to the finite conductivity of the soil, so a power absorption takes place in the ground plane reducing the radiated power.

If the E-field is plotted just over the ground as a function of position along the x or y-axis, the Sommerfeld-Norton decay of the field amplitude can be seen.

**Multihole coupler between two waveguides**

Two parallel waveguides are coupled by means of eight holes made in the adjacent face between them. The waveguide metallic surface is modeled using a thin-wire grid aproximation having small holes compared to the wavelength (about 0.1 lambda in size), which is enough in this case. The near E-field can be plotted along the x-axis to show the waveguide transmission mode.

**Parabolic reflector antenna (dish antenna)**

The reflector is modeled by a grid of straight segments. The hole sizes are small compared to the wavelength near the center of the parabola, buy they aproach half-wavelength away from the center. Most real parabolic antennas are built in this way, so this is a good approximation in those cases.

A three-elements Yagi antenna is located at the focus point of the parabola and its radiation pattern is pointing towards the reflector (secondary radiator). This Yagi antenna then simulates a primary radiator.

A high gain is obtained as can be seen by plotting the radiation pattern, which shows a main lobe pointing towards the parabola axis (y-axis).

**Parabolic reflector antenna (CMoM model of dish antenna)**

The reflector is modeled by a grid of curved segments (CMoM: Conformal Method of Moments). The hole sizes are small compared to the wavelength near the center of the parabola, buy they aproach half-wavelength away from the center. Most real parabolic antennas are built in this way, so this is a good approximation in those cases. The curved segments are a better approximation than straight segments when a continuous metallic dish surface is used as a reflector.

A three-elements Yagi antenna is located at the focus point of the parabola and its radiation pattern is pointing towards the reflector (secondary radiator). This Yagi antenna then simulates a primary radiator.

A high gain is obtained as can be seen by plotting the radiation pattern, which shows a main lobe pointing towards the parabola axis (y-axis).

**Plane wave reaching an airplane**

Simulation of a plane wave reaching the path of an airplane.

An external plane wave reaches the airplane from its tail. The wave E-field is oriented along the plane wings. The RCS (Radar Cross Section) can be analized by plotting the far-field pattern which shows the re-radiated power. The near field is calculated just in front of the plane in order to analize the wave transmission after crossing the plane.

**RLC circuit**

Frequency sweep simulation of an RLC circuit.

The series RLC circuit is modeled using thin-wires for the conductors and lumped load impedances for its resistive, inductive and capacitive components. The size of the structure is just 1.6E-7 wavelengths.

By looking at the input impedance as a function of frequency, the resonance frequency can be obtained (imaginary part of input impedance goes to zero). Calculate the resonance frequency using standard circuit theory and you will see the great accuracy of this model.

**Two dipole antennas on a ship sailing in the ocean**

This simulation shows a wire grid model of a ship sailing in the ocean and having two dipole antennas at its top. A perfect ground plane is used to simulate the ocean since it is practically a perfect conducting surface at 10 MHz (saltwater is a good conductor at those frequencies).

The radiation pattern shows the distorsion of the ideal donut-shaped dipole patterns due to the electromagnetic interaction between the antennas and the ship.

**Square loop antenna**

The total length of the loop is about 0.4 wavelengths, so the current distribution shows a semi-cycle of a sine function. The radiation pattern is not donut-shaped since the size of the loop is comparable to the wavelength. In order to obtain a donut-shaped pattern, the frequency must be decreased until the loop size approach one-tenth of the wavelength.

**Lossless transmission line**

Frequency sweep simulation of a lossless transmission line.

The transmission line is made of one horizontal conductor above a perfect ground plane. A voltage source is placed at one line end and the other end is short-circuited against ground.

By plotting the input impedance as a function of frequency the resonance frequencies can be obtained (imaginary part of input impedance goes to zero). The current distribution along the line can also be plotted to see the accuracy of the calculation compared to transmission line theory.

**Lossy transmission line**

Frequency sweep simulation of a lossy transmission line.

The transmission line is made of one horizontal conductor above a perfect ground plane. A voltage source is placed at one line end and the other end is short-circuited against ground. The horizontal conductor has a finite resistivity of 0.01 Ohm meters, so a loss of power occurs along the line.

By plotting the input impedance as a function of frequency the resonance frequencies can be obtained (imaginary part of input impedance goes to zero), which are offset from the lossless line. The current distribution along the line can also be plotted to see the effect of power losses.

**Directional V-antenna**

The horizontal arms of the V-antenna are 3 wavelengths long, so six semi-cycles of a sine function can be seen as a current distribution along the arms. The vertical wires are half-wavelength long, so they behave as half-wave center-fed dipoles.

A directional radiation pattern is obtained having a main lobe pointing towards the x-axis and the radiation resistance is 73 Ohm, the same value for an infinitely thin half-wave dipole.

**Rectangular waveguide**

Frequency sweep simulation of a rectangular waveguide.

The metallic surface of the waveguide is modeled by means of a grid of thin wires. The size of the grid holes is lower than one-tenth of the wavelength (0.1 lambda), so this is enough to obtain reliable results in this case.

The near E-field has been calculated along the x-axis, which is perpendicular to the waveguide, in order to visualize the behavior of the waveguide modes.

**3-elements Yagi-Uda antenna**

Simulation of a Yagi antenna that consists of three linear wires. A directional radiation pattern is obtained as can be expected. The current distribution on the array can be plotted as a color map in order to compare the current intensities between the elements of the array.

**5-elements Yagi-Uda antenna**

Simulation of a Yagi antenna that consists of five linear wires. The driven element is a folded dipole which does not change the radiation pattern shape but it changes the input impedance for an easier impedance matching.

A directional radiation pattern is obtained as can be expected. The current distribution on the array can be plotted as a color map in order to compare the current intensities between the elements of the array.

**7-elements Yagi-Uda antenna**

Simulation of a Yagi antenna that consists of seven linear wires. A directional radiation pattern is obtained as can be expected. The current distribution on the array can be plotted as a color map in order to compare the current intensities between the elements of the array.

It is interesting to compare this antenna with the 3- and 5-elements Yagis to see the increase in the antenna gain and the appearance of secondary lobes in the radiation pattern.

**Inverted V antenna**

Inverted Vee over real ground. The operating frequency is 7.2 MHz which corresponds to a wavelength of almost 40 meters. The V center is at 50 feet above ground. The length of each arm is 33 feet with a 22 degrees drop angle.

A voltage source at the top center is feeding the antenna. The source voltage is 300 V in order to get almost 1000 W of input power.

**Radio mast above a radial wire ground screen**

Radiating towers or radio masts can be modeled in AN-SOF with a high degree of detail. This example shows a quarter-wave monopole antenna connected to a radial wire ground screen on a real ground plane. A simplified model is also shown, where the tower is modeled by a single vertical wire having a triangular cross section.