Calculators

This is probably one of the most useful utilities in Antenna Magus. It started as an in-house application used by the engineers to read off design values from scanned graphs (mostly from published papers that were only available in *.pdf or in hardcopy). After showing this to other engineers and seeing their excitement we decided to include this as a utility in Antenna Magus.

Simply select your scanned graph image, specify anchor values and follow the trace(s) with your mouse. Apply the spline or linear function and export the XY values to a TSV (tab seperated values) file. It supports both polar and cartesian graphs.

While the chart is being traced, values relevant to the indicated data type are automatically extracted, making it easy to determine quantities such as bandwidth, sidelobe level etc. of the data. These values can then in turn be used for design or specification refinement.

Read more about how to use the Chart Tracing Tool.

The equation below shows the relationship between a decibel value and a linear voltage/power ratio. This calculator is can be used in one of three ways:

• A decibel value can be specified and the linear voltage and power ratios will be returned.
• A linear voltage ratio can be specified and the decibel value together with the linear power ratio is returned.
• A linear power ratio can be specified and the decibel value together with the linear voltage ratio is returned.

dB = 20log₁₀(voltage ratio) = 10log₁₀(power ratio)

This calculator allows the conversion between various two-port parameters. The two-port parameters include Z (impedance), Y (admittance), ABCD (chain) and S (scattering).

Most microwave textbooks [e.g. Pozar] provide very useful conversion formulas to switch between various two-port parameter conventions. Often only conversions for simplified cases are provided, namely where the impedance values of port 1 (source) and port 2 (load) are real, equal, or where a common port and system impedance is enforced.

The voltage standing wave ratio (VSWR), reflection coefficient (Τ), return loss and mismatch loss are all dependant on one or the other, as can be seen by the equations below. 

This calculator solves the Friis transmission equation for any of its variables. The Friis transmission equation relates the power received by an antenna to the power radiated by another antenna, a specified distance away (in free space). Modified forms of the basic Friis equation allow for inclusion of many system factors, including antenna mismatch, absorption in the propagation medium, cable loses, etc. The Antenna Magus calculator includes antenna mismatch effects, as shown below. Polarization and physical misalignment are not compensated for, but may be considered by adjusting the figures used for the gain of the respective antennas.

This calculator solves the well-known Radar range equation for any of its variables. The Radar range equation relates the power received by the radar receiver to the power transmitted by the radar transmitter, the radar cross section of the target, the gains of the antennas, the frequency and the distance between the antennas and the target. The form of the equation used in this calculator allows for bi-static radar, but does not consider polarization mismatch or gain compensation for misaligned antennas.

The signal-to-noise-ratio (SNR) is a criterion of detectability in a communication link. In basic terms, it compares the level of the desired signal to the level of background noise. A ratio in excess of 1:1 indicates more signal than noise.

The equation used in this tool is show in the image above. The parameters used in the equation are transmitted power (Pt), transmitter antenna effective aperture (Aet), receiver antenna effective aperture (Aer), transmitter-receiver distance (r), wavelength (λ), bandwidth (B), Boltzmann constant (k) and system temperature.

A radio telescope is a remote sensing device whether it is earth-based and pointed at the sky for observing celestial objects or on an aircraft or satellite and pointed at the earth. The equation assumes that the radiation detected or sensed by the telescope originates in the objects being observed, known as passive remote sensing.

The antenna is part of the receiving system consisting, in general, of an antenna, a receiver and a transmission line which connects them. The temperature of the system is a critical factor in determining the sensitivity and signal-to-noise ratio of a receiving system.

A communication satellite functions as a radio relay in space. The communication link may be between stations on earth, or between antennas from other satellites.

This calculator determines the electrical characteristics for the given physical properties of a microstrip line, or vice-versa. The effect of the metal thickness is taken into consideration in the calculations.

This calculator determines the impedance for a specified physical coax, or will calculate the inner or outer diameter for the given parameters. Other transmission line parameters such a capacitance and inductance per unit length are also calculated.

This calculator determines the electrical characteristics for the given physical properties of a coplanar waveguide structure, or vice-versa. The effect of the metal thickness is taken into consideration in the calculations.

This calculator determines impedance for the given physical properties of a grounded coplanar waveguide structure.

This calculator is used to determine the cutoff frequency, wave impedance and the guided wavelength of the first 5 dominant modes for the defined circular waveguide.

This calculator is used to determine the cutoff frequency, wave impedance and the guided wavelength of the first 5 dominant modes for the defined rectangular waveguide.

This calculator calculates an approximate gain for given beamwidths, or vice-versa. The exact gain will depend on many factors, but this handy calculator provides a useful rule of thumb guideline. The calculator allows the specification of both the vertical and horizontal beamwidths separately.

This calculator calculates the expected gain for an aperture of a given area and efficiency. It can also invert the equation to solve for any of the other parameters. For instance, it can be used to calculate the aperture efficiency of a horn antenna.

The total antenna efficiency takes into account losses at the input terminals and within the structure of the antenna. The losses may be due, to:

• Reflections due to the mismatch between the transmission line and the antenna
• I2R losses (conduction and dielectric)

This tool calculates the total antenna efficiency using the following equation:

e₀ = e_r e_cd

where

e₀ = total antenna efficiency

e_r = reflection (mismatch) efficiency = (1 - |Τ|2)

e_cd = antenna radiation efficiency

Τ = voltage reflection coefficient at the input terminals of the antenna [Τ=(Z_in- Z₀)/( Z_in- Z₀) where Z_in = antenna input impedance, Z0 = characteristic impedance of the transmission line].

Total antenna efficiency takes into account the reflection, conduction and dielectric losses of an antenna. The dielectric and conduction losses are difficult to compute and in most cases are measured. Even with measurements, they are difficult to separate and are usually lumped together to form the radiation efficiency (ecd). The radiation efficiency is defined as the ratio of the power delivered to the radiation resistance (Rr) to the power delivered to the radiation resistance and the conduction-dielectric resistance (RL), or in equation form:

Every object with a physical temperature above absolute zero radiates energy. The amount of energy radiated is usually represented by an equivalent temperature.

If an antenna maintained at a certain physical temperature (Tp) is connected to a receiver by a length of transmission line (L), with a constant temperature (To) throughout, and having uniform attenuation (α), the effective antenna temperature at the receiver terminal is:

The parameters used in the equation are:

T_ant = antenna temperature at the receiver terminals (K)
T_a = antenna noise temperature at the antenna terminals (K)
T_AP = antenna temperature at the antenna terminals due to physical temperature (K)
T_p = antenna physical temperature (K)
α = attenuation coefficient of transmission line (Np/m)
εA = thermal efficiency of the antenna
L = length of the transmission line (m)
T_o = physical temperature of the transmission line (K)

The realized gain of an antenna is calculated by considering the total efficiency of the antenna, along with its directivity.

The total efficiency of the antenna considers the losses due to reflections at the input terminals as well as losses within the structure of the antenna.

Total efficiency e₀ may be written as:

This calculator plots the approximate aperture and feed distribution of a typical axissymetrical parabolic reflector topology. The feed / aperture distribution is determined based on the the shape modifier (P) derived for the given focal length to diameter ratio (F/D), edge taper (ET) and aperture / feed distribution efficiency (ade / fde) [Rahmat-Samii].

For a specific parabolic reflector dish and feed antenna, the gain pattern may be calculated using the handy Pattern approximation tool. This tool allows the user to consider the theoretical gain and pattern performance of larger reflectors (which could result in long simulation times) or predict the influence of parameters like blockage ratio or feed distribution efficiency.

The Radar Cross Section (RCS) of an object is its effective area intercepting the incident power density, which when scattered isotropically would result in the received backscatter power. The estimation assumes that the polarizations are matched.

Skin depth is a measure of electrical conduction within a conductor. At DC (0 Hz) the current is equally distributed over the cross section of a conductor. As the frequency increases, the current distribution changes with the highest current density near the surface of the conductor.