VisTools

This section describes the calculations in the Visualyse Interplanetary stand-alone tool kit, VisTools.

• dB Calculation
• Frequency to Wavelength
• Path Loss
• Field of View
• Peak Gain
• Half Power Beamwidth
• Relative Gain
• Temperature to Noise
• Link Budget

dB Calculation

The $\mathrm{dB}$ tool converts between $\mathrm{dB}$ (d) and absolute (a) using:

$$\begin{array}{rl}& a=10^{d/10}\\ & d=10{\log }_{10}(a)\end{array}$$

Frequency to Wavelength

The Frequency tool converts between frequency $f$ and wavelength $\lambda$ using:

$$c=f\lambda$$

where $c$ is the speed of light

Path Loss

The Pathloss tool calculates the free space path loss. The parameters used are:

• Frequency and Frequency units
• Path Length
• Path Loss

Each of these three can be calculated from the other using:

$$L_{fs}=22.0+20{\log }_{10}\left(\frac{Df}{c}\right)$$

Field of View

The field of view tool provides information about circular orbits in terms of field of view and orbit period. The parameters are:

• height of satellite
• distance to horizon
• half of field of view, $\theta$
• orbital period

as shown in the figure below:

The equations are:

$$\begin{array}{rl}& \theta =\arcsin \left[\frac{R_e}{R_e+h}\right]\\ & D^2={\left(h+R_e\right)}^2-R_e^2\\ & P=2\pi \sqrt{\frac{a^3}{\mu }}\end{array}$$

where:

$$\begin{array}{rl}& \mu =\mathrm{GM}\text{ is the gravitational constant for the Earth }\\ & a=\text{ semi-major axis of orbit }\end{array}$$

Peak Gain

This tool calculates peak gain based on the following parameters:

• frequency and frequency units $f$
• dish size D
• efficiency $\eta$
• peak gain $G_{\max }$

These parameters are related using the following equation:

$$G_{\max }=\eta {\left(\frac{\pi \mathrm{D}f}{c}\right)}^2$$

Half Power Beamwidth

The Theta-3dB tool calculates half power beamwidth based upon the following parameters:

• peak gain, ${\mathrm{G}}_{\max }$
• efficiency, $\eta$
• half power beamwidth, ${\theta }_{3\mathrm{dB}}$

These parameters are related using the following equation:

$$G_{\max }=\eta {\left(\frac{\pi 70}{{\theta }_{3dB}}\right)}^2$$

Relative Gain

The relative gain tool calculates offaxis gain within the main lobe for a pure parabolic dish, based upon the following parameters:

• Gain relative to peak, ${\mathrm{G}}_{\text{rel }}$
• Half power beamwidth, ${\theta }_{3\mathrm{dd}}$
• Offaxis angle, $\theta$ These parameters are related using the following equation:

$$G_{rel}=-12{\left(\frac{\theta }{{\theta }_{3dB}}\right)}^2$$

Temperature to Noise

The noise tool converts between temperature in Kelvin to noise in $\mathrm{dBW}/\mathrm{Hz}$. The following parameters are used:

• Temperature $\mathrm{T}$ in Kelvin
• Noise $\mathrm{N}$ in $\mathrm{dBW}/\mathrm{Hz}$

These parameters are related using the following equations:

$$N=k+10{\log }_{10}T$$

where $\mathrm{k}$ is Boltzmann's constant in $\mathrm{dBW}/\mathrm{Hz}/\mathrm{K}$.

Link Budget

These various tools are combined to produce a link budget tool with the following parameters:

• Frequency, f, entered either directly or using the frequency tool
• Transmit power, P, entered directly, or calculated from transmit EIRP
• Transmit peak gain ${\mathrm{GTX}}_{\max }$, entered either directly or using the peak gain tool
• Transmit relative gain ${\mathrm{GTX}}_{\text{rel, }}$, entered either directly or using the offaxis gain tool
• Transmit eirp, EIRP, either entered directly or calculated from $\mathrm{C}$ or using:

$$EIRP=P+G^E{T}_{\max }+G_{\text{Tel }}$$

• Free space path loss, ${\mathrm{L}}_{\mathrm{fs}}$, either entered directly or using the pathloss tool
• Other losses, ${\mathrm{L}}_{\text{other }}$, entered directly
• Receive peak gain ${\mathrm{GRX}}_{\max }$, entered either directly or using the peak gain tool
• Receive relative gain ${\mathrm{GRX}}_{\text{rel }}$, entered either directly or using the offaxis gain tool
• Receive power, C, either entered directly or calculated from EIRP or $\mathrm{C}/{\mathrm{N}}_0$ or using

$$\mathrm{C}=\mathrm{EIRP}-{\mathrm{L}}_{\mathrm{fs}}-{\mathrm{L}}_{\mathrm{other}}+{\mathrm{GRX}}_{\max }+{\mathrm{GRX}}_{\mathrm{rel}}$$

• Receive noise, ${\mathrm{N}}_0$, either entered directly or using the noise tool
• Receive $C/{\mathrm{N}}_0$, either entered directly or calculated using:

$$\mathrm{C}=\mathrm{C}-{\mathrm{N}}_0$$

Note that: - If $C$ is changed directly the $C/N_0$, EIRP and transmit power fields update accordingly

• If the EIRP field is changed directly, the $C,C/N_0$, and transmit power fields update accordingly
• If the transmit power field is changed directly, the EIRP, $C$ and $C/N_0$, fields update accordingly
• If the $\mathrm{C}/{\mathrm{N}}_0$ field is changed directly the C, EIRP, and transmit fields update accordingly