Definition of Terms

• **BW** - the bandwidth of the transmitted optical signal, in hertz

• **C/N** - the Carrier to Noise ratio

• **DETdarkcurrent** - the dark current, which is the residual electric current flowing from your photodetector when no photons are arriving, measured in amperes (A)

• **DETeff** - a unitless quantity representing detection efficiency

• **DETgain** - a unitless receiver gain

• **DETimpedance** - the impedance within the photodetector, measured in Ohms (Ω)

• **DETnoisefigure** - the equivalent to the difference between the noise output of your optical receiver and an ideal optical receiver with the same gain and bandwidth, at a standard noise temperature, generally 290 Kelvin, measured in dB

•** DETnoisetemp** - the effective noise temperature of your optical receiver, in degrees Kelvin (K)

• **e** = 1.60217662 x 10^-19 coulombs, equivalent to the charge of one electron

• **E** - photon energy

• **f** - the frequency of the transmitted optical signal, in hertz

• **h** = 6.62607004 x 10^-34 m^2kg/s, or Planck’s constant

• **k** = 1.38064852 x 10^-23 m^2kg/s^2K, or the Boltzmann constant

• **Nd** - the noise in photon detection rate caused by dark current, in hertz

• **Ns** - the power detected, in watts

• **Nt** - the noise in photon detection rate caused by thermal noise, in hertz

• **POWERrcvd** - the signal power that reaches the optical detector, in watts

The equation that STK uses to compute C/N for a laser link is:

• C/N = Ns/(2BW) x Ns/(Ns x DETnoisefigure + Nd + Nt)

In this expression, Ns/(2BW) represents the photon detection rate per bandwidth, and Ns/(Ns x DETnoisefigure + Nd + Nt) represents the energy per photon to noise power spectral density. When multiplied, these two quantities yield the carrier-to-noise, or signal-to-noise, ratio, C/N.STK uses a few intermediate expressions before calculating the carrier-to-noise ratio:
• Ns = DETeff x POWERrcvd / (h x f)

In this expression, Ns represents the power detected in watts. DETeff is a unitless quantity representing detection efficiency, equivalent to the fraction (# photons detected over time period T)/(# photons arrived during time period T). (DETeff x POWERrcvd) divided by the energy per photon (h x f) is equivalent to the photon detection rate in hertz.
• Nd = DETdarkcurrent/ (DETgain^2 x e)

In this expression, Nd represents the photodetector dark current. DETdarkcurrent represents dark current, which is the residual electric current flowing from your photodetector when no photons are arriving; it is measured in amperes (A). (DETdarkcurrent) divided by the charge of an electron scaled by the photodetector gain squared (DETgain^2*e) is equivalent to the noise in photon detection rate caused by dark current, in hertz.
• Nt = 2 x k x DETnoisetemp/(DETgain^2 x e^2 x DETimpedance)

In this expression, Nt represents the thermal noise energy. DETnoisetemp, measured in degrees Kelvin (K), is the effective noise temperature of your optical receiver, generally understood to be the sum of the receiver temperature and the temperature of any blackbody background radiation. DETgain is a unitless receiver gain, equivalent to the fraction (optical receiver output current in A)/(receiver input photocurrent in A). DETimpedance is measured in Ohms (Ω), and represents the impedance, or opposition to current, within the photodetector. (2*k*DETnoisetemp) divided by the charge of an electron scaled by the photodetector gain squared and multiplied by the photodetector load impedance (DETgain^2*e^2*DETimpedance) is equivalent to the noise in photon detection rate caused by thermal noise, in hertz.DETeff, DETdarkcurrent, DETnoisetemp, DETnoisefigure, DETgain, and DETimpedance are all properties of the optical detector your laser link is using. You can configure these properties in the “Optical Detector” section in the “Model Specs” tab when using the Laser Receiver Model in STK.
You can use the Script Plugin Laser Receiver and Script Plugin Laser Transmitter model to define a link based on traditional communications link properties (like transmission power, transmitter and receiver gain, and design frequency) instead of defining a laser link by configuring properties of the optical photodetector. You can generate a Script Plugin Laser Transmitter and Receiver in MATLAB, VBScript, or Perl.