Receiver Noise Temperature

The following is a calculation and measurement of the noise temperature of the receiver.

Every component in the receiver chain contributes thermal noise. The radiometer output power is the sum of soil emission and receiver noise (TrecT_\mathrm{rec}​). The figure below shows the main components contributing toTrecT_\mathrm{rec}​.

Theoretical Calculation

The combined noise figure of the cascading system is:

NFsystem=Lantenna+Lswitch+NFLNA+Lbandpass+NFamp1GLNA+LCable+NFADC1GLNAGamp\mathrm{NF}_\mathrm{system} = \mathrm{L}_\mathrm{antenna} + \mathrm{L}_\mathrm{switch} + \mathrm{NF}_\mathrm{LNA}+ \dfrac{\mathrm{L}_\mathrm{bandpass} + \mathrm{NF}_\mathrm{amp}-1}{\mathrm{G}_\mathrm{LNA}} + \dfrac{L_\mathrm{Cable} + \mathrm{NF}_\mathrm{ADC} - 1}{\mathrm{G}_\mathrm{LNA} \cdot \mathrm{G}_\mathrm{amp}}

TrecT_\mathrm{rec} is calculated based on the following assumptions for Loss L\mathrm{L}, noise figure NF\mathrm{NF}, and gain G\mathrm{G}:

Lantenna=0.75dB(estimated)Lswitch=0.65dBNFLNA=0.5dBGLNA=20.5dBLbandpass=1.5dBNFamp=2.5dBGamp=20.0dBLCable=1.0dB(estimated)NFADC=3.0dB(estimated)\begin{aligned} \mathrm{L}_\mathrm{antenna} &= 0.75\,\mathrm{dB}\,\,\mathrm{(estimated)}\\ \mathrm{L}_\mathrm{switch} &= 0.65\,\mathrm{dB}\\ \mathrm{NF}_\mathrm{LNA} &= 0.5\,\mathrm{dB}\\ \mathrm{G}_\mathrm{LNA} &= 20.5\,\mathrm{dB}\\ \mathrm{L}_\mathrm{bandpass} &= 1.5\,\mathrm{dB}\\ \mathrm{NF}_\mathrm{amp} &= 2.5\,\mathrm{dB}\\ \mathrm{G}_\mathrm{amp} &= 20.0\,\mathrm{dB}\\\mathrm{L}_\mathrm{Cable} &= 1.0\,\mathrm{dB}\,\,\mathrm{(estimated)}\\\mathrm{NF}_\mathrm{ADC} &= 3.0\,\mathrm{dB}\,\,\mathrm{(estimated)}\\\end{aligned}

The noise figures of the amplifiers, as specified in their data sheets, and the noise temperatures of the resistors, which are affected by their losses, are dependent on their physical temperatures. Thus, we can calculate the overall noise temperature of the system for two realistic operating temperatures.

Receiver Phys. Temp.Receiver Noise Temp.Remark

10 deg C

141 K

After sensor startup on a cool day.

50 deg C

163 K

After about 20-30 minutes of data collection on a warm day.

For this table, we assume the physical temperature of the antenna to be constant at 20 degrees Celsius and only change the physical temperature of the electronic receiver components.

The temperature of the PCB is measured by a digital sensor and recorded as "lna_temperature_degC" in the raw data file.

In summary, the noise temperature of the receiver varies from 140 to 160 Kelvin, depending on the temperature of the receiver components.

Measurement

Coming soon...

Script to Calculate the Receiver Noise Temperature

Below is a Python script which can be used to calculate the receiver noise temperature at different antenna and component temperatures.

import numpy as np

T_phys_Antenna_degC = 20
T_phys_PCB_degC = 10

Antenna = {"Loss": {"dB": 0.5}}
Switch = {"Loss": {"dB": 0.65}}
LNA = {"NF": {"degC": [-40, 85], "dB": [0.5, 0.68]}, "Gain": {"degC": [-40, 85], "dB": [21.05, 20.6]}}
BP = {"Loss": {"dB": 1.5}}
Amp = {"NF": {"degC": [-40, 85], "dB": [2, 3]}, "Gain": {"degC": [-40, 85], "dB": [20, 19.2]}}
Cable = {"Loss": {"dB": 1}}
LMS = {"NF": {"degC": [-40, 85], "dB": [3, 3]}, "Gain": {"degC": [-40, 85], "dB": [35, 35]}}

NF_LNA = np.interp(T_phys_PCB_degC, LNA["NF"]["degC"], LNA["NF"]["dB"])
NF_Amp = np.interp(T_phys_PCB_degC, Amp["NF"]["degC"], Amp["NF"]["dB"])
NF_LMS = np.interp(T_phys_PCB_degC, LMS["NF"]["degC"], LMS["NF"]["dB"])
Gain_LNA = np.interp(T_phys_PCB_degC, LNA["Gain"]["degC"], LNA["Gain"]["dB"])
Gain_Amp = np.interp(T_phys_PCB_degC, Amp["Gain"]["degC"], Amp["Gain"]["dB"])

NF_Chain = Switch["Loss"]["dB"] + NF_LNA + (BP["Loss"]["dB"] + NF_Amp - 1)/Gain_LNA + (Cable["Loss"]["dB"] + NF_LMS - 1)/(Gain_LNA*Gain_Amp)

NT_Chain = (T_phys_Antenna_degC + 273.15) * (pow(10, (Antenna["Loss"]["dB"]/10))-1) + (T_phys_PCB_degC + 273.15) * (pow(10, (NF_Chain/10))-1)

print(NT_Chain)

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