Thaddeus Johnson and Torie Hadel Cascaded Noise Figure and the Importance of Dicke Switching in Radiometric Applications Thaddeus Johnson and Torie Hadel

Radiometers, Noise Temperature, and Dicke Switches Introduction Thaddeus Johnson Bachelors in Electrical Engineering Worked in Microwave Systems Lab (MSL) and Micron Torie Hadel Worked in CSU Semiconductor Processing Lab and Intel Senior Design Project: Radiometer-on-a-Chip Our goal by then end of the project is to have tested and improved the device model for the Dicke switch and to give those recommendations to JPL. 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

What is a black body? Blackbody Radiator A black body is something that is both a perfect emitter and absorber of electromagnetic radiation. The power emitted from a black body can be quantified in something called the brightness temperature. For an ideal blackbody the brightness temperature can be extracted from the emitted power with the expression P=kTBB Where: P=emitted power [W] k=Boltzmann’s constant [J/K] TB=brightness temperature [K] B=bandwidth of system [Hz]

Radiometers, Noise Temperature, and Dicke Switches Noisy Components Thermal noise, also known as Nyquist noise, is caused by thermal vibrations of bound charges Noisy devices are characterized by noise figure F which describes the degradation of signal-to-noise ratio between the input and output of the device 𝐹= 𝑆𝑖 𝑁𝑖 𝑆𝑜 𝑁𝑜 ≥1 Si, Ni are input signal and noise powers So, No are output signal and noise powers A more useful way of quantifying noise in a radiometer is noise temperature 𝑇𝑁= 𝐹−1 𝑇𝑜 where TN is noise temperature and T0=290K This noise temperature can be modeled as an input to the radiometer and we can consider the system noiseless Similar to power of blackbody radiation, the noise power is described by the law: 𝑃𝑁=𝑘𝑇𝑁𝐵 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

Radiometers, Noise Temperature, and Dicke Switches What is a radiometer? A radiometer is a passive receiver that is designed to measure a selected frequency range of a scene’s emitted electromagnetic radiation An antenna is positioned at the front end of a radiometer to measure the brightness temperature, TB, of the radiation and provide an equivalent noise temperature, TA, to the system The performance of a radiometer is characterized by its accuracy and precision Accuracy is dependent on the calibration of the radiometer Precision is dependent on the radiometric resolution Radiometers can be applied to measure water vapor profiles, wind vectors, sea water salinity, cloud liquid water etc. Two common types of radiometers are Total Power Radiometers (TPR) and Dicke Radiometers 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

Radiometric Resolution Radiometric resolution is the minimum change in TSYS (TA+TREC) that will produce a detectable change in VO. The radiometric resolution of an ideal TPR is 𝛥𝑇𝑁= 𝑇𝑆𝑌𝑆 𝐵𝜏 Gain and noise fluctuations can be integrated into the ideal equation to calculate a more accurate version of radiometric resolution for a TPR Δ𝑇𝑇𝑃𝑅= Δ𝑇𝑁 2+ Δ𝑇𝐺 2 1/2 = 𝑇𝑆𝑌𝑆 1 𝐵𝜏 + Δ𝐺𝑆2 𝐺𝑆2 1/2 Gain fluctuations are often the limiting factor in achieving high radiometric resolution. This is dependent upon integration time as the 1 𝐵𝜏 factor becomes more important as the integration time decreases.

Radiometric Uncertainty Gain Fluctuations Δ𝑇𝐺 Noise Fluctuations 𝛥𝑇𝑁 A low pass filter (LPF) used at the output of a radiometer smooths out high frequency noise fluctuations in VO with frequencies > 1/𝜏 where 𝜏 is the integration time. The remaining error that is not filtered out is defined as 𝛥𝑇𝑁= 𝑇𝑆𝑌𝑆 𝐵𝜏 An increase in GS will be incorrectly interpreted by the system as an increase in TSYS. Primarily caused by the RF and IF amplifiers. The undesired increase in TSYS due to gain fluctuations of the system can be defined as Δ𝑇𝐺=𝑇𝑆𝑌𝑆( Δ𝐺𝑆 𝐺𝑆 ) The bulk of the gain fluctuations occurs at a frequency below 1Hz, known as 1/f noise. GS =Average system gain ΔGS= rms value of gain variation

Calibration Techniques Internal Calibration External Calibration Built into front end of receiver (i.e. matched load, noise diode, cold FET) Does not calibrate components proceeding it; however, it doesn’t require moving parts that may be needed to view the external calibration source Observe some source that closely models a black body (i.e. temperature controlled microwave absorber) Complete calibration – takes all components of the radiometer into account 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

Total Power Radiometer A total power radiometer (TPR) uses a square law detector so that the output voltage is linearly proportional to the input power. The antenna looks at an object with brightness temperature TB and measures power radiated 𝑃𝐴=𝑘𝑇𝐵𝐵 The receiver introduces noise with power 𝑃𝑅𝐸𝐶=𝑘𝑇𝑅𝐸𝐶𝐵 The output of the square law detector is VO which is given by:

Dicke Radiometer Essentially a TPR with three extra components: A switch connected at the receiver input, a reference load and a synchronous demodulator placed between the square-law detector and the LPF. The switch alternates the receiver input between the antenna and a constant noise source at a switching frequency high enough to keep Δ𝐺𝑆, also called the 1/f noise, constant for each input. This frequency is generally higher than 1Hz. The switch looks at the antenna and the constant noise source, or reference, for equal amounts of time over the integration time 𝜏. These added components allow for a large portion of the gain and noise fluctuations to be cancelled out by subtracting the measured reference voltage from the measured antenna voltage provided that the switching frequency is high enough. 𝑉𝑜𝑢𝑡,𝐷𝑅=𝐶𝑑𝐺𝑘𝐵 𝑇𝐴+𝑇𝑅𝐸𝐹 −𝐶𝑑𝐺𝑘𝐵=𝐶𝑑𝐺𝑘𝐵 𝑇𝐴−𝑇𝑅𝐸𝐹

Dicke Radiometer

Dicke Radiometer The radiometric resolution of an unbalanced Dicke Radiometer is It is unbalanced because 𝑇𝐴≠𝑇𝑅𝐸𝐹; if 𝑇𝐴=𝑇𝑅𝐸𝐹, then it is said to be a balanced radiometer and the effects of gain variation drop out. The radiometric resolution of a balanced Dicke radiometer is given by: Notice that this is very similar to the radiometric resolution of an ideal TPR. The factor of two comes from the fact that the system is spending half its time looking at the reference load and half the time looking at the antenna.

Comparison of a Dicke Radiometer and a TPR The advantages of a Dicke radiometer over a TPR can be seen through comparing the equations for radiometric resolution and output voltage. Total Power Radiometer

Cascaded Noise Temperature Typically an input signal to a system, such as a Dicke radiometer, will travel though a cascade of components Each component in the system will be characterized with its own noise temperature Noise temperature of a cascaded system is given by 𝑇𝑐𝑎𝑠=𝑇𝑁1+ 𝑇𝑁2 𝐺1 + 𝑇𝑁3 𝐺1𝐺2 +… The gain of the first stage dominates the noise characteristics of a cascaded system. To achieve good cascaded noise performance, the first stage should have a low noise figure and some gain. If a first stage has a gain less than unity, it not only will it add noise, but will increase the effects of noise in the proceeding stages G1 G2 G3 TN1 TN2 TN3 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

Radiometers, Noise Temperature, and Dicke Switches Front End Stage It is shown from the cascaded noise figure characteristics that the first stage in a radiometer is critical to radiometric resolution Dicke switches, which are used as the first stage in a Dicke Radiometer, are known have a less than unity gain This in turn increases the cascaded noise temperature of the receiving system, so why are we using it? The gain cancellation that we get with a Dicke switch far outweighs the impacts of noise temperature due to the relationship explained earlier: *Note: Note this only holds true for long integration times 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches

Radiometers, Noise Temperature, and Dicke Switches Questions? 9/9/2011 Radiometers, Noise Temperature, and Dicke Switches