Cascaded Noise Figure and the Importance of Dicke Switching in

Radiometric Applications

Thaddeus Johnson andTorie Hadel

Introduction

Thaddeus Johnson– Bachelors in Electrical Engineering– Worked in Microwave Systems Lab (MSL) and Micron

Torie Hadel– Bachelors in Electrical Engineering– 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.

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Blackbody Radiator

• What is a black body?

– 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]

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 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 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:

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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

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• 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 – Gain and noise fluctuations can be integrated into the ideal

equation to calculate a more accurate version of radiometric resolution for a TPR

– Gain fluctuations are often the limiting factor in achieving high radiometric resolution. This is dependent upon integration time as the factor becomes more important as the integration time decreases.

Radiometric Resolution

Gain Fluctuations • 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

• The bulk of the gain fluctuations occurs at a frequency below 1Hz, known as 1/f noise.

Noise Fluctuations • A low pass filter (LPF) used at

the output of a radiometer smooths out high frequency noise fluctuations in VO with frequencies > where is the integration time.

• The remaining error that is not filtered out is defined as

Radiometric Uncertainty

GS =Average system gainrms value of gain variation

Calibration Techniques

Internal 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

External Calibration• 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

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• 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

– The receiver introduces noise with power

– The output of the square law detector is VO which is given by:

Total Power 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 , 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 .

• 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.

Dicke Radiometer

Dicke Radiometer

• The radiometric resolution of an unbalanced Dicke Radiometer is

• It is unbalanced because ; if , 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.

Dicke Radiometer

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

• 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

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G1 G2 G3

TN1 TN2 TN3

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

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Questions?

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