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Cascaded Noise Figure and the
Importance of Dicke Switching in
Radiometric Applications
Thaddeus Johnson and
Torie 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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Radiometers, Noise Temperature, and Dicke Switches
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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
𝐹=𝑆
𝑜
𝑁𝑖
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
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Radiometers, Noise Temperature, and Dicke Switches
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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
• 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
1 2
2
/
1
Δ𝐺𝑆
1 2
2
2
Δ𝑇𝑇𝑃𝑅 = Δ𝑇𝑁 + Δ𝑇𝐺
= 𝑇𝑆𝑌𝑆 𝐵𝜏 + 𝐺 2
𝑆
– Gain fluctuations are often the limiting factor in achieving high
radiometric resolution. This is dependent upon integration time
1
as the factor becomes more important as the integration time
𝐵𝜏
decreases.
Radiometric Uncertainty
Gain Fluctuations Δ𝑇𝐺
• 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
Δ𝐺
Δ𝑇𝐺 = 𝑇𝑆𝑌𝑆( 𝑆)
𝐺𝑆
• The bulk of the gain
fluctuations occurs at a
frequency below 1Hz, known
as 1/f noise.
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
GS =Average system gain
ΔGS = rms 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
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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
• 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
𝑇𝑁2 𝑇𝑁3
𝑇𝑐𝑎𝑠 = 𝑇𝑁1 +
+
+⋯
𝐺1 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
G2
G1
TN1
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TN2
G3
TN3
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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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