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Radiometer systems

Radiometer systems. Chris Allen (callen@eecs.ku.edu) Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm. Outline. Equivalent noise temperature Characterization of noise Noise of a cascaded system Noise characterization of an attenuator

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Radiometer systems

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  1. Radiometer systems • Chris Allen (callen@eecs.ku.edu) • Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

  2. Outline • Equivalent noise temperature • Characterization of noise • Noise of a cascaded system • Noise characterization of an attenuator • Equivalent-system noise power at the antenna terminals • Equivalent noise temperature of a superheterodyne receiver • Radiometer operation • Effects of gain variations • Dicke radiometer • Examples of developed radiometers • Synthetic-aperture radiometers

  3. Radiometer systems • A radiometer is a very sensitive microwave receiver that outputs a voltage, Vout, that is related to the antenna temperature, TA. • Based on the output voltage, the radiometer estimates TA with finite uncertainty, T, which is referred to as the radiometer’s sensitivity or radiometric resolution. • Radiometric resolution is a key parameter that characterizes the radiometer’s performance. • An understanding of the factors affecting radiometer’s performance characteristics requires an understanding of noise, radiometer design, and calibration techniques.

  4. Equivalent noise temperature • In any conductor with a temperature above absolute zero, the electrons move randomly with their kinetic energy proportional to the temperature T. • The randomly moving electrons produce a fluctuating voltage Vn called thermal noise, Johnson noise,or Nyquist noise. Other kinds of noise include quantum noise (related to the discrete nature of electron energy), shot noise (fluctuations due to discrete nature of current flow in electronic devices), and flicker noise (also known as pink noise or 1/f noise) that arises from surface irregularities in cathodes and semiconductors. • Thermal noise is characterized with a zero mean, Vn = 0, and is has equal power content at all frequencies, hence it is often called white noise.

  5. Equivalent noise temperature • For a conductor with resistance R connected to an ideal filter with bandwidth B, the output noise power Pn is • where k is Boltzmann’s constant (1.38  10-23 J K-1), T is the absolute temperature (K). • The thermal noise power delivered by a noisy resistor at temperature T is found by replacing the noisy resistor with a noise-free resistor and a voltage generator Vrms. • The reactance X represents the resistor’s inductive and capacitiveaspects.

  6. Why V2rms = 4 R k T B ? • Experimental studies in 1928 by J.B. Johnson and theoretical studies by H. Nyquist of Bell Laboratories showed that the mean-squared voltage from a metallic resistor is • Therefore when attached to a matched load, RL = R, the voltage developed across the load is cut in half(voltage divider) and therefore the mean-squared voltage is reduced by a factor of 4 • The power transferred to the matched load is • Open circuit voltage

  7. Is it really white noise • Quantum theory shows that the mean square spectral density of thermal noise is • At “low” frequencies this expression reduces to • For most applications where To  290 K (63 ºF) [which conveniently simplifies the numerical work as kTo = 4 x 10-21 J] • If the resistance is at To then Gv(f) is essentially constant for • This conclusion holds even for cryogenic temperatures (T  0.001 To)

  8. Equivalent noise temperature • Now replace the noisy resistor with an antenna with radiometric antenna temperature TA′. TA′ is the antenna weighted apparent temperature that includes the self-emission of the lossy antenna. • If the same average power is delivered into the matched load, then we can relate TA′ to the thermodynamic temperature T of the resistor.

  9. Characterization of noise • Now consider the added noise of a linear two-port device (e.g., amplifier, filter, attenuator, cable). • Input to this device is a signal, Psi, and noise, Pni. Output from this device is a signal, Pso, and noise, Pno. • The signal-to-noise ratio, SNR, can be determined at the input as well as the output. • For an ideal component (e.g., ideal amplifier), the input signal and noise would both be amplified by the same gain resulting in an SNRout = SNRin. • However noise sources within the component will cause SNRout < SNRin.

  10. Characterization of noise • The ratio of SNRin to SNRout is called the noise figure, F. • where T0 is defined to be 290 K. • Therefore F  1 and is may be expressed in decibels

  11. Characterization of noise • The noise added by the two-port component, Pno, is • and the total output noise power, Pno, is • The two-port device may be treated as an ideal (noise-free) device with an external noise sourceadded to the device’s input.

  12. Characterization of noise • Alternatively the noise added by the two-port component, Pno, can be expressed in terms of an equivalent input noise temperature, TE, such that • Therefore if the noise power input to the device is characterized in terms of its noise temperature, TI, then the output noise temperature is TI + TE such that

  13. Characterization of noise

  14. Characterization of noise • Example cases • The NEXRAD (WSR-88D) weather radar has an effective receiver temperature of 450 K. • Therefore its receiver noise figure is F=1+TE/T0so F = 2.55 or 4 dB. • The SKYLAB RADSCAT radiometer had a 7.1-dB receiver noise figure. • Therefore its effective receiver temperature was where F = 5.1 so that TE = 1200 K.

  15. Noise of a cascaded system • Now consider a system composed of two components (systems) in cascade (i.e., connected in series). • Assuming B1 = B2, it can be shown that

  16. Noise of a cascaded system • So the gain of the first component reduces the impact of the second component’s noise characteristics on the overall system’s noise performance. • For a system with N components or subsystems cascaded • Clearly if components with “large” gain values are placed nearest the input, their noise characteristics will determine the system’s noise characteristics.

  17. Noise characterization of an attenuator • Next consider an attenuator with a physical temperature Tp and a loss factor L. • For L > 1, Pout < Pin. • Examples include a lossy cable, a filter with insertion loss, or an RF switch. • For L = 1 dB, L =1.26; if L = 1.5 dB, then Pout = 70.8% of Pin • The noise figure, F, of an attenuator is • where T0 = 290 K. If TP = T0, then F = L. • Similarly the equivalent temperature is

  18. Noise of a cascaded system • Example • Given: • F1 = 2 • L = 3 dB, F2 = 2 • G3 = 30 dB, F3 = 5 • Find Fsys for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB (a) G1 = 5 dB or 3, Fsys = 2 + (2-1)3 + (5-1)(3/2) = 5 (b) G1 = 10 dB or 10, Fsys = 2 + (2-1)10 + (5-1)5 = 2.9 (c) G1 = 30 dB or 1000, Fsys = 2 + (2-1)1000 + (5-1)500 = 2.01 • Therefore, if G1» L  Fsys  F1

  19. Noise of a cascaded system • Example • Given: • F1 = 2, TE1 = 290 K • L = 3 dB, F2 = 2, TE2 = 290 K • G3 = 30 dB, F3 = 5, TE3 = 1160 K • Find TE for G1 = (a) 5 dB, (b) 10 dB, (c) 30 dB (a) G1 = 5 dB or 3, TE = 290 + 2903 + 1160(3/2) = 1160 K (b) G1 = 10 dB or 10, TE = 290 + 29010 + 11605 = 551 K (c) G1 = 30 dB or 1000, TE = 290 + 2901000 + 1160500 = 293 K • Therefore, if G1» L  TE  TE1

  20. Equivalent-system noise power at the antenna terminals • Losses in the antenna (radiation efficiency, l< 1) add noise to the antenna’s output • And transmission-line losses raise the receiver’s equivalent input noise temperature

  21. Equivalent-system noise power at the antenna terminals • The overall system input noise temperature, TSYS, is Assuming the antenna and transmission line are at the same temperature, TP. • Recall that TA, the desired parameter, must be estimated from PSYS • Estimation of TA from PSYS requires accuracy and precision Accuracy: conformity of a measured value to its actual value without bias Bias: a systematic deviation of a value from a reference value Precision: ability to produce the same value on repeated independent observations

  22. Equivalent-system noise power at the antenna terminals • Calibration provides a means to achieve the desired accuracy. • A linear transfer function relates Vout to TA′ • Find a and b using two different calibration temperatures, TCAL thus removing any systematic biases. • Why is Vout TA′? Isn’t TA′  P instead of V?

  23. Equivalent-system noise power at the antenna terminals • Vout is the output of a square-law detector

  24. Equivalent-system noise power at the antenna terminals • Precision relates to T, the radiometric resolution which is the smallest detectable change in TA′. • Determination of T requires an understanding of the signal’s statistical properties. • Consider the total-power radiometer • Total-power radiometer block diagram

  25. Equivalent-system noise power at the antenna terminals • The total system input noise power is PSYS where • and • The average power at the IF amplifier output, PIF, is • PIF

  26. Equivalent-system noise power at the antenna terminals

  27. Equivalent-system noise power at the antenna terminals • The instantaneous IF voltage, VIF(t), has the characteristics of thermal noise, i.e., Gaussian probability distribution and a zero mean and  standard deviation, while the envelope of VIF(t) has a Rayleigh distribution • For a Rayleigh distribution, the mean value of Ve2 is

  28. Equivalent-system noise power at the antenna terminals • After the square-law detector we have Vd = Cd Ve2 where Cd is the power-sensitivity constant of the square-law detector (V W-1) and Vd is the output voltage. • Vd will have an exponential distribution • with the property that the variance of Vd is d, which leads to d / Vd = 1. • This is significant since the variance is the uncertainty, so the measured uncertainty = the mean value.

  29. Equivalent-system noise power at the antenna terminals • So without additional signal processing, a measured value of 250 K would have an uncertainty of ±250 K! (unacceptable) • To reduce the measurement uncertainty, multiple independent samples of the signal are averaged. • The low-pass filter which acts as an integrator, performs this averaging. • Assuming the signal is constant over the averaging interval, the mean value should remain unchanged while the variance is reduced. • Here B is the RF bandwidth and  is the integration time (s) constant which is related to the low-pass filter’s bandwidth by BLPF  1/(2 ), Hz.

  30. Equivalent-system noise power at the antenna terminals • So the ratio of the measurement uncertainty to the measured value is • and since TSYS = TA′ + TREC′ • So the measurement uncertainty due to noise processes, TN, is

  31. Equivalent-system noise power at the antenna terminals • Besides uncertainties due to noise processes, variations in the receiver gain will also introduce measurement uncertainty, TG. • Since Vd = CdG k B TSYS, variations in G will cause variations in the detected signal, Vd. • The uncertainty resulting from gain variations is • where GS is the average system power gain and GS is the RMS variation of the power gain. • The magnitude of GS can be reduced (though not to 0) by periodically calibrating the radiometer output voltage when inputting a known noise source.

  32. Equivalent-system noise power at the antenna terminals • The combination of these two uncertainty terms, TN and TG , produce an total uncertainty, T through a root-sum-square (RSS) process • or

  33. Equivalent-system noise power at the antenna terminals • Example Radiometer center frequency, f = 1.4 GHz Bandwidth, B = 100 MHz Receiver noise temperature, TREC′ = 600 K (F = 3 or 4.9 dB) Antenna temperature, TA′ = 300 K Low-pass filter bandwidth, BLPF = 50 Hz ( = 10 ms) System gain, GS = 50 dB ± 0.044 dB over 10 ms interval • Find T and determine which factor (noise or gain variation) dominates.

  34. Equivalent-system noise power at the antenna terminals • Example (cont.) • Find TN: TSYS = TREC′ + TA ′ = 600 + 300 = 900 K • TN = TSYS (B )- ½ = 900 (108 ·10-2)- ½ = 0.9 K • Find TG: GS = 50 dB or 100,000 • GS + GS = 50.044 dB or 101,018 • GS  GS = 49.956 dB or 98,992 • so |GS|  1013 • GS / GS = 1013/100,000 = 1% • TG = TSYS (GS / GS) = 9 K • T = [TN2 + TG2] ½ = [(0.9)2 + (9)2]½ = 9.05 K

  35. Equivalent-system noise power at the antenna terminals • Example (cont.) • T = 9.05 K and is dominated by TG (9K) • To reduce the affect of TG so that it is comparable to TNrequires that GS/GS = 0.001 or G = 100 so that GS = 100,000 ± 100 or GS = 50 dB ± 0.004 dB over a 10 ms interval • A study of GS properties shows the following: GS varies as 1/f for f  1 kHz, GS  0 worst for f < 1 Hz • Therefore we want  < 1 ms to make TG small.However to make TN small we want  > 1 ms.

  36. Dicke radiometer • The Dicke radiometer solves the dilemma concerning . Synchronous switching and detection permits fs > 1 kHz with  » 1 ms

  37. Dicke radiometer • The Dicke radiometer alternates between two configurations, one where it samples the TA′ and the other where it samples a reference load, TREF. • When the switch connects the antenna to the receiver • When the switch connects the reference load to the receiver • These are combined in the synchronous detector to form • The ½ term is due to the dwell time in each switch position • Notice that TREC′ cancels out

  38. Dicke radiometer • Vd SYN is integrated in the low-pass filter to yield VOUT • where GS is a constant representing the radiometer’s transfer characteristics. • The low-pass filter not only integrates the signal but also rejects the components at fs and its harmonics that are introduced by the square-wave modulation. • This requires that fs 2 BLPF. • Under these conditions VOUT  (TA′ – TREF) and is independent of TREC′.

  39. Dicke radiometer • To evaluate the Dicke radiometer’s sensitivity T begin with • Three components contribute to T Gain variations Noise uncertainty in TA′ Noise uncertainty in TREF • So that

  40. Dicke radiometer • Now it might appear that we’re no better off than we were with the total-power radiometer (and maybe worse off with 3 terms comprising T now) • However notice the difference in TG total power Dicke • In the Dicke radiometer this term (which dominated T in the total-power radiometer) is significantly smaller.

  41. Dicke radiometer • Example Bandwidth, B = 100 MHz Low-pass filter bandwidth, BLPF = 0.5 Hz ( = 1 s) Receiver noise temperature, TREC′ = 700 K (F = 3.4 or 5.3 dB) Reference temperature, TREF = 300 K System gain variations, GS/GS = 1% • When viewing a 0-K target (TA′ ~ 0 K) T (total-power) = 7.0 K [TG = 7.0 K, TN ANT = 0.07 K] T (Dicke) = 3.0 K [TG = 3.0 K, TN ANT = 0.1 K, TN REF = 0.14 K] • When viewing a 300-K target (TA′ ~ 300 K) T (total-power) = 10.0 K [TG = 10.0 K, TN ANT = 0.1 K] T (Dicke) = 0.2 K [TG = 0.0 K, TN ANT = 0.14 K, TN REF = 0.14 K] (Note that TREF – TA′ = 0, a balanced condition)

  42. Balanced Dicke radiometer • Operating in a balanced mode requires adjusting TREF. • Using a “cold” noise source and a variable attenuator (TP = 290 K) permits balanced mode operation for a wide range of targets.

  43. Radiometer calibration • As mentioned earlier calibration is needed for accurate measurements. • For ground-based systems warm calibration targets are abundant so the cold target calibration poses a challenge. • Shown here is a cryoloadthat is useful for periodiccalibration of modest-sized antennas. • When filled with liquidnitrogen this cold target hasa radiometric temperature ofaround 77 K.

  44. Radiometer calibration • Another approach that may accommodate modest-sized as well as medium sized antennas is the bucket method that uses the naturally cold sky as a cold target. • As seen previously, TSKY is dependent on the operating frequency and on the weather conditions. • For clear-sky conditions the zenithsky temperature will rangebetween about 5 and 120 K. • Using this calibration technique the antenna efficiency, l, can be estimated.

  45. Radiometer calibration • Calibration of spaceborne radiometer systems requires features that enable periodic calibration during flight.

  46. Scanning Multichannel Microwave Radiometer (SMMR) • Flew on two platforms SEASAT (28 June 1978 to 10 October 1978) NIMBUS-7 (26 October 1978 to 20 August 1987) • Intended to obtain ocean circulation parameters such as sea surface temperatures, low altitude winds, water vapor and cloud liquid water content on an all-weather basis. • Ten channels: five frequencies, dual polarized • Mechanically scanned antenna

  47. Scanning Multichannel Microwave Radiometer (SMMR)

  48. Scanning Multichannel Microwave Radiometer (SMMR) • Antenna system • Shared 79-cm diameter offset parabolic reflector used by all channels • Mechanical scanning, 42 off-nadir look angle, ±25 azimuth angle range, scan period 4.096 s • Provided constant 50.3 incidence angle across 780-km swath • Offset-fed parabolic reflector geometry

  49. Scanning Multichannel Microwave Radiometer (SMMR) • Antenna scan characteristics

  50. Radiometer antennas • Antennas pose a challenge in some radiometer applications. • Spatial resolution (x, y) is set by the antenna beamwidth. • Consider an antenna with L  20  or  = 3. • A spot diameter at nadir of 520 m results at aircraft altitudes (10 km). • At spacecraft altitudes (700 km) a spot diameter at nadir of 37 km is produced. • To achieve a finer resolution requires a smaller beamwidth, i.e., a larger antenna. • In addition, mechanical beamsteering limits the scan rate and reliability.

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