Sandra Cruz Pol 3/17/14 - Engineeringece.uprm.edu/~pol/pdf/Radiometer.pdf · 2014-03-17 · Sandra...

Sandra Cruz Pol 3/17/14

INEL 6069Title goes here 1

3/17/14 UPR, Mayagüez Campus

Radiometer Systems

INEL 6669 microware remote sensing S. X-Pol

3/17/14

Rx

Tx

Rx

Radar

(active sensor) Radiometer

(passive sensor)

Microwave Sensors


Radiometers

Ø Radiometers are very sensitive receivers that measure thermal electromagnetic emission (noise) from material media.

Ø The design of the radiometer allows measurement of signals smaller than the noise introduced by the radiometer (system’s noise).


Topics of Discussion

Ø Equivalent Noise Temperature v Noise Figure & Noise Temperature

q Cascaded System q Noise for Attenuator q Super-heterodyne Receiver

v System Noise Power at Antenna

Ø Radiometer Operation v Measurement Accuracy and Precision v Effects of Rx Gain Variations

3/17/14

Topics of Discussion… Ø Dicke Radiometer

v Balancing Techniques q Reference -Channel Control q Antenna-Channel Noise-Injection q Pulse Noise-Injection q Gain-Modulation

v Automatic-Gain Control (AGC) v Noise-Adding radiometer v Practical Considerations &Calibration

Techniques 3/17/14

Radiometer’s Task: Measure antenna temperature, TA’ which is proportional to TB, with sufficient radiometric resolution and accuracy

Ø TA’ varies with time. Ø An estimate of TA’ is

found from v Vout and v  the radiometer

resolution ΔT.

Rad

iom

eter

TA TA’

Vout

TB



3/17/14

Noise voltage

Ø The noise voltage is

Ø the average=0 and the rms is

kTBRkThf

hfBRehfBRV

JeansRayleighkThfn 4

/4

14/ =≅−

=

kTBRVV nrms 422 ==

3/17/14

Noisy resistor connected to a matched load is equivalent to… [ZL=(R+jX)*=R-jX]

kTBR

kTBRR

VVIVP rmsrmsnn ==⎟

⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛==4

422

Independent of f and R!,

3/17/14

Equivalent Output Noise Temperature for any noise source

BkTP Eno =

TE is defined for any noise source when connected to a matched load. The total noise at the output is

AT Ideal Bandpass Filter

B, G=1 ZL

BkTP AA'=

Receiver antenna

'AT

3/17/14

Noise Figure, F Ø Measures degradation of noise through the device

Ø  is defined for To=290K (62.3oF!, this = winter in Puerto Rico.)

noso

nisi

oo

ii

PPPP

NSNSF

//

//

==

oE TFT )1( −=

Total output signal Total output noise

Noise introduced by device

input signal

input thermal noise

3/17/14

Noise Figure, F

Ø Noise figure is usually expressed in dB

Ø Solving for output noise power

nonino

siso

PGPPGPP

Δ+=

=

BGkTP

BkTPBGkT

GPPPP

PPPPF

o

no

o

noo

niso

nosi

noso

nisi

Δ+=

Δ+===

1

1//

FFdB log10=

niono FGPBFGkTP == BGkTFP ono )1( −=Δ

3/17/14

Equivalent input noise TE

Ø Noise due to device is referred to the input of the device by definition:

Ø  So the effective input noise temp of the device is

Ø Where, to avoid confusion, the definition of noise has been standardized by choosing To=290K (room temperature)

BGkTBGkTFP Eiono =−=Δ )1(

oEoE TTFTFT /1or )1( +=−=

Examples: 1dB NF is

and 3dB NF is What is TE for F=2dB?

170K

75K

288K




Cascade System

( )( )BTTkGG

PPGG

BGTTTkGG

PGPGGPGGP

E

Ein

EE

EEnino

+=

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

++=

121

21

1

21121

2212121

1

21 GTTT E

EE +=

1

21

11GFF

TTFo

E −+=+=

3/17/14

Noise of a cascade system

12121

3

1

21 ...

1...11

−

−++

−+

−+=

N

N

GGGF

GGF

GFFF

12121

3

1

21 ...

...−

++++=N

ENEEEE GGG

TGGT

GTTT

3/17/14

Noise for an Attenuator

BkTBkTLPLP

PBkTL

P

BkTPPPGL

EpnoE

nopno

pno

o

i

=−=Δ=

Δ+=

=

>==

)1(

1

1/1

LTTLFTLT

where

op

pE

=−+=

−=

/)1(1

)1(

3/17/14

Antenna, TL and Rx

RECp LTTL +−= )1(1

21'GTTT E

EREC +=

dBLKTKTExample

prec 5.,290,50:

=== KTyields

REC 5.91'...=

Receiver

TE2

Transmission

Line, TE1

Superheterodyne Receivers Ø  Rx in which the RF amplifier is followed by a mixer that

multiplies the RF signal by a sine wave of frequency LO generated by a local oscillator (LO). The product of two sine waves contains the sum and difference frequency components

Ø  The difference frequency is called the intermediate frequency (IF). The advantages of superheterodyne receivers include v doing most of the amplification at lower frequencies (since IF<RF),

which is usually easier, and v precise control of the RF range covered via tuning only the local

oscillator so that back-end devices following the un-tuned IF amplifier, multichannel filter banks or digital spectrometers for example, can operate over fixed frequency ranges. 3/17/14

)t] cos[-)t]-cos[(t)t)sin(2sin( RFLORFLORFLO ωωωωωω +=

3/17/14

RF amp Grf ,Frf ,Trf

Superheterodyne receiver

...+++=MRF

IF

RF

MRFREC GG

TGTTT

Mixer GM,FM,TM

IF amp Gif ,Fif ,Tif

LO

Pni Pno

G=30dB F=2.3dB

G=23dB F=7.5dB

G=30dB F=3.2dB

Example: Trf=290(10.32-1)=638K Tm=1,340K Tif=203K TREC=? KTREC 34.639...

20010203

101340638 33 =+

⋅++=



3/17/14

Equivalent System noise power at antenna terminals

Ø Taking into consideration the losses at the antenna and T.L. with a physical temperature of Tp:

Receiver

Transmission

Line

Psys = P 'A+P 'REC = k T 'A+T 'REC( )B

Given TA = ξTA '+ (1−ξ )Tothen,P 'A = kTAB = k ξTA '+ (1−ξ )To[ ]BandP 'REC = kT 'REC B = k (1− L)To + LTREC[ ]B

3/17/14

Equivalent System noise power at antenna terminals

Ø Then the total noise for the system is:

Receiver

Transmission

Line

PSYS = P 'A+P 'REC = k TA +T 'REC( )B = kTsysBkTsysB = k ξTA

' + (1−ξ )Tp + (L −1)Ttl + LTREC"# $%B

orTsys = ξTA + (1−ξ )To + (L −1)Ttl + LTREC

For radiometer , Psys = Prec

For Radar, S/N= Pr/Psys

3/17/14

Summary

Ø Antenna

Ø Antenna + losses

Ø Receiver

Ø Receiver + T.L.

Ø All of the above BkTPPPPP

sysSYS

REC

REC

A

A

=

=

=

=

=

'

'

3/17/14

Measurement Accuracy and Precision

Ø Accuracy (“certeza”) – how well are the values of calibration noise temperature known in the calibration curve of output corresponding to TA

‘ . (absolute cal.)

Ø Precision (“precisión”)– smallest change in TA‘

that can be detected by the radiometer output.(sensitivity) ΔT


Total Power Radiometer

Super-heterodyne receiver: uses a mixer, L.O. and IF to down-convert RF signal. Usually BRF>BIF


Detection- power spectra @:

Psys = PA' +PREC

'

= kTsysBwhereTsys = TA

' +TREC'

PSYS =GkTsysB

vIF (t) = ve(t)cos[2π fIFt +φ(t)]VIF (t) = 0



3/17/14

Noise voltage after IF amplifier

Therefore the time average value of pIF (t) is

PIF =12Ve

2

IF

PIF (t) = v2IF (t) = ve

2 (t) 12+

12

cos[4π fIFt + 2φ(t)]!"#

$%&

PIF (t) = 12

ve2 (t) +

12ve

2 (t) cos[4π fIFt + 2φ(t)]

The average IF power is equal to the average of the square of vIF(t)

vIF (t) = ve(t)cos[2π fIFt +φ(t)]

The instantaneous IF voltage has a time-varying envelop ve(t) and phase angle φ(t):

VIF (t) = 0 with zero average

3/17/14

Noise voltage after detector, Vd

IF x2

square-law detector

Ve Vd

The output of the square-law detector is: vd (t) =Cdve

2 (t) Vd =CdVe2

where Cd is the detector constant, e.g. Cd = 7µV / µWbut for simplicity we have assigned it to be =1.

The average value of detector voltage is

Vd =Ve2 = 2PIF = 2GkTSYSB

The detector voltage is proportional to the square of the envelop voltage:

3/17/14

Noise voltage after Integrator

Ø  For averaging the radiometer uses an Integrator (low pass filter). It averages the signal over an interval of time τ with voltage gain gI.

Ø  Integration of a signal with bandwidth B during that time, reduces the variance by a factor N=Bτ, where B is the IF bandwidth.

The voltage at the output of the low-pass filter

vout (t) =gI

τvd (t ')dt '

t−τ

t

∫if Bτ >>1 vout ≈Vout = gIVd =GSTsys

x2

integrator

Low-pass τ, gI

Vout Vd Ve

Radiometric Resolution, ΔT

Ø  The output voltage of the integrator is related to the average input power, Psys

Vout = gI Vd

x2

integrator

Low-pass τ, gLF

=GSTSYS

TA =Vout

GS

−TREC'

Vout Vd Ve

whereGS = 2gIGkTSYSB

GS is the overall system gain factor.

Which can be solved forTA:

Noise averaging

Ø  By averaging a large number N of independent noise samples, an ideal radiometer can determine the average noise power and detect a faint source that increases the antenna temperature by a tiny fraction of the total noise power.

http://www.cv.nrao.edu/course/astr534/Radiometers.html http://www.millitech.com/pdfs/Radiometer.pdf

3/17/14

Radiomter resolution ΔT→ 0 as τ →∞

The IF voltage Ø Is a sum of noise signals with same frequency

Ø In phase-domain

Ø Since summing Ns random noise sources, Ve has probability density function pdf given by (see section 5.7 Ulaby & Long 2013)

Ø With an associated standard-deviation to mean ratio:

3/17/14

vIF (t) = Vi cos[2π fIFt +φi ]i=1

Ns

∑

VIF =Veejφ = Vie

φi

i=1

Ns

∑

p(Vd ) =1Vde−Vd /Vd

sdVd

=σ d

Vd=1 Before integration



The detection voltage Vd

has a DC component and an AC component.

•  The DC component is proportional to the Tsys •  The AC component are related to the fluctuations related

to the statistical uncertainties of measurement. sd =Vd

Before integration the uncertainty is so large that it’s equal to the signal we want to detect. So we need to filter the AC AC component which is equivalent to integrating (averaging) over time. 3/17/14

Integration

Ø Averaging over a B bandwidth and during τ time, reduces the variance by a factor N=Bτ

Ø Total rms uncertainty

sout2

Vout2 =

sd2

Vd2 =

1Bτ

Still have fluctuations after LPF but are smaller

soutVout

=1Bτ

3/17/14

Radiometric Sensitivity

Since and then

Ø The Noise-caused uncertainty

Ø It’s the minimum (statistically) detectable change in radiometric antenna temperature of the observed scene.

ΔTSYSTSYS

=1Bτ

ΔT = ΔTSYS =TSYSBτ

=TA +TREC

'

BτRadiometric Sensitivity (or resolution)

Vout =GSTSYSsoutVout

=1Bτ

3/17/14

Total-power radiometer

This doesn’t take into account variations in Gain

Ø It’s also known as

Where the bandwidth is called the predetection bandwidth and given a nonuniform transfer funcition is given by

ΔTIDEAL =TSYSBτ

Ideal total-power radiometer

B =H ( f )df

0

∞

∫#

$%

&

'(

2

H 2 ( f )df0

∞

∫

Receiver Gain variations ΔT is due to various causes… 1.  Noise-caused uncertainty

2.  Gain-fluctuations uncertainty

Ø Total rms uncertainty

ΔTN =TSYSBτ

ΔTG = TSYSΔGS

GS

( ) ( )22GN TTT Δ+Δ=Δ

Example Radiometer at f=30GHz With T’Rec=600K Observing TA=300K Using B=100MHz and τ =0.01sec With gain variations of Find the radiometric resolution, ΔT

01.=Δ

S

S

GG

Total-power radiometer resolution including gain variations ΔTN = 0.9K ΔTG = 9K ΔT = 9.05K

Also, Try with 10-5 gain variation and no RF amp (TREC’=3000K)

Gain Variations and the Dicke radiometer

Ø  As you can see gain variations in practical radiometers, fluctuations in atmospheric emission, and confusion by unresolved radio sources may significantly degrade the actual sensitivity compared with the sensitivity predicted by the ideal radiometer equation.

Ø One way to minimize the effects of fluctuations in both receiver gain and atmospheric emission is to make a differential measurement by comparing signals from two adjacent feeds. The method of switching rapidly between beams or loads is called Dicke switching after Robert Dicke, its inventor. [Using a double throw switch.]

3/17/14



Dicke radiometer

VdAnt = 2GkB TA +TREC '( ) for 0 ≤ t ≤ τ s / 2

VdRef = 2GkB TREF '+TREC '( ) for τ ss / 2 ≤ t ≤ τ s

The radiometer voltage is:

1fs= τ s << τ

Unity-gain amplifiers (-) & (+)

The switching rate is fs switching period τs is much shorter than integration time.: 3/17/14

Dicke Radiometer

• Dicke Switch

• Synchronous Demodulator

Noise-Free Pre-detection Section

Gain = G Bandwidth = B

Switching rate, fs= 1/τs

fs ≥ 2BLF

Nyquist sampling theorem

Dicke radiometer

This is independent of the receiver noise temperature!

vout (t) =gIτ

vdAnt (t)dt

t−τ

t−τ /2∫ − vd

Ref (t)dtt−τ /2

t∫#

$%&'(

The radiometer switches rapidly between reference and antenna using the Dicke switching

Vout =12gI Vd

Ant −VdRef( )

Vout =12gIGkB TA −TREF( ) = 1

2GS TA −TREF( )

3/17/14

Dicke Radiometer resolution

( ) ( )[ ]'''21

RECREFRECASout TTTTGV +−+=

( )REFAS

SG TT

GGT −

Δ=Δ '

The output voltage of the low pass filter in a Dicke radiometer looks at reference and antenna at equal periods of time with the minus sign for half the period it looks at the reference load (synchronous detector), so The receiver noise temperature cancels out and the total uncertainty in T due to gain variations is

Dicke radiometer resolution Ø The uncertainty in T due to noise when looking

at the antenna or reference (half the integration time)

Ø Unbalanced Dicke radiometer resolution

( ) ( ) ( )[ ]( ) ( ) ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ+

+++=

Δ+Δ+Δ=Δ

2222

222

''2''2

refAS

SRECrefRECA

refNantNG

TTGG

BTTTT

TTTT

τ

( )τBTT

T RECrefrefN

'2 +=Δ( ) ( )

ττ BTT

BTTT RECARECA

antN''2

2/'' +=

+=Δ

Example: B=100MHz, τ=1s, T’rec= 700K, ΔG/G=.01, Tref=300K for T’A=0K and 300K, for Total P radiometer and Dicke radiometer 3/17/14

Balanced Dicke

( ) ( ) ( )[ ]( ) ( ) ( )

( )ideal

RECASYS

refAS

SRECrefRECA

refNantNG

TBTT

BTT

TTGG

BTTTT

TTTT

Δ=+

==Δ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ+

+++=

Δ+Δ+Δ=Δ

2''22

''2''2

222

222

ττ

τ

A balanced Dicke radiometer is designed so that TA’= Tref at all times. In this case,



3/17/14

Balancing Techniques

Ø Reference Channel Control Ø Antenna Noise Injection Ø Pulse Noise Injection Ø Gain Modulation Ø Automatic Gain Control

3/17/14

Reference Channel Control

Tref =TNL+T atten

E

L

Tref =TNL+ 1− 1

L"

#$

%

&'To

Vout Synchronous Demodulator

Tref

Pre-detection

G, B, TREC’

Feedback and

Control circuit

Switch driver and Square-wave generator, fS

Integrator

τ

L

Variable Attenuator at ambient

temperature To

Vc

TN Noise Source

TA’

oref

Nref

refA

TTLTTL

TT

=∞=

=≈

=

if

1 if

'

Force T’A= T ref

*Measures vc

Vc

Tc

Vout =?

TEatten = (L −1)Tp

3/17/14

Reference Channel Control

TN and To have to cover the range of values that are expected to be measured, TA’

Ø  If 50k<TA’< 300K

Ø  Use To= 300K and need cryogenic cooling to achieve TN =50K. Ø  But L cannot be really unity, so need TN < 50K. To have this cold

reference load, one can use v  cryogenic cooled loads (liquid nitrogen submerged passive matched

load) v  active “cold” sources (COLDFET); backward terminated LNA can

provide active cold source.

oAN TTT ≤< '

3/17/14

Cryogenic-cooled Noise Source

Ø When a passive (doesn’t require power to work) noise source such as a matched load, is kept at a physical temperature Tp , it delivers an average noise power equal to kTpB

Ø Liquid N2 boiling point = 77.36°K

Ø Used on ground based radiometers, but not convenient for satellites and airborne systems.

3/17/14

Active “cold or hot” sources

Ø  http://www.maurymw.com/

Ø  http://sbir.gsfc.nasa.gov/SBIR/successes/ss/5-049text.html

3/17/14

Active noise source: FET

Ø The power delivered by a noise source is characterized using the ENR=excess noise ratio

where TN is the noise temperature of the source and To is its physical temperature.

ENRENRTT

kBTTTkB

PPPENR

dB

o

N

o

oN

o

on

log10

1)(

)( =

−=−

=−

=

Example for 9,460K: ENR= 15 dB



3/17/14

Antenna Noise Injection

⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

==

cA

c

NA

orefA

FT

FT

T

TTT

11''

"

"

Variable Attenuator


Tref

Coupler Pre-detection

G, B, Trec’

Feedback

and

Control circuit


Integrator

τ

L

Vc

TN

Noise Source

TA’ TA”

LT

LTT NoN +⎟

⎠

⎞⎜⎝

⎛ −=11'

T’N

Force T”A= T ref = T o

Fc = Coupling factor of the directional coupler

*Measures vc

3/17/14

Antenna Noise Injection

Ø Combining the equations and solving for L

from this equation, we see that To should be >TA’ Ø If the control voltage is scaled so that Vc=1/L,

then Vc will be proportional to the measured temperature,

( )( )'1 AoC

oN

TTFTTL−−

−=

( )( )'1

AooN

CC TT

TTFV −−

−=

'AT

3/17/14

Example: Antenna Noise Injection

( ) KBTTT

L KT

FKTK

RECo

N

c

A

02.2'250-1.93between vary tohas

ENR) (22dB 000,50100)(Coupler ldirectiona dB20

30050 '

≈+

=Δ

=

=

≤≤

τ

( )( )'1 from

AoC

oN

TTFTTL−−

−=

Find the necessary values of the Attenuator L, to measure this range of Temperatures and the resolution for this balanced Dicke radiometer given:

Choose To=310K

TREC = 700K,B =100MHz, τ = .01sec

3/17/14

Example: Antenna Noise Injection

Ø If 50K< TA’< 300K, need to choose To>300K, say To=310K

Ø If Fc=100(20dB) and Tn=50,000K

Ø Find L variation needed:

( )( )'1 AoC

oN

TTFTTL−−

−=

L =1.93 (2.9dB) for TA' = 50K

L = 50.2(17dB) for TA' = 300K

3/17/14

Antenna Noise Injection Resolution

Ø  For expected measured values between 50K and 300K, Tref is chosen to be To=310K, so

Ø Since the noise temperature seen by the input switch is always To , the resolution is

( )τBTTT RECo '2 +

=Δ

∞≠L

3/17/14

Pulse Noise Injection

TA" = Tref = To

TA" =

TN'

Fc+TA

' 1− 1Fc

"

#$

%

&'

⎟⎠

⎞⎜⎝

⎛ −+=L

TLT

T oN

N11'


Tref

Coupler Pre-detection

G, B, Trec’

Feedback

and

Control circuit


Integrator

τ

Pulse-

Attenuation

Diode sw

itch

f r

TN Noise Source

TA’ TA”

TN’

*Measures fr

⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

ono

on

Non L

TLTT 11'

fR = proportional to TA'

⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

offo

off

Noff L

TLT

T 11'



3/17/14


Ø Reference T is controlled by the frequency of a pulse

Ø The repetition frequency is given by

''' )1( OFFRpRpONN TffTT ττ −+=

c

NA

coA F

TTF

TT'

'" 11 +⎟⎟⎠

⎞⎜⎜⎝

⎛−==

( ) ( )( ) ( ) poON

Aoc

pOFFON

ACOFFoCR TT

TTFTT

TFTTFfττ −

−−=

−

−−−= '

'

''

'' ))(1(1

For Loff high, Toff = To, is proportional to T’A

⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

offo

off

Noff L

TLT

T 11'

τR τp T’on

T’off


⎪⎩

⎪⎨

⎧

≤≤

≤≤

=

for

0for

'

'

'

RpOFF

pON

N

tT

tTT

ττ

τ

τR τp Pulse repetition frequency = fR = 1/τR

Pulse width is constant = τp Square-wave modulator frequency fS< fR/2

Switch ON – minimum attenuation Switch Off – Maximum attenuation

off

N

offoOFF L

TL

TT +⎟⎟⎠

⎞⎜⎜⎝

⎛−=11'

Example:For Lon = 2, Loff = 100, τp = 40 µs, To = 300K and TN = 1000K, F=20dB

Diode switch

TN

TN’

T’on

T’off

We obtain Ton= 650K, Toff= 307K

fR ≅FC −1( ) To −TA'( )TON' −To( )τ p

( )τBTTT RECo '2 +

=Δ

3/17/14

Example; Pulse Noise-Injection

With:

τ p = 20µ secFc =10dBTo = 315KENR = 20dBLon =1.5dBLoff = 50dB60K ≤ TA ' ≤ 300K

Find frequency range needed

Answers :Fc =10TN = 31,815KTOFF = 315KTON = 22615KTA ' = 60K, fr = 5kHzTA ' = 300K, fr = 302Hz

fR =(Fc −1)(To −TA

' )TON' −To( )τ p

off

N

offoOFF L

TL

TT +⎟⎟⎠

⎞⎜⎜⎝

⎛−=11'

⎟⎟⎠

⎞⎜⎜⎝

⎛−+=

ono

on

Non L

TLTT 11'

ENR = TNTo−1

ENR(dB) =10 logENR

τ s >> τ Rfs << fRfs = switching freq., ex. 50HzfR = pulse repetition freq.

3/17/14

Gain-Modulation

Vout

Synchronous Demodulator Pre-detection

G, B, Trec’

Control circuit


Integrator

τ

v c

Tref

TA’

*Measures vc

Fixed attenuator

Lo

Variable attenuator

Lv

( ) ( )

( )( ) ocref

cA

vc

crefv

cAo

vout

LTTTT

Lv

TTL

TTL

Lv

11

: thatso voltagecontrol theScale

11:condition hemaintain t to vary 0, for

'Re

'

'Re

'

'Re

''Re

'

+

+==

+=+

=

Drawback: slow variations of receiver noise temperature, yields error in reading.

3/17/14

Automatic-Gain-Control AGC

Ø  Feedback is used to stabilize Receiver Gain Ø Use sample-AGC not continuous-AGC since this would

eliminate all variations including those from signal, TA’.

Ø Sample-AGC: Vout is monitored only during half-cycles of the Dicke switch period when it looks at the reference load.

Ø Hach in 1968 extended this to a two-reference-temperature AGC radiometer, which provides continuous calibration. This was used in RadScat on board of Skylab satellite in 1973.

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Automatic Gain-Control (AGC)

Vagc

Synchronous Demodulator

2fs

Pre-detection

G, B, Trec’

Feedback

amplifier


Integrator

τ

Gv

Reference Switch

2fs

T2 T1

gv

Synchronous Demodulator

fs fs

Hach radiometer: insensitive to variations from G, and Trec’.



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Dicke Switch

Ø Two types v Semiconductor diode switch, PIN v Ferrite circulator

Ø Switching rate, fS , v High enough so that GS remains constant over one

cycle. v To satisfy sampling theorem, fS >2BLF http://envisat.esa.int/instruments/mwr/descr/charact.html

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Dicke Input Switch

Important properties to consider

Ø Insertion loss Ø Isolation Ø Switching time Ø Temperature stability

http://www.erac.wegalink.com/members/DaleHughes/MyEracSite.htm

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Radiometer Receiver Calibration

Ø Most are linear systems

Ø Hach-radiometer is connected to two known loads, one cold (usually liquid N2), one hot.

Ø Solve for a and b. Ø Cold load on satellites

v use outer space ~2.7K

)(

)(

bTaibTai

coldcal

coldout

hotcal

hotout

+=

+=

rcAout fvbTai or or )( ' ==+=

hotoutv

coldoutv

hotcalT

coldcalT

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Imaging Considerations

Ø Scanning configurations v Electronic (beam steering)

q Phase-array (uses PIN diode or ferrite phase-shifters, are expensive, lossy)

q Frequency controlled

v Mechanical (antenna rotation or feed rotation) q Cross-track scanning q Conical scanning (push-broom) has less variation in

the angle of incidence than cross-track

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Uncertainty Principle for radiometers

Ø  For a given integration time, τ, there is a trade-off between v spectral resolution, B and v radiometric resolution, ΔT

Ø For a stationary radiometer, make τ larger. Ø For a moving radiometer, τ is limited since

it will also affect the spatial resolution. (next)

τBMT =Δ

M= figure of merit

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Airborne scanning radiometer



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Airborne scanning

Consider a platform at height h, moving at speed u, antenna scanning from angles θs and –θs , with beamwidth β, along-track resolution, Δx

Ø The time it takes to travel one beamwidth in forward direction is

Ø The angular scanning rate is

Ø The time it takes to scan through one beamwidth in the transverse direction is the dwell time

1

2tsθω =

Sd

tθβ

ωβ

τ21==

uxt Δ

=1

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Dwell time Ø Is defined as the time that a point on the

ground is observed by the antenna beamwidth. Using

Ø For better spatial resolution, small τ

Ø For better radiometric resolution, need large τ

Ø As a compromise, choose

( )hu

xt

ssd θθ

βωβ

τ22

21 Δ

===

hx β=Δ

τθsuhx 2=Δ

τBMT =Δ

dττ =

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Radiometer Uncertainty Eq.

Ø Equating, we obtain;

suhMBxT θ2=ΔΔ

Radiometric resolution

Spatial resolution

Spectral resolution

This equation applies for this specific scanning configuration.

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Problem: A 1GHz balanced Dicke radiometer with a 100 MHz bandwidth is to be flown on a satellite at an altitude of 600 km with average speed of 7.5 km/s. Ø The radiometer uses a 10-m diameter antenna, and the

receiver is characterized by T’rec=1000K and Tref=300K. Take antenna efficiency k=1.5 [β≅k λ/l]

Ø The radiometer integration time is chosen to be equal to 0.1 of the dwell time of the antenna beam for a point on the ground. If the antenna is fixed so that its main beam is always pointed in the nadir direction,

Ø What will ΔT be?

= 0.1678 K

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WindSat first images @ Ka

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Ø Ideal radiometer

Ø “Real” radiometer

Usually we want ΔT=1K, so we need B=100MHz and τ =10msec τ⋅

+=Δ

BTTT NA

B, G

radiometer TA Pn=k B G TA

B, G

radiometer

TA =200K

Pn=k B G (TA + TN) TN =800K

Sandra Cruz Pol 3/17/14 - Engineeringece.uprm.edu/~pol/pdf/Radiometer.pdf · 2014-03-17 · Sandra...

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Transcript of Sandra Cruz Pol 3/17/14 - Engineeringece.uprm.edu/~pol/pdf/Radiometer.pdf · 2014-03-17 · Sandra...