04/21/23 UPR, Mayagüez Campus

Radiometer Systems

INEL 6669 microware remote sensing

S. X-Pol

04/21/23

RxTx Rx

Radar

(active sensor)Radiometer

(passive sensor)

Microwave Sensors

04/21/23 UPR, Mayagüez Campus

Radiometers

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

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

04/21/23 UPR, Mayagüez Campus

Topics of Discussion

Equivalent Noise TemperatureNoise Figure & Noise Temperature

Cascaded SystemNoise for AttenuatorSuper-heterodyne Receiver

System Noise Power at AntennaRadiometer OperationMeasurement Accuracy and PrecisionEffects of Rx Gain Variations

04/21/23

Topics of Discussion…

Dicke RadiometerBalancing Techniques

Reference -Channel ControlAntenna-Channel Noise-InjectionPulse Noise-InjectionGain-Modulation

Automatic-Gain Control (AGC) Noise-Adding radiometerPractical Considerations &Calibration

Techniques

04/21/23

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

TA’ varies with time.

An estimate of TA’ is found from Vout and the radiometer

resolution T.

Rad

iom

eter

TA

TA’

Vout

TB

04/21/23

Noise voltage

The noise voltage is

the average=0 and the rms is

kTBRkThf

hfBR

e

hfBRV

JeansRayleighkThfn 4

/

4

1

4/

kTBRVV nrms 422

04/21/23

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

kTBR

kTBR

R

VVIVP rmsrms

nn

4

4

22

Independent of f and R!,

04/21/23

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

ATIdeal Bandpass Filter

B, G=1

ZL

BkTP AA'

Receiverantenna

'AT

04/21/23

Noise Figure, FMeasures degradation of noise through the device

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

noso

nisi

oo

ii

PP

PP

NS

NSF

/

/

/

/

oE TFT )1(

Total output signal

Total output noise

Noise introduced by device

input signal

input thermal noise

04/21/23

Noise Figure, F

Noise figure is usually expressed in dB

Solving for output noise power

nonino

siso

PGPP

GPP

BGkT

P

BkT

PBGkT

GPP

PP

PP

PPF

o

no

o

noo

niso

nosi

noso

nisi

1

1

/

/

FFdB log10

niono FGPBFGkTP BGkTFP ono )1(

04/21/23

Equivalent input noise TE

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

So the effective input noise temp of the device is

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

BGkTBGkTFP Eiono )1(

oEoE TTFTFT /1or )1(

Examples: 1dB NF is

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

170K

75K

288K

04/21/23 UPR, Mayagüez Campus

Cascade System

BTTkGG

PPGG

BG

TTTkGG

PGPGGPGGP

E

Ein

EE

EEnino

121

21

1

21121

2212121

1

21 G

TTT E

EE

1

21

11

G

FF

T

TF

o

E

04/21/23

Noise of a cascade system

12121

3

1

21 ...

1...

11

N

N

GGG

F

GG

F

G

FFF

12121

3

1

21 ...

...

N

ENEEEE GGG

T

GG

T

G

TTT

04/21/23

Noise for an Attenuator

BkTBkTLPLP

PBkTL

P

BkTP

P

PGL

EpnoE

nopno

pno

o

i

)1(

1

1/1

LTTLF

TLT

where

op

pE

/)1(1

)1(

04/21/23

Antenna, TL and Rx

RECp LTTL )1(1

21'

G

TTT E

EREC

dBLKTKT

Example

prec 5.,290,50

:

KT

yields

REC 5.91'

...

ReceiverReceiver

TTE2E2

Transmission

Line, TE1

Superheterodyne Receivers 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

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

IF<RF), which is usually easier, and 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.

04/21/23

)t] cos[-)t]-cos[(t)t)sin(2sin( RFLORFLORFLO

04/21/23

RF amp G rf ,F rf ,T rf

Superheterodyne receiver

...MRF

IF

RF

MRFREC GG

T

G

TTT

MixerGM,FM,TM

IF amp G if ,F if ,T if

LO

Pni Pno

G=30dBF=2.3dB

G=23dBF=7.5dB

G=30dBF=3.2dB

Example:Trf=290(10.32-1)=638KTm=1,340KTif=203KTREC=?

KTREC 34.639...20010

203

10

1340638

33

04/21/23

Equivalent System noise power at antenna terminals

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

ReceiverReceiver Transmission

Line

04/21/23

Equivalent System noise power at antenna terminals

Then the total noise for the system is:

ReceiverReceiver Transmission

Line

For radiometer , Psys = Prec

For Radar, S/N= Pr/Psys

04/21/23

Summary

Antenna

Antenna + losses

Receiver

Receiver + T.L.

All of the aboveBkTP

P

P

P

P

sysSYS

REC

REC

A

A

'

'

04/21/23

Measurement Accuracy and Precision

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

‘ . (absolute cal.)

Precision (“precisión”)– smallest change in TA

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

04/21/23 UPR, Mayagüez Campus

Total Power Radiometer

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

04/21/23 UPR, Mayagüez Campus

Detection- power spectra @:

04/21/23

Noise voltage after IF amplifier

IF

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

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

with zero average

04/21/23

Noise voltage after detector, Vd

IFx2

square-lawdetector

Ve Vd

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

04/21/23

Noise voltage after Integrator

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

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

x2

integrator

Low-pass , gI

VoutVdVe

Radiometric Resolution, T

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

x2

integrator

Low-pass , gLF

VoutVdVe

GS is the overall system gain factor.

Which can be solved forTA:

Noise averaging

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

04/21/23

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

In phase-domain

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

With an associated standard-deviation

to mean ratio:

04/21/23

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.

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.

04/21/23

Integration

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

Total rms uncertainty

Still have fluctuations after LPF but are smaller

04/21/23

Radiometric Sensitivity

Since and then

The Noise-caused uncertainty

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

Radiometric Sensitivity (or resolution)

04/21/23

Total-power radiometer

This doesn’t take into account variations in Gain

It’s also known as

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

Ideal total-power radiometer

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

2.Gain-fluctuations uncertainty

Total rms uncertainty 22GN TTT

Example Radiometer at f=30GHzWith T’Rec=600KObserving TA=300KUsing B=100MHz and =0.01secWith gain variations of

Find the radiometric resolution, T

01.

S

S

G

G

Total-power radiometer resolution including gain variations

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

Gain Variations and the Dicke radiometer 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.

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.]

04/21/23

Dicke radiometer

The radiometer voltage is: Unity-gain amplifiers(-) & (+)

The switching rate is fs switching period s is muchshorter than integration time.:

04/21/23

Dicke Radiometer

•Dicke Switch

•Synchronous Demodulator

Noise-Free

Pre-detection Section

Gain = G

Bandwidth = B

Switching rate, fs= 1/s

Nyquist sampling theorem

Dicke radiometer

This is independent of the receiver noise temperature, TREC’!

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

04/21/23

Dicke Radiometer resolution

'''2

1RECREFRECASout TTTTGV

REFAS

SG TT

G

GT

'

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

The uncertainty in T due to noise when looking at the antenna or reference (half the integration time)

Unbalanced Dicke radiometer resolution

2

222

222

''2''2

refAS

SRECrefRECA

refNantNG

TTG

G

B

TTTT

TTTT

B

TTT RECref

refN

'2

B

TT

B

TTT RECARECA

antN

''2

2/

''

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

04/21/23

Balanced Dicke

ideal

RECASYS

refAS

SRECrefRECA

refNantNG

TB

TT

B

TT

TTG

G

B

TTTT

TTTT

2''22

''2''2

222

222

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

04/21/23

Balancing Techniques

Reference Channel ControlAntenna Noise InjectionPulse Noise InjectionGain ModulationAutomatic Gain Control

04/21/23

Reference Channel Control

VoutSynchronousDemodulator

Tref

Pre-detection

G, B, TREC’

Feedback

and

Control circuit

Switch driver andSquare-wave generator, fS

Integrator

LVariableAttenuatorat ambient

temperature

To

Vc

TN

Noise Source

TA’

oref

Nref

refA

TTL

TTL

TT

if

1 if

'

Force T’A= T ref

*Measures vc

Vc

Tc

Vout =?

04/21/23

Reference Channel Control

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

If 50k<TA’< 300K

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

cryogenic cooled loads (liquid nitrogen submerged passive matched load)

active “cold” sources (COLDFET); backward terminated LNA can provide active cold source.

oAN TTT '

04/21/23

Cryogenic-cooled Noise Source

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

Liquid N2 boiling point = 77.36°K

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

04/21/23

Active “cold or hot” sources

http://www.maurymw.com/

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

04/21/23

Active noise source: FET

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.

ENRENR

T

T

kBT

TTkB

P

PPENR

dB

o

N

o

oN

o

on

log10

1)(

)(

Example for 9,460K: ENR= 15 dB

04/21/23

Antenna Noise Injection

cA

c

NA

orefA

FT

F

TT

TTT

11'

'"

"

VariableAttenuator

VoutSynchronousDemodulator

Tref

Coupler Pre-detection

G, B, Trec’

Feedback

and

Control circuit

Switch driver andSquare-wave generator, fS

Integrator

L Vc

TN

Noise Source

TA’TA”

L

T

LTT N

oN

11'

T’N

Force T”A= T ref = T o

Fc = Coupling factor of the directional coupler

*Measures vc

04/21/23

Antenna Noise Injection

Combining the equations and solving for L

from this equation, we see that To should be >TA’

If the control voltage is scaled so that Vc=1/L, then Vc will be proportional to the measured temperature,

'1 AoC

oN

TTF

TTL

'1Ao

oN

CC TT

TT

FV

'

AT

04/21/23

Example: Antenna Noise Injection

K

B

TTT

L

KT

F

KTK

RECo

N

c

A

02.2'2

50-1.93between vary tohas

ENR) (22dB 000,50

100)(Coupler ldirectiona dB20

30050 '

'1 from

AoC

oN

TTF

TTL

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

04/21/23

Example: Antenna Noise Injection

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

If Fc=100(20dB) and Tn=50,000K

Find L variation needed:

'1 AoC

oN

TTF

TTL

04/21/23

Antenna Noise InjectionResolution

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

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

B

TTT RECo '2

L

04/21/23

Pulse Noise Injection

LT

L

TT o

NN

11'

VoutSynchronousDemodulator

Tref

Coupler Pre-detection

G, B, Trec’

Feedback

and

Control circuit

Switch driver andSquare-wave generator, fS

Integrator

Pu

lse-

Atte

nu

atio

n

Dio

de

sw

itch

f r

TNNoise Source

TA’TA”

TN’

*Measures fr

ono

on

Non L

TL

TT

11'

offo

off

Noff L

TL

TT

11'

04/21/23

Pulse Noise Injection

Reference T is controlled by the frequency of a pulse

The repetition frequency is given by

''' )1( OFFRpRpONN TffTT

c

NA

coA F

TT

FTT

''" 1

1

poON

Aoc

pOFFON

ACOFFoCR TT

TTF

TT

TFTTFf

'

'

''

'' ))(1(1

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

offo

off

Noff L

TL

TT

11'

R

pT’on

T’off

Pulse Noise Injection

for

0for

'

'

'

RpOFF

pON

N

tT

tT

T

R

p Pulse repetition frequency = fR = 1/R

Pulse width is constant = p

Square-wave modulator frequency fS< fR/2

Switch ON – minimum attenuation

Switch Off – Maximum attenuation

off

N

offoOFF L

T

LTT

11'

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

Diode switch

TN

TN’

T’on

T’off

We obtain Ton= 650K, Toff= 307K

B

TTT RECo '2

04/21/23

Example; Pulse Noise-Injection

With:

off

N

offoOFF L

T

LTT

11'

ono

on

Non L

TL

TT

11'

Summary

04/21/23

Summary

04/21/23

Cont… Source: “Microwave Radiometer Resolution Optimization Using Variable Observation Times, “ by Adriano Camps and Jose Miguel Tarongí

04/21/23

04/21/23

Gain-Modulation

Vout

SynchronousDemodulator

Pre-detection

G, B, Trec’

Control circuit

Switch driver andSquare-wave generator, fS

Integrator

v c

Tref

TA’

*Measures vc

Fixed attenuator

Lo

Variable attenuator

Lv

ocref

cA

vc

crefv

cAo

vout

LTT

TT

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.

04/21/23

Automatic-Gain-Control AGC

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

eliminate all variations including those from signal, TA’.

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

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.

04/21/23

Automatic Gain-Control (AGC)

Vagc

SynchronousDemodulator

2fs

Pre-detection

G, B, Trec’

Feedback

amplifier

Switch driver andSquare-wave generator, fS

Integrator

Gv

Reference

Switch

2fs

T2T1

gv

SynchronousDemodulator

fs

fs

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

04/21/23

Dicke Switch

Two types Semiconductor diode switch, PINFerrite circulator

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

one cycle.To satisfy sampling theorem, fS >2BLF

http://envisat.esa.int/instruments/mwr/descr/charact.html

04/21/23

Dicke Input Switch

Important properties to consider

Insertion loss IsolationSwitching timeTemperature stability

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

Radiometer Receiver Calibration

Most are linear systems

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

Solve for a and b.Cold load on satellites

use outer space ~2.7Khttp://ipnpr.jpl.nasa.gov/progress_report/42-154/154G.pdf

)(

)(

bTai

bTaicold

calcoldout

hotcal

hotout

rcAout fvbTai or or )( '

hotoutv

coldoutv

hotcalTcold

calT

04/21/23

Imaging Considerations

Scanning configurationsElectronic (beam steering)Phase-array (uses PIN diode or ferrite phase-

shifters, are expensive, lossy) Frequency controlled

Mechanical (antenna rotation or feed rotation)Cross-track scanningConical scanning (push-broom) has less

variation in the angle of incidence than cross-track

04/21/23

Uncertainty Principle for radiometers

For a given integration time, , there is a trade-off between spectral resolution, B andradiometric resolution, T

For a stationary radiometer, make larger.

For a moving radiometer, is limited since it will also affect the spatial resolution. (next)

B

MT

M= figure of merit

04/21/23

Airborne scanning radiometer

04/21/23

Airborne scanning

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

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

The angular scanning rate is

The time it stays while scanning through one (1) beamwidth in the transverse direction is the dwell time

1

2

ts

Sd

t

21

u

xt

1

04/21/23

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

ground is observed by the antenna beamwidth. Using

For better spatial resolution, small

For better radiometric resolution, need large

As a compromise, choose

hu

xt

ssd

22

21

hx

suhx 2

B

MT

d

04/21/23

Radiometer Uncertainty Eq.

Equating, we obtain;

suhMBxT 2

Radiometric resolution

Spatial resolution

Spectralresolution

This equation applies for this specific scanning configuration.

04/21/23

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. The radiometer uses a 10-m diameter antenna, and the receiver is characterized by Trec’=1000K and Tref=300K. Take antenna efficiency k=1.5 [k /l]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,What will T be? = 0.1678 K

04/21/23

WindSat first images @ Ka