signals, antenna and measurements

8/10/2019 signals, antenna and measurements

1/19

Spectral Measurements

Case A: Bandwidth exceeds that of

available amplifiers

TA(f)

S(f)

channels

f1

fNreceivers and antennas

detector noise, detect directly or

split frequencies and then detect

before amplification or detection

f1

fN

f1

fN

f

Receivers-G1

1) Extreme bandwidth: use multiple

2) If signal large compared to

3) Use passive frequency splitters


2/19

Spectral Measurements

Case B: Bandwidth permits amplificationf1

fN further frequency splitting

Case C: Bandwidth permits digital spectral analysis

(

fResolution

-~)f(V 2M

2N

)f()( NN

(Permits ~100 more B per cm2 silicon)(Reference: Van Vleck and Middleton, Proc. IEEE, 54, (1966)

)

G2

1) Amplify before either detection or

1) If computer resources permit, compute

N2B

:transformpointNpermultiplysNlogN

2) Or 1-bit (or n-bit) samples)(N

spectraMaverage


3/19

Examples of Passive Multichannel Filters

IN

f1 fnf2

Zo

2. Waveguides

f1 resonant

cavities at ff

virtual

short

/4

fN

RCVRRCVR

f1 f3f2

filters

passive

channel-dropping filters

Zo at f1

f

G3

1. Circuits


4/19

Examples of Passive Multichannel Filters

3. Prism

-bound electron(s)

red blue fo

f

prism

5. Cascaded Dichroics

plane wave

f2 >fn-1(f1>f2>fn)

4. Diffraction grating

(f)

G4


5/19

Digital spectral analysis example: autocorrelation

0 0 f

() (f)[W Hz-1]

analog signals

Possible analog implementation:

1) max lag = max = NT2) sample lag, T sec

3) finite integration time

>> max

)(v

BRF

0f

fRF

0f

fIF

delay line

LO

local oscillator

v(t)

)T(v

)(v

)NT(v

NT = max

BBRF

G5

:onbasedis

T2


6/19

Resolution of autocorrelation analysis

)(W)()( yv =1)

W(

)

0

M = NT-

M

0f

0f

B

v(f) W(f)

~1/2 M Hz

Thus

v(f)

)f(W)f()f( vv

M

=

7777 W(f)

f0

G6

m


7/19

Aliasing in autocorrelation spectrometers

)f(I)f(

)t(i)(

)f(

)(

v

v

v

v

=

=

7777

2)

i(t)

T0t

I(f)

0f(Hz)

-1/T

Aliasing is spectral overlap

-1/T 0 1/T 2/T

B)f(

v

3) Finite averaging time adds noise to )f(,)( vv

G7

1/T 2/T


8/19

Autocorrelation of hard-clipped signals

A/D

( )2

counte

r

delay line

LO

x(t)

vo(t)1

v(t)

)(v

hard clipping

A/D

1

+1

-1

0t

+1 if v(t) > 0

Receivers-I1


9/19

Analysis of 1-bit autocorrelation

( ) ( ) 0-

0xt 212211


10/19

Power spectrum for 1-bit signal

Change

variables

x2

x1

dr

rdr

x1 = r cos x2 = r sin dx

1dx

2= rdr d

( )

=

2

0 0

1

12r

2

2

x 1e

12

12rdd4)( 2

2

(

)( )

= 2

0

21

12

1d4

I3

2sin

21

21

2sin


11/19

Power spectrum for 1-bit signal

(

)( )

=2

0

2

112

1d4

( )

(

)

1sin22

141dsin11

414 1

0x

+

=

=

( )

( )

=

xv 2sin

( ) ( )( )Tx

)Where =

0 b0

p(b)p(a)

b

(see Burns & Yao, Radio Sci., 4(5) p. 431 (1969))

2Let

I4

a

21

2sin

21

-v(tsgnv(t)sgn

exactnotbif

biashas:Note


12/19

Spectral response & sensitivity: autocorrelation receiver

;B

f1

f

T)f( effrms

channel bandwidth

(S. Weinreb empirical result,

MIT EE PhD thesis, 1963)

Apodizing weighting functions:

f

1.099

0.87

0.69

N

s

Nfs

Ns

first

sidelobe

-7 dB

-16 dB

-29 dB

Note trade between spectral resolution, sidelobes in (f) and Trms

=

=

N;NT1f

Ms

uniform

raised cosine

blackman

0

0

0

I5

6.1

f60.0

f13.1

taps#


13/19

Spectral response & sensitivity: autocorrelation receiver

If N delay-line taps, how many spectral samples Ns?

1W()

0 M

Say uniform weighting of ():

Then B = Ns f = Ns /2M) where spectral resolution f 1/2mfor orthogonal channels from boxcar W()

(

)

(

)B2N Ms ====

W(f) for adjacent channel

M

f

In practice: raised cosine widens f by 1/0.6 1.7, so Ns N/1.7

W(f)

I6

(1

taps#Nratenyquistat2B1TBNT2

21


14/19

Types of power

Delivered

AvailableExchangeable

( )

{

}

{ }j tev t R t sin t

=

+

Vg

gZ

LZRg g

+

-

+

-

V

{

}( )

=

gZP

PVIR21P

LDavailable

Dedelivered

Receivers-K1

Receivers Gain and Noise Figure

Ve Re V cos Im V

+ j X

Zifi.e.,,Pmax


15/19

Delivered and Available Power

{

}( )

=

gZP

PVIR21P

LDavailable

Dedelivered

RL

ge ZR-

ge ZR

PD

0Zf ge

Zifi.e.,,Pmax

R:I

optionpowerleexchangeab

ZIm

R:I


16/19

Definition of Gain

gZ LZG1 2

Gpower (= Gp)

12 DDPP

Gavailable

(= GA

) 12 AA

PP

Gtransducer (GT)power

12 AD

PPGexchangeable (=GE)

1

2

E

E

P

P

Ginsertion (= GI)

1

2

D

D

P

Pwithamplifier

without

amplifier

Note: GA, GEdont depend on ZLdo depend on Zg (via PE2)

K3


17/19

Definition: Signal-to-Noise Ratio (SNR)

First define:

N1 =

N2

=

S1 =

S2 =

1zWH

222111 NSSNR;NS

Vg

1 2

gZ

LZ

F

G

gE =

K4

exchangeable noise power spectrum @ Port 1

same, at 2

exchangeable signal power spectrum @ Port 1

same, at 2

SNRDefine

ZfGRecall


18/19

Definition: Noise Figure F

kTNNS

NS

SNR

SNRF oo1

22

11

2

1

[Ref. Proc. IRE, 57(7), p.52 (7/1957); Proc. IEEE, p.436 (3/1963)]

S2 = GES1 (see definition of GE)

N2 = GEN1 + N2T transducer noise

( )N

1NGNGS

NSF

111

11 +=+

= ( )EG

o

R

o

R

1 T

TN1F ==

K5

K290T,where,

GNT2

T2Glet

T2

GkT

GkT

GNexcess noise figure

receiver noise temperature


19/19

Receiver Noise Example

(6FT

F(2FT

)F(1TT1FT

R

R

o

RR

==

===

==+==

Examples:

Excess noise corresponds toreceiver noise temperature TR

+ 1

TR = (F 1) To

290K

noiseless

G, FTA

+1

TA

N2T

TA

TR

K6dB)5.7~FK1500

dB)3K290

dB0K0

F,G

F,G

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