relating cascaded noise figures to real world performance

7/27/2019 Relating Cascaded Noise Figures to Real World Performance

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16 www.rfdesign.com J anuary 2003

A c o m m o n i s s ue t h a t o f t en a r i s e s i s , a f t e rt h e d e s i g n a n d b u i l d o f a r e ce i v er , i t i sde termined tha t t he sensi t iv i ty is worse than ofthe calcula ted model. A signif icant am ount oft ime can be spent determining the exact prob-le m a n d w h y t h e ca s ca d e d n o i s e f i g u r e e qu a -t ions did not a ccura tely represent the predictedsensit ivity.

Th e s o lu t ion u s u a l l y in v o lv e s i s s u in g n e w component requirements (lower LNA noise fig-ure or more ga in) and /or chan ging t he front -end

architecture (removing loss in the front-end).N o i s e f i g u r e i s a c r i t i c a l p a r a m e t e r w h e n

designing receivers . In crit ical s it uat ions a fra c-

t ion of a dB can make a huge dif ference in thel ink budge t and can p lay a b ig par t in winningor losing contracts . Many t imes decreasing thenoise f igure of a receiver ma y be m uch cheapert h a n in c r ea s in g t h e p ow e r o f t h e t r a n s mi t t e r .

Predict ing accurate noise f igure then becomesof paramount importance.

Receiver Sensitivity DefinedThe sensit ivity of a receiver is equivalent to

the thermal noise a t the input p lus the noisefigure and minimum acceptable s ignal-to-noiser a t i o (s e e f i g u r e 1 t h e v e r t i c a l a x i s i sdB m/Hz ). The r eceiver design er t ypically onlyh a s c on t r o l ov e r t h e n o i s e f i g u r e s i n c e t h ereceiver operat ing temperature determines thetherma l noise an d the type of modulat ion usual-ly de termines the minimum acceptab le s igna l-to-noise ratio.

The cascaded noise f igure is defined by the

following equa t ion:

Where the power gains and noise factors arethe l inear , and not the logar i thmic , quant i t ies .

Note that the cascaded noise f igure is solelybased on the individua l noise f igure and ga in ofeach sta ge. The cascaded noise f igure equa t ionswork well unt il the mixer enters the equat ion.Mixers equally convert the in-channel noise aswell as the image noise into the mixer output .I t i s o f t e n a s s u m e d t h a t t h e i m a g e n o is e i saccounted for in t he cascaded noise f igure equa -t ion it isn t .

The cascaded noise f igure equat ions assumethat noise contribution due to the image is zero.In many cases, in receiver design, this can be adangerous assumption tha t w ill only lead to a newdesign pa ss or failing sensitivity requirements.

When software design tools or spreadsheetsdo not account for image noise power a cross thec h a n n e l b a n d w i d t h , t h e n s i m u l a t i o n r e s u l t sonly show best-case noise f igure instead of theworst case scenario. Worst-case noise f igure ismuch more important than best-case noise f ig-ure s ince typical receiver requirements guaran-t e e s e n s i t i v i t y b e t t e r t h a n a s p ec i fi e d l ev e l .Worst-case noise f igure is necessary in deter-

min in g w or s t -ca s e s e n s it i v i t y . A s a m a t t e r o ffact , i f there is no image noise reject ion at a ll ,the tr ue cascaded noise f igure will be 3 dB high-e r t h a n in d ica t e d t h r ou g h t h e ca s ca d e d n o i s efigure equat ions. This would mean double thet r a n s m i t t e r o u t p u t p o w e r t o c om p e n s a t e f o rthis s imple oversight .

Image and Noise Rejection IssuesIma ge signal r eject ion a nd ima ge noise rejec-

t ion can mean two d i f fe rent th ings . For exam-

F FF

G

F

G G

F

G G Gcascade

n

n

= +

+

+ +

1

2

1

3

1 2 1 2

1 1 1

1.. .

.. .

Figure 1. Noise and receiver sensitivity

Relating Cascaded

Noise Figures to Real-world PerformanceWhen th e devi ces per formance

fai l s to meet speci fi cati on, i ti snt always the component s.

Someti mes i ts th e math

By Rulon VanDyke

time & frequency


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image f requency ( IMGF) , and imagec h a n n e l p o w e r ( I M G P ) a l o n g t h ei n p u t t o o u t p u t p a t h . Th e c h a n n e lb a n d w id t h u s e d fo r t h e s e me a s u r e -ments is 1 Hz, since continuous wave(CW) signa ls ar e used in this exa mple.

The true cascaded noise figure andt h e p r e d i ct e d n o i s e f i g u r e i s a l s o

shown on the level diagram in f igure4. Image noise can easily be detectedon a level diagram since the noise fig-ure will jump up at t he mixer output .

N e xt , i n t e g r a t i n g t h e s i m p l e 1s t

or d e r b a n d p a s s f i l t e r ( ima g e n o i s er e je c t ion f i l t e r ) a f t e r t h e L N A w i l lprovide about 20 dB of re ject ion a t

t h e i m a g e f r e q u e n c y o f 1 8 6 0 M H z(see f igure 5) . Af te r re-running thesimulat ion a noise f igure of 3.66 dB,w h i c h i s 0 . 0 4 d B h i g h e r t h a n t h ecascaded noise f igure equat ions pre-

d i c t , i s a c h i e v ed . Th i s i s b e ca u s et h e r e i s s t i l l a s m a l l a m o u n t o fi m a g e n o i s e c o n t r i b u t i o n a n d t h eVSWR effects of the f i l ters have alsobeen accounted for .

F i g u r e 6 s h ow s a t a b l e o f t h er e s u l t s of t h e l i n e u p w i t h i m a g en o i s e r e j e c t i o n f i l t e r e n a b l e d .Compa r in g CN P a n d I M G P me a s ur e -ments , the des igner can quickly seethe amount of image noise reject ionn e e d e d t o m i n i m i z e t h e i m p a c t o fi m a g e n o i s e . Th i s c a n b e s e en b ycompar ing the resul t s shown in f ig-ure 3 wit h t hose of f igure 6.

S i n c e t h e s o f t w a r e u s e d f o r t h i sp a r t i c u l a r s c e n a r i o i s a c h a n n e l -b a s e d t o o l t h a t i n t e g r a t e s p o w e rspectral density over a channel band-w i d t h , m e a s u r e m e n t s s h o w p o w e rw i t h i n a c h a n n e l a l o n g a u s er -defined path. The CNP measurementin tegra tes the absolute power o f a l lof the noise within the channel band-width at the channel frequency. TheI M G P m e a s u r e m e n t i n t e g r a t e s t h ea b s o lu t e p ow e r o f a l l o f t h e e n e r g ywith in the channe l bandwid th a t theimage frequency.

Obvious ly , the IMGF wi l l becomet h e C F a t t h e o u t p u t o f t h e m i xe r .Such image measurements he lp theRF designer determine the amount ofimage rejection needed in the designe l imina t ing t he guesswork and wa i t -an d-see sensit ivity approach.

ConclusionThe spect ra l domain eng ine used

in th is scena rio in gives RF designersthe a b i li t y t o v iew, a na lyze , and opt i-mize designs in a m an ner to opt imizet ime and resources. Modern softwarenow includes compensat ion for t radi-t ionally t roublesome an omalies tha toften don t show up until the receive

had been built and tested.With such tools , broadband noise ,

f or e x a m p l e , ca n a u t o m a t i c a l l y b efo lded in to the output o f the mixer .S u c h c a s c a d e d N F m e a s u r e m e n t swill automatically take into consider-at ion this folded noise (such as im agen o i s e). F u r t h e r m o r e , t h e c a s c a d e dnoise f igure measurement can easilyb e s w e p t o v er f r e q u e n c y a n d t h eresults displayed on a level diagram

Figure 6. Channel noise and image channel power with an image noise filter

Figure 7. The cascaded noise figure versus frequency

Figure 5. A typical receiver front-end with image noise rejection after the LNA


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or in a table (see figure 7) for a fre-quency channel sweep on a level dia-g r a m a n d f i g u r e 8 f o r a r e c e i v e rfront-end Monte Ca rlo ana lysis .

F u r t h e r m o r e , i m p e d a n c e m i s -

mat ches a re aut omat ica l ly accountedg iv in g t h e R F d e s ig n e r a comp le t epicture of the design before commit-t ing to layout . Design trade-offs andexact performance requirements canbe determined an d opt imized for eachs tage and d i f fe rent RF archi tecturescan be compared. This e liminat es theover s impli f ica t ion typica l ly crea tedi n o t h e r R F d e s i g n t o o l s , s p r e a d -s h e et s , a n d m a t h p a c k a g e s. Th ewa i t -and-see approach to rece iversensit ivity can be elimina ted.

Figure 8. A Monte Carlo analysis of the receiver


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RF Design www.rfdesign.com 25

About the authorRulon Van Dyke is the lead engineer in systems simulat ion a t Eagleware Corp.

(www.eagleware.com). He received both a B S degree an d MS degree in electricalengineering from Brigham Young University in 1990. For 10 years, he designedfirst-, second-, and third-generation digital cellular transceivers and base stations

for AT&T B ell La bs a nd Lu cent Technologies. In 2001, he joined Ea glew a re todevelop Spectra sys, wh ich is t he softw are used in t his a rticle. He ma y be reacheda t r u l o n @e a g l e w a r e. c om , or a t (678) 291-0995 voice or (678) 291-0971 fa x.

relating cascaded noise figures to real world performance

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