[RFD0009] Improving the Vector Network Analyzer s Dynamic Range

8/13/2019 [RFD0009] Improving the Vector Network Analyzer s Dynamic Range

1/4

82 www.rfdesign.com September 2000

t est & m easu r em en t

Avector network a nalyzer s a bili ty toi d e n t i f y t h e c h a r a c t e r i s t i c s o f acomponent makes i t a rguably, as theN a t i o n a l I n s t i t u t e o f S c i e n c e a n d

Technology (NIST) puts i t , the mosti m p o r t a n t t o o l o f t h e R F a n dmicrowa ve engineer.

The capabili t ies of the vector net-work analyzer (VNA) itself define how accurate its device characterization willbe. One of the most important of thesecapabili t ies is dynamic range, i .e. theinstruments measurement sensit ivity.Dyn am ic ra nge is often the key determi-n a n t o f m e a s u r e m en t p er f or m a n c e.Fortunately, i t is possible to optimizet h e d y n a m i c r a n g e o f a n y V N A t oachieve the best results, and with theleast impact on other instrument para -me te r s such a s measurement speed .This requires an understanding of dy-namic range and its impact on overallinstrum ent performan ce.

D y n a m i c r a n g e i s es s en t i a l l y t h erange of power levels over which theinst rument can make measurements.The highest measurable power levelbe fore un accep tab l e l eve l s o f e r ro r soccur is called P MAX . This specification isusually determined by the network ana -lyzer receivers compression specifica-t ion. The nominal power avai lable a tthe test port from the network analyz-ers source is called P ref . The minimumpower level the syst em can measure (itssensitivity) is called P mi n and is set bythe receivers noise floor. The value ofP mi n depends on IF bandwidth, averag-ing, an d test-set configurat ion.

Th e r e a r e a l s o t w o c a t e g o r i e s ofdynamic range; receiver dynamic range(P ma xP mi n ) and system dynamic range(P ref P min ), as show n in Figur e 1. Syst emdynamic range is the span that can berealized without amplification, such aswhen measuring passive componentsl ike a t tenuators and f i l te rs . Receiver

dynamic range is the measurement sys-tems true dynamic range, if i t is con-sidered to be a receiver. An amplifiermay be required to realize the receiv-er s full dynamic range, and it can t akethe form of a device under test or anexternal amplifier.

Noise floor: coming into focusTh e t e r m n o i s e f l oo r h a s b e en

bandied about the engineering commu-nity for years. This has resulted in thiskey ingredient in determining dyna micrange having several definit ions. Thedifferences in these definitions are sig-ni f icant enough tha t i t i s desi rable tostandardize on one. Figure 2 shows there su l t s o f an expe r iment compar ingsome common noise floor definit ions.Gauss i an random no i se wi th a no i sepower of 100 dB m w as simulated, andthe no i se f l oor was ca l cu l a t ed us ingfour definitions.

The solid line shows the RMS valueof the noise, wh ich is equal t o the noisepower of 100 dBm. The dashed line(101 dBm) is the mean value of the lin-ear m agn itude of the noise, converted todBm. The dotted line (102.4 dBm) isthe mean value of the log magnitude ofthe no i se . F ina l ly, t he do t -dash l i ne(92.8 dBm) is the sum of the mean

va lue o f t he l i nea r magn i tude o f t henoise and three times its standard devi-at ion, converted to dBm.

A step beyondSometimes it is necessary to increase

the VNAs dynamic range beyond whati s a c h i e v a b l e w i t h t h e i n s t r u m e n t sd e f a u l t s e t t i n g s . N o i s e f l o o r a n ddynamic range can be improved signifi-cantly through averaging, or by reduc-i n g s y s t e m b a n d w i d t h ( I F B W ) .Smoothing is another technique oftenconsidered to be akin to averaging andI F B W a d j u s t m e n t , b u t i t d o e s n otreduce the noise f loor. Smoothing isadjacent-point averaging of the format-t e d d a t a , s i m i l a r t o v i d e o f i l t e r i n g .Trace - to - t r ace (o r sweep- to - sweep)averaging operates on the pre-format-ted vector data, so that i t can actuallyreduce the noise power. This key differ-ence is responsible for the inability ofs m o o t h i n g t o r e d u c e n o i s e f l o o r ,although it does reduce small peak-to-peak var iat ions of noise on a tra ce.

The advantage of averagingNetwork analyzers perform sweep-

to-sweep averaging by taking an expo-nentially weighted average of the datapoints from each sweep. Exponentiallyweighting the samples in the data seta l l ows ave rag ing to p roceed wi thou tt e r m i n a t i o n , e v e n a f t e r t h e d e s i r e daveraging factor has been reached. Thea v e r a g i n g i s p e r f o r m e d o n c om p l e xd a t a , w h i c h m e a n s t h a t t h e d a t a a r eaveraged vectorially.

M a n y s i g n a l a n a l y z e r s u s e s c a l a ra v e r a g i n g , w h i c h m i t i g a t e s o n l y t h evariance of the noise. It does not a ffectthe a verage noise level . When a t ra ce

Improving the vector networkanalyzers dynamic rangeA t ech n i qu e for ch oosi n g th e best com bi n at i on of m easur em en t speed an d systemsensi ti vi ty for speci fi c devi ce char acter i zati on si tu at i ons.

By Bar ry Br ownan d

J i n B a i n s

Figure 1. Dynamic range definitions.

Figure 2. Random noise simulation.


2/4


t h a t c o n t a i n s b o t h c o h e r e n t s i g n a lan d uncorrela t ed noise i s avera ged inth e vector sense, the n oise componentwi l l approach zero, and the resul t ingt r a c e w i l l s h o w t h e d e s i r e d s i g n a lwith less noise present. When viewedwith the log magni tude format on thenetwork analyzer display, i t becomesc l ea r t ha t t he ave rage no i se l eve l i sr e d u c e d a n d a n i m p r o v e m e n t i ndyna mic range is a chieved.

Using the averaging funct ion avai l -able in most vector network analyzers,signa l-to-noise ra tio is improved by 3 dBfor every factor-of-2 increase in aver-ages . Th i s i s a power fu l me thod fo rreducing noise floor. However, i t alsoreduces measurement speed becausew h e n t w o t r a c e s m u s t b e a v e r a g e d ,measurement time doubles.

Av e r a g i n g c a n o n l y b e u s e d o nratioed measurements. It will not workon measurements using a single receiv-er chann el. Averaging is not a llowed onunratioed measurements because phaseis random in this mode and averaging(which i s pe r fo rmed in t he complexdomain), will always cause the result toapproach zero.

Reducing IF bandwidthTh e I F B W o f t h e s y s t e m c a n b e

al tered via the f ront panel or remoteprogramming, and its value will affectthe digi ta l f i l te r ing tha t i s performedon the data collected in the analyzer sr e c e i v e r s . D e c r e a s i n g I F B W w i l lreduce noise floor by filtering out noisetha t i s ou t s ide t he bandwid th o f t hedigital fi l ter.

The low-level noise that is present inthe analyzers receiver chain is causedby thermal noise rising from the ther-ma l agita tion of electrons in resista nces.Consequently, it is directly proportionalto bandwidth. The mean-square valueof the therma l noise volta ge is given by:

where:

k is B oltzma nns consta nt (1.38 e -23

joules/Kel vin )T i s t h e a b s o l u t e t e m p e r a t u r e i ndegrees KelvinR is the resistive component in ohmsB is the bandwidth in Hertz

The noise power delivered to a com-plex conjugat e loa d is:

This is the familiar kTB relation-ship for noise power 2.

Noise is ran dom in nat ure and is con-sidered nondeterministic because i t iscaused by a collection of small eventsand exhibits a Ga ussian probability dis-tribution (which can be proved by thecentra l limit theorem 3).

A high level of confidence in the rela-tionship betw een noise floor a nd IF B Wmakes it possible to precisely calculatethe noise floor reduction achieved bydecreas ing t he IF BW. An empi r i ca ls tudy was pe r fo rmed us ing the PNAne twork ana lyze r i n which the RMSnoise level was measured a t f ive CWfrequenc i e s (1, 3 , 5 , 7 , and 9 G Hz) .

There were 801 points in the sw eep andthe IF BW was set to 1 Hz, 10 Hz, 100Hz, 1 kHz and 10 kHz. The noise floorof the VNA was measured with no sig-nal present at the test ports. In Figure3, the observed re la t ionship betweenthe noise f loor and the IF BW showsthat the PNAs RMS noise floor closelyf o l lo w s t h e t h e or e t i c a l e x p e ct a t i o n .Devia tion from th eory is n egligible.

As with averaging, decreasing IF BWto reduce noise floor reduces measure-ment speed. It could be expected that afac to r-o f -10 dec rea se i n IF BW wi l lreduce the noise floor by 10 dB a nd w illcause a factor-of-10 increase in mea-surement t ime, but this i s not a lwaystrue because the digital filters used in anetwork analyzer at different IF band-widths may vary in shape. In the othermodels, the PNA Series for example ,sweep time increases by a factor that isless than 10 for a factor-of-10 reductionin IF BW. This means that to achievethe same reduct ion in noise f loor, IF

B W reduction w ill reduce measur ementspeed less tha n avera ging will.

Choosing a methodTo ach ieve no i se f l oor r educ t ion ,

averaging can be increased or IF BWreduced. If measurement speed is not ofparamount concern, either method willwork equa lly well. The time required toacqu i re and p rocess da t a fo r a t r ace(called cycle t ime), includes not onlysweep time, but also retra ce time, band-crossing time, and display updat e time.

Because ave rag ing requ i re s t ak ingmul t iple t races and updat ing the dis-p l a y e v e r y t i m e , i t g e n er a l l y t a k e slonge r t o use ave rag ing than IF BWreduction, especially if many averagesare required. It is important to remem-ber that the digital filtering performed

for the various IF BWs causes much ofthe di fference in impact on measure-ment time. This effect manifests itselfi n t he sweep t ime componen t o f t hecycle time. So to determine the effect ofthe two noise-floor-reduction methodson measurement time, it is appropriateto consider sw eep tim e only.

Consider the PNA Series set up in a10 KHz IF BW. If an improvement of10 dB is desired in dynamic range, i tc a n b e a c h i e v e d b y a v e r a g i n g 1 0sweeps or sett ing the IF BW to 1 kHz.Ta ble 1 on page 88, show s the effecton sweep time for the two approachesto achieve a dynamic range improve-ment of 10 or 20 dB .

Thi s example use s a f a i r l y f a s t IFBW, and shows that IF BW reductionproduces a benefit over avera ging w henattempting to improve dynamic range.However, now consider a slower sweepmode (i.e., lower IF BW). If the PNA isset at an IF BW of 100 Hz and a noisefloor reduction of 10 dB is desired, aver-aging w ith a factor of 10 can be applied,or the IF BW can be reduced to 10 Hz.Ta ble 2 on page 88, shows th e impact onsweep time.

The increa se in cycle time closely par-allels the increase in sweep time. It isevident that using IF BW reduction toattain increased dynamic range has anadvantage over averaging (in terms ofimpact on measurement speed) if then e t w o r k a n a l y z e r i s i n a f a s t s w e e pmode. With a slow sweep mode, impacton measurement speed is essent ia l lythe sa me for either of the t wo methods.

There are other factors to considerw h e n d e c i d i n g w h i c h m e t h o d t ochoose for increasing dynamic rangein a given measurement appl ica t ion.

P E

R kT B n = =

2

4

E RkT B 2 4=

Figure 3. RMS noise floor vs. IF BW with 801

points in a CW sweep.


3/4

Using averaging to reduce noise floorallows the user to observe the traces ont h e P N A s c r e e n a s t h e a v e r a g i n gprocesses, which some designers mayfind useful. IF BW reduction works onboth r a t i oed and un ra t i oed measure -ment s (un l ike ave rag ing which on lyworks in ra tioed mode), which can be thedetermining fa ctor in some situa tions.

T h e P N A s e r i e s p r o v i d e s a l a rg ese lec t ion of IF BWs, which gives thedes igne r f l ex ib i l i t y i n de s i red no i sef l o o r r e d u c t i o n w h i l e i n c u r r i n g t h esma l l e s t poss ib l e r educ t ion in mea -s u r e m e n t s p e e d . I n m a n y p r a c t i c a ls i t u a t i o n s , d y n a m i c r a n g e i sincreased by using a combinat ion ofave ra g ing and IF B W ad jus tment .

The segmented sweepApplications in w hich speed a nd w ide

d y n a m i c r a n g e m u s t b e op t i m i z edrequire the use of a segmented sweepfeature. It is valuable when measuringfilters tha t demand simultaneous char-acterization of the passband at a highpower level, and th e reject ba nd a t a low power level. Segmented sweep allowsthe use r t o b reak a f r equency sw eepinto mul t iple segments, each wi th i t sown stop and start frequency, IF BW,p o w e r l e v e l , a n d n u m b e r o f p o i n t s .When measuring a filter, the IF BW inthe passband can be set wide for a fastsweep rate, as long as high level tracenoise is kept sufficiently small.

In the reject band, where noise floorcontr ibutes signi f icant ly to measure-ment error, the IF BW can be set low

enough to achieve the desired reductionin average noise level. To increase thedynamic range of the analyzer even fur-ther, segmented sweep can be used inconjunction with a re-configuration ofthe test-set. This configuration does notprohibit the user from performing a fullt w o - p o r t c a l i b r a t i o n , w h i c h m a y b ed e s i r ed f o r e n h a n c e d a c c u r a c y. A nincrease in dynamic range of 12 to 13dB can be achieved with t his method byreversing the directional coupler in thereceiving t est port.

In short...Network a nalyzer dynamic range is

the mos t c r i t i c a l pa rame te r i n manym e a s u r e m e n t s i t u a t i o n s . R ed u c i n gnoise floor through averaging or IF BWr e d u ct i o n c a n i n c r e a s e t h e d y n a m i cr a n g e o f a n a l y z e r s . H o w e v e r , e a c hmethod has disadvantages tha t de ter-mine its suitability in certain cases, andeach has a unique effec t on measure-ment speed. Beyond these two meth ods,fu r the r dynamic range improvementc a n b e o bt a i n e d , a n d m e a s u r e m e n tspeed reta ined, by using th e segmentedsweep feature found in some networkanalyzers and a configurable test set.

References

1] Robert A. Witte, Spect r um a nd N etw ork M easurement s, Upper S addleRiver, New J ersey, P rentice Ha ll PTR,Inc., 1993.

2] H.L. Krauss, C.W. Bost ian, andF.H. Raab, Solid State Radi o Engin eer- ing, New York, NY: J ohn Wiley & Sons,Inc. 1980, pp. 11-24.



4/4

3] Alberto Leon-G a rcia , Pr oba b i l i t y a n d R a n d o m P r o ces s f o r E l ec t r i c a l En gin eeri ng, 2nd ed. , New York, NY:Addison-Wesley P ublishing Compa ny,Inc., 1994.


About the authorsB a r r y B r ow n i s a h a r d w a r e

design engineer in the ComponentTest Unit of Agilent Technologies.A gradua t e o f Purdue and S t anfordUniversi t ies, he has been involvedwi th t he des ign o f vec to r ne tworkan alyzers since 1976. J in B ains i s am a n u f a c t u r i n g d e v el o pm e n t e n g i -neer with Agilent Technologies. Hehas more than f ive years of experi -

e n c e w i t h n e t w o r k a n a l y z e r s .B a i n s h a s a B S E E f r o m U C D a v i s ,and is current ly working towards aMSEE f rom S tanford Unive r si t y.

Noise floor Sweep timereduction (dB) increase factor

100 Hz 10 averages 10 10

10 Hz 0 averages 10 9.9100 Hz 100 averages 20 1001 Hz 0 averages 20 99.5

Table 2. Sweep time impact with slow IF BWs.

Noise floor Sweep timereduction (dB) increase factor

10 kHz 10 averages 10 101 kHz 0 averages 10 7.7510 kHz 100 averages 20 100100 Hz 0 averages 20 74.8

Table 1. Sweep time impact with fast IF BWs.

Documents

[RFD0009] Improving the Vector Network Analyzer s Dynamic Range