SPARQ Dynamic Range Peter J. Pupalaikis VP & Principal Technologist

Transcription

1 SPARQ Dyamic Rage Peter J. Pupalaiis VP & Pricipal Techologist Summary This paper discusses the dyamic rage of the SPARQ sigal itegrity etwor aalyzer ad cosiders the impact of several ey specificatios. It further compares dyamic rage ad ey specificatios of two competitive time-domai istrumets ad provides derivatios ad experimetal results that support the calculatios. Dyamic Rage The expressio for dyamic rage of ay TDR based measuremet istrumet ca be expressed accordig to the followig equatio which is derived i Appedix A - Derivatio of Dyamic Rage: Appedix A - Derivatio of Dyamic Rage: S R A T Ta rac eq ( ) Log act f T oise + P( f) + ( C+ F) CM( f) 6, Where: f is frequecy (GHz) T is the amout of time to average over Ad where for the SPARQ istrumet: [] The Dyamic Rage Equatio A. V is the sigal step amplitude f.4 GHz is the bad limit o oise (ot bad limited so set to Nyquist rate).5 MS/s is the effective actual sample rate (actual sample rate is GS/s) act Ta 45 s frac % is the equivalet time acquisitio legth ormal pulser mode (5 MHz) is the fractio of the acquisitio cotaiig reflectios omial 4.8 GS/s is the equivalet time sample rate eq oise 46 is the trace oise with o badwidth limitig (is -5 bad limited to 4 GHz) is the pulser respose as fuctio of frequecy (db) approximately a liear rise to + 4 GHz (falls to db at approximately 65 GHz). f P( f ) db 4 F 3.5 db is the switch matrix loss 4 GHz) C.6 is the user cable loss 4 GHz) CM ( f ) SE f DE is a cable model that has db loss at 4 GHz derived i Appedix B - Calculatio of the Cable Model where: SE.33 is the si-effect loss (db/sqrt(ghz)) DE.44 is the dielectric loss (db/ghz) The SPARQ taes oe acquisitio cosistig of 5 hardware averages per secod ad uses such acquisitio ( secod) i preview mode, such acquisitios ( secods) i ormal mode, ad such acquisitios ( secods) i extra mode. If we collect all of the costats i this equatio, we obtai the followig equatio for SPARQ dyamic rage:

2 SPARQ Dyamic Rage S R ( f, T ) f + Log( T) Log( f ) SPARQ [] Note that i [], the cable loss is eglected as exteral cables ad cable specificatios are geerally user determied ad therefore dyamic rage is typically specified at the istrumet ports. SPARQ Dyamic Rage 9 8 dyamic rage (db) frequecy (GHz) Extra Mode ( secods, acquisitios,5 total averages) Normal Mode ( secods, acquisitios,5 total averages). Preview Mode ( secod, acquisitio,5 total averages) Figure - SPARQ Dyamic Rage Dyamic Rage Cosideratios The Dyamic rage equatio [] has several implicatios worth discussig. First the obvious oes. Regardig frequecy, the dyamic rage drops at db per decade (or 6 db per octave). This ca be cosidered as the effect of the dropoff i frequecy compoets of a step. If the waveform utilized could be a impulse, this effect could be avoided. This effect is couteracted by the expressio P(f ) which accouts for practical step resposes.

3 SPARQ Dyamic Rage Next is the obvious fact that the dyamic rage is strogly depedet o the step size. It goes up by 6 db for every doublig of the step amplitude, although the high frequecy cotet is also accouted for i P (f ) (which is ot cocered with the differece betwee pulser or sampler respose). Dyamic rage is directly proportioal to the radom oise ad also losses i the cablig ad fixturig, but this is also couteracted by highsample rate. Dyamic rage goes up by 3 db for every doublig (or db for every te times icrease) i either the actual sampler sample rate or the time oe waits for acquisitios to traspire. Dyamic rage is strogly affected by the legth of the acquisitio i time as idicated by the squared term Ta i the deomiator. The reaso why it is squared is two-fold. Oe effect is the amout of oise let ito the acquisitio. Remember that the actual sigal the icidet wavefrot is cotaied i a very small time locatio, yet the oise is spread over the etire acquisitio. As the acquisitio legth icreases, the amout of oise icreases with o icrease i sigal. The term frac which accouts for deoisig algorithms that serve maily to restrict the acquisitio to areas actually cotaiig sigal couteracts this effect. The secod effect is the effect o averagig. Loger acquisitios tae more time to acquire. Now some more complicated cosideratios that are ot ecessarily obvious. First is the effect of the badwidth limit o the oisef. I may cases, oise i equivalet time sampler arragemets is essetially white. This is especially true if a major source of the oise comes from quatizatio effects i the ADC. This meas that all of the oise power is preset up to the Nyquist rate. I this case, f ad these terms cacel. I this eq case, the dyamic rage is completely idepedet of the equivalet time sample rate. This may seem couterituitive because icreasig the sample rate causes more oise to fall outside the spectrum of iterest due to eve oise spreadig, but this effect is fully couteracted by the icrease i acquisitio time ad therefore the decrease i the umber of acquisitios that ca be averaged. I the case where the trace oise is specified with a badwidth limit (as i most cases), the the dyamic rage is actually pealized by which seems ufair util ( f ( ) Log eq you cosider that uless the Nyquist rate is set exactly equal to this limit frequecy, the acquisitios are eedlessly oversampled (eedless i theory, ot ecessarily i practice due to aliasig cosideratios). To mae a proper compariso of bad limited ad o bad limited oise, oe must compare usig this adjustmet. SPARQ Dyamic Rage Techology SPARQ is desiged with several ey trade-offs which affect dyamic rage. Namely, it is built to be simultaeously low cost ad much easier to use. The low cost ad ease of use is accomplished partly by utilizig oly a sigle pulser ad two samplers, the primary source of cost i TDR based istrumets. The ability to utilize a miimum set of pulser/samplers dovetails well with its desig for ease of use. This is because the sigle pulser ad each sampler must be able to be coected to each port of the SPARQ durig measuremets, ecessitatig a high-frequecy switch arragemet. This switch arragemet also provides for the capability to coect to iteral stadards allowig the uit to calibrate to a iteral referece plae without multiple coectios ad discoectios of the device uder test. This iteral calibratio capability meas that the uit is affordable ad is much simpler to operate. This capability comes with a large dyamic rage price tag because the switch system adds loss to the system ad eve more importatly, it adds legth. As we see i the dyamic rage equatio, the losses i the path betwee the iteral pulser/samplers ad the ports o the frot of the uit cotribute twice to the dyamic rage reductio because the sigal must get from the pulser to the port, go through the DUT ad the retur from the port to the sampler. I fact, this loss degrades the SPARQ s dyamic rage by about 7 db. But the legth is a eve bigger 3

4 SPARQ Dyamic Rage pealty because geerally the acquisitio legth must be exteded by at least four times the added legth. This accouts for a roughly 3 db reductio i dyamic rage. The total price paid for ecoomy ad ease of use is approximately db i dyamic rage. If the desig eded there, perhaps SPARQ would simply be a cheaper, less precise way to mae measuremets, but i fact may special techology features are embodied i the SPARQ to ot oly couteract the db reductio, but to provide higher dyamic rage tha ay other TDR based solutio. The first techology is the pulser/sampler respose. Most TDR systems utilize a reasoably large amplitude pulse of 5 mv which is flat with frequecy. SPARQ uses a similarly sized pulse, but provides a pulse respose that rises by db at 4 GHz. I fact, the respose of the pulser/sampler passes bac through zero db at aroud 65 GHz. The pulser ad sampler are very high frequecy. Others do t provide such pulse resposes because the pulse does ot loo very good it exhibits about 8-% overshoot maig it less attractive for older traditioal TDR applicatios where the respose to the pulse was examied visually. The SPARQ s primary missio is to provide S- parameters ad calibrated time-domai resposes ad here the eed is for dyamic rage ad precisio over visual attractiveess of the raw pulse. This provides a et db improvemet i dyamic rage through oflatess..6 amplitude (V).4. magitude (db)... time (s). 5 5 frequecy (GHz). Figure SPARQ ulta-fast pulser time ad frequecy domai respose The secod techology is the LeCroy pateted coheret-iterleaved-samplig (CIS) time base. Traditioal TDR systems are based o sequetial samplig which is very slow ad suffers from time base o-liearities. Some eve stitch together sequetial acquisitios which adds to eve more error. The time base oliearity will ot be see as a dyamic rage degradatio but rather as a accuracy degradatio. The LeCroy CIS timebase produces a sample cloc that is slightly offset from MS/s as it samples the repeatig 5 MHz repeatig TDR pulse. This allows for much higher sample rates with o time base oliearity issues. The CIS time base is ot oly more precise, it is much simpler to build ad operate which eables fast averagig to be performed i hardware. The speed of the samplig system accouts for a -8 db improvemet over other sequetially sampled istrumets. Ufortuately, whe samplers are utilized at higher sample rates, sampler oise icreases also, so the et improvemet is perhaps oly 6 db or so whe factorig i the icreased sampler oise. As a fial ote, because this advatage relies heavily o fast averagig, it is importat i the desig of the istrumet to esure that this averagig truly results i icreased dyamic rage. Measuremets of this are show i Appedix C - Effects of Averagig The fial ey techology is a method of removig oise usig digital sigal processig 4

5 SPARQ Dyamic Rage techiques called wavelet deoisig. Techiques lie this are used i radar, imagig, ad electrocardiogram systems. The effects of this techique are hard to quatify exactly, but the simplest way to loo at it is that it couteracts the effects of maig the acquisitio duratio loger to the extet that the algorithm removes oise wherever reflectios (i.e. sigal) is ot preset. For short devices this results i a db improvemet or so i dyamic rage for loger devices the improvemet ca be extreme. Whe ports of a device exhibit extremely large isolatio, wavelet deoisig techiques result i dyamic rage improvemets far i excess of db gai (db) gai (db) frequecy (GHz) 3 4 frequecy (GHz) Figure 3 Compariso of o-deoised (left) ad wavelet deoised crosstal measuremet These three techologies allow a SPARQ to gai coservatively 6 db improvemets i dyamic rage allowig it to trade bac db for its lower cost ad ease of use ad still maitai a 6 db improvemet. This is half the oise or double the frequecy, whichever way you wat to loo at it. The compariso of SPARQ dyamic rage is quatified ad compared to the specificatios of competitive istrumets i the followig sectio. Note that the fial dyamic rage calculated ca be read directly from the competitor data sheets ad that the calculatios show here are either exact or eve more optimistic tha specified for competitive istrumets. 5

6 SPARQ Dyamic Rage Compariso with Other TDR Based Solutios Calculatio of Tetroix Specificatios LeCroy SPARQ Agilet 86C Dyamic Rage Score DSA8 Normalized Log Startig db 5 db 5 db Poit 3,4, Sample Rate Log( ) 5 Noise (@ 4 GHz Badwidth) 4 GHz + act Step Amplitude ( ) Losses module to 4 GHz Electrical Legth module to port 3 MS/s Coheret Iterleaved Samplig (CIS) (.5 MS/s effective) 6 5 averages + db + oise 5 7 uv (-5 ) 7 + P( 4) + db + db + Log A mv - db F 3.5 db -7 db 5 + Log L 4 5 L 4 Deoisig Log( frac) 3.6 s 5 KS/s Sequetial Samplig 5 averages 37 uv (-56 ) 8 +6 db db 5 mv db s +3 db 4 KS/s Sequetial Samplig 4 averages -6 db 63 uv (-5 ) 9 + db db mv - db db s +3 db + Wavelet Hard Threshold 4 Noe Noe Total 5 db 44 db 5 3 db 6 Table - Compariso of TDR Dyamic Rage. Utilizes Tetroix DSA8 samplig oscilloscope ad 8E TDR module as specified by Tetroix for 4 GHz measuremets.. Utilizes Agilet 86C samplig oscilloscope ad 54754A TDR module ad PSPL 4 NLTS ad 868A sampler module as specified by Agilet for 4 GHz measuremets. 3. Assumes step amplitude of 5 mv, 5 KS/s actual sample rate, -5 oise (badlimited to 4 GHz), db respose at 4 GHz, o losses from module to port, 5 s acquisitio legth, frequecy of 4 GHz, secods of acquisitios averaged, GS/s equivalet time sample rate. Result is rouded up to Note that 8 GS/s sample rate is utilized sice all oise specificatios are provided badlimited to 4 GHz. The dyamic rage equatio shows SNR improvig with sample rate which is ot the case whe oise is bad limited. The appropriate settig of sample rate for bad limited oise is twice the bad limit. 5. Note that 45 s is used for acquisitio legth, eve though 5 s has bee specified. Half a divisio is utilized for edge placemet. 6. Although CIS is much faster, oly 5% of samples acquired are used due to the fact that CIS acquires a full cycle of the s pulse repetitio period. Other advatages to CIS are timebase liearity, but this beefit ot quatified i dyamic rage. 7. Spec is -46 white oise to Nyquist rate of GHz which is 4 db improvemet whe badlimited to 4 GHz validated by measuremet. 8. Uses typical specificatio of 37 uv which is much smaller tha guarateed specificatio of 48 uv 9. Spec is 7 uv at 5 GHz badwidth so assume db improvemet whe badlimited to 4 GHz. Gai is supplied at expese of pulse overshoot specs which are irrelevat i SPARQ actual pulse frequecy respose db at typically 65 GHz. Datasheet idicates 4 produce mv output step amplitude equal to iput strobe amplitude.. Losses due to cables ad switches that facilitate iteral calibratio capability. 3. The SPARQ has about 3.6 s electrical legth which requires 4.4 extra s of acquisitio. This correctio credits competitive uits i both averagig time ad oise from this extra acquisitio legth. 4. Patet Pedig, assumes % of waveform actually cotais reflectios, which is very coservative. 5. This umber ca be read almost directly from Tetroix specificatio. Tetroix shows 45 db at 5 averages at 4 GHz. The averagig used i this compare is secods which, with the legth credit, is averages which accouts for the db. 6. Agilet shows db at 3 GHz with 64 averages. We compare 4 averages, but cosiderig the electrical legth module to port, we compare 56 averages. Degrade further by a extra db to accout for the fact that our umbers are at 4 GHz, extrapolates to 8 db accordig to Agilet supplied dyamic rage data. We caot explai the deviatio betwee the 3 db calculated here ad Agilet s supplied data of 8 db. 6

7 SPARQ Dyamic Rage Appedix A - Derivatio of Dyamic Rage Withi the SPARQ, we acquire step waveforms, therefore we start with a acquired sigal defied as follows: w s [3] where w is the step waveform actually acquired, sis the step portio cotai the sigal of iterest, ad ε is the oise sigal which we assume to be white, ormally distributed, ucorrelated oise. The sigal cotet i the step is i the form of the frequecy cotet of the derivative, so the derivatio must cosider this. Sice durig calculatio we do t ow the differece betwee the oise ad the step, we must tae the derivative of both. We will be approximatig: + ε d d wt ( ) ( s( t) + ε ( t) ) dt dt d d d s( t) + ε ( t) x( t) + ε ( t) dt dt dt Whe we covert the two sigals we are iterested i to the frequecy domai: [4] X DFT ( x( t)) d D DFT ε ( t) dt [5] We will calculate the dyamic rage as a sigal-to-oise ratio (SNR) ad defie this for each frequecy as: X S R D I order to calculate the SNR, we calculate the frequecy cotet of each of these compoets separately ad tae the ratio. We start with the oise compoet. [6] Give a oise sigal ε which cotais oly ucorrelated, ormally distributed, white oise, it has a mea of ad a stadard deviatio of σ, which is the same as sayig it has a root-mea-square (rms) value of σ. We have K poits of this sigal ε, K. If we calculate the discrete-fourier-trasform (DFT) of this oise sigal, we obtai + frequecy poits K, : where the frequecies are defied as: E K jπ K εe [7] f 7

8 SPARQ Dyamic Rage Where is the sample rate. [8] By the defiitio of the rms value ad by the equivalece of oise power i the time domai ad frequecy domai, we ow the followig: ε σ K E is the last frequecy bi cotaiig oise due to ay bad limitig of oise effects. [9] We defie a average value of Ea that satisfies this relatioship: Ad therefore: Ea σ Ea [] Ea f f is the frequecy limit for the oise calculatig by substitutig σ K for i [8]. [] We, however, are taig the derivative of the sigal. The derivative i discrete terms is defied as: Where we have: d dt ε ( t) ε ε dε Ts Ts is the sample period. Usig the same equivalece i [9] ad defiig D DFT( dε ), K dε σ D [3] Usig the Z-trasform equivalet of the derivative i the frequecy domai, ad a average value for the oise i D it ca be show that: [] K dε σ j e Ts f π Ea [4] 8

9 SPARQ Dyamic Rage Therefore, the average oise compoet at each frequecy is give by: D e f jπ Ts Ea [5] We ca mae a approximatio that allows oe to gai further isight by expadig the umerator term i a series expasio: f jπ e πf + O Which allows us to approximate the oise compoet as: πf Ts Ea D f 3 πf σ Now that we have the oise compoet of dyamic rage, we move to the sigal compoet. K f [6] [7] Without regard to the rise time or the frequecy respose of the step, which we will cosider later, we defie the sigal such that, i the discrete domai, the itegral of the sigal forms a step: s s + x Ts A x is a impulse such that x A ad is zero elsewhere such that sforms a step that rises to Ts amplitude A at time zero ad stays there. X DFT(x) ad therefore the sigal compoets at each frequecy is defied as: [8] Agai, to gai further isight, we defie: X A Ts A [9] Where Ta is the acquisitio duratio. Therefore: K K Ts Ta [] X A Ta Usig [6], the ratio ca therefore be expressed as: [] 9

10 SPARQ Dyamic Rage S R X D A K f Ta π σ Sice these are voltage relatioships, we ca express the SNR i db as: [] Ad usig [], fially: S R A K f Log Ta π σ Log Ta A 4 π K σ [3] S R A Log Ta 4 π σ We would lie to express the oise i, so we have: Ad therefore: oise Log Log ( σ ) ( σ ) + 3. [4] [5] Substitutig [6] i [4]: σ oise [6] S R A Log Ta 4 π A Log Ta 4 π The, to clea thigs up, we extract some costats: oise oise [7] Ad therefore: Log 6 8 π [8] S R A Log Ta oise 6 [9]

11 SPARQ Dyamic Rage Now let's cosider some other factors. First, that there is a frequecy respose of the pulse, ad a frequecy respose of the sampler. These resposes ca be aggregated ito a sigle respose. Sice, i decibels, it is simply the frequecy respose of the step calculated by taig the DFT of the derivative of the step (isolatig oly the sampled icidet waveform) ad calculatig i db, this value ca simply be added to the dyamic rage: A S R Log Ta oise + P ( f) 6 [3] Next, we cosider the effects of averagig. Averagig the waveform achieves a 3 db reductio i oise with every doublig of the umber of averages. This leads to a improvemet of dyamic rage by: ( avg) Log( avg) Log Which allows us to isert this directly ito the umerator: A avg S R Log Ta oise + P ( f) 6 [3] We really do t wat to cosider dyamic rage i terms of umber of averages ad istead to prefer to cosider the amout of time we are willig to wait. The amout of averages tae i a give amout of time is give by: act avg Ta eq T I [33], we ow eed to distiguish what is meat by sample rate. sample rate ad replaces what we previously called. eq becomes the equivalet time act is the actual sample rate of the system ad T is the amout of time over which acquisitios are tae. Substitutig [33] i [3], we obtai: Log A S R Ta oise + P ( f) 6 act eq T [34] Next, we cosider the losses i the cablig ad fixturig betwee the pulser/sampler ad the deviceuder-test (DUT). Sice the cablig ad fixturig is coaxial ad similar, both of these resposes follow a respose shape that we call a cable model which cosists of si-effect loss that is a fuctio of the square-root of the frequecy ad a dielectric loss that is a fuctio of frequecy. We ca fit a curve to the fixturig ad cablig that is a fuctio of these effects that has bee scaled to have a loss of db at 4 GHz. This is show i [3] [33] Appedix B - Calculatio of the Cable Mode. This curve ca the be applied to the fixture ad cable resposes defied as a sigle umber at 4 GHz: CM ( f ) SE f DE [35]

12 SPARQ Dyamic Rage Where SE is the si-effect loss i db Hz ad DE is the dielectric loss i db Hz. Where F ad C are the loss i the fixturig ad cablig respectively at 4 GHz, the equatio for dyamic rage becomes: ( ) Log A S R f Ta oise + P act T ( f) + ( C+ F) CM( f) 6 [36] Cosiderig the fact that the sigal must pass through the cablig ad fixturig twice. There is oe fial cosideratio. That is the effect of deoisig algorithms. Deoisig algorithms have the effect of removig broadbad oise from the acquisitio primarily through meas of detectig where ucorrelated oise is preset i the sigal i time. It is difficult to quatify these effects, but a eq coservative method cosiders the fact that the primary oise reductio occurs where there are o reflectios. I other words, if we loo at a deoised waveform, the primary effect is to remove the oise i the locatios i the waveform devoid of reflectios. The effect o oise, agai coservatively speaig, is to retai oly the portio of the waveform that cotais reflectios. Here, we will assume that the oise remais i these portios. Thiig this way, we ca defie a variablefrac that cotais the fractioal portio of the acquisitio that actually cotais reflectios relative to the portio that does ot. This value is DUT depedet ad modifies the acquisitio duratio Ta. Of course, frac is used whe deoisig is ot employed: S R A T Ta rac eq ( ) Log act f oise + P( f) + ( C+ F) CM( f) 6 [37] Dyamic Rage Equatio *************************************

13 SPARQ Dyamic Rage Appedix B - Calculatio of the Cable Model Give a magitude respose M for frequecy poitsf for + frequecy poits, we first defie the magitude respose ormalized to have a gai of d db at the last frequecy poit f. We defie a object fuctio to fit to as: V LogM d Log The cable mode fuctio is defied as: ( M ) T f ( f, ) x f x x [38] F x f [39] The model is determied by fittig values for x to V : H, F, x x Ad solvig for x : H, F, x x x ( f ) f ( f ) f T T ( H H) H V A example ormalized cable ad fit for a SPARQ are show i Figure 4. Here, the costats are: SE.33 x DE.44 db GHz db GHz [4] [4] [4] [43]..4 gai (db) frequecy (GHz) Actual Data (ormalized to - 4 GHz). Fit Data Figure 4 Fit of Cable Model to Normalized Cable Measuremet 3

14 SPARQ Dyamic Rage Appedix C - Effects of Averagig I the calculatio of dyamic rage, there is a assumptio that the dyamic rage icreases by db if we icrease the umber of averages by a factor of. There are three mai operatig modes of the SPARQ. These modes are preview, ormal, ad extra with 5, 5, ad 5 averages, respectively. Here we show the effects of the averagig i these modes ad show that that each mode truly gais db of dyamic rage as we icrease the averagig tefold for each mode improvemet. Further, we show the poit where averagig produces dimiishig returs. I order to test that averagig truly improves the dyamic rage, we set up the SPARQ to compute the stadard deviatio of a s portio of the TDR trace while the pulser is tured off ad coected to a 5 Ohm termiatio. Because we eed to compute a large data set, we record the cumulative average of 3 acquisitios with o hardware averagig, the cumulative average of acquisitios with 5 hardware averages per acquisitio, ad the cumulative average of 6 acquisitios with, hardware averages per acquisitio. These sets of data are tae usig iteral software tools to avoid the fact that most of the tools that are exposed to the user have a limit of 6 bits of precisio. These three sets of data are aggregated ad sorted ito oe large set of data that cotais from to 6, averages. We the fit the data to the followig fuctio: A ( avg, A) A F + [44] The motivatio for this fuctio is as follows: A cotais the ucorrelated oise (oise that ca be averaged away). A cotais the correlated oise (oise that caot be averaged away). Ideally, A is as low as possible to reflect a low oise sampler, A is zero meaig that cotiued averagig improves the oise forever. Whe we fit the data we obtai the followig values: A. 3mV or A. 63µ V or The variace is 3.9e. Note that the oise used for a SPARQ sampler is ot show bad limited ad improves by 4 db to -5 whe bad limited to 4 GHz. The result of the fit is show i Figure 5 where it is see that all of the SPARQ averagig modes have a db oise improvemet ad that i fact aother factor of beyod extra mode would brig the oise close to the best oise achievable. 4

15 SPARQ Dyamic Rage Preview Mode Noise () 7 8 db decade db Normal Mode Extra Mode 9 decade mi oise floor Number of Averages Fitted Curve. Fitted Curve (ucorrelated oise oly) Fitted Curve (correlated oise) Empirical Noise Measuremets Fitted Curve at Measured Data Poits Noise at Stadard SPARQ Operatig Modes (preview,ormal,extra) Figure 5 Effect of Averagig o Noise 5

16 SPARQ Dyamic Rage Appedix D Coheret Iterleaved Samplig Mode (CIS) Calculatios eq is the equivalet time sample rate (GS/s). SP 48 is the samples per patter specified for the CIS timebase: SP 4.8 eq GS/s [45] This correspods to a Nyquist rate of.4 GHz ad a sample period of eq Ts eq 4.883ps. We have two modes of operatio, which refer to the electrical legth of the DUT. These are ormal mode ad log mode. Normal mode utilizes a 5 MHz pulser repetitio rate ad log mode utilizes a MHz pulser repetitio rate. The duty cycle is a miimum of 3 percet i both modes, which leads to a maximum acquisitio duratio of: PR 5 MHz repetitio rate i ormal mode. avg 5 is the umber of hardware averages per sigle CIS mode acquisitio. T is the time spet acquirig (s). act rate. The update rate is: MS/s is the CIS mode actual sample avg T PR eq act [46] is the acquisitio time i secods for a sigle, hardware averaged acquisitio (5 times). Sice DC 3 % is the duty cycle of the pulser Ta s ad is the maximum max DC PR 6 acquisitio duratio i ormal mode. We use Ta 45 s as the acquisitio duratio for ormal mode to mae sure we fit it divisios at 5 s/div mius half a divisio to positio the TDR pulse edge. 6