DSO Bandwidth test SDS1104X-E DSOX1102G TO1104 GDS1054B - Page 1
Forum section: electronics / testgear

author: TK
author_rank: Super Contributor
timestamp: May 04, 2019, 03:49:21 pm
content: I had the opportunity to test the Bandwidth on the following Digital Storage Oscilloscopes:Siglent SDS1104X-E (100MHz 1GSa/s 4 channels)Siglent SDS1104X-E software modded to SDS1204X-E (200MHz 1GSa/s 4 channels) (Indicated as SDS1104X-E* in the table)Siglent SDS1202X-E (200MHz 4 channels) (As tested by TAUTECH)Keysight DSOX1102G (EDUX1002G uphacked to DSOX1102G) (2GSa/s 2+1 channels)GWInstek GDS1054B (software license hacked to 300MHz) (1GSa/s 4 channels)Micsig TO1104 (1GSa/s 4 channels)Agilent 54622D (200MSa/s 2+16 channels) NOTE: Frequency over 200MHz is indicated as ">200MHz" but can see a very well defined sinewave up to 600MHz (Added 5-May-2019)HP 54645D (2+16 channels) (Added 5-May-2019)I used an Agilent signal generator to output a 0dBm (632 mVpp) signal.Agilent Signal Generator --> N to SMA connector --> SMA - SMA cable --> SMA to BNC --> BNC 50ohm passthrough --> DSOFrequencySDS1104X-ESDS1104X-E*SDS1202X-EDSOX1102GGDS1054BTO110454622D54645D10 MHz645 mVpp652 mVpp640 mVpp640 mVpp630 mVpp644 mVpp641 mVpp643 mVpp100 MHz500 mVpp596 mVpp608 mVpp625 mVpp485 mVpp516 mVpp497 mVpp546 mVpp200 MHz70 mVpp500 mVpp508 mVpp215 mVpp224 mVpp257 mVpp250 mVpp287 mVpp300 MHz---348 mVpp352 mVpp28 mVpp47 mVpp49 mVpp106 mVpp72 mVpp350 MHz---186 mVpp240 mVpp---23 mVpp---72 mVpp---400 MHz---125 mVpp180 mVpp---9 mVpp---53 mVpp---500 MHz---40 mVpp------------26 mVpp---600 MHz------------------10 mVpp---EDIT 5-MAY-2019: Added SDS1104X-E software modded to 200MHz (SDS1104X-E*), Agilent 54622D and HP 54645DEDIT 7-MAY-2019: Added SDS1202X-E (TAUTECH)

author: hgjdwx
author_rank: Regular Contributor
timestamp: May 05, 2019, 05:31:22 am
content: The worst must be SDS1104X-E. The best?

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 08:17:04 am
content: Quote from: TK on May 04, 2019, 03:49:21 pmBecause there was also modified Good Will 1054B compared to unmodified others so here is modified SDS1104X-E --> SDS1204X-ESDS1104X-E (sw-mod to 1204X-E)Generator Hewlett-Packard 8642B (also checked with HP power meter that levels are well inside specs or much better)Generator output: N-BNC adapter Suhner.Cable: M17/084 (RG223) 150cm + Suhner BNC'sScope input: Terminator Tektronix 011-0049-00Generator output level set value 0.0dBmScope 100mV/div.10 MHz 636mV100MHz 561mV200MHz 494mV300MHz 342mV350MHz 256mV400MHz 171mVhere also member @lzyengineer measurements:SDS1104X-E original + modhttps://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/msg2326518/#msg2326518And in other place can find my measurements also with both: 1104X-E and after mod.Example in this thread after this message it starthttps://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/msg1624558/#msg1624558But is it so that more is better? Not always.All channels on 500MSa/s. SDS1104X-E have good DSP filter for reject aliasing!~-36dB @ fNyquistSo, for avoid alias effects with measurements example with SDS1204X-E user need really know least some basic fundamentals. - Mirror have also its backside.But here bit more fair, both modified. Siglent for 200MHz and GoodWill for 300MHzSDS1104X-E modGDS1054B modresponds SDS1204X-Ewith 300MHz licenseFrequency@rf-loop@TK10 MHz636 mVpp630 mVpp100 MHz561 mVpp485 mVpp200 MHz494 mVpp224 mVpp300 MHz342 mVpp47 mVpp350 MHz256 mVpp23 mVpp400 MHz171 mVpp9 mVpp

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 09:31:16 am
content: A picture update..

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 09:57:35 am
content: Quote from: imo on May 05, 2019, 09:31:16 amFor SDS1204X-E..........a very accurate picture.From my own tests ~230 MHz @ -3dB.

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 10:08:31 am
content: Better the 1104X-E 200M should follow the shape of the 1104X-E 100M (or DSOX) above, but with the corner shifted to 200M, imho..

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 10:17:22 am
content: Quote from: imo on May 05, 2019, 10:08:31 amI can do -3dB points forrealSDS1104X-E and SDS1204X-E if you want........I have to do my pre-dispatch checks so no real problem to use my 510 MHz HP RF gen orSDG3021XSDG3032X.

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 10:18:51 am
content: Make it at all above freqs, I will update the picture then..

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 10:31:57 am
content: Quote from: tautech on May 05, 2019, 09:57:35 amAnd previously (my previously made quality control's) SDS1104X-E's out from box:individual units I have measured have been between~>120MHz --- ~<130MHz -3dB vs 1MHzSo this previous table is bit odd because TK did not measured any scope real -3dB pointJump from 100 directly to 200MHz and then between 300 and 400 also 350.Proportionally jump from 100 to 200 is like jump from 300 to 600 or 200 to 400 so it is more than odd, specially because he test 50 - 100MHz nameplate scopes. Peoples are some times ranting biased sellers but is it so that some times owners are even more biased or what to think. But yes, nice test.

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 10:57:22 am
content: Quote from: rf-loop on May 05, 2019, 10:31:57 amAgree 1000%-3dB point is what matters however can be useful to know how high we can get stable performance albeit with significant attenuation. You saw me push SDS2202X-E to 520 MHz in another thread to make a point and I know the SDS1kX-E cannot be pushed that high.Back to BW measurements..........

author: TK
author_rank: Super Contributor
timestamp: May 05, 2019, 11:11:27 am
content: I agree that the correct way is to measure -3dB but I saw several members asking for the max frequency that the scope (modded or original) can measure, so I tested to get to that value as soon as possible.I will mod my sds1104x-e to sds1204x-e and edit my original results

author: nctnico
author_rank: Super Contributor
timestamp: May 05, 2019, 11:17:56 am
content: Still the graph in the 3rd reply post gives a good indication. Let's not get over obsessed with the precise -3dB point.

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 11:47:34 am
content: Scopes tested straight from box. Tests = warm up.SDS1104X-ESDS1204X-ESource SDG3021X (modded to 3.2 GHz model)BNC cheap 1 GHz Siglent cableTermination 50 ohm 1x TekLevel 0dBmAmplitude can be taken from OSD p-p measurements.SDS1104X-E ....much as expected.Images 27, 28, 29(200 MHz) and 30.(300 MHz)SDS1204X-E..............pushed.(Frequency counter becomes unstable @ 400+ MHz)Images 31, 32, 33, 34, 36(350), 35(400), PNG450, PNG500, PNG550 and PNG600

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 11:48:08 am
content: Quote from: nctnico on May 05, 2019, 11:17:56 amYes. Only that it is quite common practice to measure -3dB point.But as you said "Let's not get over obsessed"But because typically 100MHz scopes have BW limit slope between 100 and 200MHz it is bit rough only measure 100 and 200MHz point (and after then draw straight line between these points as @imo)

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 11:56:50 am
content: Quote from: tautech on May 05, 2019, 11:47:34 amWhat happen in image 29?I expect roughly around -6dBSome thing is now wrong.Oh... this trigger freq counter.. true signal is 200M..

author: David Hess
author_rank: Super Contributor
timestamp: May 05, 2019, 12:28:52 pm
content: With manufacturers like Rigol producing DSOs with unspecified and variable full power bandwidth, these tests are close to useless without specifying the input sensitivity. In the past this was not a consideration because the full power bandwidth was always higher than the bandwidth at any input sensitivity which was a result of operating the input stages over a much smaller signal range.

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 12:31:05 pm
content: Quote from: David Hess on May 05, 2019, 12:28:52 pmSpecified in the OP and plainly visible in every screenshot.

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 12:52:33 pm
content: Quote from: David Hess on May 05, 2019, 12:28:52 pmPlease explain.If I measure freq response using (example) 5, 10, 20, 50, 100, 200, 500mV, etc/div and so on and show all these results. Or if I measure freq response for 100mV/div and show result. What is then wrong there. Can you say this response is not true with used setup. Do you mean all this is bullshit.What is wrong. If it is wrong, please give explanation and instructions how to measure.Or is it just only wrong because these are made in China.I have repaired and calibrated several Tektronix old and also made frequency response measurements as told in Tek service manuals. Are these also useless.Measured frequency response is just as result is in told situation. Or do you claim this result is wrong. If it is wrong please come here and show how it need measure so that also you are satisfied.

author: David Hess
author_rank: Super Contributor
timestamp: May 05, 2019, 12:55:51 pm
content: Quote from: tautech on May 05, 2019, 12:31:05 pmSignal level is not the input sensitivity and there are no screenshots associated with TK's post.

author: nctnico
author_rank: Super Contributor
timestamp: May 05, 2019, 12:58:05 pm
content: Quote from: rf-loop on May 05, 2019, 12:52:33 pmDavid has a good point. On the lower sensitivity settings there usually is a pre-amplifier which also affects the frequency response. And the attenuators may behave differently at various frequencies as well. So if you want to do a really accurate frequency response graph then you'd need to do this using multiple v/div settings. But then again this is not a very useful exercise because near the bandwidth most (non-sinusoidal) signals will be distorted anyway.

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 01:08:13 pm
content: A picture update..

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 01:12:25 pm
content: Quote from: nctnico on May 05, 2019, 12:58:05 pmYes, of course.But still, if measure 100mV/div frequency respose using ok setup it IS 100mV/div frequency response in used setup and not bullshit. Bllshit is if after then claim it tell something what is not measured. Predictors and clairvoyants are a separate issue.But, of course, and who even think other, it is NOT whole scope frequency response over whole signal level range with all sensitivity settings. If it is measured using one V/div range with one signal input level and explained setup it is response just with it and nothing else. This is true what ever we test. Result tell only how it is with used setup and nothing else.

author: TK
author_rank: Super Contributor
timestamp: May 05, 2019, 01:15:57 pm
content: Quote from: hgjdwx on May 05, 2019, 05:31:22 amI updated the original test to include the SDS1104X-E software hacked to 200MHz, so far it is the 2nd best on my test

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 01:16:09 pm
content: Quote from: imo on May 05, 2019, 01:08:13 pmWrong, there is err...afaik.Look tautech 1104X-E result. Where from you get 150MHz data point?This around -18dB point is 200MHz!

author: TK
author_rank: Super Contributor
timestamp: May 05, 2019, 01:16:31 pm
content: Quote from: imo on May 05, 2019, 01:08:13 pmA picture is worth a thousand words (or numbers in this case)

author: David Hess
author_rank: Super Contributor
timestamp: May 05, 2019, 01:26:44 pm
content: Quote from: rf-loop on May 05, 2019, 12:52:33 pmThat would be one way and in practice because of the common designs now, it may be the only way without knowing more about the vertical signal chain.The problem comes about when a gain stage has a limited full power bandwidth (slew rate). In the past, all of the attenuation stages were very early in the signal chain so every stage operated with the same signal level. With the input always attenuated down to say 5mV/div, each stage saw the same signal level. (1) Later designs changed this a little and replaced some of the high impedance attenuators at the input with low impedance attenuators immediately after the high impedance buffer but the result was the same as long as the buffer always operated within its full power bandwidth.Now it is common to have those low impedance attenuators after the early gain stages which results in the early gain stages operating over a much wider signal range requiring a correspondingly higher full power bandwidth. This is reflected in measurements of instruments like the Rigol DS1000Z series where bandwidth varies markedly with sensitivity, over more than a 2:1 range.QuoteThose old Tektronix oscilloscopes had full power bandwidths in excess of their bandwidth so it was never a problem.QuoteI am claiming that with a modern oscilloscope, the measurement cannot be replicated without knowing the input sensitivity because many oscilloscopes now have wildly varying bandwidth with different input sensitives. This has shown up repeated on this forum with users making rise time and bandwidth measurements of Rigol DS1000Z DSOs which vary over more than a 2:1 range depending on the test conditions.(1) Often old oscilloscopes had a small number of switched gain stages which were used at the highest sensitivities but at least the manufacturers specified the bandwidth if it differed. For instance an old 200 MHz Tektronix TDS410A is 200 MHz from 5mV/div to 10V/div, 150 MHz at 2mV/div, and 95 MHz at 1mV/div.However this is the opposite of what is going on now where bandwidth decreases when an input attenuator is removed because of pull power bandwidth (slew rate) limits. Slew rate limiting causes harmonic distortion however it is very difficult to discern from the shape of the waveform with the harmonics all above the -3dB bandwidth.

author: tautech
author_rank: Super Contributor
timestamp: May 05, 2019, 01:29:06 pm
content: Quote from: rf-loop on May 05, 2019, 01:16:09 pmYes counter error when 1104X-E is pushed past its -3dB point.......but it might also be some trigger level hysteresis.Will add some more scopes tomorrow when I do their checks before they need to be delivered.Now

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 01:37:24 pm
content: A picture update v3.PS: not enough colors, sorry

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 01:45:59 pm
content: Quote from: imo on May 05, 2019, 01:37:24 pmAnd still same error.

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 01:59:48 pm
content: A picture update v4.Fixed the TAU 1104 100M.PS: plz provide the numbers only..

author: nctnico
author_rank: Super Contributor
timestamp: May 05, 2019, 02:05:43 pm
content: I have two remarks: it would be better not to use the polynomal fit because you don't have enough points. Also the frequency axis would be better if it where logarithmic.

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 02:12:10 pm
content: Quote from: David Hess on May 05, 2019, 01:26:44 pmOh these. Wellll...I have laughed many times looking many of these. Some times it looks that some peoples do not even know what they are doing with things what they have get to hand or table for playing. But if it is fun and educating, perhaps it is cheap and health way to keep fun and learn. Good and healthy value for spent money.

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 02:18:20 pm
content: Quote from: nctnico on May 05, 2019, 02:05:43 pmAnd same for a straight lines.

author: iMo
author_rank: Super Contributor
timestamp: May 05, 2019, 02:43:51 pm
content: Guys, no rocket science here, just depicting a trend based on a few measurement points..

author: rf-loop
author_rank: Super Contributor
timestamp: May 05, 2019, 03:28:54 pm
content: Quote from: imo on May 05, 2019, 02:43:51 pmYes free for artists.

author: tautech
author_rank: Super Contributor
timestamp: May 06, 2019, 08:44:50 am
content: OK so if TK can bring an 2GSa/s entry level DSO into this comparison then so shall I.Signal source SSG3021X and setup as before, 0dBm into 50 ohm Tek termination and 100mV/div unless shown otherwise.SDS2022X-E stock 200 MHz $619 model.Completely missed 900 MHz.Pushed to 1 GHz !At the start of aliasing.

author: Rerouter
author_rank: Super Contributor
timestamp: May 06, 2019, 08:51:33 am
content: Tautech, can I ask why you did not increase the VDIV for most of the screens, the measure command is more accurate when the wave is at least 65% of the screen height,

author: tautech
author_rank: Super Contributor
timestamp: May 06, 2019, 09:00:00 am
content: Quote from: Rerouter on May 06, 2019, 08:51:33 amLook at the OP, all measurements were done @ 100mV/div.If we think about it, what David Hess bought to the discussion is valid in that displayed/measured accuracy could be compromised if different vertical attenuations are selected. A valid point IMO.It certainly would affect the BW roll off curve however probably just to a small degree.So we just compare apples with apples @ 100mV and call it quits at that and let the viewers decide which are the lemons.

author: rf-loop
author_rank: Super Contributor
timestamp: May 06, 2019, 10:41:50 am
content: Quote from: David Hess on May 05, 2019, 01:26:44 pmHereis small simple form test what show that least in Siglent whole range starting from 500uV/div is roughly same when compare 10MHz and 200MHz using all steps from 500uV/div up to 2V/div (can not higher level due to lack of trusted high level signal source with enough flatness.) But test include 2 lower bands all steps and band 3 first step. THis do not proof anything and test was with simplest method but it give some image that least not any dramatical Band Width differences between input sensitivity (V/div) settings. (like example ion older Tek analog scopes where are some times significant differences specially in highest sensitivities, depending model)https://www.eevblog.com/forum/testgear/siglent-sds1204x-e-released-for-domestic-markets-in-china/msg2390184/#msg2390184

author: TK
author_rank: Super Contributor
timestamp: May 06, 2019, 10:43:10 am
content: Quote from: tautech on May 06, 2019, 09:00:00 amI am sorry to have caused a confusion... I started at 100-200mV/div and went down all the way to 2-10mV/div for the higher frequencies.The objective of the test was to get the highest possible frequency that the instrument can measure

author: tautech
author_rank: Super Contributor
timestamp: May 07, 2019, 09:23:28 am
content: For shits and giggles let's run the 200 MHz 1 GSa/s 2ch SDS1202X-E, the first of the X-E scopes but without some of the nice features added into the 4ch X-E range and 2kX-E models.Source as before; SSG3021X, 0dBm into Tek 1x 50 ohm termination.

author: rf-loop
author_rank: Super Contributor
timestamp: May 07, 2019, 12:44:29 pm
content: Nice alias signals in 600, 700 and 800MHz images(600 ---> 400MHz alias700 ---> 300MHz alias800 ---> 200MHz alias)500 can see because sampling and signal is not perfectly synch and same with fN.This is why real best modification is reduceanalogBW (aka example make 200MHz LPF more steep after corner freq, With 500MSa/s this situation is lot of more "terrible", real trap to peoples who have lack of enough experience and knowledge. As can see even with 1GSa/s it is not good except that many times probing make some freq rejection but better solution is if front end is bit more designed. Personally I'm not satisfied with these too widely open analog front ends with very lazy slope down after corner. Looks like it is not designed at all for this matter. These alias productions smudge also many other signals where is markable amount of example harmonics. Oscilloscope need design for analyze unknown signals. Example inputting extremely fast changing signal may produce "what ever" miracles and phenomena what are then wondered here and there.

author: tinhead
author_rank: Super Contributor
timestamp: May 08, 2019, 09:13:00 am
content: Quote from: rf-loop on May 07, 2019, 12:44:29 pmthis is what of the reason why i use, when unsure or for RF, my DIY active probes with LPF from minicircuits with my SDS1204X-EI have only 550 and 600MHz models here, these here are for sure better ->https://www.minicircuits.com/WebStore/dashboard.html?model=BLP-450%2B

author: nctnico
author_rank: Super Contributor
timestamp: May 08, 2019, 09:48:30 am
content: It is much less of a problem then you might think. To avoid aliasing the front end should attenuate around 40dB to 50dB at fNyquist * 1.2. Sure you can lower the V/div setting to see a signal but that has no real value. If you are looking at a signal within the oscilloscope's bandwidth you'll use 8 bits of ADC resolution at most and with multiple traces on screen likely 6 or 7 bits. If the higher harmonics above the Nyquist frequency are attenuated by 40dB to 50dB they won't trouble you at all.

author: rf-loop
author_rank: Super Contributor
timestamp: May 08, 2019, 10:34:41 am
content: Quote from: tinhead on May 08, 2019, 09:13:00 amThis is produced using freq hopping sinewave(yes there is also rf generator harmonics what also produce aliasing but they are buried behind others in display)sweep so that it leave enough spacing for also get alias peaks visible. So, it is not beautiful image but it is ok for this purpose. So it is swept using constant level signal from 10MHz to 1000MHz (not true constant level at scope BNC input point but enough for this purpose.)In this tiny example fNyquist is 250MHz (500MHz sampling frequency)(maximum if all 4 channels are in use)What other things these aliases do. They can example distort square/pulse etc waveforms of course specially if signal have fast edges where higher level harmonics goes over fN.For peoples who do not know alias things at all, clarify: These arrows mean freq sweeping up direction(example in image (blue arrow) if signal input is 300MHz then FFT show alias 200MHz. and then when inout freq rise alias goes down.. until 0, after then when signal still rise then alias freq rise etc..

author: iMo
author_rank: Super Contributor
timestamp: May 08, 2019, 10:50:19 am
content: Where to place a few pF to make the BW shape better (1204X-E)?

author: rf-loop
author_rank: Super Contributor
timestamp: May 08, 2019, 11:05:08 am
content: Quote from: imo on May 08, 2019, 10:50:19 amWhat is better shape?If want better shape then filter need follow ADC sampling frequency and so on.Here same experimental with 1GHs ADC sampling frequency.Then if have BW limited more steep with this 500MSa/s then can ask is it ok anymore for this next.As previous, also this is produced using freq hopping sinewave(yes there is also rf generator harmonics what also produce aliasing but they are mostly buried behind others in display)sweep so that it leave enough spacing for also get alias peaks visible when freq rise and aliases start fold back from fNyquist.Of course often we use oscilloscope with usual passive probes. This is also filter.Then, example, if we look, say example square waves. Harmonics levels are not at all same as fundamental freq. (3th level 1/3, 5th: 1/5, 7th 1/7, 9th 1/9 etc... IF square is ideal square with 0 risetime, what is is never).So in practice this is not at all as bad situation what it first may feel example if look these images where input freq is constant level over whole sweep freq range. But important is that users undestand these basics in theory and also his scope and his probes etc. Enough knowledge and scope do not fool user so easy.Also when look these images, there vertical scale is LOG. Normally when we use time domain, vertical scale is linear. Why I draw there 26dB range. If example normal time domain display we have 1Vrms sinewave on the screen. When it drop 26dB there is 50mV on display. (5%)If we have 10M square and think its harmonics example 11th. It is 110MHz but it is dropped say example over 20dB... if it have very fast edges it may easy have exaple 31th harmonic 310MHz. But it is perhaps -30dB down from fundamental level. If Sampling freq is 500M (as previous image) it is aliasing, its alias is 190MHz but if we are in time domain display with linear vertical and our fundamental is example 6div height, how is level of this harmonics. Can you see its effect. If front end attenuate 310MHz example 5dB then this harmonic alone is around 0.1div or so. In practice, no visible effect in this square wave shape.But, with FFT we really need care about alias frequencies. There these can mess lot of.Just example. Some RF generator 3rd harmonic can be example -30dBc.If some one is looking 124.9MHz carrier on FFT and example case he is using 500MSa/s.Say example he look 0dBm carrier. 3rd harmonic -30dBc (374.7MHz)Now he can see 124.9MHz 0dBm peak and he can also see 125.3MHz peak level -36dBm. (If scope attenuate 6dB 375MHz.) And then user wonder why there is fundamental carrier 124.9MHz and after then 400kHz higher also signal. Think these with different frequencies and different waveforms with different harmonics. In some cases this situation with many aliases can be really confusing.Keep care and not input over fN frequencies (including harmonics and nonharmonics)