AH 2700A. Attenuator Pair Ratio for C vs Frequency. Option-E 50 Hz-20 khz Ultra-precision Capacitance/Loss Bridge

Transcription

1 0 E ttenuator Pair Ratio or vs requency NEEN-ERLN 700 Option-E 0-0 k Ultra-precision apacitance/loss ridge ttenuator Ratio Pair Uncertainty o in ppm or ll Usable Pairs o Taps /08/0 E E E E E E E E k k k 0k 0k NEEN-ERLN 300 ainbridge Road leveland, Ohio U.S.. E olor vs Tap oltage Website: ino@andeen-hagerling.com all: ax: E dditional eatures o the Option-E version o the k bridge The 700 Option-E is an enhanced precisioersion o the basic 700 bridge. Much like the 00 Option-E, the 700 Option-E oers higher precision and signiicantly enhanced calibration and veriication eatures over its non-option-e base model. Please reer to the regular 700 brochure or a description o basic eatures. eatures in common with the 00 Option-E * Quantitatively improved speciications ull report o all nternal calibration points Real-time temperature corrections Selected hardware or higher perormance eatures New to the 700 Option-E mproved hardware to reduce noise and or better thermal perormance ynamic ierential Non-Linearity (NL) mode New speciications or non-linearity and noise ttenuator Pair Ratio speciication and reporting o the attenuator tap used by each measurement Expanded cable and UT correction commands UT stray capacitance loading correction based on NST Special Publication 0-76 User-settable time out-o-calibration warnings User-settable temperature out-o-calibration warnings eriication/alibration Reports s part o the nternal veriication report, all versions o the 700 report the elapsed operating time and temperature dierence between the conditions used to obtain the currently stored calibration values and the conditions used to obtain the new veriication data. Non-Option-E bridges also report only the one nternal calibration point that is urthest rom its nominal value. Option-E bridges produce a more detailed report which includes the status o each o the nternal calibration points in the bridge. *00 bridges are no longer available. Real-time Temperature orrections n 700 Option-E contains additional nternal calibration data in the orm o temperature coeicients (T s) or all nternal calibration points. This T data is generated when the bridge is manuactured and is considered to be permanent unless the main board or standard capacitor assembly is replaced. The T data is used to adjust the nternal calibration data so that it is correct or the temperature at which the bridge is operating. New Noise and NL Speciications The resolution and non-linearity uncertainty speciications as deined or the basic 700 bridge have been revised or the Option-E version. The resolution speciication has been supplemented by two new speciications in the 700 Option-E:. The irst is an nput Noise speciication. This is shown graphically on page. The units are ppm/ where reers to the measurement rate, not the test requency. This new noise speciication puts an upper limit on the amount o random noise in the measurements while being independent o NL perormance described next.. The second new speciication is ierential Non-Linearity (NL). This speciication puts an upper limit on the magnitude o tiny, local steps in the measurement results that occur as a unction o capacitance or loss. NL behaves like the mathematical derivatives o these measurement result unctions. n all current and previous resolution speciications, this NL uncertainty and the nput Noise are combined within the resolution speciication. n the 700 Option-E bridge, the new NL and noise specs are also speciied separately. This can help better understand the eects that limit resolution. New ntegral Non-linearity Speciication n the 700 Option-E, a new and dierent ntegral Non-Linearity (NL) speciication replaces the non-option-e 700 Non-Linearity spec. This spec uses a commonly accepted method o deining NL as a deviation rom a straight line o the transer curve o the measured value o capacitance (or loss) versus the actual value. deally, the lower ends o the transer curve and the

2 straight line are deined to pass through =0. n most cases, the upper ends o the curve and the line are deined to pass through the highest capacitance (or loss) reachable by the transormer attenuator tap used to make the current reading. This curve is likely composed o quadratic and higher order curves, all o which are so small that we are unable to quantiy their nature. Thereore, we deine our NL spec to be within a band whose width has a ixed height centered on the straight line. This width is speciied as a unction o requency or capacitance and loss as a set o six equations and two graphs shown later herein. This set gives one NL speciication unction or each transormer attenuator tap, through, as listed in Table on page 3. When to use NL versus NL? NL uncertainty is important when accurately comparing measurements o two capacitors having closely similar values. NL uncertainty is important when comparing the sum o the capacitances o two capacitors measured individually against measurements o them taken when connected in parallel. ll three measurements must be made on the same attenuator tap. ynamic ierential Non-Linearity (NL) This is a new eature which can substantially reduce the magnitude o NL step laws in the measured data. t does this by averaging the measured data in regions where these steps are prone to occur. NL s availability is dependent on the test requency and the average time according to Table below. Where possible, NL is enabled by deault, but can be disabled i desired. verage time setting Table : verage Times and requencies or which NL can be Enabled <6 Enableable nactive nactive nactive 7 Enableable Enableable nactive nactive 8 Enableable Enableable Enableable nactive 9 Enableable Enableable Enableable Enableable The ttenuator Pair Ratio Uncertainty Spec Each 700 capacitance bridge contains ratio transormers collectively having a set o eleven selectable attenuator taps that allow a variable voltage to be supplied to the (igh) terminal o the bridge. y selecting one o these taps at a time, this voltage can be very precisely set to cover a range rom zero to volts thereby allowing the bridge to measure correspondingly larger capacitance values using eleven distinct ranges covering over 00 p on the tap range to over.6 on the tap range. The tap range can be calibrated directly by measuring a traceable reerence capacitor having a value compatible with this range such as 00 p. Such direct calibration o the other ten ranges is less desirable due to the limited stability o capacitors having larger values. nter-comparison o measurements made on adjacent ranges allows all the ranges to be calibrated relative to each other and especially o each to the tap range. t the same time, uncertainties can be determined or all pairs o ranges (attenuator taps). These uncertainties are used to create the ttenuator Pair Ratio Uncertainty Speciications (PR) or and shown as graphs on pages and. The non-option-e 700 bridge PR uncertainties are incorporated only into its accuracy speciications. PR uncertainty is undamentally dierent rom all the other uncertainties or bridges in that PR only applies to a pair o measurements. t gives an uncertainty based on that pair's not having used the same attenuator tap or both measurements. the same attenuator tap is used or both members o the pair, then the PR uncertainty is zero. pplication o PR Suppose your lab has a very stable 00 p reerence capacitor with a high accuracy traceability certiicate. urther suppose you have other capacitors having an array o capacitance values. You would like to calibrate these capacitors relative to your traceable 00 p reerence capacitor and you would like to provide a certiicate o traceability with these capacitors. Using 700 bridges, there are three ways to do this:. You can use the capacitance calibration procedure described in the manual to calibrate your 700 non- Option-E bridge. This will allow that bridge to make traceable measurements throughout its range having uncertainties given mainly by the published accuracy speciication or that 700. This is a sae way to make traceable measurements, but will not give the tightest possible uncertainties because the accuracy speciication already allows or a relatively large traceability uncertainty. This traceability uncertainty may be larger than necessary i your traceable 00 p reerence capacitor has a tighter certiication.. You can apply the same procedure described above but using an 700 Option-E bridge. Since the published uncertainties or this bridge will be smaller, you will be able to produce tighter certiicates o traceability than with paragraph above. 3. You can use an 700 Option-E bridge to accurately measure your traceable 00 p reerence capacitor and record the results (without changing the calibration o your bridge). ll subsequent capacitance measurements made with this bridge can then be corrected by the ratio between the earlier recorded results and the traceable certiied value o your 00 p reerence capacitor. The uncertainty calculations or these measurements should not include the published accuracy speciication or your 700 Option-E. nstead, the calculation should include the sum o the traceable uncertainty o your 00 p reerence and the Noise, NL, and T or the measurement o your 00 p reerence. n addition, each subsequent capacitance measurement must add the sum o its own Noise, NL, and T. stability uncertainty is not needed unless enough time has passed to justiy it. One more uncertainty must be added to this list. This is the ttenuator Pair Ratio (PR) uncertainty. This is needed only or whichever subsequent measurements were made using a dierent attenuator tap than was used by the measurement o the 00 p reerence capacitor. The attenuator tap used is reported by each measurement result. Expanded able orrection ommands orrection Models The cable correction model or the non-option-e 700 allows the user to speciy the electrical parameters o the dual coaxial cable that connects the bridge to the UT. These include the capacitance per meter, inductance per meter, and resistance per meter, as well as the length o the cable. This model does not take into account any requency dependent behavior o the cable. To make requency dependent corrections in a non-option-e bridge, you must speciy the cable parameters or each requency at which a measurement is to be taken. nput Noise o p in ppm/ MeasurementRate ttenuator Pair Ratio o vs requency 0k 0k 0k k k k olor vs Tap oltage 00 nput Noise o p vs. requency 0 E E 0 00 p 0 p 0.0 n p k k k 0k 0k 0 E u 00 n 0 n E E ttenuator Ratio Pair Uncertainty o (bsolute, not ppm) or ll Usable Pairs o Taps nput Noise o (0-6 ) in ppm/ MeasurementRate 0k 0k 0k k k k n p k k k 0k 0k E nput Noise o vs. requency p 0 p E 0. E E E E 0. u 00 n 0 n k k k 0k 0k

3 NL o p in ppm NL o p in ppm NL o p vs. requency k p 0. 0 p 0. n 0 n/00 n/ μ 00 p k k k 0k 0k NL o p vs. requency k k p 0. 0 p E k k k 0k 0k NL o (0-6 ) (bsolute, not ppm) k k k NL o vs. requency 0 00 p 0 p n 0 n/00 n/μ 00 p k k k 0k 0k n contrast, each 700 Option-E bridge comes with a OX-TP--N one meter cable. This cable has doublebraided silver plated shields and gold plated N connectors. This construction allows the cable s electrical parameters and its requency dependent behavior to be more accurately and stably deined. The 700 Option-E bridge introduces a new ability to select correction models or speciic cable types and UT conigurations. These models have a built-in knowledge o electrical parameters or speciic cable and UT types. This includes the requency dependence o these parameters i it s signiicant. One o these models is or use with the OX-TP--N cable alone. nother is or use with that cable together with the TT two-terminal to three-terminal adapter. These correction models are selectable by deault as an alternative to the ability to speciy individual cable electrical parameters or cable correction. UT Loading orrections Stray capacitance rom high-to-ground ( ) and low-to-ground ( L ) at the UT causes the measured capacitance to be larger than it should by amounts that are proportional to and L. Loading errors like these are discussed in NST Special Publication The 700 Option-E allows the user to enter the values or and L at the UT when using any o the correction models associated with the OX-TP--N cable. When using these models, the bridge will always automatically correct the measurement results or these stray capacitances. and L have never been entered, then deault values will be used. The Speciication Equations The speciications below give various perormance uncertainties as a unction mainly o capacitance, loss and requency. See page o the basic 700 brochure or deinitions o all the input variables used. Other helpul relations are on page 4 herein. Table. apacitance and conductance ranges or the preerred limiting voltages with k. or < k, multiply Limit by in k. T, and T are used by the speciication equations. ttenuator Tap Limit ( T ) apacitance range Range o ; is in k T.00 - to 0 p -0.8 to 8 ns to 0 p -.6 to 6 ns to 0 p -4 to 40 ns to 00 p -8 to 80 ns 0 0 E to 00 p -6 to ns to 60 p -48 to 480 ns to 6,00 p -0 to 00 ns to,000 p -400 to 4000 ns ,00 to 6,000 p -00 to,000 ns ,000 to 0,000 p to 40,000 ns ,000 to,000 p -,000 to 0,000 ns ccuracy in ppm ollowing calibration: : T is ound in Table T : T : -- / T -- / R P : 00 R p T R 3 p S : s T s p 0 R S : s T s 0. 0 p E The length o the cables connecting the 700 to the UT has a negligible eect on the accuracy or small capacitances. This assumes that the coaxial 0. shield on these cables has 00% coverage. uncorrected by the LE command, cables similar to R-8 will increase the capacitance readings at k by about 40 ppm per meter o cable pair and per µ o capacitance being measured k k k 0k 0k The accuracy Y years ollowing calibration may be calculated rom the expression YS where is the desired accuracy expression rom above and S is the corresponding stability per year below. 0 3 NL o (0-6 ) (bsolute, not ppm) NL o vs. requency

4 Resolution in absolute units:* ccuracy o p vs. requency ccuracy o vs. requency : : R P : 0R p R p n 3 c s S : n 40 3 c s 0 s 0 - s p where n c =.4t -/ and = 0.0l(0./)(R S l0) l/ ( ) l/ t -/. is ound in Table. The series resistance R S needed or may be calculated using R S = l0 6 /((l )). Resolution in ppm:* : n ---- v n 3 c : / p : n 3 c n 3 c ns R S : n 40 s 3 c k n 3 c : n ---- v n 40 3 c n 3 c R P : 0 R p n ---- v n 40 3 c S : n 40 s 3 c ivide result by to get absolute resolution or / ccuracy o p in ppm 00k 0k 0k 0k k k k k p 0 p p 0 p 00 n 0 n 00 p k k k 0k 0k μ μ 00 n 0 n Stability/Year o p vs. requency n n 00 p ccuracy o (0-6 ) (bsolute, not ppm) 00k 0k 0k 0k k k k p p μ μ 00 n 00 n 0 n 0 n 0 p 0 p n 00 p 00 p k k k 0k 0k Stability/Year o vs. requency 0k n.3 R S : *Resolution is the smallest repeatable dierence in readings that is guaranteed to be measurable at every capacitance or loss value. Useul resolution is typically a actor o ten better. nput Noise: S : R S : n s 3 c : : : R P : R ---- p s s R s --- s ---- s Useul Unit onversions The relationships below can be useul or converting rom one kind o units to another. Particularly useul are conversions rom other units to the units o or or use in Table on page 3. = = R p = s 0 6 = R p s = s Rs = s Rs Stability/Year o p in ppm 0k k k k p 0 p p 0 p 00 n 0 n n 00 p k k k 0k 0k μ μ 00 n 0 n n 00 p 9 Stability/Year o (0-6 ) (bsolute, not ppm) 0k k k k p p p 0 p u 00 n 0 n n 00 p k k k 0k 0k u 00 n 0 n n 00 p

5 Resolution o p in ppm Temperature oeicient o p in ppm 0k 0k 0k k k k n n k k k 0k 0k Resolution o p vs. requency p p 0 p 0 p 00 p 00 p μ μ 00 n 00 n 0 n 0 n u Temperature oeicient o p vs. requency k k p p 0 p 00 p 0 p 00 p u k k k 0k 0k u u 00 n 00 n 0 n 0 n n n 8 Temperature oeicient o (0-6 ) (bsolute, not ppm) Resolution o (0-6 ) (bsolute, not ppm) 0k 0k 0k k k k Resolution vs. requency p p 0 p 0 p 00 p 00 p u u 00 n 00 n 0 n 0 n n n k k k 0k 0k Temperature oeicient o vs. requency k k u u 00 n 00 n 0 n 0 n n n k k k 0k 0k p 00 0 p p 00 p 00 p 0 p ttenuator Pair Ratio (PR) Uncertainty in ppm: : log T T : : log T T R P : --- log T T S : log T T R S : --- log T T ierential Non-Linearity (NL) in ppm: ntegral Non-Linearity (NL) in ppm: : : T : : T : R P : S : R S : --- log T T : e : e : e R P : 0 R P e S : e R S : e T T T T max This NL uncertainty speciies the maximum dierence o the sum o the capacitances o two capacitors measured individually against measurements o them taken when connected in parallel. This speciication is valid only i all three measurements are taken using the same attenuator tap. max s discussed in more detail on page, the PR speciication gives the additional uncertainty between a pair o measurements made using two dierent attenuator taps, T and T. These can have values rom to. or a given pair o taps, the values o,, T and T can be ound in Table on page 3. ll usable pairs o taps are plotted in graphs on pages &. This NL speciication assumes that the NL correction eature is disabled. Enabling NL can oten improve NL substantially. The eature s eect is to reduce the mathematical derivative o the measurement results as a unction o capacitance or loss The six equations to the let give the NL uncertainty or each attenuator tap. These range rom to and are listed in Table on page 3. The value o T is given there also. The two equations above give the NL uncertainty or smaller capacitance ranges bounded by 0.0 and max where max can have values o.0 and 0.0 p.

6 Stability in ppm per year: : : : -- / R S : s s Temperature coeicient relative to change in ambient temperature in ppm per : : T where T is ound in Table / : : R P : S : R S : SELETE SPETONS N RPL ORM ccuracy speciications versus and loss There are six contour plots on the next page. The irst three graphs are contour plots o the accuracy o capacitance () versus and conductance (). The irst o these graphs applies at 00, the second one at k and the third one at 0 k. The accuracy in the area within or below each contour is equal to or better than the labeled accuracy (in percent) or that contour. These graphs show that the accuracy o depends not only on the value o but also on the value o the loss. Each contour was plotted using the maximum possible voltage. The graph in the middle o the right column is a contour plot o the accuracy o the dissipation actor () versus and. The accuracy in the area within each contour is equal to or better than the labeled accuracy (in percent) or that contour. This graph shows that the accuracy o depends not only on the value o but also on the value o. ccuracy speciications at selected voltages The irst graph in the bottom row on the next page is a contour plot o the accuracy o versus and. The accuracy in the area within or below each contour is equal to or better than 0.00%. The second graph in the bottom row on the next page is a contour plot o the accuracy o versus and. The accuracy in the area within each contour is equal to or better than 0.03%. 6 / 0 R P : 0 R p R p 0 S : s s T / T / R p T -- - R R p 0 p T s 0 6 T / 0 s s 0 s These graphs show how the accuracy o and depends on the measurement voltage. Each contour represents operation at the labeled voltage which is one o the voltages in Table on page 3. The gray regions are out o range. Option-E Specs ompared to non-option-e Selected speciications or both the 700 Option-E and non-option-e are shown in the graphs below. Speciications or the non-option-e 700 are shown in red while speciications or the Option-E are shown in green. Speciications versus requency There are 6 graphs on pages 8- o plots versus requency or capacitance and loss. These include the accuracy, resolution in ppm, temperature coeicient, accuracy, stability, NL, NL, input noise, and Ppeciications. These plots were generated by using the speciication equations presented on pages 3-6. The exception is that the equations or are multiplied by to get units o absolute. Most graphs contain a set o curves or various values o capacitance. These values range rom one emtoarad up to one microarad. The graphs show that the speciications tend to be best or capacitance values in the region o 0 p to n and worst at either extreme o capacitance. These graphs assume that the capacitance o the UT is o good quality implying a small dissipation actor (<~0.00). Most curves were plotted using the maximum possible voltage. - 0 in ns in ns in ns ccuracy o p vs. p and using maximum voltages requency = 00 0% % 0.% 0.0% 0.00% requency = k ccuracy represented by each contour is 0.00% in p % 0% % 0.% 0.0% 0.00% ccuracy o p vs. p and using maximum voltages 0 6 requency = 0 k % % 0.% 0.0% 0.00% 0.00% in p 0% % 0.% 0.0% 0.00% ccuracy o p vs. p and using selected voltages in p % 7 in ns (tan ) (tan ccuracy o p vs. p and using maximum voltages ccuracy o vs. p and using selected voltages requency = k 0% % 0.% 0.0% 0.00% % ccuracy represented by each contour is 0.03% % % 0-0% % 0.% % 0.00% % in p ccuracy o vs. p and using maximum voltages 0 4 0% % 0.% 0.03% requency = k in p % % 0.% 0.03% 0.00 requency = k in p