Specifying Calibration Standards and Kits for Agilent Vector Network Analyzers. Application Note

Transcription

1 Speciying Calibration Standards and Kits or Agilent Vector Network Analyzers Application Note

2 Table o Contents Introduction... 3 Measurement errors... 3 Measurement calibration... 3 Calibration Kits... 4 Connector deinitions... 5 Calibration standards deinition... 6 Class assignment Modiication Procedure PNA calibration kit entry/modiication procedure Calibration kit modiication/entry procedure Appendix A: Dimensional Considerations in Coaxial Connectors mm coaxial connector interace mm, 2.4-mm, 1.85-mm, 1.0-mm coaxial connector interace Type-N coaxial connector interace Appendix B: Derivation o Coaxial Calibration Coeicient Model Appendix C1: Derivation o Waveguide Calibration Coeicient Model Appendix D: Data-based Calibration Standard Deinition File Format Example ile Preliminary #PNA keywords Reerences Web Resources

3 Introduction Measurement errors Measurement errors in network analysis can be separated into two categories: random and systematic errors. Both random and systematic errors are vector quantities. Random errors are non-repeatable measurement variations and are usually unpredictable. Systematic errors are repeatable measurement variations in the test setup. Systematic errors include impedance mismatch, system requency response and leakage signals in the test setup. In most microwave measurements, systematic errors are the most signiicant source o measurement uncertainty. The source o these errors can be attributed to the signal separation scheme used. Numerous publications are available on vector network analyzer (VNA) calibration techniques. Reerences [1], [2], [3], [4], [5], [6], [7] and [8] are just some o the published work. Agilent s application notes: , and also provide insights on VNAs and VNA error correction. It is recommended that a user be amiliar with these calibration techniques and terminologies to get the maximum understanding rom this application note. Measurement calibration A measurement calibration is a process which mathematically derives the systematic error model or the VNA. This error model is an array o vector error coeicients used to establish a ixed reerence plane o zero phase shit, zero relection magnitude, lossless transmission magnitude and known impedance. The array o coeicients is computed by measuring a set o known devices or calibration standards connected at a ixed measurement plane. Dierent calibration techniques are used to solve dierent error models. The deinition o calibration standards and types are set up dierently or the applicable calibration techniques. Solving the ull 2-port twelve term error model using the short/open/ load/ thru (SOLT) calibration method is an example o only one o the many measurement calibrations available. The type o measurement calibration selected by the user depends on the device to be measured (i.e., 1-port or 2-port device) the calibration standards available and the extent o accuracy enhancement desired. A combination o calibrations can be used in the measurement o a particular device, such as adapter removal calibration or noninsertable devices. The accuracy o subsequent device measurements depends on the accuracy and stability o the test equipment, the accuracy o the calibration standard model, and the calibration method used in conjunction with the error correction model. This application note covers calibration standard deinitions, calibration kit content and its structure requirements or Agilent s vector network analyzers. It also provides some examples o how to set up a new calibration kit and how to modiy an existing calibration kit deinition ile. 3

4 Calibration Kits A mechanical calibration kit consists o a set o physical devices called standards, as shown in Figure 1. Each standard has a precisely known magnitude and phase response as a unction o requency. In order or the VNA to use the standards o a calibration kit, each standard must be assigned or organized into standard classes which correspond to the calibration method used by the VNA. Agilent currently supplies mechanical calibration kits with 1.0-mm, 1.85-mm, 2.4-mm, 3.5-mm, 7-mm, and Type-N 50 ohm, Type-N 75 ohm, Type-FD 75 ohm and 7-16 coaxial connectors. Rectangular waveguide calibration kits include X, P, K, R, Q, U, V and W bands. Calibration or microstrip and other non-coaxial media is described in Product Note A: Agilent Network Analysis Applying the 8510 TRL Calibration or Non-Coaxial Measurements, literature number E. A calibration kit may support many calibration methods. Figure 1. Mechanical cal standards and cal kit 4

5 Connector deinitions In addition to calibration standard deinitions and standard class assignments, calibration kits also provide deinitions o connectors. Agilent s PNA network analyzer amily uses the connector deinition to deine connector (Figure 2): Frequency Range Gender (male, emale, no gender) Impedance Media (coax, waveguide, etc) Cuto Frequency (waveguide) Height/Width Ratio (waveguide) Figure 2. PNA connector entry screen A calibration kit may be deined with multiple connectors. Each 1-port calibration standard must be associated with a deined connector. Two port standards, such as thrus and adapters, may be associated with two dierent deined connectors. 5

6 Calibration standards deinition The S-parameters o VNA calibration standards must be deined suiciently and accurately to satisy the requirements o the calibration methods or which they will be used. Calibration standards may be deined in various ways. Agilent s VNAs support two types o calibration standard deinitions: calibration coeicient model and data-based model. Calibration coeicient model The majority o VNAs deine calibration standards by using a transmission line model or 2-port standards and a terminated transmission line model or 1-port standards. (See Figure 3.) Transmission line Z C ; delay; loss Z T Figure 3. Terminated transmission line model The transmission line and termination may be represented by a signal low graph as illustrated in Figure G 1 e - γ 1+ G 2 G i G 1 G G2 G 1 G T 1+ G 2 e - γ 1+ G 1 Figure 4 Signal low graph o terminated transmission line model Figure 5 shows the same terminated transmission line model in cascade parameter ormat:, deine XI and Xo a b [ T XI ] [ T L ] [ T XO ] [ G L ] Figure 5. Cascade parameter representation o terminated transmission line model Where Zc Zr Z Γ1 = ; Γ2 = Γ1 ; ΓT = Z + Z Z c r γ = α+ jβ ; l = length o line; T T Z + Z Z ^ characteristic impedance o line c Z ^ reerence impedance (connector impedance or system impedance) r α ^ propagation loss constant o line β ^ propagation phase constant o line r r (1.1) 6

7 Γ [ ] ] ][ γ l 1 1 Γ1 e ( ) [ ; L = 1 + Γ1 Γ1 1 ] [ ] [ 0 e 1 1 Γ1 ΓT ; ΓL = ( 1 Γ )[ [ ] Γ 1 ] [ 1 ] b b = ; =[TXI [ TL T ][ Γ ] a a i XO L [ T ] = T XI [ TXO] = Γ i 1 2γl 2γl Γ1 ( 1 e Γ1ΓT)+ e Γ = 2γl 2γl 1 Γ e Γ + Γ 1 e 1 T 1 [ 1 T ] ( ) 0 γ l ] (1.2) (1.3) (1.4) Transmission line characteristic impedance and propagation constants can be derived rom the line s physical properties [9], [10]. Agilent s VNA uses oset delay, oset loss and oset Z 0 instead o Z C, and gl to model the transmission line. With these oset deinitions, the VNA can compute the transmission line s characteristic impedance and, propagation phase and loss constants o the calibration standard without deining the dielectric constant o the calibration standard s transmission medium which may be dierent rom that o the device under test. This assumes that the oset loss and oset delay values were derived using the same dielectric constant. Oset delay Oset delay is the dispersion ree, TEM mode, electrical delay in seconds. ε r l ( Oset delay )= ; c l = physical oset length rom reerence plane (1.5) ε = r relative permittivity (dielectric constant) o transmission medium = in sea level and 50% humididty c = speed o light in vacuum = x 10 8 m/s Note that the reerence plane o coaxial connectors is deined as the mating plane o the outer conductors. Appendix A on page 30 illustrates the physical oset length deinition o certain coaxial connector types. 7

8 Oset loss Oset loss is in G½/sec. It is the propagation loss per unit length o the transmission line at a normalization requency, such as 1 GHz, multiplied by the speed o light in the transmission medium. For coaxial devices, it can be calculated rom the loss magnitude data at 1 GHz. S 21 data: Linear mag: Oset loss ( ) = Log mag (db): Oset loss Oset Z0 ( Oset delay) -ln ( 10 db GHz Oset Z 1 0 ( ) 10 )( ) ) = *ln( S ) GHz Oset delay (1.6) S 11 data: (1.7) For best results, curve it the measured data to the unction. See Appendix B on `b page 32 or details For rectangular waveguide transmission lines, loss is not a simple unction o requency. In most cases, the 1 GHz data point is not available. Since the loss o most waveguide standards are very small and are usually used way above cut o, the oset loss term is assumed to be 0. The waveguide loss model is not supported by all VNAs until recently. Agilent s PNA series o network analyzers now include a waveguide loss model. See Appendix C on page 35. ( oset loss) = ln( ) µ 0 ( oset delay)( ) ε 0 c [ ( ) ] 2 1 c h c ( ) w (1.8) Oset Z 0 Oset Z 0 is the lossless characteristic impedance o the transmission line. For coaxial transmission lines, the lossless characteristic impedance is Z µ 0 r µ r D ( ) ( ) ( ) ln ( ) εr d 1 µ D 0c = ln = µ 2π ε d 2π = relative permeability constant o the transmission medium D = outer conducter inner diameter, d = center conductor outer diameter (1.9) Z C, the transmission line characteristic impedance that includes skin loss eects can be derived rom the oset Z 0 and oset loss terms. Waveguide oset Z 0 and characteristic impedance is normalized to 1. 8

9 Oset terms and transmission line parameters For coaxial transmission lines the ollowing expressions relate the oset terms to the transmission line s electrical parameters. See Appendix B on page 32 or their derivation. [ ] 10 9 ; requency in Hz αl = ( oset loss )( oset delay ) 2oset ( Zo) βl = 2π( oset delay )+ αl Zc = ( oset Zo)+ ( 1 j) ( ) oset loss 4π 10 9 (1.10) For rectangular waveguide transmission lines [11] the ollowing expressions relate the oset terms to the transmission line s electrical parameters. See Appendix C on page 35 or details. c βl = 2π ( oset delay ) 1 ; = waveguide cut o requency α c ( ) l ( oset loss)( oset delay ) 2 ε0 ( ) ( µ ) c 0 [ h c w ( ) ] 2 1 c ( ) (1.11) Waveguide impedance varies as a unction o requency. In such cases, normalized impedance measurements are typically made. When calibrating in waveguide, the impedance o a matched load is used as the impedance reerence. The impedance o this load is matched to that o the waveguide characteristic impedance across the guide s requency bandwidth. Normalized impedance is achieved by setting OFFSET Z 0 to 1 ohm or each standard and setting system Z 0 (SET Z 0 ) to 1 ohm. 9

10 Terminating devices Short Many vector network analyzers assume that the short is an ideal short and has a relection coeicient o 1. This may be adequate at low requencies and or large connector sizes, such as 7 mm and larger. However, at higher requencies and or smaller connectors, 3.5 mm and smaller, at least a third order polynomial inductance model, L S, is required. Loss o the short circuit is assumed to be insigniicant. L = L + L+ L + L ; Z = j πl Γ S S 2 S S Z = Z S S Z + Z r r (1.12) In some cases (when the phase response is linear with respect to requency) the response o a short can be modeled as an equivalent incremental length. Open Open circuits radiate at high requencies. This eectively increases the electrical length o the device and can be modeled as a requency dependent capacitor, C 0, (also known as ringing capacitance). At low requencies, a ixed capacitance value may be suicient. Most network analyzers use a third order polynomial capacitance model. Radiation loss is assumed to be insigniicant. C = C + C+ C + C ; Z = 0 0 j2πc Γ 0 Z = Z Z + Z 0 r 0 r 0 (1.13) In some cases (when the phase response is linear with respect to requency) the response o an open can be modeled as an equivalent incremental length. Fixed load The ixed load is assumed to be a perect termination, G L = 0. However, i an oset transmission line with a inite delay and loss is speciied, and an oset Z 0 is not equal to the reerence impedance, the total relection is NOT zero. This is as deined in equation (1.4). Arbitrary impedance An arbitrary impedance device is similar to a ixed load except that the load impedance is NOT perect. The previous generations o VNA, such as the Agilent 8510, 87xy series and the early irmware releases o the PNA series, use a ixed resistance value. A complex terminating impedance has been added to the PNA series to allow or more accurate modeling o circuit board and on-waer devices. Z ZA = R+ ji ; ΓA = Z A A Z + Z r r (1.14) 10

11 Oset loads Note The 8510 assumes that the irst oset has zero delay and the second oset has the required delay. Thereore, the oset delay value o the oset load must be the dierence in delay between the two osets. Figure 6. PNA oset load entry screen An oset load can be considered a compound standard consisting o 2 known osets (transmission lines) o dierent length and a load element (Figure 6). The deinition o the osets is the same as all oset transmission lines. The shorter o the two osets can be a zero length oset. The load element is deined as a one-port relection standard. An oset load standard is used when the response o the oset standards is known more precisely than the response o the load element. Measurement o an oset load standard consists o two measurements, one with each oset terminated by the load element. The requency range o the oset load standard should be set so that there will be at least a 20-degree separation between the expected response o each measurement. In cases where more than two osets are used the requency range may be extended as the internal algorithm at each requency will search through all o the possible combinations o osets to ind the pair with the widest expected separation (to use in determining the actual response o the load element.) When speciying more than two osets, the user should deine multiple oset load standards. When assigning multiple oset load standards to SOLT classes or the PNA. it is usually beneicial to speciy use expanded math when possible. See the section on SOLT class assignment on page 16. Sliding load A sliding load is deined by making multiple measurements o the device with the sliding load element positioned at various marked positions o a long transmission line. The transmission line is assumed to have zero relections and the load element has a inite relection that can be mathematically removed, using a least-squares-circle-itting method. For best results, try to move the load element in the same direction, do not move it back and orth. Also, try to slide in non-uniorm, not equally spaced, increments. 11

12 Data-based standard model The data-based standard model is a new eature in Agilent s network analyzers. It allows a calibration standard to be deined by a data ile that contains requency data, S-parameter data and uncertainty data. The data ile may be created using actual measured data rom a reerence metrology laboratory, model data rom device modeling sotware or combinations o both. See Appendix D on page 37 or details on data ile ormats. Figure 7 shows how the data-based standard bypasses the itting process and eliminates any errors that may have been associated with the itting. Fitting errors are usually negligible or requencies below 30 GHz. However, at higher requencies multiple requency banded models or the same standard have been used to avoid errors due to itting. The data-based standard avoids this problem altogether by interpolating on the data directly. The data-based calibration standard also eliminates shortcomings o itting non-coaxial or waveguide standards to the models based on a coaxial or waveguide structure. This increased lexibility also enables the user to more easily deine custom calibration standards that do not accurately it existing calibration coeicient models. This can be especially useul or dispersive transmission line structures. The data may be obtained by device modeling based on physical dimensions or rom accurate measurements. Compute nominal response rom nominal dimensions Fit nominal response to polynomial model Nominal data-based model (eliminates itting errors) Nominal polynomial model (includes itting errors) Figure 7. Data-based vs. polynomial model The actory data-based models are similar to polynomial models in that they are a generic nominal model or a particular part number. Thus, a replacement calibration standard can be ordered or a calibration kit and used without having to modiy the data-based model. Data-based standards also open the opportunity o enhancing the accuracy o a particular calibration kit. For example, calibration with a broadband load calibration kit is usually less accurate than calibration with either a TRL calibration kit or sliding load calibration kit. The main source o degradation is the accuracy o the ixed load model. The generic model or a ixed load is that its relection coeicient is equal to zero at all requencies. As an alternative, a ixed load can be characterized using a more accurate calibration. The resulting characterization data, with uncertainties, is used as the databased standard deinition o that particular load. Figure 8 shows how the data iles can be created. Figure 9 shows the data entry screen or data-based standards. Calibrations using the ixed load and its associated data-based model will have an accuracy approaching the accuracy o the system that characterized the ixed load. The residual directivity error now depends on the uncertainty o the characterization rather than the speciication o the load. 12

13 Compute nominal response rom nominal dimensions Characterize actual response or a particular standard (or example, a ixed load) Nominal data-based model (valid or a particular part number) Data-based model (valid or a particular standard) Figure 8. Nominal vs. customized data-based ile Figure 9. Data-based standard setup screen Maximum/minimum requency The maximum and minimum requency entries deine the applicable requency range o the calibration standard. The applicable range may be limited by the model data, accuracy o the model or the physical dimensions o the calibration standard. A ixed load, or example, may be used at low requencies while a sliding load may be used at high requencies. For waveguide, the minimum requency is the waveguide cut-o requency. Although the PNA s SmartCal (guided cal) no longer uses the minimum requency o a calibration standard as the cut-o requency or dispersion correction, it is still recommended that the minimum requency equals the cut-o requency or backward compatibility. 13

14 Class assignment Calibration kit class assignment organizes calibration standards into a ormat which is compatible with the error models used in measurement calibration. Each calibration standard is assigned with a standard number. That number is then assigned to a class or calibration measurement that is required or the calibration method selected. Some standards may have multiple standard numbers assigned or dierent calibration methods or dierent standard deinitions. This may be necessary to optimize the accuracy o the standard model or a given requency band and/or calibration requirement. For the 8510 VNA, a calibration kit may contain up to 21 standards. There is no limit on the PNA SmartCal (guided cal). The required number o standards will depend on requency coverage and calibration methods supported. A single standard class is a standard or group o (up to 7 or most VNA) standards that comprise a single calibration step. The standards within a single class are assigned to locations A through G as listed in the Class Assignments table. It is important to note that each and every class must be deined over the entire requency range or which the calibration is made, even though several separate standards may be required to cover the ull measurement requency range. Not all VNAs support the same set o calibration methods and calibration kits. Check the instrument s documentation or its capabilities. The ollowing sections provide detailed descriptions o the various VNA class assignment structures. VNA calibrations are test-port speciic and thereore class assignments are structured around port numbers. Since only 1-port and 2-port calibration standards are available, calibration kit class assignments are 2-port based, only one port pair can be calibrated at a time. Standard types Calibration standards are assigned to the ollowing standard types (Figure 10): OPEN, SHORT, LOAD, THRU, ADAPTER (8510) and DATA BASED STANDARD (PNA) Figure 10. Calibration standard selections 14

15 An OPEN calibration standard assumes that the polynomial coeicients represent a capacitance model and computes its relection coeicients according to equation (1.13). The VNA assumes that each capacitance coeicient is scaled to a deault exponent C0= sxx. xxx10 F; C2= sxx. xxx10 F/ Hz ; s sign( + or ) C1 = sxx.xx x 10 F/ Hz ; C3= sxx. xxxx10 F/ Hz 3 (1.15) All Agilent VNA models use the same scaling actor. A SHORT calibration standard assumes that the polynomial coeicients represent an inductance model and computes its relection coeicients according to equation (1.12). The deault exponents or inductance terms are: L0= sxx. xxx10 H; L2= sxx. xxx10 H/ Hz L1 = sxx.xx x 10 H/ Hz ; L3= sxx. xxxx10 H/ Hz ; s sign( + or ) (1.16) Four types o LOAD standards are available: a ixed load, sliding load, arbitrary impedance and oset load. The deault setting or ixed load is delay=0, loss=0 and Z0=50 ohms; a perect termination. A sliding load triggers prompts or multiple slide positioning and measurements. A minimum o 6 slide positions is recommended. Arbitrary impedance requires a terminating impedance entry, a real value only or most VNA and complex value or the PNA. Oset load requirements are explained in the Terminating Device section on page 10. A DATA BASED STANDARD is deined by a data ile. See Appendix D on page 37 or the requirements and ormat o data iles. Calibrations and class assignments Assigning standards to class Calibration kits can be created to support SOLT calibrations, TRL calibrations, or both. Class assignments are a way or the calibration kit ile to guide the selection o standards during the calibration process. When assigning standards to a class or the PNA SmartCal (guided cal) the order in which the standards appear indicates the deault preerence or the calibration kit. As the internal PNA irmware searches or the appropriate calibration standard to use at a given requency it starts at the top o the list and searches until it inds a standard that can be used at that requency. For this reason it is important to list the preerred standards irst. For example, a calibration kit that includes a sliding load usually also includes a broadband load i the broadband load is listed beore the sliding load, the sliding load will not come up as a deault selection. For the 8510 and its derivatives (87xy and unguided cal o the PNA), the order o standard assignment within a given class is not important. The order o the standard measurements is important. When two standards have overlapping requency bands, the last standard to be measured will be used. The order o standard measurement between dierent classes is not restricted, although the 8510 requires that all standards that will be used within a given class are measured beore proceeding to the next class. Multiport calibrations use a series o one-port and two-port calibration standards and are comprised o a series o two-port SOLT and /or TRL calibrations. 15

16 SOLT class assignment In the simplest case, an SOLT calibration consists o two one-port calibrations ollowed by orward and reverse transmission and relection measurements on a thru standard. The thru standard can be a deined thru or an unknown thru. The simplest thru standard is a zero-length thru which is simply the connection o port i to port j. Selecting the radio button corresponding to a particular class enables modiication o both the standards included in the class, and a user-deined label associated with the class. The user-deined class label is visible during unguided calibration on the PNA. Each one-port calibration requires relection measurements on at least three known and distinct standards. S 11 A, S 11 B, and S 11 C represent the three relection standard classes or port i while S 22 A, S 22 B, and S 22 C represent the three relection standard classes or port j. Most o the time S 11 A and S 22 A have the same standards, S 11 B and S 22 B have the same standards, and S 11 C and S 22 C have the same standards. The standards assigned to each class may have dierent connector deinitions, dierent requency coverage, and dierent standard types. Some calibration kits, such as the Agilent 85059A 1.0 mm precision calibration kit, use a combination o open, short, load and oset short standards to calibrate over a very wide requency range. Both shorts and opens are assigned to the S 11 A class as illustrated by Figure 11. Label is just a name assigned to that class. This label is used or on-screen prompts or sotkey labels during the calibration measurement process. Figure 11. Example opens and shorts in the same class Four calibration classes are associated with the thru standard measurements, namely: FWD TRANS, FWD MATCH, REV TRANS, and REV MATCH. Except or rare occasions, these classes will all contain the same standards; the LINK FWD TRANS, FWD MATCH, REV TRANS, and REV MATCH checkbox acilitates the common manipulation or these classes. 16 Unchecking the LINK option provides the ability to deine dierent standards or each o these classes. This option would be used in the rare case where an external testset may require manipulation between the various measurements o the thru standard. In this case assigning dierent standards or each class will result in a separate prompt during calibration. Normally, one thru standard would be assigned to the FWD TRANS and FWD MATCH classes and a dierent thru standard, with an identical model, would be assigned to the REV TRANS and REV MATCH classes. This would result in two separate prompts during the calibration sequence.

17 The unknown thru calibration is one o the thru choices o the PNA. It does not require a thru standard deinition. Any two port passive reciprocal device can be used as the unknown thru device. A low-loss device, less than 20 db loss, is preerred but not a requirement. Adapter class is set up in the 8510 or adapter removal calibration. It deines the electrical delay o the adapter in order to determine the correct S 11 and S 22 response o the adapter. The delay value need not to be very accurate. However, the correct phase, within ± 90, or all the measurement requency points must be provided. A class assignment table is a very useul tool to help organize calibration standard assignments or data entry. All calibration kit operating and service manuals provide examples and blank orms o assignment tables. Compare the SOLT class assignment table (Table 1) with the PNA s cal kit editor SOLT class assignment edit screen (Figure 12) to see the mapping relationships. The SOLT class assignment table maps directly into the 8510 s modiy cal kit class entry ormat. Table 1. SOLT class assignment table or the 85052D kit CLASS A B C D E F G Class Label S 11 A 2 15 Open S 11 B 1 7 Short S 11 C 3 14 Load S 11 A 2 15 Open S 22 B 1 7 Short S 22 C 3 14 Load Forward transmission Thru Reverse transmission Thru Forward match Thru Reverse match Thru Adapter 15 Adapter Figure 12: PNA s cal kit editor modiy SOLT class screen or 85052D kit 17

18 Traditionally, relection calibrations have been computed using the measured response o three calibration standards at each requency. For port i, at each requency three standards are selected, one each rom S 11 A, S 11 B, and S 11 C and used to compute the systematic error terms associated with port i. Similarly S 22 A, S 22 B, and S 22 C are used or port j. Each class may include more than one standard, the speciied minimum and maximum requency o each standard in the class is used to determine which standard to use or a particular requency. Usually, when multiple standards are listed in a class their requency ranges have a inite overlap. For the 8510 and unguided calibration on the PNA, the last standard measured is used in the overlap region. Usually the load classes or a sliding load kit are deined with three load standards a low band load, a sliding load and a broadband load. Oten the low band load and the broadband load are the same physical device. The low band load has a reduced requency range and is intended to be paired with the sliding load to cover the ull requency range o the kit. For users who desire a quicker, less accurate calibration, the broadband load is deined to cover the ull requency range. In the 8510 and PNA unguided calibration, i a user measured a sliding load then measured a broadband load, the calibration would be computed using only the broadband load ignoring the sliding load altogether. SmartCal (guided cal) in the PNA avoids this problem altogether by selecting the standards based on the order they are listed in the class, thus a sliding load will always have priority over a broadband load when it is listed beore the broadband load. Expanded calibration is a weighted least squares solution that uses the measurement o three or more standards. The least squares solution works well when all observations are trusted to the same degree. That is to say the actual response o each standard is known with the same accuracy. This is a reasonable assumption or ECal, but may not be valid when a least squares approach is applied to calibrations using other calibration kits due to the physical property dierences o the standards. Expanded math is a weighted least squares solution approach that provides a simple solution to handle the case where the observations are not all trusted to the same degree[12]. I the observations are all independent but not equally trusted, an optimal solution is best obtained by multiplying each equation by a weighting actor that includes both the accuracy o the standard s model and the proximity o the standard s response to the response o the other measured calibration standards. The accuracy o the standard model is explicitly deined or data-based standards, or the other standards a nominal accuracy is assigned to provide a relative weighting or the weighted least squares solution, Table 2. Deault relative accuracy o cal standards types. The measurement o a standard is included in the weighted least squares solution over the requency range where the accuracy o the standard is deined; this requency range is greater than or equal to the requency range where the standard is selected speciied by the min/max requencies. To avoid conusion in the ollowing table, FMin and FMax correspond to the minimum and maximum requency speciied or the standard while UMin and UMax correspond to the minimum and maximum connector requency. Also in the ollowing table, endpoints are given; nominal accuracy at a given requency is computed as a linear interpolation between the appropriate endpoints. Note Nominal accuracy does not correspond to the accuracy o the calibration standards or any particular calibration kit nominal accuracy should simply be considered as a deault weighting. Table 2. Deault relative accuracy o cal standards types Standard Nominal accuracy Frequency range type UMin FMin UMax UMin UMax Open 0.01 UMax/10 12 Minimum connector Maximum connector requency requency Short UMax/10 13 Minimum connector Maximum connector requency requency Fixed load *UMax/10 12 Minimum connector Maximum connector requency requency Sliding load FMin/2 Maximum connector requency 18

19 When use expanded math when possible is checked the solution at each requency all o the measured one-port standards will be included in the solution i requency alls between UMin and UMax. For example, consider a sliding load calibration that includes requencies in both the low band load and sliding load requency ranges. The open, short, low band load and sliding load will be measured. At each requency between UMin and UMax o the sliding load the computation will use expanded math. Using expanded math in this case will blend the transition between the low band load requency range and the sliding load requency range. As another example, the 85058B 1.85 mm calibration kit has a low-band load, an open and a series o short standards with varying osets. There is a minimal set o standards deined that would insure calibration with three standards is possible at each requency. The minimum and maximum requency ranges or each standard combined with the class assignments will determine a set o three standards or each requency resulting in a series o requency ranges where only three standards would be required. I the VNA spans more that one o these requency ranges there will be more than three relection standards connected. In the case o the 85058B, in addition to blending the transitions between the requency ranges, the overall accuracy o the calibration improves when using expanded math. There is an option to measure all mateable standards in class measuring all o the standards results in the best accuracy or kits like the 85058B and the 85059B. It is advantageous to measure all o the standards or some calibration kits, but not or others. For example, in the case o the sliding load kit discussed earlier, selecting measure all standards in class would result in measuring the low-band load, the sliding load and the broadband load. There is no advantage to measuring two ixed loads when doing a sliding load calibration. TRL class assignment The TRL/TRM amily o calibration is deined by the TRL thru, relect and line classes plus TRL options. Table 3 shows the TRL portion o a typical VNA class assignment table. Table 3. TRL class assignment table Class A B C D E F G Class label TRL thru thru TRL relect 2 4 short TRL line/match line/load TRL options: Calibration reerence impedance: System Z 0 Line Z 0 Test port reerence plane: Thru Relect (PNA only) q LRL line auto characterization 19

20 Figure 13. TRL edit class screen TRL is a generic name that represents a class o calibrations that allow partially known calibration standards to be used. In general, the thru standard is assumed to be ully known with perect match; the relect standard is assumed to have a high relection with unknown amplitude and partially known phase. The line standard is assumed to have the same propagation characteristics as the thru standard with partially known phase. Table 4 provides a mapping o speciic calibration types to the TRL class. Table 4. Mapping TRL standards to TRL class 20 Thru class Relect class Line class TRL Zero length thru with Unknown equal relect Line with S 11 = S 22 = 0 (thru/relect/ S 11 = S 22 = 0, S 21 = S 12 = 1 on port i and port j. phase approximately known. line) Phase approximately Bandwidth limited to avoid known. phase o ±20. LRL Line1 with S 11 = S 22 = 0, Unknown equal relect Line2 with S 11 = S 22 = 0 (line/relect/ S 21 and S 12 both known on port i and port j. phase approximately line) with same propagation Phase approximately known. Bandwidth limited characteristics as Line2. known. so phase is at least ±20 dierent rom phase o Line 1. TRM Zero length thru with Unknown equal relect Can be deined as ixed (thru/relect/ S 11 = S 22 = 0, S 21 = S 12 = 1 on port i and port j. loads on ports i and j match) Phase approximately S 11 =S 22 = 0. Can also be known. deined as very long lossy line. LRM Line with S 11 = S 22 = 0, Unknown equal relect Can be deined as ixed (line/relect/ S 21 and S 12 both known. on port i and port j. loads on ports i and j match) Phase approximately S 11 = S 22 = 0. Can also be known. deined as very long lossy line. TRA Zero length thru with Unknown equal relect Attenuator between ports (line/relect/ S 11 =S 22 =0, S 21 =S 12 =1 on port i and port j. I and j S 11 =S 22 =0. Deined attenuator) Phase approximately as lossy line. known. LRA Line with S 11 =S 22 =0, S 21 Unknown equal relect Attenuator between ports I (line/relect/ and S 12 both known. on port i and port j. and j S 11 = S 22 = 0. Deined attenuator) Phase approximately as lossy line. known.

21 The generalized TRL algorithm assumes the characteristic impedance o the line standard equals the desired system characteristic impedance. The calibration reerence Z 0 option allows or adjustments to the calibration to account or small perturbations between the system Z 0 and the line characteristic impedance Z c. This is derived rom the deined Oset Z 0 and Oset Loss terms. See equation (2B.5) in Appendix B on page 32 I line Z 0 is selected, no adjustments are made. Caution: Do not select System Z 0 i oset Z 0 o the line or match standard is very dierent rom system Z 0. TRL calibration is computed initially at a reerence plane that corresponds to the middle o the thru. In this case, the line standard can be assumed to be the portion o the line standard let over ater subtracting a length equal to the length o the thru standard. Ater the error coeicients are computed, they are adjusted to establish a testport reerence plane based on either the model o the thru standard or the model o the relect standard. When selecting the relect standard to set the testport reerence plane, the assumption is that the relect standard is precisely known as both magnitude and phase o the relect standard will be used to compute the testport reerence plane. Selecting the thru standard to set the reerence plane obviously works or a zero length thru. In the case when the thru standard is a line with non-zero length, the model o the thru standard is used to compute the testport reerence plane. In the case o coax or waveguide, using the model o the thru standard alone will provide excellent results. In the case o other dispersive media such as microstrip, the thru standard alone may give less than optimal results. One option would be to design the test ixture and calibration standards so that the testport would be located in the middle o the thru. Another alternative would be to select LRL line auto characterization. One o the by-products o the TRL algorithm is a computed value or the line standard propagation constant. This would include any dispersive eects o the transmission medium. When LRL line auto characterization is set the propagation characteristics o the thru standard are computed rom the computed propagation characteristics o the line standard and the deined delays or both the thru and line standards. Note, LRL line auto characterization will only be used at requencies where both the THRU and LINE standards are delay lines and where the oset impedance o the THRU and LINE standards are equal. Table 5. TRL options and meaning Calibration reerence plane set LINE standard is a match standard Reerence plane set by THRU standard deinition LINE standard is a Reerence plane set rom Reerence plane Reerence plane delay line with deined estimated LINE propagation set by THRU set by REFLECT oset Z 0 EQUAL to constant and speciied standard deinition standard deinition deined oset Z 0 delays o THRU and o THRU standard LINE standards. LINE standard is a delay line with deined oset Z 0 NOT EQUAL to deined oset Z 0 o THRU standard Reerence plane set by THRU standard deinition 21

22 Modiication Procedure Calibration kit modiication provides the capability to adapt to measurement calibrations to other connector types. Provided the appropriate standards are available, cal kit modiication can be used to establish a reerence plane in the same transmission media as the test devices. Additionally, the modiication unction allows the user to input more precise physical deinitions or the standards in a given cal kit. The process to modiy or create a cal kit consists o the ollowing steps: Note Calibration kit entry and modiication procedures or the Agilent ENA series o network analyzers are well documented in the Calibration Chapter o the ENA User s Guide, thereore, they are not covered in this document. 1. Select Modiy Cal Kit 2. Select Kit, Import Kit or Create New 3. Deine the connector(s) [coax, waveguide etc.] 4. Select Standards 5. Deine the standards 6. Select Assign Classes 7. Enter the standard types and classes 8. Select Name or Rename Kit 22

23 PNA calibration kit entry/modiication procedure Use the Advance Modiy Cal Kit Wizard on the PNA s [Calibration] pull down menu to create or modiy a calibration kit or the PNA. Or, download a PC executable PNA Cal Kit Editor program. The PC version may not be as updated as the PNA s built-in version. Newer versions can process kit data created by an older version. The reverse may not be true. The PNA s built-in cal kit editor will show a list o all cal kits iles currently available and can be selected or modiication. All current Agilent mechanical calibration kits are preinstalled in the actory cal kit ile directory. I the kit o interest is not on the list, import the kit (instructions ollow). Once on the list, select the kit, then click on [Edit Kit]. Cal Kits can be imported rom other directories, the disc drive or the USB drive. Almost all previous versions o network analyzer data iles can be imported. Some user created 8510 cal kit iles and 87xx cal kit iles may not import properly. Check the kit s content ater download to make sure all data entries are correct. Note that PNA versions o all the Agilent 8510 calibration kits were pre-installed in the actory cal kit directory. With the PC version, select a kit and then select [Edit] >[Modiy]. Figure 14. Select and modiy cal kit 23

24 The cal kit s connector amily can be renamed. The APC 7 connector amily is being changed to 7mm. To set up a new kit, the connector amily must be deined beore adding calibration standards. Any changes to the connector deinition must also be perormed beore editing the calibration standards. With the amily name changes, all the kit s cal standard connector designations in the description ield and the kit description ield are updated as shown below I the connectors [Add or Edit] eature is selected, the Add or Edit connector screen appears. The media section deines the transmission line type COAX, WAVEGUIDE or others when available. I WAVEGUIDE is selected, the Cuto Frequency and Height/Width Ratio entries are required. Male and emale connectors must be speciied separately. More than one connector amily can be deined or a kit. This shows the eect o a connector amily name change rom APC 7 to 7mm. Next press the [Add] button to add the standards. Figure 15. Deine a new connector amily 24

25 Add any one o the supported standard types. I open is selected, the open edit screen will appear, as shown on the right. The short standard edit screen is very similar to the open s. The load standard edit screen is shown below. Enter all the ields. Make sure the units o measurements, such as the exponents, are correct,. There are 4 load types. Each activates a dierent set o data entry ields. Fixed and sliding loads are similar. Note, Arbitrary impedance activates the complex impedance entry ield. Figure 16. Add standards 25

26 Oset load activates the Oset Load Deinition ield. The Thru/Line/Adapter edit/entry screen is activated by choosing the thru standard type. Note that connectors need to be deined or both ports. They can be used to deine an adapter. Use [Browse] to locate the data-based ile and upload it. I successul, the ile inormation screen will summarize the ile s content. File inormation is only available at initial installation. Subsequent viewing o an existing standard is not yet supported Ater all the standards are deined. They need to be assigned to classes. Class assignment details were discussed earlier in this application note. The inal step is to complete the kit description and save the kit. Figure 17. Complete standard deinitions and assign to classes 26

27 8510 Calibration kit modiication/entry procedure Calibration kit speciications can be entered into the Agilent 8510 vector network analyzer using the disk drive, a disk drive connected to the system bus, by ront panel entry, or through program control by an external controller. Disk procedure This is an important eature since the 8510 can only store two calibration kits internally at one time, while multiple calibration kits can be stored on a single disk. Below is the generic procedure to load or store calibration kits rom and to the disk drive or disk interace. To load calibration kits rom disk into the Agilent 1. Insert the calibration data disk into the network analyzer (or connect compatible disk drive to the system bus). 2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL; then press the ollowing display sotkeys: LOAD CAL KIT 1-2 CAL KIT 1 or CAL KIT 2 (This selection determines which o the non-volatile registers that the calibration kit will be loaded into.) FILE #_ or FILE NAME (Select the calibration kit data to load.) LOAD FILE. 3. To veriy that the correct calibration kit was loaded into the instrument, press the CAL key. I properly loaded, the calibration kit label will be shown under CAL 1 or CAL 2 on the CRT display. To store calibration kits rom the Agilent onto a disk 1. Insert an initialized calibration data disk into the network analyzer or connect compatible disk drive to the system bus. 2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL; then press the ollowing CRT displayed sotkeys: STORE CAL KIT 1-2 CAL KIT 1 or CAL KIT 2 (This selection determines which o the non-volatile calibration kit registers is to be stored.) FILE #_ or FILE NAME (Enter the calibration kit data ile name.) STORE FILE. 3. Examine directory to veriy that ile has been stored. This completes the sequence to store a calibration kit onto a disk. 27

28 To generate a new cal kit or modiy an existing one, either ront panel or program controlled entry can be used. In this guide, procedures have been given to deine standards and assign classes. This section will list the steps required or ront panel entry o the standards and appropriate labels. Front panel procedure: (P-band waveguide example) 1. Prior to modiying or generating a cal kit, store one or both o the cal kits in the s non-volatile memory to a disk. 2. Select CAL menu > MORE. 3. Prepare to modiy cal kit 2: press MODIFY To deine a standard: press DEFINE STANDARD. 5. Enable standard no. 1 to be modiied: press 1, X1. 6. Select standard type: SHORT. 7. Speciy an oset: SPECIFY OFFSETS. 8. Enter the delay rom Table 1: OFFSET DELAY, , ns. 9. Enter the loss rom Table 1: OFFSET LOSS, 0, X Enter the Z0 rom Table 1: OFFSET Z0, 50, X Enter the lower cuto requency: MINIMUM FREQUENCY, GHz. 12. Enter the upper requency: MAXIMUM FREQUENCY, GHz. 13. Select WAVEGUIDE. 14. Prepare to label the new standard: press PRIOR MENU > LABEL STANDARD > ERASE TITLE. 15. Enter PSHORT 1 by using the knob, SELECT > LETTER sotkey and SPACE sotkey. 16. Complete the title entry by pressing TITLE DONE. 17. Complete the standard modiication by pressing STANDARD DONE (DEFINED). Standard #1 has now been deined or a 1 /8 l P-band waveguide oset short. To deine the remaining standards, reer to Table 1 and repeat steps To deine standard #3, a matched load, speciy ixed. The ront panel procedure to implement the class assignments o Table 2 or the P-band waveguide cal kit are as ollows: 1. Prepare to speciy a class: SPECIFY CLASS. 2. Select standard class S 11 A. 3. Direct the network analyzer to use standard no. 1 or the 11A class o calibration: l, X1, CLASS DONE (SPECIFIED). 28

29 Change the class label or S 11 A: LABEL CLASS, 11 A, ERASE TITLE. 1. Enter the label o PSHORT 1 by using the knob, the SELECT sotkey and the SPACE sotkey. 2. Complete the label entry procedure: TITLE DONE > LABEL DONE. Follow a similar procedure to enter the remaining standard classes and labels as shown in the table below: Finally, change the cal kit label as ollows: 1. Press LABEL KIT > ERASE TITLE. 2. Enter the title P BAND. 3. Press TITLE DONE > KIT DONE (MODIFIED). The message CAL KIT SAVED should appear. This completes the entire cal kit modiication or ront panel entry. An example o programmed modiication over the GPIB bus through an external controller is shown in the Introduction To Programming section o the 8510 Network Analyzer Operating and Service Manual (Section III). Table class assignment table Standard class Standard numbers Class label S 11 B 2 PSHORT 2 S 11 C 3 PLOAD S 22 A 1 PSHORT1 S 22 B 2 PSHORT2 S 22 C 3 PLOAD FWD TRANS 4 THRU FWD MATCH 4 THRU REV TRANS 4 THRU REV MATCH 4 THRU RESPONSE 1, 2, 4 RESPONSE 29

30 Appendix A: Dimensional Considerations in Coaxial Connectors This appendix describes dimensional considerations and required conventions used to determine the physical oset length o calibration standards in sexed coaxial connector amilies. Precise measurement o the physical oset length is required to determine the OFFSET DELAY o a given calibration standard. The physical oset length o one and two-port standards is as ollows. One-port standard Distance between calibration plane and terminating impedance. Two- port standard Distance between the Port 1 and Port 2 calibration planes. The deinition (location) o the calibration plane in a calibration standard is dependent on the geometry and sex o the connector type. The calibration plane is deined as a plane which is perpendicular to the axis o the conductor coincident with the outer conductor mating surace. This mating surace is located at the contact points o the outer conductors o the test port and the calibration standard. To illustrate this, consider the ollowing connector type interaces: 7-mm coaxial connector interace The calibration plane is located coincident to both the inner and outer conductor mating suraces as shown in Figure 18. Unique to this connector type is the act that the inner and outer conductor mating suraces are located coincident as well as having hermaphroditic (sexless) connectors. In all other coaxial connector amilies this is not the case. 3.5-mm, 2.4-mm, 1.85-mm, 1.0-mm coaxial connector interace The location o the calibration plane in these connector standards, both sexes, is at the outer conductor mating surace as shown in Figure

31 Type-N coaxial connector interace Note During measurement calibration using the 8510 and its derivatives, standard labels or the calibration standard indicate both the standard type and the sex o the calibration test port, (M) or (F). The sex (M) or (F) indicates the sex o the test port, NOT the sex o the standard. This port sex labeling convention must be observed and ollowed so that the correct calibration standard is connected to the calibration port. This is especially important or calibration kits that have dierent calibration coeicients or the male and emale standards, such as the Type-N, 1.85-mm and 1.0-mm calibration kits. The location o the calibration plane in Type-N standards is the outer conductor mating suraces as shown in Figure 19. For the PNA amily, the device label uses M or F to indicate the sex o the calibration standard instead o the test port. (M) or (F) & sex o the test port, M or F & sex o the calibration standard Figure 18. Location o coaxial connector calibration plane Figure 19. Type-N connector calibration plane 31

32 Appendix B: Derivation o Coaxial Calibration Coeicient Model D d e r s Figure 20. Coaxial transmission line characteristics All transmission lines may be deined by their characteristic impedance (Z C ), propagation loss constant (a), propagation phase constant (b), and length. They are related to the calibration coeicients - Oset Z 0, Oset Loss, and Oset Delay - as ollows: Recall that: Transmission loss and phase = e ( α + jβ)= ( R+ jωl) G+ jωc Zc = R+ jωl G jω C ( ) ( ) ( + ) ( ) - α+j β l R distributed resistance oset line; L G C distributed inductance oset line; distributed conductance oset line; distributed capacitance oset line; ω 2π ; requency in Hz; l length (2B.1) Assume that R is small and G=0, including the sel inductance o imperect conductors, the second order approximation o the transmission line characteristics are: (2B.2) L= L + L = L + R Z c o i o ( α+ jβ) jω LC 1+ ( 1 j) Lo C o ω [ ( ) R [ 1 + ( 1 j) ( 2ω L o ) ] R 2ω L o ] 32

33 For coaxial transmission lines, let: (2B.3) Rν Oset loss = 9 ε 10 Oset dela y l ε r = = ν π µ R = + σ πd π D c r ( ) LC o Given: L o ( ) ( ) µ 0 D 2πεoε r 1 = ln ; C = ; ε o = 2π d ln Dd µ ν Lo µν o Oset Z o = = ln C 2π ε r ( ) D d ( ) o 2 (2B.4) Substituting the oset deinitions back to the transmission line equations (2B.2): (2B.5) The short s inductance may be determined rom physical properties o the shorting plane, as presented in reerence [10]. The computed results are then curve itted to a third order polynomial unction. 2 Z jω L ; L = L + L+ L + L T T T ω LT 2 jarctan( Z ) r T Γ ( 1) e 3 3 (2B.6) 33

34 At low requencies where the inductance is reasonably linear, it may be modeled as an extra delay term. φ ( ) 2πLT = 2arctan = 2π( delay) Z r (2B.7) The open s ringing capacitance may be determined using three dimension microwave structure simulators. However, the mechanical structure o the open assembly can be quite complex and can cause simulation problems. It may be more realistic to measure the open s response using TRL or oset short calibration techniques where opens are not employed as calibration standards. The measured results are then curve itted to a third order polynomial capacitance model. Z Γ T T 1 2 ; CT = C0+ C1 + C2 + C3 jω C () 1 e T 2 jarctan (ωc T Z R ) 3 (2B.8) At low requencies where the capacitance is reasonably linear, it may be modeled as an extra delay term. φ ( T r ) = 2arctan 2πC Z = 2π( delay) (2B.9) 34

35 Appendix C1: Derivation o Waveguide Calibration Coeicient Model r h s e r w Figure 22. Rectangular waveguide dimensions and properties The physical properties o a rectangular waveguide are illustrated in Figure 22. ( ) ( ) 2 2π εr λ0 β = 1 ; λ0 = wave length in guide medium ν 2we (2C.10) [13] 2 w = e eective guide width = ( 4 π) r w h α π µ ρ h [ 2 h λ ε w ( e 2w ) ] e ( ) µ 2 0 λ 1 0 ( 2w ) 0 0 e 1 ; ρ = σ (2C.11) resistivity o conductor λ 0 ν ν = ; 2we = λc guide cut o wave length = Then λ0 2w e = c ; ν speed o light in ree space c (2C.12) 35 35

36 To structure the waveguide loss equation in calibration coecient ormat or the VNA, oset loss must be in G ohm/s. The equation may be reormulated as ollows: 2 2h c 1 π µ ρ ε w α ; c 0 0 e h c µ 0 2 c 1 (2C.13) πµ ρ ν ε let oset loss ; oset delay = h ε ν r 0 c r 2 2h c 1 ε 0 w e then α oset loss oset delay ; (2C.14) µ 0 c 2 c 1 The combine propagation constant is: 2 2h c 1 2 w ε γ α β π 0 c 2 µ c 1 0 e c j oset loss j 2 1 oset delay ; (2C.15) 36

37 Appendix C2: Derivation o Circular Waveguide Calibration Coeicient Model Figure 23: Circular waveguide dimensions and properties Given the physical properties o a circular waveguide as illustrated by Figure 23. (C2.1) [i ] (C2.2) (C2.3) To structure the waveguide loss equation in calibration coeicient ormat or the VNA, oset loss must be in G ohm/s. The equation may be reormulated as ollows, to be consistent with coaxial and rectangular waveguide structures: (C2.4) Note that the term is equivalent to, height/width ratio, o rectangular waveguides. Use this as the height/width ration value in calibration coeicients. 37

38 (C2.5) The combine propagation constant is: (C2.6) 38

39 Appendix D: Data-based Calibration Standard Deinition File Format A beta release o the calibration kit editor is available at pna/dbcal.html. This editor will allow the creation o kits that include data-based standards. Data-based standards are described by a data list. A data-based standard should include a list o requencies, the actual response or each s-parameter at each requency and an estimate o the accuracy o the actual response to be used in determining the weighting actor. Currently only one-port devices are supported. Support or two-port devices will be added later. Example ile CITIFILE A #PNA Rev A #PNA STDTYPE DATABASED COMMENT MODEL: COMMENT SERIAL NUMBER: NOMINAL #PNA STDREV Rev A #PNA STDLABEL SHORT 1 -M- #PNA STDDESC 1.85 mm male [SHORT 1] #PNA STDFRQMIN 0 #PNA STDFRQMAX #PNA STDNUMPORTS 1 COMMENT 1.85 mm known so #PNA DEFINECONNECTOR statement non needed COMMENT #PNA DEFINECONNECTOR 1.85 mm COAX #PNA CONNECTOR mm MALE COMMENT PINDEPTH is optional, only applies to coax devices #PNA PINDEPTH NAME DATA COMMENT This section describes the s parameter data and weighting COMMENT actor or the calibration standard COMMENT COVERAGEFACTOR is used to scale the weighting actor COMMENT S[i,j] is sij or the standard. Supported ormats: RI COMMENT U[i,j] is the weighting actor or sij. COMMENT Supported U[i,j] ormats: RI, MAG #PNA COVERAGEFACTOR 2 COMMENT note number o points is 509 below VAR Freq MAG 509 DATA S[1,1] RI DATA U[1,1] MAG VAR_LIST_BEGIN VAR_LIST_END BEGIN -1, , , , END BEGIN END 39

40 Preliminary #PNA keywords The PNA currently does not recognize the ollowing keywords (they are ignored). Future revisions will include the ollowing keywords to allow the data-based standard to be completely deined by the CITIFILE. Table 7. #PNA keyword table (preliminary) Statement Explanation #PNA REV s #PNA revision #PNA STDTYPE s Calibration standard type s can be DATABASED #PNA STDREV s Standard revision #PNA STDLABEL s Standard label #PNA STDDESC s Standard description #PNA STDFRQMIN Min requency or standard selection (may be dierent rom range o use) (Hz) #PNA STDFRQMAX Max requency or standard selection (may be dierent rom range o use) (Hz) #PNA STDNUMPORTS d Number o ports, deault 1 #PNA PINDEPTH d 1 2 Indicates pin depth or coaxial connectors to allow or pin depth compensation to the model d= port number 1= value included in the model data (mm) 2= actual value (mm) #PNA DEFINECONNECTOR s1 1 2 s2 <> Deines connector (NOT NEEDED IF PREDEFINED) s1= connector ID 1= minimum requency (Hz) 2= maximum requency (Hz) s2= connector type can be COAX, WAVEGUIDE, <> is an optional list o parameters to speciy values needed or connector type. <> is ignored or COAX <> the irst element is cuto requency or WAVEGUIDE <> to be determined or other types #PNA CONNECTOR d s1 s2 Connector assignment d= port number s1= connector ID corresponding to predeined ID or one deined by DEFINECONNECTOR s2= connector sex can be MALE, FEMALE, NONE #PNA COVERAGEFACTOR Coverage actor or weighting deault = 1 40

41 Reerences 1. D. Rytting. (Mar. 1987). An Analysis o Vector Measurement Accuracy Enhancement Techniques, Hewlett-Packard RF & Microwave Measurement Symposium and Exhibition. 2. D. Rytting. (Mar. 1987). Appendix to an Analysis o Vector Measurement Accuracy Enhancement Techniques, Hewlett-Packard RF & Microwave Measurement Symposium and Exhibition. 3. D. Rytting. (1996). Network Analyzer Error Models and Calibration Methods, RF & Microwave Measurements or Wireless Applications, ARFTG/NIST Short Course Notes. 4. G.F. Engen, C.A. Hoer. (Dec. 1979). Thru-Relect-Line: An Improved Technique or Calibrating the Dual 6-Port Automatic Network Analyzer, IEEE Trans Microwave Theory Tech., vol. MTT-27, pp R.A. Speciale. (Dec. 1977). A Generalization o the TSD Network Analyzer Calibration Procedure, Covering N-port Scattering Parameter Measurements, Aected by Leakage Errors, IEEE Trans. Microwave Theory Tech., vol MTT-24, pp E.J. Eul, B. Schiek. (Apr. 1991) A Generalized Theory and New Calibration Procedure or Network Analyzer Sel-Calibration, IeEE Trans. Microwave Theory Tech., vol 39, pp R.B. Marks. (Fall 1997). Formulations o the Basic Vector Network Analyzer Error Model Including Switch Terms, 50th ARFTG Conerence Digest, pp D. Blackham, K. Wong. (July 2005). Latest Advances in VNA Accuracy Enhancements, Microwave Journal, pp K.H. Wong. (Dec. 1988). Using Precision Coaxial Air Dielectric Transmission Line as Calibration and Veriication Standards, Microwave Journal, pp K.H. Wong. (June 1992). Characterization o Calibration Standards by Physical Measurements, 39th ARFTG Conerence Digest. 11. N. Marcuvitz. (1986). Waveguide Handbook, McGraw-Hill, NY, Reprint Peter Peregrinus Lt. 12. G. Strang. (1980). Linear Algebra and Its Applications, 2nd ed. New York, New York: Academic Press, Inc. 13. D.J. Bannister, E.J. Griin, T.E. Hodgetts. (Sep 1989). On the Dimensional Tolerances o Rectangular Waveguide or Relectometry at Millimetric Wavelengths, NPL Report DES N. Marcuvitz, (1986) Waveguide Handbook, Sec. 2.3, IEE Electromagnetic Waves Series 21, Peter Peregrinus Ltd. 41

42 Web Resources For additional literature and the latest product inormation, visit our Web sites: PNA series network analyzers: network analyzers: Electronic Calibration Modules (ECal): Agilent Updates Get the latest inormation on the products and applications you select. LXI is the LAN-based successor to GPIB, providing aster, more eicient connectivity. Agilent is a ounding member o the LXI consortium. Agilent Channel Partners Get the best o both worlds: Agilent s measurement expertise and product breadth, combined with channel partner convenience. Agilent Advantage Services is committed to your success throughout your equipment s lietime. We share measurement and service expertise to help you create the products that change our world. To keep you competitive, we continually invest in tools and processes that speed up calibration and repair, reduce your cost o ownership, and move us ahead o your development curve For more inormation on Agilent Technologies products, applications or services, please contact your local Agilent oice. The complete list is available at: Americas Canada (877) Brazil (11) Mexico United States (800) Asia Paciic Australia China Hong Kong India Japan 0120 (421) 345 Korea Malaysia Singapore Taiwan Other AP Countries (65) Europe & Middle East Belgium 32 (0) Denmark Finland 358 (0) France * *0.125 /minute Germany 49 (0) Ireland Israel /544 Italy Netherlands 31 (0) Spain 34 (91) Sweden United Kingdom 44 (0) For other unlisted Countries: Revised: October 14, 2010 Product speciications and descriptions in this document subject to change without notice. Agilent Technologies, Inc , Printed in USA, March 28, EN