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Agilent’s PNA network analyzer family uses the connector definition to define connector (Figure 2): • • • • • • Frequency Range Gender (male. etc) Cutoff Frequency (waveguide) Height/Width Ratio (waveguide) Figure 2. calibration kits also provide definitions of connectors. Two port standards. female. 5 .Connector definitions In addition to calibration standard definitions and standard class assignments. PNA connector entry screen A calibration kit may be defined with multiple connectors. such as thrus and adapters. waveguide. may be associated with two different defined connectors. no gender) Impedance Media (coax. Each 1-port calibration standard must be associated with a defined connector.
delay.1) γ = α + j β .) Transmission line Z C . Calibration standards may be defined in various ways. l = length of line.Calibration standards definition The S-parameters of VNA calibration standards must be defined sufficiently and accurately to satisfy the requirements of the calibration methods for which they will be used. Calibration coefficient model The majority of VNAs define calibration standards by using a transmission line model for 2-port standards and a terminated transmission line model for 1-port standards. Terminated transmission line model The transmission line and termination may be represented by a signal flow graph as illustrated in Figure 4. define XI and Xo a [ T XI ] b Figure 5. loss ZT Figure 3. Z c ^ characteristic impedance of line Z r ^ reference impedance (connector impedance or system impedance) α ^ propagation loss constant of line β ^ propagation phase constant of line 6 . Cascade parameter representation of terminated transmission line model [ TL ] [ T XO ] [ GL ] Where Γ1 = Zc − Zr Z − Zr . Agilent’s VNAs support two types of calibration standard definitions: calibration coefficient model and data-based model. Γ T = T Zc + Zr ZT + Zr (1.:. (See Figure 3. Γ 2 = − Γ1 .
[10]. With these “offset” definitions.2) ] = [ e− γ l 0 ΓT 1 0 e γl [ ΓL ] = [ ] ] (1. propagation phase and loss constants of the calibration standard without defining the dielectric constant of the calibration standard’s transmission medium which may be different from that of the device under test. “Appendix A” on page 30 illustrates the physical offset length definition of certain coaxial connector types.000649 in air @ sea level and 50% humididty εr = relative permittivity (dielectric constant) of transmission medium c = speed of light in vacuum = 2.5) c l = physical offset length from reference plane = 1. ( Offset delay ) = l εr .Γi = b . offset loss and offset Z0 instead of ZC. Offset delay Offset delay is the dispersion free. Agilent’s VNA uses offset delay. (1. TL Γ1 1 1 −Γ1 .4) Transmission line characteristic impedance and propagation constants can be derived from the line’s physical properties [9]. the VNA can compute the transmission line’s characteristic impedance and. electrical delay in seconds. and gl to model the transmission line. 7 . a [ TXI ] = [TXO] = Γi = [ ] ( )[ ] [ ( )[ ] 1 1 + Γ1 1 1 − Γ1 b = [ TXI ][ TL ] [ TXO ] [ ΓL ] a 1 Γ1 . TEM mode.99792458 x 108 m/s Note that the reference plane of coaxial connectors is defined as the mating plane of the outer conductors. This assumes that the offset loss and offset delay values were derived using the same dielectric constant. − Γ1 1 (1.
ln (10) dB1GHz 10 Offset Z 0 ) (Offset delay) (1. multiplied by the speed of light in the transmission medium. See “Appendix B” 109 For rectangular waveguide transmission lines. the lossless characteristic impedance is Offset Z0 Z0 = ( ) 1 2π μ 0c D μ ε ln d = 2π () ( ) μr D ln εr d () (1. Waveguide offset Z0 and characteristic impedance is normalized to “1”. In most cases. Since the loss of most waveguide standards are very small and are usually used way above cut off. 8 . The waveguide loss model is not supported by all VNAs until recently. curve fit the measured data to the on page 32 for details.8) 2 Offset Z0 is the lossless characteristic impedance of the transmission line. loss is not a simple function of frequency. d = center conductor outer diameter ZC.ln( S11 1GHz ) ( Offset Z0 Offset delay ) ) Log mag (dB) : (Offset loss) = ( . it can be calculated from the loss magnitude data at 1 GHz. such as 1 GHz. the 1 GHz data point is not available. S21 data: S11 Linear mag: Offset loss) = − 2 * ln S21 1GHz Log mag (dB): (Offset loss) = data: (1.7) Linear mag: ( ( . f `b function. See “Appendix C” on page 35. For coaxial transmission lines. the offset loss term is assumed to be “0”.ln (10)dB1GHz 20 )( f Offset Z0 Offset delay For best results.Offset loss Offset loss is in G½/sec. Agilent’s PNA series of network analyzers now include a waveguide loss model. ( offset loss) = ( offset delay) − ln S21 @ f ( )( μ0 ε0 ) fc f [ ] 1− 1+ 2h fc w f ( ) ( ) fc f 2 (1. It is the propagation loss per unit length of the transmission line at a normalization frequency. the transmission line characteristic impedance that includes skin loss effects can be derived from the offset Z0 and offset loss terms. For coaxial devices.6) )( Offset Z 0 Offset delay ) (Offset loss) = .9) μr = relative permeability constant of the transmission medium D = outer conducter inner diameter.
See “Appendix C” on page 35 for details. See “Appendix B” on page 32 for their derivation. the impedance of a “matched” load is used as the impedance reference. f ≡ frequency in Hz (1. In such cases. Normalized impedance is achieved by setting OFFSET Z0 to 1 ohm for each standard and setting system Z0 (SET Z0) to 1 ohm. When calibrating in waveguide.10) ( offset loss f 4π f 109 ) For rectangular waveguide transmission lines [11] the following expressions relate the offset terms to the transmission line’s electrical parameters. 9 . The impedance of this load is matched to that of the waveguide characteristic impedance across the guide’s frequency bandwidth. β l = 2πf ( offset delay ) 1 − fc . normalized impedance measurements are typically made. f fc = waveguide cut off frequency ( ) 2 (1. (offset loss)( offset delay ) 2 ( offset Zo) β l = 2πf ( offset delay ) + α l αl = Zc = ( offset Zo) + ( 1 − j ) [ ] f 109 .
3. 87xy series and the early firmware releases of the PNA series. Radiation loss is assumed to be insignificant. Z 0 = Γ0 = Z 0 − Zr Z 0 + Zr 1 j 2πfC0 (1. (also known as fringing capacitance). However. This is as defined in equation (1. This effectively increases the electrical length of the device and can be modeled as a frequency dependent capacitor. if an offset transmission line with a finite delay and loss is specified. A complex terminating impedance has been added to the PNA series to allow for more accurate modeling of circuit board and on-wafer devices.4). such as 7 mm and larger. and an offset Z0 is not equal to the reference impedance. At low frequencies. However. at higher frequencies and for smaller connectors. use a fixed resistance value. the total reflection is NOT zero. GL = 0.5 mm and smaller. at least a third order polynomial inductance model. Arbitrary impedance An arbitrary impedance device is similar to a fixed load except that the load impedance is NOT perfect. This may be adequate at low frequencies and for large connector sizes. Γ A = ZA −Z r ZA +Z r (1. C0. C0 = C 0 + C1f + C 2f 2 + C 3f 3 . Open Open circuits radiate at high frequencies. Z S = j 2πfLS ΓS = ZS − Z r ZS + Z r (1. is required. L S = L0 + L1f + L 2f 2 + L 3f 3 . LS. The previous generations of VNA.14) 10 . Z A = R + jI .13) In some cases (when the phase response is linear with respect to frequency) the response of an open can be modeled as an equivalent “incremental” length. Fixed load The fixed load is assumed to be a perfect termination. Most network analyzers use a third order polynomial capacitance model. such as the Agilent 8510.Terminating devices Short Many vector network analyzers assume that the short is an ideal short and has a reflection coefficient of –1. Loss of the short circuit is assumed to be insignificant. a fixed capacitance value may be sufficient.12) In some cases (when the phase response is linear with respect to frequency) the response of a short can be modeled as an equivalent “incremental” length.
PNA offset load entry screen An offset load can be considered a compound standard consisting of 2 known offsets (transmission lines) of different length and a load element (Figure 6). For best results. The transmission line is assumed to have zero reflections and the load element has a finite reflection that can be mathematically removed. Sliding load A sliding load is defined by making multiple measurements of the device with the sliding load element positioned at various marked positions of a long transmission line. The definition of the offsets is the same as all offset transmission lines. Therefore. not equally spaced.) When specifying more than two offsets. try to move the load element in the same direction. do not move it back and forth. Also.Offset loads Note The 8510 assumes that the first offset has zero delay and the second offset has the required delay. The shorter of the two offsets can be a zero length offset. The frequency range of the offset load standard should be set so that there will be at least a 20-degree separation between the expected response of each measurement. try to slide in non-uniform. Measurement of an offset load standard consists of two measurements. An offset load standard is used when the response of the offset standards is known more precisely than the response of the load element. one with each offset terminated by the load element. the user should define multiple offset load standards. the offset delay value of the offset load must be the difference in delay between the two offsets. Figure 6. using a least-squares-circle-fitting method. When assigning multiple offset load standards to SOLT classes for the PNA. increments.. 11 . The load element is defined as a one-port reflection standard. it is usually beneficial to specify “use expanded math when possible”. See the section on “SOLT class assignment” on page 16.
For example. The resulting characterization data.Data-based standard model The data-based standard model is a new feature in Agilent’s network analyzers. a replacement calibration standard can be ordered for a calibration kit and used without having to modify the data-based model. a fixed load can be characterized using a more accurate calibration. The data-based calibration standard also eliminates shortcomings of fitting non-coaxial or waveguide standards to the models based on a coaxial or waveguide structure. calibration with a broadband load calibration kit is usually less accurate than calibration with either a TRL calibration kit or sliding load calibration kit. However. This can be especially useful for dispersive transmission line structures. It allows a calibration standard to be defined by a data file that contains frequency data. 12 . S-parameter data and uncertainty data. The generic model for a fixed load is that its reflection coefficient is equal to zero at all frequencies. is used as the databased standard definition of that particular load. The data may be obtained by device modeling based on physical dimensions or from accurate measurements. Data-based vs. Fitting errors are usually negligible for frequencies below 30 GHz. As an alternative. The data file may be created using actual measured data from a reference metrology laboratory. Data-based standards also open the opportunity of enhancing the accuracy of a particular calibration kit. Figure 8 shows how the data files can be created. Thus. The main source of degradation is the accuracy of the fixed load model. The residual directivity error now depends on the uncertainty of the characterization rather than the specification of the load. Calibrations using the fixed load and its associated data-based model will have an accuracy approaching the accuracy of the system that characterized the fixed load. with uncertainties. Figure 9 shows the data entry screen for data-based standards. at higher frequencies multiple frequency banded models for the same standard have been used to avoid errors due to fitting. Figure 7 shows how the data-based standard bypasses the fitting process and eliminates any errors that may have been associated with the fitting. See Appendix D on page 37 for details on data file formats. model data from device modeling software or combinations of both. polynomial model The factory data-based models are similar to polynomial models in that they are a generic nominal model for a particular part number. The data-based standard avoids this problem altogether by interpolating on the data directly. This increased flexibility also enables the user to more easily define custom calibration standards that do not accurately fit existing calibration coefficient models. Fit nominal response to polynomial model Compute nominal response from nominal dimensions Nominal polynomial model (includes fitting errors) Nominal data-based model (eliminates fitting errors) Figure 7.
Data-based standard setup screen Maximum/minimum frequency The maximum and minimum frequency entries define the applicable frequency range of the calibration standard. Although the PNA’s SmartCal (guided cal) no longer uses the minimum frequency of a calibration standard as the cut-off frequency for dispersion correction. for example. A fixed load. accuracy of the model or the physical dimensions of the calibration standard. Nominal vs. it is still recommended that the minimum frequency equals the cut-off frequency for backward compatibility. For waveguide. The applicable range may be limited by the model data.Compute nominal response from nominal dimensions Nominal data-based model (valid for a particular part number) Characterize actual response for a particular standard (for example. a fixed load) Data-based model (valid for a particular standard) Figure 8. customized data-based file Figure 9. may be used at low frequencies while a sliding load may be used at high frequencies. the minimum frequency is the waveguide cut-off frequency. 13 .
A single standard class is a standard or group of (up to 7 for most VNA) standards that comprise a single calibration step. It is important to note that each and every class must be defined over the entire frequency range for which the calibration is made. ADAPTER (8510) and DATA BASED STANDARD (PNA) Figure 10. For the 8510 VNA. even though several separate standards may be required to cover the full measurement frequency range. SHORT. Each calibration standard is assigned with a standard number. LOAD. Calibration standard selections 14 . Some standards may have multiple standard numbers assigned for different calibration methods or different standard definitions. The following sections provide detailed descriptions of the various VNA class assignment structures. calibration kit class assignments are 2-port based. VNA calibrations are test-port specific and therefore class assignments are structured around port numbers. a calibration kit may contain up to 21 standards.Class assignment Calibration kit class assignment organizes calibration standards into a format which is compatible with the error models used in measurement calibration. That number is then assigned to a class or calibration measurement that is required for the calibration method selected. THRU. Not all VNAs support the same set of calibration methods and calibration kits. Standard types Calibration standards are assigned to the following standard types (Figure 10): OPEN. The required number of standards will depend on frequency coverage and calibration methods supported. Since only 1-port and 2-port calibration standards are available. There is no limit on the PNA SmartCal (guided cal). The standards within a single class are assigned to locations A through G as listed in the Class Assignments table. only one port pair can be calibrated at a time. This may be necessary to optimize the accuracy of the standard model for a given frequency band and/or calibration requirement. Check the instrument’s documentation for its capabilities.
13). although the 8510 requires that all standards that will be used within a given class are measured before proceeding to the next class.xxxx −45 F /Hz 3 All Agilent VNA models use the same scaling factor. the order of standard assignment within a given class is not important. For this reason it is important to list the preferred standards first. s ≡ sign (+or −) 10 (1. TRL calibrations. s ≡ sign (+or −) 10 L1 = sxx. Arbitrary impedance requires a terminating impedance entry.An OPEN calibration standard assumes that the polynomial coefficients represent a capacitance model and computes its reflection coefficients according to equation (1. The order of the standard measurements is important. arbitrary impedance and offset load.15) 10 C1 = sxx.xxx10−24 H /Hz .xxx10−12 H . A sliding load triggers prompts for multiple slide positioning and measurements.12). loss=0 and Z0=50 ohms. Calibrations and class assignments Assigning standards to class Calibration kits can be created to support SOLT calibrations. The default exponents for inductance terms are: L 0 = sxx. See “Appendix D” on page 37 for the requirements and format of data files.16) Four types of LOAD standards are available: a fixed load.xxx −36 F /Hz2 . a real value only for most VNA and complex value for the PNA. A SHORT calibration standard assumes that the polynomial coefficients represent an inductance model and computes its reflection coefficients according to equation (1. Multiport calibrations use a series of one-port and two-port calibration standards and are comprised of a series of two-port SOLT and /or TRL calibrations. A DATA BASED STANDARD is defined by a data file. The VNA assumes that each capacitance coefficient is scaled to a default exponent. 15 . C3 = sxx. As the internal PNA firmware searches for the appropriate calibration standard to use at a given frequency it starts at the top of the list and searches until it finds a standard that can be used at that frequency. L 2 = sxx. the last standard to be measured will be used. C 2 = sxx. When two standards have overlapping frequency bands.xxx10−27 F /Hz . Offset load requirements are explained in the “Terminating Device” section on page 10. or both. a calibration kit that includes a sliding load usually also includes a broadband load—if the broadband load is listed before the sliding load.xxx10 −15 F . The default setting for fixed load is delay=0. The order of standard measurement between different classes is not restricted. When assigning standards to a class for the PNA SmartCal (guided cal) the order in which the standards appear indicates the default preference for the calibration kit. For the 8510 and its derivatives (87xy and unguided cal of the PNA).xxx −33 H /Hz2 .xxxx −42 H /Hz3 10 (1. C0 = sxx. A minimum of 6 slide positions is recommended. For example. sliding load. the sliding load will not come up as a default selection. a perfect termination. Class assignments are a way for the calibration kit file to guide the selection of standards during the calibration process. L 3 = sxx.
and REV MATCH. and REV MATCH checkbox facilitates the common manipulation for these classes.SOLT class assignment In the simplest case. Some calibration kits. Each one-port calibration requires reflection measurements on at least three known and distinct standards. and a user-defined label associated with the class. namely: FWD TRANS. The simplest thru standard is a zero-length thru which is simply the connection of port i to port j.0 mm precision calibration kit. Unchecking the “LINK” option provides the ability to define different standards for each of these classes. In this case assigning different standards for each class will result in a separate prompt during calibration. and different standard types. The standards assigned to each class may have different connector definitions. and S11C represent the three reflection standard classes for port i while S22A. one thru standard would be assigned to the FWD TRANS and FWD MATCH classes and a different thru standard. 16 . load and offset short standards to calibrate over a very wide frequency range. S11A. S11B and S22B have the same standards. different frequency coverage. Both shorts and opens are assigned to the S11A class as illustrated by Figure 11. such as the Agilent 85059A 1. This would result in two separate prompts during the calibration sequence. Normally. Except for rare occasions. FWD MATCH. Selecting the radio button corresponding to a particular class enables modification of both the standards included in the class. Figure 11. This option would be used in the rare case where an external testset may require manipulation between the various measurements of the thru standard. these classes will all contain the same standards. S22B. The user-defined class label is visible during unguided calibration on the PNA. REV TRANS. This label is used for on-screen prompts or softkey labels during the calibration measurement process. an SOLT calibration consists of two one-port calibrations followed by forward and reverse transmission and reflection measurements on a thru standard. Most of the time S11A and S22A have the same standards. use a combination of open. Example – opens and shorts in the same class Four calibration classes are associated with the thru standard measurements. S11B. FWD MATCH. short. and S22C represent the three reflection standard classes for port j. with an identical model. and S11C and S22C have the same standards. The thru standard can be a defined thru or an “unknown thru”. would be assigned to the REV TRANS and REV MATCH classes. Label is just a name assigned to that class. REV TRANS. the LINK FWD TRANS.
It does not require a thru standard definition. All calibration kit operating and service manuals provide examples and blank forms of 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 delay value need not to be very accurate. less than –20 dB loss.The unknown thru calibration is one of the thru choices of the PNA. It defines the electrical delay of the adapter in order to determine the correct S11 and S22 response of the adapter. Any two port passive reciprocal device can be used as the “unknown thru” device. Adapter class is set up in the 8510 for adapter removal calibration. Table 1. The SOLT class assignment table maps directly into the 8510’s modify cal kit class entry format. for all the measurement frequency points must be provided. is preferred but not a requirement. the correct phase. However. A class assignment table is a very useful tool to help organize calibration standard assignments for data entry. A low-loss device. .
S11B. In the 8510 and PNA unguided calibration. The least squares solution works well when all observations are trusted to the same degree.01 0. at each frequency three standards are selected. less accurate calibration. Usually the load classes for a sliding load kit are defined with three load standards—a low band load. Default relative accuracy of cal standards types. Similarly S22A. Standard type Open Short Fixed load Sliding load Nominal accuracy UMin 0. nominal accuracy at a given frequency is computed as a linear interpolation between the appropriate endpoints. the specified minimum and maximum frequency of each standard in the class is used to determine which standard to use for a particular frequency. Usually. SmartCal (guided cal) in the PNA avoids this problem altogether by selecting the standards based on the order they are listed in the class. The accuracy of the standard model is explicitly defined for data-based standards. The low band load has a reduced frequency range and is intended to be paired with the sliding load to cover the full frequency range of the kit. for the other standards a nominal accuracy is assigned to provide a relative weighting for the weighted least squares solution. FMin and FMax correspond to the minimum and maximum frequency specified for the standard while UMin and UMax correspond to the minimum and maximum connector frequency. one each from S11A. To avoid confusion in the following table. This is a reasonable assumption for ECal. Expanded calibration is a weighted least squares solution that uses the measurement of three or more standards. and S11C and used to compute the systematic error terms associated with port i. the broadband load is defined to cover the full frequency range.003 UMin Minimum connector frequency Minimum connector frequency Minimum connector frequency FMin/2 Frequency range UMax Maximum connector frequency Maximum connector frequency Maximum connector frequency Maximum connector frequency 18 . That is to say the actual response of each standard is known with the same accuracy. endpoints are given. S22B.003 0. Table 2.01 0. but may not be valid when a least squares approach is applied to calibrations using other calibration kits due to the physical property differences of the standards.Traditionally. this frequency range is greater than or equal to the frequency range where the standard is selected specified by the min/max frequencies. Each class may include more than one standard. reflection calibrations have been computed using the measured response of three calibration standards at each frequency.005 0. a sliding load and a broadband load. and S22C are used for port j. For the 8510 and unguided calibration on the PNA. the calibration would be computed using only the broadband load ignoring the sliding load altogether. when multiple standards are listed in a class their frequency ranges have a finite overlap. thus a sliding load will always have priority over a broadband load when it is listed before the broadband load. Often the low band load and the broadband load are the same physical device. 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]. The measurement of a standard is included in the weighted least squares solution over the frequency range where the accuracy of the standard is defined. if a user measured a sliding load then measured a broadband load. Table 2. the last standard measured is used in the overlap region.003 FMin UMax UMax/1012 UMax/1013 3*UMax/1012 0. If the observations are all independent but not equally trusted. For port i. For users who desire a quicker. an optimal solution is best obtained by multiplying each equation by a weighting factor that includes both the accuracy of the standard’s model and the proximity of the standard’s response to the response of the other measured calibration standards. Also in the following table. Default relative accuracy of cal standards types Note Nominal accuracy does not correspond to the accuracy of the calibration standards for any particular calibration kit—nominal accuracy should simply be considered as a default weighting.
Using expanded math in this case will blend the transition between the low band load frequency range and the sliding load frequency range. Table 3. consider a sliding load calibration that includes frequencies in both the low band load and sliding load frequency ranges. There is no advantage to measuring two fixed loads when doing a sliding load calibration. There is an option to “measure all mateable standards in class” measuring all of the standards results in the best accuracy for kits like the 85058B and the 85059B. If the VNA spans more that one of these frequency ranges there will be more than three reflection standards connected. low band load and sliding load will be measured. The minimum and maximum frequency ranges for each standard combined with the class assignments will determine a set of three standards for each frequency resulting in a series of frequency ranges where only three standards would be required. There is a minimal set of standards defined that would insure calibration with three standards is possible at each frequency. an open and a series of short standards with varying offsets.When “use expanded math when possible” is checked the solution at each frequency all of the measured one-port standards will be included in the solution if frequency falls between UMin and UMax. the overall accuracy of the calibration improves when using expanded math. The open.85 mm calibration kit has a low-band load.. the 85058B 1. At each frequency between UMin and UMax of the sliding load the computation will use expanded math. For example. the sliding load and the broadband load. reflect and line classes plus TRL options. Table 3 shows the TRL portion of a typical VNA class assignment table. short. in addition to blending the transitions between the frequency ranges. selecting measure all standards in class would result in measuring the low-band load. As another example. For example. but not for others. TRL class assignment The TRL/TRM family of calibration is defined by the TRL thru. in the case of the sliding load kit discussed earlier. It is advantageous to measure all of the standards for some calibration kits.
Can also be defined as very long lossy line. Bandwidth limited so phase is at least ±20° different from phase of Line TRL (thru/reflect/ line) LRL (line/reflect/ line) 1.Figure 13. the reflect standard is assumed to have a high reflection with unknown amplitude and partially known phase. Line with S11=S22=0. known. Mapping TRL standards to TRL class Thru class Reflect class Zero length thru with Unknown equal reflect S11= S22 = 0. the thru standard is assumed to be fully known with perfect match. Can also be known. The line standard is assumed to have the same propagation characteristics as the thru standard with partially known phase. Phase approximately known. TRL edit class screen TRL is a generic name that represents a class of calibrations that allow partially known calibration standards to be used. loads on ports i and j Phase approximately S11 = S22 = 0. Line class Line with S11 = S22 = 0 phase approximately known. defined as very long lossy line. Table 4. S21 = S12 = 1 on port i and port j. In general. and j S11 = S22 = 0. Defined Phase approximately as lossy line. LRM (line/reflect/ match) TRA (line/reflect/ attenuator) LRA (line/reflect/ attenuator) 20 S11 =S22 = 0. with same propagation Phase approximately characteristics as Line2. S21=S12=1 on port i and port j. TRM fixed (thru/reflect/ j match) Zero length thru with Unknown equal reflect Can be defined as loads on ports i and S11 = S22 = 0. known. Unknown equal reflect S21 and S12 both known on port i and port j. on port i and port j. Line with S11 = S22 = 0. Defined Phase approximately as lossy line. on port i and port j. Bandwidth limited to avoid phase of ±20°. Unknown equal reflect Can be defined as fixed S21 and S12 both known. S21 = S12 = 1 on port i and port j. I and j S11=S22=0. Phase approximately known. . known. S21 Unknown equal reflect Attenuator between ports I and S12 both known. Line1 with S11 = S22 = 0. Zero length thru with Unknown equal reflect Attenuator between ports S11=S22=0. Table 4 provides a mapping of specific calibration types to the TRL class. Line2 with S11 = S22 = 0 phase approximately known.
One option would be to design the test fixture and calibration standards so that the testport would be located in the middle of the thru. See equation (2B.. the line standard can be assumed to be the portion of the line standard left over after subtracting a length equal to the length of the thru standard. In the case when the thru standard is a line with non-zero length. the model of the thru standard is used to compute the testport reference plane.The generalized TRL algorithm assumes the characteristic impedance of the line standard equals the desired system characteristic impedance. One of the by-products of the TRL algorithm is a computed value for the line standard propagation constant. LRL line auto characterization will only be used at frequencies where both the THRU and LINE standards are delay lines and where the offset impedance of the THRU and LINE standards are equal. Selecting the thru standard to set the reference plane obviously works for a zero length thru. Caution: Do not select System Z0 if offset Z0 of the line or match standard is very different from system Z0. no adjustments are made. TRL calibration is computed initially at a reference plane that corresponds to the middle of the thru. After the error coefficients are computed. This would include any dispersive effects of the transmission medium. the assumption is that the reflect standard is precisely known as both magnitude and phase of the reflect standard will be used to compute the testport reference plane. When LRL line auto characterization is set the propagation characteristics of the thru standard are computed from the computed propagation characteristics of the line standard and the defined delays for both the thru and line standards. Another alternative would be to select LRL line auto characterization. using the model of the thru standard alone will provide excellent results. the thru standard alone may give less than optimal results. This is derived from the defined Offset Z0 and Offset Loss terms. The calibration reference Z0 option allows for adjustments to the calibration to account for small perturbations between the system Z0 and the line characteristic impedance Zc. they are adjusted to establish a testport reference plane based on either the model of the thru standard or the model of the reflect standard. In the case of coax or waveguide. Reference plane set by THRU standard definition Reference plane set by THRU standard definition Reference plane set by REFLECT standard definition 21 . Note. In the case of other dispersive media such as microstrip. In this case.5) in “Appendix B” on page 32 If line Z0 is selected. When selecting the reflect standard to set the testport reference plane. Table 5.
] 4. Select Standards 5. Select Kit. The process to modify or create a cal kit consists of the following steps: Note Calibration kit entry and modification procedures for the Agilent ENA series of network analyzers are well documented in the Calibration Chapter of the ENA User’s Guide. 1. therefore. Provided the appropriate standards are available. Define the connector(s) [coax. the modification function allows the user to input more precise physical definitions for the standards in a given cal kit. Enter the standard types and classes 8.Modification Procedure Calibration kit modification provides the capability to adapt to measurement calibrations to other connector types. Import Kit or Create New 3. Select Modify Cal Kit 2. Additionally. Select Name or Rename Kit 22 . waveguide etc. they are not covered in this document. cal kit modification can be used to establish a reference plane in the same transmission media as the test devices. Define the standards 6. Select Assign Classes 7.
import the kit (instructions follow). The PC version may not be as updated as the PNA’s built-in version. Cal Kits can be imported from other directories. Almost all previous versions of network analyzer data files can be imported. All current Agilent mechanical calibration kits are preinstalled in the factory cal kit file directory. The PNA’s built-in cal kit editor will show a list of all cal kits files currently available and can be selected for modification. Figure 14. the disc drive or the USB drive. The reverse may not be true. select a kit and then select [Edit] >[Modify]. download a PC executable PNA Cal Kit Editor program. Select and modify cal kit 23 . Or.PNA calibration kit entry/modification procedure Use the “Advance Modify Cal Kit Wizard” on the PNA’s [Calibration] pull down menu to create or modify a calibration kit for the PNA. With the PC version. then click on [Edit Kit]. Once on the list. Note that PNA versions of all the Agilent 8510 calibration kits were pre-installed in the factory cal kit directory. Some user created 8510 cal kit files and 87xx cal kit files may not import properly. If the kit of interest is not on the list. Check the kit’s content after download to make sure all data entries are correct. select the kit. Newer versions can process kit data created by an older version.
If WAVEGUIDE is selected. WAVEGUIDE or others when available. the connector family must be defined before adding calibration standards. Define a new connector family 24 . The APC 7 connector family is being changed to 7mm. the Cutoff Frequency and Height/Width Ratio entries are required. More than one connector family can be defined for a kit. Male and female connectors must be specified separately. To set up a new kit. Figure 15. the Add or Edit connector screen appears. all the kit’s cal standard connector designations in the description field and the kit description field are updated as shown below If the connectors [Add or Edit] feature is selected. The media section defines the transmission line type – COAX. Any changes to the connector definition must also be performed before editing the calibration standards.The cal kit’s connector family can be renamed. This shows the effect of a connector family name change from APC 7 to 7mm. With the family name changes. Next press the [Add] button to add the standards.
Enter all the fields. If open is selected. The short standard edit screen is very similar to the open’s. Arbitrary impedance activates the complex impedance entry field. such as the exponents. There are 4 load types. the open edit screen will appear. Each activates a different set of data entry fields. Make sure the units of measurements.. Note. The load standard edit screen is shown below. Figure 16.Add any one of the supported standard types. are correct. Fixed and sliding loads are similar. as shown on the right. Add standards 25 .
After all the standards are defined. Use [Browse] to locate the data-based file and upload it. The Thru/Line/Adapter edit/entry screen is activated by choosing the thru standard type. If successful. Class assignment details were discussed earlier in this application note. File information is only available at initial installation. 26 . Note that “connectors” need to be defined for both ports. Subsequent viewing of an existing standard is not yet supported Figure 17. They need to be assigned to classes.Offset load activates the “Offset Load Definition” field. Complete standard definitions and assign to classes The final step is to complete the kit description and save the kit. They can be used to define an adapter. the file information screen will summarize the file’s content.
a disk drive connected to the system bus. To store calibration kits from the Agilent onto a disk 1. To load calibration kits from disk into the Agilent 1.) LOAD FILE. Insert the calibration data disk into the network analyzer (or connect compatible disk drive to the system bus). then press the following display softkeys: LOAD CAL KIT 1-2 CAL KIT 1 or CAL KIT 2 (This selection determines which of the non-volatile registers that the calibration kit will be loaded into. Examine directory to verify that file has been stored. select STORAGE IS: INTERNAL or EXTERNAL. This completes the sequence to store a calibration kit onto a disk.) FILE #_ or FILE NAME (Enter the calibration kit data file name. Below is the generic procedure to load or store calibration kits from and to the disk drive or disk interface.8510 Calibration kit modification/entry procedure Calibration kit specifications can be entered into the Agilent 8510 vector network analyzer using the disk drive. 3. then press the following CRT displayed softkeys: STORE CAL KIT 1-2 CAL KIT 1 or CAL KIT 2 (This selection determines which of the non-volatile calibration kit registers is to be stored. Insert an initialized calibration data disk into the network analyzer or connect compatible disk drive to the system bus. or through program control by an external controller. select STORAGE IS: INTERNAL or EXTERNAL. while multiple calibration kits can be stored on a single disk.) FILE #_ or FILE NAME (Select the calibration kit data to load. Disk procedure This is an important feature since the 8510 can only store two calibration kits internally at one time. To verify that the correct calibration kit was loaded into the instrument. Press the DISC key. If properly loaded. 3. 2. the calibration kit label will be shown under “CAL 1” or “CAL 2” on the CRT display. by front panel entry. press the CAL key. 27 . 2.) STORE FILE. Press the DISC key.
18. a matched load. 3. Select standard class S11A. Enter the loss from Table 1: OFFSET LOSS. X1. 13. 12. Direct the network analyzer to use standard no. 10. Enter the upper frequency: MAXIMUM FREQUENCY. Prepare to specify a class: SPECIFY CLASS. 28 . Prepare to modify cal kit 2: press MODIFY 2. Enable standard no. 1 for the 11A class of calibration: l. refer to Table 1 and repeat steps 4-17. store one or both of the cal kits in the ’s non-volatile memory to a disk.0108309. 2. 0. 5. To define standard #3.To generate a new cal kit or modify an existing one. 16. 6. Enter the Z0 from Table 1: OFFSET Z0. X1. X1. CLASS DONE (SPECIFIED). 2. Prepare to label the new standard: press PRIOR MENU > LABEL STANDARD > ERASE TITLE. 7. Select WAVEGUIDE. Complete the title entry by pressing TITLE DONE. To define a standard: press DEFINE STANDARD. To define the remaining standards. SELECT > LETTER softkey and SPACE softkey. 0. specify “fixed. ns. X1. Enter PSHORT 1 by using the knob. procedures have been given to define standards and assign classes. 50.97 GHz. 8. Prior to modifying or generating a cal kit.” The front panel procedure to implement the class assignments of Table 2 for the P-band waveguide cal kit are as follows: 1. Enter the delay from Table 1: OFFSET DELAY. Specify an offset: SPECIFY OFFSETS. 4.487 GHz. In this guide. 3. This section will list the steps required for front panel entry of the standards and appropriate labels. 11. 9. 15. 17. either front panel or program controlled entry can be used. Complete the standard modification by pressing STANDARD DONE (DEFINED). Standard #1 has now been defined for a 1/8 l P-band waveguide offset short. Select CAL menu > MORE. Front panel procedure: (P-band waveguide example) 1. 1 to be modified: press 1. 9. Select standard type: SHORT. Enter the lower cutoff frequency: MINIMUM FREQUENCY. 14.
2. ERASE TITLE. Complete the label entry procedure: TITLE DONE > LABEL DONE. 11A. Enter the title “P BAND.” 3. Press LABEL KIT > ERASE TITLE. 1. 8510 class assignment table Standard class S11B S11C S22A S22B S22C FWD TRANS FWD MATCH REV TRANS REV MATCH RESPONSE Standard numbers 2 3 1 2 3 4 4 4 4 1. This completes the entire cal kit modification for front panel entry. Press TITLE DONE > KIT DONE (MODIFIED).Change the class label for S11A: LABEL CLASS. the SELECT softkey and the SPACE softkey. change the cal kit label as follows: 1. Enter the label of PSHORT 1 by using the knob. The message “CAL KIT SAVED” should appear. Table 6. 4 Class label PSHORT 2 PLOAD PSHORT1 PSHORT2 PLOAD THRU THRU THRU THRU RESPONSE 29 . 2. Follow a similar procedure to enter the remaining standard classes and labels as shown in the table below: Finally. 2. An example of programmed modification over the GPIB bus through an external controller is shown in the “Introduction To Programming” section of the 8510 Network Analyzer Operating and Service Manual (Section III).
is at the outer conductor mating surface as shown in Figure 18.5-mm. 2. In all other coaxial connector families this is not the case. 1.0-mm coaxial connector interface The location of the “calibration plane” in these connector standards. Unique to this connector type is the fact that the inner and outer conductor mating surfaces are located coincident as well as having hermaphroditic (sexless) connectors.4-mm. The “calibration plane” is defined as a plane which is perpendicular to the axis of the conductor coincident with the outer conductor mating surface. 3. 30 . 1. One-port standard – Distance between “calibration plane” and terminating impedance. Precise measurement of the physical offset length is required to determine the OFFSET DELAY of a given calibration standard.port standard – Distance between the Port 1 and Port 2 “calibration planes. Two.Appendix A: Dimensional Considerations in Coaxial Connectors This appendix describes dimensional considerations and required conventions used to determine the physical offset length of calibration standards in sexed coaxial connector families. consider the following connector type interfaces: 7-mm coaxial connector interface The “calibration plane” is located coincident to both the inner and outer conductor mating surfaces as shown in Figure 18. The physical offset length of one and two-port standards is as follows. This mating surface is located at the contact points of the outer conductors of the test port and the calibration standard. To illustrate this.” The definition (location) of the “calibration plane” in a calibration standard is dependent on the geometry and sex of the connector type. both sexes.85-mm.
The location of the “calibration plane” in Type-N standards is the outer conductor mating surfaces as shown in Figure 19. standard labels for the calibration standard indicate both the standard type and the sex of the calibration test port. Type-N connector calibration plane 31 . 1.Type-N coaxial connector interface Note During measurement calibration using the 8510 and its derivatives. –M– or –F– & sex of the calibration standard Figure 18. such as the Type-N. Location of coaxial connector calibration plane Figure 19. the device label uses –M– or –F– to indicate the sex of the calibration standard instead of the test port. (M) or (F) & sex of the test port. For the PNA family. This is especially important for calibration kits that have different calibration coefficients for the male and female standards.0-mm calibration kits. (M) or (F). This port sex labeling convention must be observed and followed so that the correct calibration standard is connected to the calibration port. The sex (M) or (F) indicates the sex of the test port. NOT the sex of the standard.85-mm and 1.
of distributed capacitance offset line.1) ω ≡ 2π f. Coaxial transmission line characteristics All transmission lines may be defined by their characteristic impedance (ZC).Offset Z0. f ≡ frequency in Hz. propagation loss constant (a). including the self inductance of imperfect conductors.( α +j β ) l (α + j β ) = ( R + j ω L) ( G + jω C ) Z c = ( R + jω L) ( G + jωC ) R L G C ≡ ≡ ≡ ≡ distributed resistance offset line. distributed inductance offset line. l ≡ length (2B. the second order approximation of the transmission line characteristics are: (2B. propagation phase constant (b). and length.2) L = Lo + Li = Lo + R ω ( α + j β) ≅ jω Zc ≅ Lo C 1+ (1 − j ) Lo R 1 + (1− j ) 2ω Lo C [ [ ( )] ( 2ωRL ) ] o 32 . Assume that R is small and G=0. distributed conductance offset line.as follows: Recall that: Transmission loss and phase = e . They are related to the calibration coefficients . Offset Loss.Appendix B: Derivation of Coaxial Calibration Coefficient Model s D d er Figure 20. and Offset Delay .
d μ oν Lo D ln = C 2π ε r d ( ) Substituting the offset definitions back to the transmission line equations (2B.4) Given: Lo = Offset Z o = μ ( 2π ) ln ( D ).For coaxial transmission lines.2): ( )( αl = Offset loss R = 2ω Lo 2ω (Offset Z o) [( ) f 109 (2B. as presented in reference [10]. let: (2B. The computed results are then curve fitted to a third order polynomial function.6) ΓT ≈ ( −1) e ω LT −2 j arctan Zr ( ) 33 . LT = L0 + L1 f + L2 f 2 + L3 f 3 (2B.3) Offset loss = Offset dela y = R= Rν ε r f 10 9 l εr π f μ0 1 1 + πd π D σc 0 ( ν = Lo C ) C= 2πεoε r 1 . εo = ln ( D d) μoν 2 (2B..
It may be more realistic to measure the open’s response using TRL or offset short calibration techniques where opens are not employed as calibration standards. CT = C0 + C1 f + C2 f 2 + C3 f 3 jω CT −2 j arctan (ωC T ZR) (2B. However. Δφ = 2 arctan 2πf CT Zr ( ) = 2πf (Δ delay) (2B. it may be modeled as an extra delay term. it may be modeled as an extra delay term.8) Γ T ≈ (1) e At low frequencies where the capacitance is reasonably linear. the mechanical structure of the open assembly can be quite complex and can cause simulation problems. Δφ = 2 arctan f (2πZ L ) = 2πf (Δ delay) T r (2B. ZT ≈ 1 .7) The open’s fringing capacitance may be determined using three dimension microwave structure simulators.At low frequencies where the inductance is reasonably linear. The measured results are then curve fitted to a third order polynomial capacitance model.9) 34 .
11) . Rectangular waveguide dimensions and properties The physical properties of a rectangular waveguide are illustrated in Figure 21. λ 0 = wave length in guide medium (2C. 2we = λ c ≡ guide cut off wave length = f fc λ0 f = c . ν ≡ speed of light in free space 2we f (2C.Appendix C1: Derivation of Waveguide Calibration Coefficient Model w h r s er Figure 21.12) Then 35 . β= ( 2πf ε r ν ) ( ) λ0 1− 2 we 2 . ρ= 1 ≡ resistivity of conductor σ λ0 = ν ν .
36 .2) (C2. height/width ratio. The equation may be reformulated as follows.4) Note that the term is equivalent to . Use this as the height/width ration value in calibration coefficients. of rectangular waveguides. (C2.
5) The combine propagation constant is: (C2.6) 37 .(C2.
0.00028 . the actual response for each s-parameter at each frequency and an estimate of the accuracy of the actual response to be used in determining the weighting factor.01.01.99976354927.Appendix D: Data-based Calibration Standard Definition File Format A beta release of the calibration kit editor is available at.. only applies to coax devices #PNA PINDEPTH 1 0. 70000000000 VAR_LIST_END BEGIN -1.00367766097 .1] RI DATA U[1.85 mm male [SHORT 1]” #PNA STDFRQMIN 0 #PNA STDFRQMAX 70000000000 #PNA STDNUMPORTS 1 COMMENT “1.01. Supported formats: RI COMMENT U[i..00028 0.99970950119..0.html.1] MAG VAR_LIST_BEGIN 0 10000000 15000000 .007 0.007 NAME DATA COMMENT This section describes the s parameter data and weighting COMMENT factor for the calibration standard COMMENT COVERAGEFACTOR is used to scale the weighting factor COMMENT S[i.85 mm” 0 70000000000 COAX #PNA CONNECTOR 1 “1.j] is the weighting factor for sij. A data-based standard should include a list of frequencies.. Support for two-port devices will be added later.j] formats: RI.00249289367 -0..85 mm” MALE COMMENT PINDEPTH is optional. Currently only one-port devices are supported.0 -0.com/ pna/dbcal.00 #PNA STDLABEL “SHORT 1 -M-” #PNA STDDESC “1. COMMENT Supported U[i..00 #PNA STDTYPE DATABASED COMMENT MODEL: 85058-60101 COMMENT SERIAL NUMBER: NOMINAL #PNA STDREV Rev A. This editor will allow the creation of kits that include data-based standards. 0.j] is sij for the standard.9772034982.00028 0. MAG #PNA COVERAGEFACTOR 2 COMMENT note number of points is 509 below VAR Freq MAG 509 DATA S[1.0.005 END 38 .85 mm” known so #PNA DEFINECONNECTOR statement non needed COMMENT #PNA DEFINECONNECTOR “1.01 #PNA Rev A. Data-based standards are described by a data list.14575300423 END BEGIN 0.tm. Example file CITIFILE A.
NONE #PNA COVERAGEFACTOR f Coverage factor for weighting default f = 1 39 . . Future revisions will include the following keywords to allow the data-based standard to be completely defined by the CITIFILE. Table. FEMALE.Preliminary #PNA keywords The PNA currently does not recognize the following keywords (they are ignored)..
1979). Microwave Journal. E. MTT-27. Hoer. Hodgetts. Latest Advances in VNA Accuracy Enhancements. K. Covering N-port Scattering Parameter Measurements. (Fall 1997). NY. Strang. 50th ARFTG Conference Digest.H. 14. (Apr. Affected by Leakage Errors. B. Wong. Marcuvitz. (Mar. Inc. 6. Rytting. Rytting. Linear Algebra and Its Applications. Wong. Characterization of Calibration Standards by Physical Measurements. D. D. IEEE Trans Microwave Theory Tech. K. Eul.J. 7. E. (July 2005). Hewlett-Packard RF & Microwave Measurement Symposium and Exhibition. IEEE Trans. pp. 8. IEE Electromagnetic Waves Series 21. T. pp 983-987. R. 3. Bannister. Blackham. (Sep 1989). Sec.3. 10. 78-94. Waveguide Handbook. 115-126.. (1996). R. 4. 2nd ed. G. McGraw-Hill. An Analysis of Vector Measurement Accuracy Enhancement Techniques. pp 88-92. D. N. 1991) A Generalized Theory and New Calibration Procedure for Network Analyzer Self-Calibration. Speciale. Reprint Peter Peregrinus Lt. Wong. Formulations of the Basic Vector Network Analyzer Error Model Including Switch Terms. N. G. 40 . 2. 13. Appendix to an Analysis of Vector Measurement Accuracy Enhancement Techniques.F. ARFTG/NIST Short Course Notes.A. On the Dimensional Tolerances of Rectangular Waveguide for Reflectometry at Millimetric Wavelengths. IeEE Trans. Microwave Journal.. 39th ARFTG Conference Digest. Thru-Reflect-Line: An Improved Technique for Calibrating the Dual 6-Port Automatic Network Analyzer. pp 724-731. K. Hewlett-Packard RF & Microwave Measurement Symposium and Exhibition. Using Precision Coaxial Air Dielectric Transmission Line as Calibration and Verification Standards. New York: Academic Press. pp. 9. (June 1992). (Dec. Peter Peregrinus Ltd. vol 39.References 1. NPL Report DES 95. Marcuvitz. Microwave Theory Tech.. (1986) Waveguide Handbook. vol MTT-24. Marks. (Dec. (Dec. 1100-1115. pp. 1987). A Generalization of the TSD Network Analyzer Calibration Procedure. Engen. Microwave Theory Tech.A. D. 1955. 1988). Network Analyzer Error Models and Calibration Methods. D.B. Schiek. (1980). RF & Microwave Measurements for Wireless Applications.J. 5. 11.H. Griffin. (1986).E. Rytting. 1987). New York. 1977). 12.J. 2. vol. (Mar. C.
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