«White Paper Abstract Traditionally, the calibration of Vector Network Analyzers (VNAs) has been accomplished with mechanical standards. This ...»
Electronic vs. Mechanical
Calibration Methods and Accuracy
Traditionally, the calibration of Vector Network Analyzers
(VNAs) has been accomplished with mechanical standards.
This calibration process can be laborious and error prone, but is
required to make accurate measurements. Electronic calibration
modules have been designed to make VNA calibration faster,
simpler, and easier than traditional mechanical calibration.
The purpose of this paper is to clarify the differences between electronic and mechanical calibrations and how these differences affect measurement accuracy.
Introduction VNA (Vector Network Analyzer) calibration kits require two levels of speciications, the kit level calibration standard speciications and the VNA system level calibration residual error speciications. The residual-error speciications are functions of the calibration-standard speciications, VNA system speciications and calibration methods used. A calibration kit can support many different calibration methods. Different VNAs may have different implementations of calibration methods and calibration standard deinitions.
Typically, a mechanical VNA calibration kit consists of the following
set of standards:
Opens, Shorts/Offset Shorts, Loads/Sliding Loads;
Precision offsets – waveguide or coaxial.
Calibration methods that these calibration kits can support include :
Short/Open Load/Thru (SOLT) Short/Offset Short/Load/Offset Load/Thru Thru/Relect/Line or Thru/Relect/Match (TRL/TRM).
Electronic calibration (ECal) kits consist of at least one module that can electronically connect various impedance states to the VNA’s test port . The characteristics of these impedance states are stored in EEPROM (Electrically Erasable Programmable Read-Only Memory) that can be read by the VNA or a PC controller to perform a calibration.
Different modules cover different frequency ranges. The calibration method used is similar to the open/short/load/through method or the offset shorts/through method. The Keysight Technologies, Inc. PNA Series of network analyzers can also support unknown through and external ideal through calibrations using an ECal module. Most ECal modules use four impedance states to compute the VNA’s systematic error terms to reduce calibration errors.
Some recent broadband models, such as the 10 MHz to 67 GHz model, use seven impedance states to improve calibration accuracy. Figure 1 shows a simpliied block diagram of an electronic calibration device with four relective impedance states and two through states.
03 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper
Figure 2. Mechanical calibration system standard specs and VNA system spec relationships.
Calibration standard speciications Figure 2 shows the key factors that inluence the calibration standard speciications. Different calibration standards have different key characteristics that are important for the calibration method used. The male and female shorts, for example, must be matched in electrical characteristics in order to minimize errors in TRL/TRM calibrations; but this is not critical for SOLT calibrations. On the other hand, the opens and shorts should be as close to being 180 degrees out of phase as possible over the entire applicable frequency range to minimize calibration errors using the SOLT calibration method.
04 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper Traditionally, electrical characteristics of opens and shorts are described by the calibration coeficients of the devices. Most VNAs use the following parameters to calculate the
calibration standard’s response:
Offset Delay, Offset Loss, Offset Zo, Min. Freq, Max Freq, Coax or WG, and C0, C1, C2, C3 terms for opens, L0, L1, L2, L3 terms for shorts Fixed or sliding for loads These parameters are also known as “Calibration Coeficients” of the calibration standards.1 Other Keysight VNA products use similar implementations of these calibration coeficients. Actual device deviation from this deined electrical characteristic determines the accuracy of the calibration. Speciications of calibration devices are, therefore, deined as deviations from the calibration coeficient responses.
Recently, Keysight’s PNA Series network analyzers have started using “data-based models” . The data-based models reduce the errors caused by itting of data to the calibration coeficients. Speciications of calibration devices are deined as deviations from the “nominal” data-based response plus data interpolation errors.
Sources of errors Opens and shorts Typically, the magnitude response of opens and shorts is very consistent. Their phase response, however, has more signiicant variations from device to device. The maximum phase deviation allowed from the nominal response, as deined by the calibration coeficients or data ile, provides the necessary margin to warrant VNA residual source match and relection tracking speciications. Dimensional variation is the main cause of device characteristic deviations. For very broadband requirements, the calibration coeficient model error has more impact. The data based model is much more accurate.
Fixed loads Usually, the calibration coeficients deine ixed loads as perfect system impedance terminations with zero relection. The offset terms may be used to create an imperfect load that matches the actual relection of the device. The actual relection coeficient or return loss of ixed loads is the primary error. If the actual data is used, then the uncertainty of the actual data becomes the primary error.
Arbitrary impedance Loads may be deined as arbitrary impedance standards. By using offset terms, in conjunction with a user deined terminating impedance (a real number for most network analyzers, a complex number for the PNA), a more accurate model of the load may be possible. Again, the deviation of the actual device response from the assumed calibration coeficient model is the major source of calibration error.
Sliding loads Sliding loads have an effective return loss speciication. It has the same meaning as the return loss speciication of the ixed load. It cannot be measured directly, but is calculated from a set of measurements taken with the sliding load element set at various positions.
Calibration residual errors Calibration residual errors depend on the calibration method used. The traditional method is SOLT. Three independent equations are generated from the measurement of three distinct calibration standards, open/short/load. The one-port error coeficients, directivity, source match, and relection tracking, are determined. The transmission tracking and load match terms are then determined using the through measurements. Appendix A provides the theoretical derivation of the relationship between calibration standard errors and calibration residual errors for this calibration method.
The same detail error analysis for the TRL/LRL calibration method has not been attempted. An estimate is provided by reference 
TRL residual errors:
Other publications  have applied the covariance matrix method to determine the TRL calibration errors.
Recently, the PNA has incorporated the weighted least squares method in the computation of VNA error coeficients using mechanical calibration standards. Appendix B shows the error propagation of calibration standards through the covariance matrix using the least squares approach.
Figure 3. ECal module specs in relationship to VNA system specs.
ECal impedance state speciications ECal impedance states are transfer impedance standards. The errors of their characterization are transferred to the residual errors of VNA calibration. The actual impedance of the impedance state is, therefore, less critical than their mechanical cal kit’s equivalent. The actual values of the impedance states, however, do have some impact on the sensitivity of the characterization errors. To be consistent with the mechanical cal kit speciications, it is desirable to put a max and min limit on each of the impedance states. It is the deviation from the stored EEPROM data that contributes to the calibration residual errors, NOT the speciications of each the impedance states.
06 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper ECal residual errors Sources of errors
The total impedance-state error budget includes the following factors:
– Characterization uncertainty – State stability – Drift with respect to time and operating temperature – Environmental changes – Aging – Interpolation error Characterization uncertainties are usually dominated by systematic errors. Aging phenomena is not random. These two factors are additive to the random errors – state stability, drift, and environmental changes. The random errors are RSS. Total ECal’s
state error is:
One-port residuals ECal uses a minimum of four impedance states in conjunction with the least squares it method to compute the systematic errors of the VNA. The standard residual error equations for 1-port calibration using three known standards do not apply. Instead, the covariance matrix from the least squares it solution is used to determine the residual errors. The system equations are weighted by the total uncertainty of each impedance state. The weighting factors, e1, e2, e3, …, en, are derived from the sources of errors for each impedance state. Since this is a least squares itted solution, the uncertainty terms do not propagate through to the residual calibration-error terms algebraically like the mechanical calibration kits. Appendix B shows how the errors of each impedance state propagate through to the calibration residual errors.
Two-port residuals ECal’s two-port residual computation uses the same method as the mechanical cal kit when the through is not an ideal through. Because the insertion loss of the ECal through can be as high as 7 dB, the transmission tracking and load-match errors are higher than the mechanical cal kits. If an ideal thru is used, now available as an ECal calibration option, the transmission residual errors can be better than or equal to those of the mechanical calibration kits.
07 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper Calibration Results Compared The following graphs, in Figures 4 through 8, show the vector magnitude differences of the VNA systematic-error coeficients between the reference calibration performed using mechanical standards and the calibration performed using an ECal module characterized based on the reference calibration. It is evident from these graphs that the differences are within the connector repeatability error of the 1.85 mm connector.
Thus, calibrations performed with ECal are as accurate as the original calibration used to characterize the ECal module.
Figure 4. Magnitude of [Raw Directivity (ref) – Raw Directivity (ECal)].
Figure 5. Magnitude of [Raw Source Match (ref) – Raw Source Match (ECal)].
08 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper Figure 6. Magnitude of [Raw Load Match (ref) - Raw Load Match (ECal)].
Figure 7. Magnitude of [Raw Relection Tracking (ref) - Raw Relection Tracking (ECal)].
Figure 8. Magnitude of [Raw Transmission Tracking (ref) - Raw Transmission Tracking (ECal)].
09 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper
Conclusion ECal calibration operates quite differently from traditional mechanical vector network analyzer calibration. ECal offers lexibility in non-insertable calibrations that can be dificult for mechanical calibration. Its one-port calibration accuracy depends on the accuracy of the ECal’s impedance state measurement process. For two-port and multiport calibrations, the residual errors related to the transmission terms can be improved and made equal to mechanical calibrations if an external ideal through is used (or low-loss through) instead of the internal through. ECal offers added ease-of-use with fewer connections (especially for multiport calibration) over mechanical calibration.
Fewer connections, greatly reduces connection errors as well as wear on connectors.
In summary, the speed and consistency of ECal calibration cannot be matched by mechanical calibration.
10 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper Appendix A: Calibration Kit Calibration Residual Errors – Algebraic Solution One-port residuals ,  a
11 | Keysight | Electronic vs. Mechanical Calibration Kits: Calibration Methods and Accuracy - White Paper
Figure 10. Signal low graph of transmission calibration terms.
Transmission tracking and load-match residual errors depend on the performance speciications of the cables and test sets used just as much as the calibration kit’s performance speciications. These terms are calculated from the speciications of the cal kit, test-port cables, adapters and the S-parameter test set used. The following is provided as a reference on how these terms can be derived. As a general case, a nonideal through is used to connect port 1 to port 2 during the transmission calibration.
To determine the residual load-match error of a VNA using a inite length non-ideal
through with known S11, S21, S12, S22 and their errors e11, e21, e12, e22. Assume that S21=S12:
By taking the partial derivative of L with respect to all the dependent variables and