The SOLR Calibration

There are several hybrid calibrations which use model based direct calibration techniques in conjunction with the 8-term error model’s characteristic of only requiring 7 conditions. Quick SOLT or QSOLT, developed by Andrea Ferrero, was one of the first calibration techniques to combine model based direct calibration methods with the 8-term error model [26]. Essentially QSOLT allows a user to only perform one reflectometer calibration, which gives 3 of the seven conditions, and then measure a known thru

standard that gives the remaining 4 conditions. This is very useful for coaxial calibrations in which standard connection is very time consuming.

An even more significant hybrid calibration development of Ferrero was the development of what is now known as the short-open-load-reciprocal calibration, or SOLR [6]. The SOLR calibration has a very useful and unique property in that it does not require a well known ideal transmission standard [7]. Two reflectometer calibrations are performed the same as with SOLT this gives six of the seven needed conditions for the 8-term calibration leaving only one condition to impose on the thru.

The only requirement for the transmission standard is that it be reciprocal (S21 = S ) and a rough knowledge of the phase is needed in order to make a root choice later.

of a non-ideal transmission standard for calibration, such as a 90 degree probe setup for devices with right angle footprints. On a multi-signal probe a loop back or U thru is required which is far from ideal, in this case SOLR is highly beneficial. As a result of this property it will be shown in Chapter 7 to be a very useful multiport calibration technique.

The following development of the SOLR calibration will be done using 8-term error model notation presented in 3.3.2. It is noted at this time that this is an 8-term error model calibration and therefore all raw measured calibration data must be switch

corrected in order to be accurate. Switch corrected raw data is designated by bold parameters. Then the user may choose to continue to switch correct the raw DUT data and use 8-term error correction techniques or perform an 8 to 12-term conversion in which the error terms include the switch error and regular raw DUT data may be used for 12-term correction. Both techniques are detailed in Chapter 3.

First two reflectometer calibrations must be performed by solving the linear system for each port using known modeled standards just like the SOLT calibration.

22

From this all the reflectometer terms or 6 of the seven required terms for the 8-term error model are known (e100, e111, t11, e200, e211, and t22).

The only remaining term is the transmission term t21 which is now easily found by cascading the error box A and B transmission matrix and measuring the thru. It can be

recalled from Chapter 3 that the transmission matrices A and B of the 8-term error model

Recall that a raw switch corrected transmission parameter measurement Tm is represented as shown.

From the two reflectometer calibrations A and B are known. Tm is also known because it is the raw measured data of the thru standard. Therefore, all that is not known is the transmission parameter t21 and the actual S-parameters of the thru. However, the actual S-parameters of the thru do not need to be known. Because the thru must be reciprocal it follows that if the determinant of the actual thru parameters T is taken it will be equal to unity. If the determinants of both sides of the Tm equation are taken the result is as follows.

Solving for the transmission parameter t21 gives.

( ) ( )

Now that the transmission parameter is solved for a root choice must be made because t21 can be either positive or negative. The way to determine whether it is positive or negative is by comparing the rough estimate of the thru phase to the corrected thru phase at every frequency point and determine whether a positive or negative t21 gives a closer response to the rough estimate. It can be seen by Figure 4.9 that with the corrected phase with a positive and negative transmission term only one is close to the estimate at any given point because they are 180 degrees out of phase. This demonstrates that an exact knowledge of the reciprocal thru phase is by no means necessary.

0 5 .10⁹ 1 .10¹⁰ 1.5 .10¹⁰ 2 .10¹⁰ 2.5 .10¹⁰ 3 .10¹⁰ 3.5 .10¹⁰ 4 .10¹⁰ 0

50 100 150 200

Negative transmission term -t21 Positive transmission term +t21

Rough phase estimate of the 1.13 ps thru line

Corrected Thru Transmission Phase

Frequency (Hz)

Phase (Degrees)

Figure 4.9 – The Corrected Reciprocal Transmission Phase Using Both the Positive and Negative Transmission Terms ±t21.

A simple if statement in the calibration algorithm will allow you to make the decision whether t21 should be positive or negative based on which corrected thru data, that which is calculated from +t21 or -t21, has the greatest phase difference from the rough estimate. Once t21 is calculated the final term of the 8-term error model the reverse transmission term t12 is easily calculated from the other 7 terms. Therefore, t12 can be found through the following relationship.

21

Now that all 8-terms have been found error correction can be applied to DUT measurements.

Most passive devices are inherently reciprocal for this reason in some cases the actual DUT may be used a calibration standard. The benefits of SOLT are held with SOLR such as the equal footprint layout (when using a non-zero length thru) and the compactness of the calibration standards. However, it also has the drawbacks of SOLT in terms of the need for accurate broadband standard models. The need becomes more critical in SOLR because the transmission terms are highly dependent on all of the reflectometer terms. The use of accurate models like those presented in 3.2.4 will increase the accuracy of SOLR at high frequencies. The implementation of which is shown in Chapter 5.

4.4 StatistiCAL

StatistiCAL is a kind of mix and match calibration algorithm [27,28]. It was developed by NIST in order to create a flexible and highly robust calibration algorithm. It utilizes redundant calibration standards and an orthogonal distance regression algorithm [28]. This allows Statistical to calculate errors in measurements and standard definitions in order to find an optimal solution. Using this idea, the calibrations can be made up of any combination of standards. The more that is known about the standards and the more standards measured, the more optimal the calibration. Statistical can also reduce non-systematic errors such as connection repeatability by have multiple measurements of the same calibration standard or device. The calibration begins by entering an estimate for the error boxes which can be obtained from any previous Multical calibration for a particular system and then the standards are enter and defined and measured. Once everything is measured the algorithm goes to work and produces a 12-term error coefficient file by which raw data can be corrected.

4.5 Chapter Summary

Various 12 and 8-term calibration techniques have been discussed. The direct 12-term model based calibration has been developed in detail and a generalized procedure for performing self calibration techniques has been given. The various calibrations have been compared and their strengths and weaknesses discussed. It is generally accepted that Multiline TRL, despite its low frequency inadequacies, is the most robust broadband calibration algorithm. It has also been shown that through implementation of a complex load model direct calibration techniques such as SOLT, can achieve multiline TRL like

accuracy at higher frequencies and retain the low frequency accuracy of SOLT. The SOLR calibration algorithm has been developed in detail and it will be verified in the next chapter that the SOLR calibration technique can be improved by using a complex load model as well.

CHAPTER 5

COMPLEX SOLR (cSOLR) DEVELOPMENT AND VERIFICATION

5.1 Introduction

As with SOLT the reflectometer terms of the SOLR calibration are determined by finding a solution to a linear system of equations which relates raw measured data to calibration standard models. As was shown in Chapter 4 with SOLT, the standard load model is inadequate at higher frequencies and a more accurate model can be used in its place in order to achieve better broadband accuracy. This same method can be applied to the SOLR calibration to create what will be referred to as complex SOLR or cSOLR. The cSOLR calibration method will be discussed in this chapter and experimental results will be used to compare this calibration to other well-known calibrations and verify its

accuracy.