WO2008011035A2

WO2008011035A2 - Line-reflect-reflect match calibration

Info

Publication number: WO2008011035A2
Application number: PCT/US2007/016220
Authority: WO
Inventors: Leonard Hayden
Original assignee: Cascade Microtech, Inc.
Priority date: 2006-07-18
Filing date: 2007-07-17
Publication date: 2008-01-24
Also published as: TW200807601A; WO2008011035A3

Abstract

A method of compensating a calibration for a vector network analyzer [VNA] includes performing calibrations on at least a pair of por [El. E2 E3.E4] to determine error terms associated with each port [E1.E2.E3 E4] wherein at least one of the error term is based upon selecting the reactacne of the load standard from a set of potential values in a manner such that the reference reactance errors are reduced

Description

LINE-REFLECT-REFLECT MATCH CALIBRATION

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of Line-Refiect-Reflect Match

Calibration filed July 18, 2006 assigned Application No. 60/831,940.

BACKGROUND OF THE INVENTION

[0002] A calibration technique for testing a device under test.

[0003] The Line-Reflect-Reflect-Match (LRRM) vector network analyzer calibration method with automatic load inductance correction has been an accepted and reliable work horse for on-wafer probing measurement for more than a decade. LRRM is valued for its relative insensitivity to small errors in probe placement that are inherent in microwave probing. Typical LRRM calibrations compare favorably with the NIST reference multiline Thru-Reflect-Line (TRL) method yet require only simple fixed spacing standards using the same set as the Short-Open-Load-Thru (SOLT) method.

[0004] In the most common use of the LRRM algorithm, impedance standard substrate standards are positioned to allow probing using fixed spacing probes with minimal spacing, as illustrated in FIG. 1. The Line (or Thru) standard is kept electrically short and the reflect and match standards are situated at the probe tips, approximately co-located with the desired measurement reference planes. This configuration reflects design choices made to minimize impacts from non-ideal or unknown behavior of the Line standard in loss, frequency dependent delay, or impedance match. The configuration also facilitates convenient automation of the calibration using only substrate moves resulting in not only the convenience of a one- button calibration but also enhanced repeatability by avoiding probe repositioning.

[0005] As maximum testing frequency has risen to 110 GHz and beyond, the electrical length and inductive reactance of existing, commonly used calibration standards has grown to where these impacts are no longer transparent. This calibration error is not necessarily the dominant measurement error since probe to DUT positioning uncertainty also has greater impact at higher frequency. Also, less frequent but important situations (such as probe card measurement of larger die size) require electrically long lines for the Line standard used in calibration, encountering at even lower frequency the limitations [0006] An enhanced LRRM (eLRRM) technique for improved handling of non-ideal and electrically long Line standards which uses a more robust load inductance extraction method is desirable.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS [0007] FIG. 1 illustrates a calibration system.

[0008] FIG. 2 illustrates an error model.

[0009] FIG. 3 illustrates worst case error bounds from calibration comparison.

[0010] FIG. 4 illustrates expanded y-axis scale of worse case error bound traces.

[0011] FIG. 5 illustrates error magnitudes.

[0012] FIG. 6 illustrates a multiport network analyzer.

[0013] FIG. 7 illustrates a 4-port with loopbacks.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT

[0014] An enhanced eLRRM technique may be accomplished at the expense of using more a priori knowledge of at least approximate standard behavior than was required by LRRM. One implementation of an LRRM is based upon an eight-term error model. In FIG. 2, the two-port ABCD parameters (voltage-current cascade parameters) are used to describe the measurement configuration for the Line standard. This standard is labeled Thru in the FIG. 2. Thru and Line are used interchangeably when describing probing calibrations since all connection of probes requires some form of intermediate structure (like a line). No direct connection exists like would be the case for coaxial ports of different genders.

[0015] The goal of the LRRM calibration is to compute the terms of E_x and E_y from measurements of the various standards. With these terms known it becomes possible to take the raw measurement (i.e., the measurement of the error box, DUT, error box cascade) and extract the corrected DUT behavior. It is generally understood that only seven of the eight terms are necessary to be known to allow S-parameter correction since for linear devices the absolute magnitudes and phase of waves incident and exiting the devices need not be known, just their ratios. [0016] The Thru measurement along with the known behavior of the standard provides four complex equations. Each unknown reflect standard pair measurement gives one complex known created by the requirement that the paired reflects are equal at the two ports. A single match standard measurement provides a seventh complex equation when the load is known. Note: when more is known about the standards other choices may be made. For the case of the automatic determination of load inductance the system may assume the magnitude of the reflection coefficient of the open is known and that the load is an R-L series circuit with known R and unknown, frequency independent L.

[0017] The LRRM technique may start by solving for the error terms to the center of the Thru reference plane as shown in FIG. 2(b). Once this process is completed then the known Thru behavior may be used to move the reference plane to the probe tips. It may be observed that it is not just the Thru that is known but actually the behavior of the two mirror-identical half-circuits that in cascade are equal to the Thru.

[0018] Expressing the cross-talk and switching term corrected measured Thru standard ABCD parameters, E_MT, as the cascade product gives:

where the E_T/2 terms represent the behavior of the half-thru structure and the probe tip reference plane error boxes Eχ, and E_Y, can be found from the center-of-thru reference plane error boxes Eχ and E_Y using:

and

[0019] The normalized ABCD parameters of the error boxes are what is desired. Choosing Dx as the one term to leave unknown one has:

with

and

with

Since E_MT = Eχ'Eγ one can determine Ey from E_MT once E_x is known using:

where the E_MT matrix is known from the measurement term-by-term:

[0020] The next tool desired is a set of general expressions that allow one to relate the measured behavior of a one-port termination with the actual behavior of the standard. The measured impedance may be obtained from actual admittance using:

and

for ports X and Y respectively. The inverse expressions are used for correction and are:

and

[0021] For the condition of a reflect pair standard providing equal actual admittance at both ports one can equate (13) with (14) and using (9) identify the expression:

where

and

[0022] For the second reflect standard one obtains a second expression similar to (13):

where the bj, b2, and Vb terms are found using (18)-(20) except using the measured impedances from the second pair of reflects.

[0023] The two equations (15) and (21) may be solved for the two unknowns yielding:

and

[0024J From the definitions OfP₁ and P₂ in (16) and (17) one forms a quadratic equation with roots Ax/Cx and Bx

or

with solutions given by:

where the root selection is determined by trial and error using the needed sign of the corrected open reflection coefficient.

[0025] If there exists a termination (e.g., load) with known behavior at the center-of-thru reference plane, one can determine Cx from a variation on (13):

or alternatively one can determine the Cx term using the automatic load inductance extraction process outlined below.

[0026] Once the Cx is known and applying (9) one has complete determination of the normalized error boxes at the center-of-thru reference plane. Using (2) and (3) the reference planes are moved to the probe tips. In normal application the probe tip error box ABCD parameters are converted to S-parameters and the eight-term error model is converted to a twelve- term model using switching terms and cross-talk terms identified when originally computing the eight-term error model reduction.

[0027] It is desirable to automatically extract the load inductance, preferably as follows.

Using a variation of (11)

One may note the following special cases:

i. Perfect open, Yχ,_act = 0, Yχ,_meas = Cχ/Aχ ii. Perfect short, Yχ,_act→ infinity, Yχ,_meas → 1/Bχ-

These terms are independent of the load definition used in (27) and solely determined by the open and short.

[0028] If one makes an estimate of C_χ and use it to complete the correction then the resultant estimate correction of a measurement at port X would be given by:

[0029] Forming the ratio of (27) for the two situations where an estimate is used and where the actual Cx is used results in a simple relation since the fractional part of (27) drops out:

[0030] Using a load extraction method one may assume an ideal load

(Yχ,_est,load = 1 + jO) in (27) to obtain the estimate Cχ_,est. The ratio defined in (30) is determined solely by the ratio of the estimated load to the ideal load which will be the error ratio for measurement of any DUT:

[0031] For a reflect (e.g., open) standard known to be reactive only at the center-of-thru reference plane (Yχ,_act,open = O + jB_open,act) the estimated behavior (Yχ,_est,open = G_open,est + jB_open,est) is given by:

Remembering that the ratio term may be complex and equating the real parts of (32) means that:

since

Solving (36) for the load inductance yields:

where R, G, and B are the real part of the actual load impedance and the components of the estimated behavior of the open standard using the perfect assumption, all at the center-of-thru reference plane.

[00321 The use of ABCD parameters, impedances, and admittances in the derivation avoids a possible problem associated with the implicit assumption of the existence of an intermediate reference impedance.

[0033] While LRRM is functional, it does have limitations and assumptions.

One such limitation leads to the potential for a reflect singularity with a long Thru. When computing the LRRM calibration the system relies on uniqueness of the reflect standards to provide information (equations) to help solve for the error-terms (unknowns). A problem may be observed when using probe tip reflect standards and the thru line is approximately one quarter wavelength long At this frequency (and odd multiples) ideal open and shorts located at the probe tip are contributing the same information, preventing a proper cal (resonant spikes are observed on the open verification plot).

[0034] The LRRM algorithm is largely computed with a center-of-thru reference plane. Re-computing these (probe-tip) reflects for their apparent value, at a center-thru reference plane results in impedances with zero real part and opposite sign imaginary part when the resonant spikes occur. It is apparent from experimentation that the two reflects are providing the same information in this situation. The solution to the system given by (15) and (21) is singular and the denominator of (22) goes to zero. This degenerate case is inherent in the use of two reflects for calibration and cannot be readily fixed mathematically. The situation needs to be avoided either by staying with electrically short Thru standards or by the use of offset reflect standards. Reflects physically located at the center-of-Thru reference plane (or sufficiently close) will also eliminate this problem. For the Thru with delay of 1 ps this effect is not a significant contributor of error below 110 GHz but may need to be considered for higher frequencies.

[0035] Another such assumption is that the Thru impedance is matched to the system impedance, which may not be the case. The Thru impedance in the LRRM algorithm was presumed to be equal to the target system impedance. This creates a limitation when deliberately calibrating to a different system impedance (such as 75 ohms) which is at times desirable, but it also introduces errors in 50 ohm calibration when the thru deviates from 50 ohms. The impact is larger when the thru is electrically long. The thru impedance is used when shifting between the native center-of-Thru LRRM reference plane and target calibration reference planes. Thru impedance, delay, and the usual VNA offset transmission line loss model are used to calculate the known scattering behavior of the distributed elements allowing the calculation of the reference plane shift. This is used in the load inductance extraction process as well as at the end of the calibration to set the desired final reference plane (this location is determined by the defined delay/length of the thru). [0036] Typical implementations of the LRRM algorithm have implicitly assumed the Thru impedance to be equal to the target system impedance of calibration. There was no separate entry for the impedance of the Thru transmission line. For electrically short and nearly equal system and Thru impedance the error introduced as a result is small. However, for long lines even a small impedance difference can produce dramatic side effects.

[0037] More generally, any error in the known Line behavior can cause incorrect probe-tip error box determination with the greatest impact for a longer Line. Only the TRL family of calibrations currently can accurately move reference planes when faced with unknown line behavior. Determining the line behavior is a unique part of the TRL calibration process.

[0038] There are also assumptions and limitations made in the extraction of the load inductance. One such assumption is that the load Z is equal at the probe-tip and the Thru-center. The algorithm described above does not effectively allow for differences between the load measured at the probe-tip reference plane (really the edge of the thru) and measured at the center-of-thru reference plane. The algorithm can accurately give us the ratio of L_act/R_act at the center of the Thru (although this may not be true when there is loss in the Thru or when R_load ≠ Z_system)- One fundamental assumption is that the load has constant R, series R-L behavior at the location set by the thru delay and load offset entries. This means that the R(f) is a known constant R₀ at this reference plane and the L/R is known at the thru center.

[0039] The previous implementations of the LRRM algorithm improperly assumes R=R_o at the center of the thru and calculate L_act from the L_act/R_act. LRRM then (again improperly) assumes that at the load reference plane Z_load is R_o + jωL_act (using L_act from the thru-center calculation) and uses this value and the line behavior to determine the effective Z at the thru-center reference plane by reference plane shift. This Z is then used as the effective Z_o of the calibration and the error terms are corrected to renormalize the Z_o to the desired system impedance (usually 50 ohms). This error becomes more significant when L is large and when the reference plane shift is a greater phase rotation (thru electrical length larger than a small fraction of a wavelength) causing the assumptions of similar behavior at the two reference planes to fail.

[0040] A fundamental assumption in the load inductance algorithm described above for the ability to determine the L/R ratio is that the loss of the open is zero at the center-of-thru reference plane. For a line that has even a small amount of loss this assumption will not be perfectly true. A typical 2 ps Thru standard can have as much as 0.04 dB round-trip loss at 40 Ghz. While small relative to other measurement errors, this offset on the open reflection verification plot is significant compared to the default display scale and is perceived as a problem. More importantly, the effect on the extracted inductance may be significant.

[0041] Another assumption is the use of a primitive L correction when load R is not equal to Zsystem. In the LRRM algorithm, if the resistance value in the load is not equal to the target system/Thru impedance then the apparent load inductance value is changed. The situation occurs when mapping the probe-tip load to the Thru-center introducing a standing wave. The assumption of an electrically short Thru with small load L led to a correcting adjustment value determined by a simple excess inductance model. The excess inductance is the difference between the total line inductance and the inductance the line would have had if it were matched. The adjustment used in prior implementations was given by:

[0042] This calculation assumes that the thru is electrically very short and determines a single, constant-frequency correction. For significant Thru electrical length the effect is frequency dependent and improperly modeled with this approximation. The error may be significant in practical cases making this correction not generally useful. While it is not a heavily used case, the expectation is that entering a non-matched resistor value should work properly. It won't when the thru has non-zero electrical length with the previous implementation.

[0043] In order to overcome some or all of the aforementioned shortcomings an enhanced version of the LRRM technique, referred to as eLRRM, is desirable. The inadequate modeling of the Thru discussed is compensated for using a modified technique and a more robust load inductance determination technique has been developed that is better suited to the case with an electrically long Thru. [0044] To correct the limitations for the load inductance method discussed is best performed using a new paradigm. The previous method fundamentally requires moving a determined L/R ratio from one reference plane to another if longer Thrus are to be allowed. It is not feasible to make such a translation of the ratio, only for a specific impedance value.

[0045] The enhanced LRRM load inductance approach includes the following:

1. Determine a set of estimated values for the load inductance.

2. Compute the Z_load at the probe tip and then translate to the Thru-center reference plane for each value.

3. Renormalize the error box terms for each value.

4. Compute the open verification using error box corrections including moving the reference plane to the probe-tip (or offset open location) for each value.

5. Calculate a difference between the expected reflect magnitude of the reference open and the magnitude of the estimated reflection for each estimated value of load inductance.

6. Choose the inductance value that minimizes the error magnitude summed over a desired frequency range.

[0046] In the preferred implementation of eLRRM the estimated values are concentrated densely near a starting point value, but spread over a wide range. This set of estimates allows refining a value more precisely if it is close to the starting point, but will also have a reasonable opportunity to find a distant value. The determined value optionally replaces the starting point allowing repeated calculation to find and then refine the load inductance value.

[0047] The translation of the various estimated impedances to other reference planes requires a known line behavior for the various cases of length differences. In the preferred implementation one may use the offset-loss transmission line model used in many network analyzers. Parameters for the VNA model are line Z_o, line delay, and a line-loss parameter in GΩ/s. One may simplify this further by determining the line-loss parameter internally from the entered reference loss at a reference frequency for a line with reference delay. For this eLRRM model these entries are enough to determine the complete frequency dependent loss characteristic.

[0048] The use of the additional known line behavior remains a limitation since there is no clear way to determine this without resorting to variable probe spacing methods like used in the multiline TRL. When this compromise is unacceptable then it will be necessary to keep the Thru as electrically short as possible to minimize the error.

[0049] Two further variations may be considered:

1. Allow for a general but known load impedance to be used in (27).

2. Use of an additional measurement of a long-line to allow determination of the line per-unit-length propagation constant and characteristic impedance allowing precise translation of the reference planes to the probe-tips.

[0050] For investigating the algorithm behavior a number of different calibrations were computed. In each case the data were acquired using an Agilent PNA vector network analyzer, Cascade Microtech 12801 probe station, Infinity ground-signal-ground 150 um pitch probes and impedance standard substrate. The WinCal 2006 software (service pack 1 version 4.01) was used to automatically sequence measurement of the needed standards, compute the error terms using the various cases of the LRRM algorithm, and send the error terms back to the PNA. WinCal 2006 also provided the ability to correct an additional reference structure with the calibration results for purposes of recognizing the validity of the calibration. For LRRM the open reflects are often used for this purpose, although use of any S- parameter of any particular structure is supported.

[0051] In FIGS. 3-5 computed calibration comparisons are used as the measure of calibration performance. The plotted curves are error-bounds for the measurement difference between two calibrations for a worst-case passive DUT. The trusted 1 ps Thru cal is used as the reference.

[0052] The singularity in calibration associated with conjugate reflects behavior at the Thru-center reference plane was presented. While this limitation of LRRM is encountered when using electrically long Thru standards and probe tip reflects. By understanding this limitation of LRRM one can avoid it by the use of an electrically short Thru standard or locating the reflect standards close to the center of the Thru.

[0053] It is also noted that a technique that for evaluation of estimated values may rely on matching the translated impedance to the center of the Thru with the calculated L/R ratio. The L/R ratio may be determined based upon the determined Lact/Ract, as previously discussed. The techniques are generally applicable to calculating the error terms for a system with two or more ports by calculating the characteristics of pairs of ports.

[0054] Referring to FIG. 6, some multi-port network analyzers (greater than two ports) include a series of error models El, E2, E3, E4 for ports 1, 2, 3, and 4 respectively. A set of switches may be selected between a respective load and the source signal. During calibration of the system one of the ports is connected to the source (and not connected to its respective load), with the remaining ports connected to the respective internal loads. It is noted that each of the internal loads are not perfect loads so they need to be considered during the calibration. [0055] One technique to calibrate a 4-port system is to perform short-open- load test for each of the four ports. Then the 6 Thru paths are tested, for a total of 10 separate tests. In the case of a 12 port network analyzer, this would result in 66 separate tests, which is highly burdensome. In some cases, the number of Thru tests may be reduced by inferring information. The SOLT (short-open-load-thru) technique tends to be sensitive to probe placement and tends to be sensitive to known values of the standards, and thus with a significant number of probe placements is exceptionally prone to significant errors.

[0056] Referring to FIG. 7, to perform this SOLT multi-port (4+) calibration the paths 2 and 4 are loop-backs. In practice, for high frequency calibrations, it is difficult to construct a high quality curved co-planar waveguide. Such curved co- planar waveguides tend to include additional modes of propagation which further introduce errors.

[0057] After further consideration it was determined that using the LRRM technique requires minimal knowledge of the standard except for the Thru path. Accordingly, by using the LRRM technique (or eLRRM) a 1 port calibration may be done on each of the ports to obtain information for El, E2, E3, and E4. The data obtained using the LRRM or eLRRM characterizes equivalently characterizes the short, open, and load characteristics.

[0058] With reference to the SOLR calibration technique, this leaves the . reciprocal characteristic to be determined. The SOLR calibration is desirable, especially for this high frequency calibration, is because the reciprocal is better with high frequency calibrations in the sense that it is less sensitive to lower quality loopbacks.

[0059] In the system of calibration for multi-port network analyzers, one may use a reference calibration technique to obtain the switching terms. To obtain the most accurate switching terms, preferably a full N port calibration technique is used to extract the switching terms. Also, depending on the hardware, the switching terms may be directly measured.

[0060] The terms and expressions which have been employed in the foregoing specification are used therein as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding equivalents of the features shown and described or portions thereof, it being recognized that the scope of the invention is defined and limited only by the claims which follow.

Claims

1. A method of compensating a calibration for a vector network analyzer comprising:

(a) performing calibrations on at least a pair of ports to determine error terms associated with each port;

(b) wherein at least one of said error terms is based upon selecting the reactance of the load standard from a set of potential values in a manner such that the reference reactance errors are reduced.

2. The method of claim 1 wherein said method accounts for differences between the load measured at a probe-tip reference plane and measured at a center-of- thru reference plane.

3. The method of claim 1 wherein said set of potential value is based upon said reactance of said load.

4. The method of claim 1 wherein for each of said potential values computing a load impedance at the probe tip.

5. The method of claim 4 wherein for each said computed load impedance at said probe tip translating to the thru-center reference place.

6. The method of claim 5 wherein at least one error term is renormalized based upon said translated computed load impedance.