System for setting reference reactance for vector corrected measurements

A system for calibrating vector corrected electrical measurements to adjust for distortion due to reactance in the measuring circuit, particularly that caused by variable positioning of a circuit element, such as probe or coupling. Initial error factors for directivity, source match, and frequency response, respectively, normally calculated from assumed reflection coefficients of respective primary impedance standards, are adjusted to correct for such reactance. Reflection coefficient measurements (magnitude and phase) of a further impedance standard, different from the primary standards, are obtained at multiple frequencies and corrected by the initial error factors. The corrected magnitude and phase measurements of the further impedance standard are compared with theoretical magnitude and phase values which very linearly with frequency, and the initial error factors are adjusted so as to minimize any deviation of the corrected measurements from the linear values. Thereafter, by positioning the probe or other circuit element relative to a device under test substantially identically to its previous placement relative to the further impedance standard, the adjusted error factors can be used to obtain corrected measurements with minimized magnitude and phase errors due to reactance.

BACKGROUND OF THE INVENTION 
This invention relates to vector corrected measurements of microwave 
circuits. More specifically, the invention provides a system for adjusting 
error factors, normally used to correct such measurements, to compensate 
for distortions due to imperfect assumptions of the value of reflection 
coefficients of impedance standards. Such imperfect assumptions may be 
caused, for example, by reactance in the measuring circuit due to variable 
positioning of circuit elements, such as probes, couplings, and the like. 
Microwave measurements of very small planar circuits require highly 
accurate measurements of complex (magnitude and phase) reflection and 
transmission coefficients. The measurement system, whether used in a 
one-port or two-port mode, is subject to three major sources of repeatable 
errors correctable by complex error factors referred to as directivity 
(Ed), frequency response (Er), and source match (Es). The basic approach 
to determining and using such error factors is widely published, as 
exemplified by R. F. Bauer et al. "De-embedding and Unterminating", IEEE 
Trans. on MTT, Volume MTT-22, pages 282-288 (Mar. 1974), and J. 
Fitzpatrick, "Error Models For Systems Measurement," Microwave Journal 
(May 1978). It is well known that these three error factors Ed, Es, Er are 
mathematically related to the actual one-port reflection coefficient Sa 
and the measured one-port reflection coefficient Sm by the following 
equation (or variations thereof): 
##EQU1## 
If the three error factors are known for the particular test frequency, 
the measured reflection coefficient Sm (magnitude and phase) can be 
corrected by solving the above equation for the actual reflection 
coefficient Sa. 
In practice, values of the three error factors are conventionally 
determined by measuring the reflection coefficients (at the test 
frequencies of interest) of three independent primary impedance standards 
whose actual reflection coefficients are assumed to be known constants at 
all frequencies. Although different impedance standards may be used, the 
ones most commonly employed are the open-circuit, short-circuit, and load 
(termination) impedance standards whose actual reflection coefficients for 
purposes of calculating the error factors are assumed to be 1, -1, and 0, 
respectively (or with slight known offsets). The measured reflection 
coefficient Sm of the load standard is used to find Ed from the above 
equation. Thereafter, the equation can be solved simultaneously for the 
remaining two error factors Es and Er using the measurements Sm of the 
open and short standards, respectively. 
The foregoing three assumed reflection coefficients of the impedance 
standards presume the absence of any unknown reactance affecting their 
reflection coefficients. However, it has been recognized that reactance 
does in fact affect such measurements and that the standards'reflection 
coefficients are therefore not completely known. In a technical paper by 
E. Strid, "Planar Impedance Standards and Accuracy Considerations in 
Vector Network Analysis" (June 1986), the effect of reactance on the 
assumed reflection coefficients of the foregoing impedance standards, and 
the resultant inaccuracies in error factor calculations, is discussed. 
Reactance affecting the measurements of the reflection coefficients of the 
open and short impedance standards is described as producing phase errors 
in the error factors, and thus phase errors in the ultimate corrected 
measurements of devices under test. On the other hand, reactance affecting 
the measurement of the reflection coefficient of the load impedance 
standard produces magnitude errors in the calculation of the error 
factors, and thus magnitude errors in the ultimate corrected measurements. 
However, the nature and values of the reactances, their variability with 
changes in position of a circuit element such as a probe, and the combined 
effects of two or more of these reactances have been difficult both to 
quantify and to interrelate. Accordingly, it has not previously been known 
how to adjust the error factors in a systematic or mutually compatible 
manner to compensate accurately for both magnitude and phase distortions 
caused by such reactances. 
SUMMARY OF THE INVENTION 
The present invention solves the aforementioned problem of error factor 
adjustment by providing a system for setting a reference reactance, 
analogous to a reference plane but with an inductive or capacitive 
element, at the point of connection to a device under test so as to 
compensate for distortions in measurements caused by reactance, especially 
that due to probe or other circuit element placement but not limited 
thereto. The system stems from the realization that any test device or 
impedance standard contacted by a measuring circuit has (to the first 
order) a variable inductance in series with the device or standard due to, 
and varying with, placement of the contacting circuit element such as a 
probe tip. Such series inductance decreases with increasing overlap 
between the contacting circuit element and the device or standard. 
Parallel capacitance is not likewise affected by such overlap (to the 
first order). Such series inductance is what is referred to herein as the 
reference reactance. 
The present invention quantifies the series inductance by using the 
variable-position probe or other circuit element to measure the magnitudes 
and phases of respective reflection coefficients, at different 
frequencies, of a further (i.e., fourth) impedance standard, different 
from the three primary impedance standards, and utilizing the initial 
error factors (unadjusted for such inductance) to correct such 
measurements. Thereafter, distortions in magnitude and phase of the 
corrected measurements of the further standard due to the inductance are 
determined, and the initial error factors are adjusted to minimize such 
distortions by adjusting the assumed reflection coefficients of at least 
two of the three primary impedance standards with respect to their 
imaginary components, so as to recalculate the error factors. When the 
recalculated error factors are subsequently used to correct one-port or 
two-port measurements on devices under test, with the probe or other 
circuit element positioned with an overlap substantially identical to that 
previously used to measure the further impedance standard, any magnitude 
and phase distortions due to reactance caused by positioning of the probe 
or other circuit element will be minimized. 
The calibration system of the present invention is rendered particularly 
efficient and rapid by systematizing the adjustment of the respective 
assumed reflection coefficients of the two primary impedance standards. 
The respective reflection coefficients are adjusted by respective 
imaginary increments related to each other by a predetermined ratio, so 
that both adjustments converge compatibly toward the desired result of 
minimizing magnitude and phase distortions. Moreover, when particular 
adjustment increments do not completely accomplish the desired result, 
extrapolation is used to predict what further adjustment is necessary. 
Preferably, distortions in the measurement of the reflection coefficients 
of the further (fourth) impedance standard are determined by comparing the 
corrected magnitude and phase measurements thereof with corresponding 
theoretical values which vary substantially linearly with frequency, and 
using the deviations of the corrected magnitude and phase measurements 
from the theoretical values to quantify the distortions. In this 
connection, the invention recognizes that phase deviations from the 
theoretical values can also be caused by imperfect impedance of the 
further impedance standard, and provides a means of removing from such 
deviations the variable component thereof caused by variations in such 
impedance. 
The foregoing and other objectives, features, and advantages of the 
invention will be more readily understood upon consideration of the 
following detailed description of the invention, taken in conjunction with 
the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
A typical block diagram of a conventional network analyzer for measuring 
microwave integrated circuits (such as a Hewlett Packard model HP8510 
analyzer), is shown in FIG. 1. The analyzer may be controlled by its own 
computer 10 or, alternatively, by an external computer, and is connected 
by transmissions lines 12, 14 to respective probe heads 16 of a 
conventional probe station 18. Each probe head 16 has a respective probe 
tip 20 for contacting and performing measurements on integrated circuits 
and impedance standards. The probe tip 20 may be of the coplanar wave 
guide type shown, for example, in U.S. Pat. No. 4,697,143, which is 
incorporated herein by reference. The probe tip 20 shown in FIGS. 2-5 is 
of a relatively simple coplanar type having one signal conductor 22 and a 
pair of ground conductors 24. 
For purposes of conventional determination of the three initial error 
factors Ed, Er, and Es, three primary impedance standards provided on an 
impedance standard substrate are contacted by the probe tip 20 to measure 
their respective reflection coefficients. A typical short-circuit standard 
as shown in FIG. 2 is a planar conductive strip 26 contacted in unison by 
the signal conductor 22 and ground conductors 24 of the probe tip 20. The 
variable reactance component of the measurement is caused principally by 
the variable distance 28 by which the probe tip overlaps the edge of the 
short-circuit strip 26. A typical exemplary load standard is shown in FIG. 
3, and comprises a pair of 100 ohm resistors 30 separating a signal 
conductor 32 from a pair of ground conductors 34. Similarly, the reactance 
variable is caused primarily by the variable overlap distance 36. The 
open-circuit standard, as depicted in FIG. 4, is preferably created by 
lifting the probe tip 20 at least ten mils into the air above the 
impedance standard substrate. The open standard is unaffected by probe 
placement since no interaction of the probe tip with another device is 
necessary, and whatever reactance may exist in the measurement of the open 
standard is therefore relatively fixed. However, even though the reactance 
of this standard is not physically variable, it is possible to vary it 
mathematically as part of the adjustment system of the present invention 
if desired. 
In addition to the foregoing three primary impedance standards, the system 
of the present invention utilizes a fourth impedance standard. The fourth 
standard may be an open or shorted stub, a high-Q capacitor, or a high-Q 
inductor. A typical open-stub standard is depicted in FIG. 5, comprising a 
relatively long central planar signal conductor strip 38 with a pair of 
ground conductor strips 40 on either side thereof electrically isolated 
therefrom. Again, variable reactance affecting the measurement of the 
reflection coefficient of the open stub depends on the probe tip overlap 
distance 42. After the initial error factors have been adjusted by the 
system of the present invention to compensate for the reactance caused by 
the overlap distance 42, such overlap distance will be maintained in 
subsequent measurements by the probe tip 20 of devices under test, so that 
the same reactance is maintained and the adjusted error factors can 
thereby accurately compensate for such reactance in the subsequent 
measurements. 
FIGS. 6A and 6B show an exemplary simplified logic flow diagram in 
accordance with which the computer 10 is programmed to perform the 
adjustment of the initial error factors Ed, Er and Es to correct for 
reflection coefficient magnitude and phase distortions caused by probe 
positioning during the measurement of the reflection coefficients of the 
impedance standards. First, the reflection coefficients S open, S short, S 
term, and S stub of the standards are measured and stored at each 
frequency for which subsequent measurements of devices under test will be 
made. The assumed imaginary components of the reflection coefficients of 
the three primary impedance standards are then entered (C open, L short, L 
term). There may all be zero, in which case the assumed reflection 
coefficients of the open, short and load standards will be 1, -1, and 0, 
respectively. Alternatively, a known imaginary component such as that for 
the open standard may be entered if known. In any case, the initial error 
factors Ed, Er, and Es are then calculated in the conventional manner for 
each frequency using the equation set forth in the Background of the 
Invention. Once the three initial error factors are known for each 
frequency, measurements at each frequency of the magnitude and phase of 
the reflection coefficient of the open stub impedance standard are 
corrected by the initial error factors to find actual .vertline.S stub 
.vertline. (magnitude) and actual &lt;S stub (phase) for each frequency. 
These corrected measurements will yield the "unadjusted for reactance" 
curves of FIG. 7 (magnitude) and FIG. 8 (phase), respectively. In the 
absence of reactance in the corrected measurements, the corrected 
magnitude should ideally decrease monotonically in proportion to the 
square root of the frequency, and the rate of change of the phase with 
frequency should be substantially linear. Accordingly, distortion in each 
corrected measurement due to the presence of such reactance is determined 
by comparing the corrected magnitude and phase measurements with 
theoretical values thereof, at the same frequencies, which vary 
substantially linearly with frequency. (With respect to magnitude, the 
linear theoretical function represents an approximation of the ideal 
square root function, with acceptably small error over the majority of the 
frequency range, permitting simpler, more rapid calculation.) These linear 
theoretical values are represented by the dashed "linear variation" lines 
of FIG. 7 and 8, respectively, which are drawn so as to have respective 
slopes equal to the respective frequency-averaged slopes of the 
corresponding "unadjusted for reactance" curves. Thereafter, deviation 
between the corrected and theoretical magnitude curves in FIG. 7, and 
deviation between the corrected and theoretical phase curves in FIG. 8, 
are calculated at each frequency. 
It does not matter whether magnitude deviations or phase deviations are 
considered first; however, for purposes of explanation, it will be assumed 
that magnitude deviations are analyzed first. The respective positive or 
negative value of the stub magnitude deviation at each measurement 
frequency is multiplied by the positive or negative sine of the 
corresponding phase measurement at such frequency. The results are then 
summed to produce a total magnitude deviation .epsilon.ml (FIG. 9) over 
the measurement frequency range. Since .epsilon.m has not previously been 
calculated, the last .epsilon.m will be zero. Therefore, in accordance 
with the logic flow chart of FIG. 6A, the imaginary component (L term) of 
the reflection coefficient of the load standard is increased by an 
arbitrary amount (e.g. 10pH), and Ed, Er and Es are recalculated. The 
resultant corrected .vertline.S stub .vertline. and &lt;S stub are likewise 
recalculated for each frequency, and .epsilon.m2 is then calculated, 
producing two different values of .epsilon.m as shown in the graph of FIG. 
9 at two different imaginary (L term) values, separated by an increment of 
10pH, of the reflection coefficient of the load standard. From these 
values of .epsilon.ml and .epsilon.m2 a further imaginary increment 
.DELTA.1 can be extrapolated so as to yield an .epsilon.m 3 intended to be 
zero (corresponding to minimum corrected magnitude deviation from linear, 
and thus minimum magnitude distortion). However, if the imaginary 
increment .DELTA.1 resulting from this extrapolation is not less than a 
predetermined minimum (such as 0.01pH), .epsilon.m3 is calculated at the 
last imaginary value, yielding a further extrapolation from .epsilon.m2 
and so on until a final increment (such as .DELTA.2), in the imaginary 
value (L term) of the reflection coefficient of the load standard, is 
reached which is below the predetermined minimum. 
Thereafter, as shown in FIG. 6B, a calculation similar to that for 
.epsilon.m is made with respect to the positive or negative value of the 
stub phase deviation at each frequency, multiplied by the positive or 
negative cosine of the corresponding phase measurement at such frequency. 
The results are summed to produce a total phase deviation .epsilon.1 over 
the frequency range, representing the effects of the last recalculation of 
Ed, Er and Es. (The cosine function removes from the phase deviation 
calculation that component thereof which is due to any imperfection in the 
impedance Zo of the stub.) Then the imaginary component (L term) of the 
reflection coefficient of the load standard is changed by a further 
arbitrary increment (such as 10pH), but in this case the imaginary 
component of the reflection coefficient of one of the other primary 
impedance standards is changed simultaneously as well. As shown in FIG. 
6B, the imaginary component (L short) of the short impedance standard can 
be changed by the same increment as that of the load standard or, 
alternatively, the imaginary component (C open) of the open impedance 
standard can be changed by an increment whose ratio to the load imaginary 
increment is inversely proportional to the square of the impedance Zo of 
the calibration. The three error factors are again recalculated, a new 
.epsilon.p2 is calculated and extrapolation from .epsilon.p2 and 
.epsilon.p1 yields a further imaginary increment in the reflection 
coefficient of the load standard. If this further increment is not below a 
predetermined minimum, further calculations of .epsilon.p and further 
extrapolations are performed until the increment is below the minimum, 
after which .epsilon.m is recalculated using the last recalculation of the 
error factors. A further extrapolation with respect to .epsilon.m is 
performed to determine whether it continues to indicate only a small 
imaginary increment below the predetermined minimum. If not, 
extrapolations with respect to .epsilon.m and .epsilon.p are repeated; but 
if so, the calibration procedure is complete and the last-recalculated 
error factors at each frequency are the ones subsequently used in 
correcting measurements of devices under test at the same frequency. In 
the latter case, the measurements of the test devices are performed with 
the overlap of the probe tip with respect to the device being identical to 
the overlap distance 42 (FIG. 5) with which the probe tip measured the 
reflection coefficients of the open stub standard at the different 
frequencies. 
As a result of the adjustments of the error factors to compensate for 
reactance, the open stub magnitude and phase deviations from linear should 
be minimized such that the corrected magnitude and phase values are 
represented by curves such as the "adjusted for reactance" curves of FIG. 
7 and FIG. 8, respectively, which are much closer to linear. 
It will be noted that, in the above procedure, the reflection coefficients 
of only two of the three primary impedance standards are adjusted to 
produce adjusted error factors. In one embodiment the imaginary components 
of the coefficients of the load and short standards are adjusted, while in 
another embodiment the imaginary components of the coefficients of the 
load and open standards are adjusted. The unchanged reflection coefficient 
of the third primary impedance standard defines the reference plane for 
measurement purposes. 
Although in both embodiments just described the imaginary component (L 
term) of the reflection coefficient of the load standard is adjusted, this 
need not necessarily be the case. The reflection coefficient of the load 
standard could, alternatively, be fixed to define the reference plane and 
adjustments necessary to minimize .epsilon.m and .epsilon.p could be 
accomplished by changing the reflection coefficients of the open and short 
impedance standards. 
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.