# ! !"
A new one-port impedance analyzer measures high-frequency devices up
to 1.8 GHz. Using a current-voltage method, it makes precise measurements over a wide impedance range. A special calibration method using a
low-loss capacitor realizes an accurate high-Q device measurement.
Many types of test fixtures are introduced because they are a key element in any test system.
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V1 = E1
V1
V2 = (-1/8)E2
Zx = Ro(1 + )/(1 - ),
E
where 1 is the gain of vector voltmeter 1, 2 is the gain of
vector voltmeter 2, = -8Vrr is the measured reflection
coefficient, Vr = V2/V1 is the voltage ratio, and r = 1/2 is
the ratio of the voltmeter gains.
V2
We define the calculated impedance sensitivity S to the voltĆ
meters' gain variance as follows:
Ix
Zx
S+
Vx
General schematic for impedance measurement using two
vector voltmeters.
parameters is called and one method is (OSL) calibration. Calculation of Zx from the
measured voltage ratio Vr according to equation 1 is called
We call a linear circuit such as the one in Fig. 2Ċone that
relates a signal source, two vector voltmeters, and a DUTĊa
Transducers are the key element in impedance
measurements. Two types of transducers of interest here are
the directional bridge and the transducer in a currentĆvoltage
(IĆV) method. Let's compare these in terms of their sensitivity
to gain variance in the vector voltmeters in Fig. 2.
Directional Bridge. Directional bridges (see Fig. 3) are used in
many network analyzers, mainly to measure impedances
near 50 ohms. In this case, the bilinear transformation is:
Zx + Ro 1 ) ,
1*
(2)
where = (Zx - Ro)/(Zx + Ro) is the reflection coefficient, Vr
= V2/V1 = (-1/8), and Ro = 50 ohms is the characteristic
impedance. The parameters in equation 1 are K1 = -8Ro, K2
= -1/8, and K3 = 8.
Now assume that the vector voltmeters in Fig. 3 are not ideal
but have some gain variance. The measured voltages V1 and
V2 and the calculated impedance Zx are:
+
V2
Ro
Ro
V1
Ro
(3)
This sensitivity can be considered as the inverse of the magĆ
nification of gain variance. The smaller S is, the smaller the
error in the calculated impedance.
For the directional bridge, equation 3 is:
S+
1 Z 2x * R 2o
Z x r
+
2 Z xR o
r Z x
S = (-1/2)Ro/Zx
for Zx Ro
S=0
for Zx = Ro
S = (1/2)Zx/Ro
for Zx Ro.
This implies that this type of transducer has little sensitivity
to the voltmeter gain variance when the DUT impedance is
near Ro (50 ohms). The gain variance of the voltmeters beĆ
haves as an offset impedance with a magnitude of (1/2)Ro
r/r when the DUT impedance is much smaller than Ro,
where r is the change in the gain ratio r. The gain variĆ
ance of the voltmeters behaves as an offset admittance with
a magnitude of (1/2)Gor/r when the DUT impedance is
much larger than Ro, where Go = 1/Ro.
Fig. 4 shows this characteristic.
I-V Method. Fig. 5 shows the simplest transducer for the IĆV
method. The bilinear transformation in this case is:
Zx = RoVrā,
We also assume that there is some gain variance in the vecĆ
tor voltmeters in Fig. 5. The measured voltages V1 and V2
are related to the calculated impedance Zx as follows:
V 1 + 1E
Ro
Zx ) Ro
V 2 + 2E
Zx
Zx ) Ro
where 1 is the gain of vector voltmeter 1, 2 is the gain of
vector voltmeter 2, and Vr = V2/V1 is the voltage ratio. Thus,
Ro
Zx
Zx = RoVr rā,
where r = 1/2 is the ratio of the voltmeter gains.
Directional bridge circuit.
October 1994 HewlettĆPackard Journal
(4)
where Ro = 50 ohms is a resistor that converts the DUT curĆ
rent to a voltage and Vr = V2/V1. The parameters in equation
1 are K1 = Ro, K2 = 0, and K3 = 0.
Ro
+
E
Z xńZ x
.
rń r
300
V1
100
Directional Bridge
Ro
Ro
High
10
E
Low
Sensitivity
Zx
Ro
1
Ro
I-V Method
0.1
V2
0.10
100m
1
10
Basic transducer circuit of the HP 4291A RF impedance anaĆ
lyzer with switch indicating circuit configurations for highĆimpedance
and lowĆimpedance measurements.
Ro 100
1k
10k
Impedance Rx (ohms)
Sensitivity of the directional bridge and IĆV methods to
voltmeter gain variance.
In this case, the sensitivity is given by:
S+
Z xńZ x
+ 1.
rń r
The error ratio (Zx/Zx)/(r/r) is always constant and equal
to unity. For example, if the voltmeter gain ratio r changes
by 1%, an impedance error of 1% is incurred for any DUT.
The foregoing analysis shows that the voltmeter gain variance
is neither suppressed nor magnified for all DUT impedances
by an IĆV method transducer. This characteristic is desirable
for wide impedance measuring capability. Therefore, we
adopted this type of transducer for the new HP 4291A
oneĆport RF impedance analyzer.
Fig. 6 shows the basic circuit of the transducer in the HP
4291A, which is a modified version of Fig. 5. The highĆ
impedance configuration (switch closed) realizes perfect open
and imperfect short conditions, while the lowĆimpedance
configuration (switch open) realizes imperfect open and
perfect short conditions.* In either switch position, the outĆ
put impedance at the DUT port is always Ro.
+
V1
Ro
E
+
V2
Zx
Fig. 7 shows the actual HP 4291A transducer circuit configuĆ
rations. A number of considerations influenced the design of
these circuits. First, because a wideband switch with small
nonlinearity and small transients over a wide signal range is
not easily realized, we divided the circuit of Fig. 6 into two
separate circuits. Second, because the minimum frequency of
the analyzer is 1 MHz, the floating voltmeter (V1), which
corresponds to the current meter, is easily realized by using
a balun. Third, we adopted a circuit in which the voltmeter
readings change by the same percentage if the floating imĆ
pedance of the balun changes. Thus, the voltage ratio Vr
does not change and stable impedance measurements are
realized.
A conceptual block diagram of the HP 4291A including the
transducer discussed above is shown in Fig. 8. Only the parts
relevant to this discussion are included. The mainframe is
similar to the HP 4396A network and spectrum analyzer.3
Two key features of the HP 4291A are time division multiĆ
plex operation and impedance ranging. Two voltmeters are
obtained by time division multiplexing one voltmeter. The
multiplexing period is 2 ms. This ensures that slow drift of
the voltmeter gain does not affect the impedance measureĆ
ment. With this method, the signal path after the multiplexer
can be extended. The HP 4291A uses a 1.8Ćm cable between
the transducer and the instrument mainframe. This allows
wide flexibility in constructing a test system using automatic
device handlers. The singleĆpath configuration results in good
temperature characteristics even with an extended cable.
At frequencies below 200 MHz there is an expanded range.
In the expanded range there is a gain difference between the
voltage channel and the current channel ahead of the multiĆ
plexer. This impedance ranging offers stable measurements
for DUTs with impedances that differ greatly from 50 ohms.
Fig. 9 shows HP 4291A impedance measurement specificaĆ
tions. General error factors are the uncertainties of standards
IĆV method.
* A perfect open condition means that voltmeter V1 reads zero with the DUT port open. A perfect
short condition means that voltmeter V2 reads zero with the DUT port shorted.
October 1994 HewlettĆPackard Journal
V2
calibration. One way to improve phase measurement accuĆ
racy is to use a phaseĆcalibrated load standard. However, it
is not guaranteed that the phase uncertainty for a calibrated
50Ćohm load is smaller than 10-3 at high frequencies, such as
1 GHz.
Ro
Another way to improve phase measurement accuracy is to
use, in addition to the normal openĆshortĆload standards, a
lowĆloss air capacitor as a second load (LOAD2). The dissipaĆ
tion factor (D) of the air capacitor should be below 10-3 at
around 1 GHz. With this method, the uncertainty in the meaĆ
sured phase is decreased from the phase uncertainty of the
50Ćohm load (LOAD1) to the uncertainty of the dissipation
factor D of the lowĆloss capacitor (LOAD2) for almost all DUT
impedances. The next section gives the details of this
method.
Ro
E
Ro
Balun
V1
Ro
Zx
(a)
V2
Ro
Ro
E
•
•
•
•
Ro
Balun
V1
Ro
Zx
(b)
(a) Actual HP 4291A transducer circuit for lowĆimpedance
measurements. (b) Circuit for highĆimpedance measurements.
used in the calibration, instabilities, and interpolation errors.
The instabilities consist mainly of connection nonrepeatabilĆ
ity, longĆterm drift, circuit nonlinearity, temperature coeffiĆ
cients, and noise. The instabilities and interpolation errors
are small enough that the impedance phase errors can be
reduced by means of the special calibration discussed next.
Normally, the accuracy requirement for impedance phase
measurements is greater than that for impedance magnitude
measurements. The HP 4291A has a special, easyĆtoĆuse,
calibration for measurements of devices having high Q
(quality factor).
Even if the stability of the instrument is good enough, accuĆ
rate Q measurements cannot be made without adequate
phase calibration. For instance, if we want to measure the Q
factor with 10% uncertainty for a DUT whose Q value is 100,
the uncertainty in phase must be smaller than 10-3. The phase
accuracy of the instrument is determined almost entirely by
the uncertainty of the 50Ćohm load standard used in the OSL
October 1994 HewlettĆPackard Journal
•
We want a calibration method that reduces the error in
phase measurement in spite of the existence of phase error
for the 50Ćohm load. We have the 50Ćohm load standard
whose impedance magnitude is known but whose impedĆ
ance phase is not. We add another load (LOAD2) whose imĆ
pedance phase is known but whose impedance magnitude is
not. We use a lowĆloss capacitor as the second load. There
are still at most three unknown circuit parameters. However,
two more unknowns related to standards are added. Let us
define the problem. There are eight real unknown parameĆ
ters:
Circuit parameter K1 (two real parameters)
Circuit parameter K2 (two real parameters)
Circuit parameter K3 (two real parameters)
The impedance phase ls1 of the 50Ćohm load (one real
parameter)
The impedance magnitude Zabs_ls2 of the lowĆloss capacitor
LOAD2 (one real parameter).
We have solved this problem analytically. For the simplest
case where both the open and the short standard are ideal,
the three circuit parameters are found as follows:
K1 = AZlsiRo
K2 = -Zsm/Ro
K3 = -YomRo
where:
Ro = characteristic impedance
A = (1 - ZlmiYom)/(Zlmi - Zsm)
Yom = measured admittance for open standard
Zsm = measured impedance for short standard
Zlmi = measured impedance for load standard i
(i = 1 for LOAD1, i = 2 for LOAD2)
Zlsi = true impedance for load standard i
Zls1 = Zabs_ls1exp(jls1)
Zls2 = Zabs_ls2exp(jls2)
ls1 = 2 - 1 + ls2
Zabs_ls2 = (A1/A2)Zabs_ls1
Zabs_ls1 = impedance magnitude for LOAD1
(50Ćohm, known)
ls2 = impedance phase for LOAD2
(lowĆloss capacitor, known)
1 = arg((1 - Zlm1Yom)/(Zlm1 - Zsm))
2 = arg((1 - Zlm2Yom)/(Zlm2 - Zsm))
(5)
Test Head
DUT
Zx
Ro
High
Signal
Source
Low
V1
V2
Test
Station
Ro
Buffer
0 dB
6 dB
18 dB
Multiplexer
Buffer
–4 dB
Buffer
Ro
DC Bias
Mainframe
0 to 36 dB
2-dB Steps
V
20 kHz
ADC
I
Cable 1.8 m
DC Bias Option
0 to 12 dB
Only the mainframe parts relevant
to this discussion are shown here.
DAC
Constant V
Constant I
Ro
E
Signal Source
1 MHz to 1.8 GHz
! " " " " ! #
"# ! " # !
100k
100 10k
10%
•
•
•
•
•
5%
2%
1K
10m
|Z|,R,X ()
|Y|,G,B (S)
1m
1%
100
100m
10
1
1
10
0.1
1M
•
10M
100M
1G
•
Frequency (Hz)
(a)
•
•
10 100k
100 10k
1m
1K
•
10m
|Z|,R,X ()
|Y|,G,B (S)
10%
5%
2%
100
100m
10
1
1
10
0.1
1M
1%
10M
100M
1G
Frequency (Hz)
(b)
(a) Errors for impedance magnitude with the transducer for
high impedance. (b) Errors for impedance magnitude with the transĆ
ducer for low impedance.
A1 = (1 - Zlm1Yom)/(Zlm1 - Zsm)
A2 = (1 - Zlm2Yom)/(Zlm2 - Zsm)
•
•
•
•
For the actual case these circuit parameters are expressed by
far more complicated equations. Therefore, we adopted
a simpler procedure consisting of two steps. Step 1 is as
follows:
Regard the impedance of the 50Ćohm load as Zls1 = 50+j0
(that is, the phase of LOAD1 is zero).
Find the circuit parameters K1, K2, and K3 by normal OSL
calibration using the load value Zls1.
Execute correction for LOAD2 and get the corrected
impedance Zcorr2.
Calculate the phase difference between the phase of
Zcorr2 and the true phase of LOAD2.
Step 2 is as follows:
• Modify the impedance of LOAD1 to Zls1 whose phase is -
and whose impedance magnitude is still 50 ohms.
• Calculate the circuit parameters again by normal OSL
calibration using the modified load impedance Zls1 .
Although this is an approximate method, it is accurate
enough for our purposes. We call this method the modified
OSL calibration.
October 1994 HewlettĆPackard Journal
The following error factors affect phase measurement
accuracy using the modified OSL calibration:
Uncertainty in the impedance magnitude of LOAD1
Impedance phase of LOAD1
Impedance magnitude of LOAD2
Uncertainty in the impedance phase of LOAD2
Uncertainty in the admittance magnitude of the open
standard.
Notice that the second and third factors would not cause any
error if we were using the analytical solution. Computer simĆ
ulations have shown that:
The phase measurement error caused by the uncertainty in
the impedance magnitude of LOAD1 is small.
The phase measurement error caused by the impedance
phase of LOAD1 is small.
The phase measurement error caused by the impedance
magnitude of LOAD2 is small.
The uncertainty in the impedance phase of LOAD2 directly
affects the phase measurement error.
For reactive DUTs, the phase measurement error caused by
the uncertainty in the admittance magnitude of the open
standard (Yopen) is reduced to RoYopen(Copen/Cls2) in
the modified OSL calibration, where Ro is the characteristic
impedance (50 ohms), Copen is the capacitance of the open
standard, and Cls2 is the capacitance of LOAD2 (lowĆloss
capacitor). In the case of resistive DUTs, the error is the
same as in the normal OSL calibration.
Fig. 10 shows the relationship between the phase error and the DUT impedance when the LOAD2 phase uncertainty
ls2 is 500×10-6 radian in the modified OSL calibration.
The relationship between and the DUT impedance is
shown in Fig. 11 when the open admittance uncertainty
Yopen is 5 fF in the modified OSL calibration.
In summary, the phase measurement error when using the
modified OSL calibration is mainly determined by the uncerĆ
tainty in the impedance phase of LOAD2 and the uncertainty
in the admittance magnitude of the open standard. We now
evaluate these two items. The D factor for the capacitor (3
pF) used in the calibration can be small because the capaciĆ
tor's dimensions are small and the space between the inner
and outer conductors is filled almost completely with air.
1
Phase Error || (radians)
10 10–1
10–2
Inductive
10–3
ls2
Resistive
10–4
Capacitive
10–5
1
10
100
1000 |Zopen|
10,000
DUT Impedance |Zx| ()
Relationship between phase measurement error and the unĆ
certainty ls2 in the impedance phase of LOAD2 (lowĆloss capacitor)
at 1 GHz for resistive and reactive DUTs. Zopen is the impedance of
the open standard (about 2000 ohms).
Phase Error || (radians)
1
National Standards (U.S.A. NIST)
10–1
Resistive
10–2
Capacitance
Capacitance
Bridge at Low
Frequency
10–3
Inductive
Attenuation
Measurement
System
Attenuation
10–4
1
1
10
100
1000 |Zopen|
IDOC, ODIC
Reference
Air Line
Capacitive
10–5
DCR
10,000
DUT Impedance |Zx| ()
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S-Parameter
Calculation
System
NBS
Monograph
96
DCR
Measurement
System
S-Parameters
Reflection Measurement
System (Network Analyzer)
Z
Z
Z
Z
Z
DCR
Quarter-Wave
Impedance
Method
Z
Open Termination
Open-Ended
Air Line
Short-Ended
Air Line
50 Load
IODC = Inside Diameter of Outer Conductor
ODIC = Outside Diameter of Inner Conductor
DCR = DC Resistance
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3/4/3/@+ :.+ 2+4-:. ,853 :.+ 8+,+8+4)+ 62'4+ 5, :.+ A
2/4+9 )'4 (+ )'2);2':+* :.+58+:/)'22? ,853 :.+/8 */3+49/549
)544+):58 :5 :.+ ,/>:;8+ :+83/4'2 '4* :5 3/4/3/@+ :.+ )54A
'4* 8+9/9:/</:? 5=+<+8 /: /9 45: +'9? :5 *+9/-4 ' 9?9:+3 :5
4+):/54 4548+6+':'(/2/:? ".+ 4+= ,/>:;8+9 8+6+':'(/2/:? /9
)'2/(8':+ :.+ */3+49/549 5, :.+ '/8 2/4+ /4 +'). /4*/</*;'2 1/:
'2359: ,/<+ :/3+9 (+::+8 :.'4 5;8 52* 54+9 ".+ :?6/)'2 454A
".+8+,58+ 542? :.+ */3+49/549 5, :.+ 8+,+8+4)+ '/8 2/4+ 5,
8+6+':'(/2/:? 5, :.+ 9;8,')+ 35;4: *+</)+ ,/>:;8+9 /9 ± 6
5;8 9:'4*'8*9 2'(58':58? /9 6+8/5*/)'22? )'2/(8':+* '2/(8'A
'4* ± 35.39 ,58 9.58:A)/8);/: 3+'9;8+3+4:9 '4* ± ,
:/54 5, :.+ /4*/</*;'2 '/8 2/4+ /9 +>+);:+* (? ' 4+:=581 '4'A
'4* ± 3! ,58 56+4A)/8);/: 3+'9;8+3+4:9
2?@+8 )'2/(8':+* ,853 :.+ 8+,+8+4)+ '/8 2/4+ ".+ A5.3 25'*
/>:;8+ )536+49':/54 /9 /4)2;*+* /4 :.+ ,/83='8+ )588+A
)'2/(8':/54 /9 *54+ 3'/42? (? :.+ 7;'8:+8A='<+ /36+*'4)+
9654*/4- :5 )588+):/54 ': :.+ ,/>:;8+ :+83/4'2 "./9 8+*;)+9
3+:.5* '4* *) 8+9/9:'4)+ 3+'9;8+3+4: ".+ 56+4 :+83/4'A
:.+ +88589 -+4+8':+* /4 :.+ )/8);/: (+:=++4 :.+ 8+,+8+4)+
:/54 /9 )'2/(8':+* (? ' )'6')/:'4)+ (8/*-+ ': 25= ,8+7;+4)/+9
62'4+ '4* :.+ ,/>:;8+ :+83/4'2 ".+ (+9: )536+49':/54
'4* (? :.+ 4+:=581 '4'2?@+8 ': ./-. ,8+7;+4)/+9 ".+ 9.58:
3+:.5* /9 :.+ ! 3+:.5* 5=+<+8 /: /9 45: +'9? :5 68+6'8+
:+83/4':/54 /9 :8+':+* '9 /*+'2 #4)+8:'/4:/+9 ,58 :.+ 9.58:
' 9:'4*'8* 25'* .'</4- +>)+22+4: ,8+7;+4)? ).'8'):+8/9:/)9 9
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):5(+8 +=2+::A')1'8* 5;84'2
5
Test Fixture
1
“Compensation”
Fixture Terminal
(Traceability Does
Not Exist)
Additional Error (%)
“Calibration”
APC-7 Terminal
(Traceability Exists)
Detailed Model
Zo1=50W
Zo2050W
l1
l2
APC-7
Terminal
0.1
Fixture Terminal
Compensation
0.01
10
Open
Black Box
Short
Open-Short-Load
Compensation
Zo = 50+j0
g = 0+jb
Open
l (>l1)
Short
Fixture Port
Extension +
Open-Short
Compensation
g + Propagation Constant of the Transmission Line
w
b+v
o
v o + Velocity of Signal Propagation in Free Space ^ 3
10 8 mńs
8.6D;17:<D47*- $ /2@<=:. ,758.6;*<276 >.:;=; !
/2@<=:. 87:< .@<.6;276 84=; 78.6D;17:< ,758.6;*<276
* 57:. :.*42;<2, *4<.:6*<2>. ?. 8:7>2-. *67<1.: ,758.6;*D
<276 /=6,<276 /2@<=:. 87:< .@<.6;276 ,75+26.- ?2<1 78.6D
;17:< ,7::.,<276 *< <1. /2@<=:. 84*6. %12; 5.<17- *;;=5.;
<1*< <1.:. 2; * ;17:< <:*6;52;;276 426. +.<?..6 <1. !D
<.:526*4 7/ <1. <:*6;-=,.: 1.*- *6- <1. &% ,766.,<7: 7/
<1. /2@<=:. ;.. 20 (1.6 <1. =;.: ;.4.,<; 76. 7/ 7=:
6.? /2@<=:.; 76 <1. ! -2;84*A *6 *88:78:2*<. /2@<=:.
87:< .@<.6;276 >*4=.E*6 .9=2>*4.6< 4.60<1 7/ 2-.*4 D715
426. 8:.>27=;4A -.<.:526.- /7: <1*< /2@<=:.E2; *=<75*<2,*44A
;.< %1. =;.: <1.6 8.:/7:5; * ,758.6;*<276 =;260 78.6 *6;17:< ,2:,=2<;
%1. -2//.:.6,. +.<?..6 <1. $ 5.<17- *6- <1. ! 5.<17- 2; <1*< <1. $ 5.<17- *;;=5.; 2-.*4 78.6 ;17:<
*6- 47*- ;<*6-*:-; ?124. <1. ! 5.<17- *;;=5.;
2-.*4 78.6 *6- ;17:< ;<*6-*:-; *6- *6 2-.*4 <:*6;52;;276
426. (. /..4 <1*< <1. *;;=58<276 7/ *6 2-.*4 <:*6;52;;276
426. 2; 57:. :.*42;<2, <1*6 <1. *;;=58<276 7/ *6 2-.*4 47*- /7:
,758.6;*<276 7>.: * ?2-. /:.9=.6,A :*60.
,<7+.: .?4.<<D!*,3*:- 7=:6*4
1000
1800
%A82,*4 .::7: ,76<:2+=<276; 7/ <1. 6.? <.;< /2@<=:.; */<.:
/2@<=:. ,758.6;*<276
20 ;17?; <1. <A82,*4 <.;< /2@<=:. .::7: ,76<:2+=<276;
?1.6 =;260 <12; ,758.6;*<276 /=6,<276 %1.;. >*4=.; *:.
*457;< <1:.. <25.; +.<<.: <1*6 <1. .::7:; /7: 7=: /7:5.: <A8.
7/ /2@<=:.;
Load
(?)
100
Frequency (MHz)
$.4.,<276 7/ * <:*6;-=,.: *; -./26.- 76 8*0. 2; 2587:D
<*6< /7: *,,=:*<. 258.-*6,. 5.*;=:.5.6< 6.? <A8. 7/
<:*6;-=,.: +*;.- 76 <1. ,=::.6<D>74<*0. 5.<17- *6- 1*>260
?2-. 258.-*6,. 5.*;=:260 ,*8*+242<A 2; =;.- 26 <1. 6.? !
# 258.-*6,. *6*4AB.: 6.? 81*;. ,*42+:*<276 <.,1D
629=. * 57-2/2.- $ ,*42+:*<276 1*; *4;7 +..6 -.>.478.-
< =;.; * 47?D47;; ,*8*,2<7: *; <1. ;.,76- 47*- *6- 5*3.;
*,,=:*<. " 5.*;=:.5.6<; 87;;2+4.
%1. *=<17: 2; 0:*<./=4 <7 )*02 $ %*6257<7 *6- (*3*5*<;= ?17 8:7>2-.- 1.48/=4 -2;,=;;276;
% )76.3=:* *6- *6;76; C201D:.9=.6,A 58.-*6,. 6*D
4AB.: Proceedings of CARTSĊEurope '93, 88 D
% )76.3=:* C .? *42+:*<276 .<17- /7: 58.-*6,. .<.:;
Proceedings of the 1994 IEEE Instrumentation and Measurement
Technology Conference, $12B=73* *8*6 *A 88 D
$ *?*+*<* *6- =32A*5* C 201D!.:/7:5*6,. DB
'.,<7: .<?7:3 *6- $8.,<:=5 6*4AB.: HewlettĆPackard Journal,
'74 67 ,<7+.: 88 D
Traceability and the HP 8510 Network Analyzer, .?4.<<D!*,3*:8=+42,*<276 67 D 7>.5+.: # .4;76 *6- # 7:A.44 Electrical Parameters of Precision,
Coaxial, AirĆDielectric Transmission Lines, $ 7670:*81 =6.