Incomplete 2-Port Vector Network Analyzer
Calibration Methods
A. Henze 1, N. Tempone 2, G. Monasterios 3, H. Silva 4
RF Metrology Laboratory – Instituto Nacional de Tecnología Industrial (INTI)
Buenos Aires, Argentina
1
ahenze@inti.gov.ar
2
ntempone@inti.gob.ar
3 guillem@inti.gov.ar
4 hsilva@inti.gov.ar

Abstract— Different types of incomplete 2-port vector
network analyzer (VNA) calibration methods are
explained. All of them are particular cases of the 12-
term error model and a comparison, including
advantages and disadvantages, between them and a Full
2-Port method, such as TOSM, is made.
Resumen— En el presente informe se explican los
distintos tipos de calibración incompleta de un VNA de 2
puertos. Todos ellos son casos particulares del modelo de
12 términos de error, y se realiza una comparación,
incluyendo ventajas y desventajas, entre ellos respecto a
un método Full 2-Port como el método TOSM.
I. INTRODUCTION
When calibrating a 2-Port VNA, Full 2-Port calibration
is usually employed [1]. There are different types of
methods depending on the error model to be considered.
The most common calibration method used for coaxial
systems is TOSM (also known as SOLT) which uses the 12-
term error model [2]. However, this method requires an 8-
step procedure to get both ports calibrated.
When is not necessary to measure all four scattering
parameters (i.e. S11, S12, S21 and S22) of the Device Under
Test (DUT) or uncertainties are not necessary to be as small
as possible, alternative calibration methods may be
employed. Advantages and disadvantages must be
previously considered in order to determine which one will
be the best option for each particular case.

II. TOSM CALIBRATION
Before measuring any DUT S-parameters, both VNA’s
ports must be first calibrated in order to calculate system
errors. Most common employed method is TOSM. It
consists in calculating 6 forward (F) and 6 reverse (R) error
terms as shown in figures 1 and 2.










Fig. 1 Forward 12-term error model flow chart
where forward error terms are
e00 : Directivity (F)
e11 : Port-1 Source Match (F)
e10e01 : Reflection Tracking (F)
e10e32 : Transmission Tracking (F)
e30 : Leakage (Crosstalk)(F)
e22 : Port-2 Load Match (F)
Fig. 2 Reverse 12-term error model flow chart

where reverse error terms are

e′33 : Directivity (R)
e′11 : Port-1 Load Match (R)
e′23e′32 : Reflection Tracking (R)
e′23e′01 : Transmission Tracking (R)
e′03 : Leakage (Crosstalk) (R)
e′22 : Port-2 Source Match (R)

Solving measured S-parameters from figures 1 and 2 [2]

( )
S
S
eeSeSe
eSee
e
a
b
=S
∆+−−
∆−⋅
+=
221122221111
22110110
00
0
0
11M 1
(1)

SeeSeSe
See
e
a
b
=S
∆+−−
⋅
+=
221122221111
213210
30
0
3
21M 1
(2)

( )
S
S
eeSeSe
eSee
e
a
b
=S
∆+−−
∆−⋅
+=
′
′
221122221111
11223223
33
3
3
22M
''''1
'''
' (3)

SeeSeSe
See
e
a
b
=S
∆+−−
⋅
+=
′
′
221122221111
120123
03
3
0
12M
''''1
''
' (4)
where

SxxM: Measured, i.e. uncorrected, S-parameters
Sxx: Corrected S-parameters
21122211 SSSS=S −∆ (5)

A. VNA Calibration
Calibration procedure consists in measuring 7 different
reference standards (2 Opens, 2 Shorts, 2 Matches and a
Thru) with known reflection and/or transmission values from
a TOSM calibration kit. In this paper reference standards are
considered to have ideal values as follows
1=ΓOPEN (6)
1−=ΓSHORT (7)
0=ΓMATCH (8)




=
01
10
THRUS (9)
To perform a complete 2-Port calibration, an 8-step
procedure must be done as follows
Step 1: Connect Open1 to Port 1
Step 2: Connect Short1 to Port 1
Step 3: Connect Match1 to Port 1
Step 4: Connect Open2 to Port 2
Step 5: Connect Short2 to Port 2
Step 6: Connect Match2 to Port 2
Step 7: Connect Match1 Port 1 / Match2 Port 2
Step 8: Connect Thru between Port 1 and Port 2

1) Port 1 Calibration: Making steps 1 to 3, an OSM
calibration [2] to Port 1 is performed and the following
forward error terms are calculated from (1)

( )11100 matchS=e M (10)

)()(
2)()(
111M111M
00111M111M
11
shortSopenS
eshortSopenS
=e
−
⋅−+
(11)
[ ] [ ]
)()(
)()(2
111M111M
00111M00111M
0110
shortSopenS
eshortSeopenS
=ee
−
−⋅−⋅−
(12)

TABLE I
PORT 1 CALIBRATION SUMMARY
Reference Error to be
corrected Description
Open1
Short1
e11 Source Match (F)
e10e01 Reflection Tracking (F)
Match1 e00 Directivity (F)

2) Port 2 Calibration: Making steps 4 to 6, an OSM
calibration to Port 2 is performed and the following reverse
error terms are calculated from (3)

( )22233´ matchS=e M (13)

)()(
´2)()(
´
222M222M
33222M222M
11
shortSopenS
eshortSopenS
=e
−
⋅−+
(14)
[ ] [ ]
)()(
´)(´)(2
´´
222M222M
33222M33222M
3223
shortSopenS
eshortSeopenS
=ee
−
−⋅−⋅−
(15)


TABLE II
PORT 2 CALIBRATION SUMMARY
Reference Error to be
corrected Description
Open2
Short2
e′11 Source Match (R)
e′23e′32 Reflection Tracking (R)
Match2 e′33 Directivity (R)

3) Isolation Ports Calibration: Step 7 is optionally made
only when very low transmission parameters must be
measured. In most cases this error term is neglected.
( )2,12130 matchS=e M (16)
( )1,21203 matchS=e M′ (17)

TABLE III
ISOLATION PORTS CALIBRATION SUMMARY
Reference Error to be
corrected Description
Match1
Match2
e30 Crosstalk (F)
e’03 Crosstalk (R)

4) Calibration between Ports: When making step 8 both
Load Match and Transmission Tracking error terms are
calculated from (1), (2), (3) and (4) as follows

eeThruS
eThruS
=e
∆−⋅
−
1111M
0011M
22 )(
)(
(18)
[ ] )1()( 221130213210 eeeThruS=ee M −⋅− (19)
eThruS
eThruS
=e
′∆−
′
−
′ )(
)(
22M
3322M
11
(20)
[ ] )1()( 113303123223 eeeThruS=ee M ′′−⋅′−′′ (21)
where
10011100. eeee=e −∆ (22)
32232233 ´´´.´´ eeee=e −∆ (23)

TABLE IV
CALIBRATION BETWEEN PORTS SUMMARY
Reference Error to be
corrected Description
Thru
e22 Load Match (F)
e’11 Load Match (R)
e10e32 Transmission Tracking (F)
e’23e’01 Transmission Tracking (R)

Equations (10) to (21) represent the 12 error terms to be
calculated.

B. DUT S-Parameters Measurement
Solving equations (1) to (4), corrected S-parameters of
the DUT can be expressed as follows [1]−[4]
( )
D
AAeeAA
=S 12212222221111
1 ⋅⋅−′⋅+⋅
(24)
( )[ ]
D
eeAA
=S 2222222121
1 −′⋅+⋅
(25)
( )
D
AAeeAA
=S 12211111112222
1 ⋅⋅′−⋅+⋅
(26)
( )[ ]
D
eeAA
=S 1111111212
1 ′−⋅+⋅
(27)
where
0110
0011
11
ee
eS
=N M
−
(28)
0123
0312
12
ee
eS
=N M
′′
′
−
(29)
3210
3021
21
ee
eS
=N M − (30)
3223
3322
22
ee
eS
=N M
′′
′
−
(31)
( ) ( ) 1122122122221111 11 eeAAeAeA=D ′⋅⋅⋅−′⋅+⋅⋅+ (32)

where Nxx are normalized S-parameters [4].

C. Full 2-Port: Advantages and Disadvantages
1) Advantages: Provides low uncertainties as all 12 error
terms are calculated and all four DUT S-parameters are
measured.
2) Disadvantages: Needs an 8-step procedure calibration.
It is always necessary to measure all four DUT S-
parameters even if only one is needed to be corrected.

III. INCOMPLETE 2-PORT VNA CALIBRATION
In the past, VNAs had only a transmission/reflection
(T/R) test set. This allowed only forward parameters to be
measured, since Port 1 acted as a source and Port 2 as a load.
Then, calibration methods used were:

• Transmission Response (TR)
• 1-Port + Normalization (1-P+N)
• Enhanced Response(ER)
• One-Path 2-Port (1-P 2-P)

Nowadays, most VNAs have a full S-parameter test set.
This allows the source to be switched to both ports, hence it
is able to measure all four S-parameters and a TOSM, i.e.
complete, calibration can be done.
However, when it is not necessary (or convenient for
some reason) to measure all four DUT S-parameters or,
uncertainties are not necessary to be as small as possible,
above mentioned incomplete calibration methods can be
used [5]. All of them are partial calibrations based on
TOSM method described in section II.
To simplify mathematical expressions, crosstalk error
terms will be considered null valued for all cases

030 =e (33)
003 =e′ (34)

IV. TRANSMISSION RESPONSE
It is the simplest 2-Port calibration method and is used
when only S21 (or S12) parameter is of interest. A Thru
reference element is connected between ports for the
calibration, so only transmission tracking error term is
partially calculated. This causes the highest uncertainties in
transmission S-parameter measurements.
A. VNA Calibration (between Ports)
From (2) and (33):

( )
( ) ( ) ( )ThrueeThruSeThruSe
ThruSee
=S
S∆+−−
⋅
221122221111
213210
21M 1
(35)

Applying (9) in (30)

2211
321021M 1
1
ee
ee=S
−
⋅
(36)

As neither e11 nor e22 are calculated, the correction term
related to them is considered null valued.

02211 =ee (37)

Replacing (37) in (36)

21M3210 S=ee (38)

Similar considerations are applied for the reverse
transmission tracking term

12M2301 S=ee ′′ (39)

B. DUT S21 (or S12) Measurement
As only S21 parameter is measured and e10e32 error term
is calculated, equation (25) is reduced to

3210
21
21
)(
ee
DUTS
=S M (40)

Similar considerations can be applied for S12

0123
12M
12
''
)(
ee
DUTS
=S (41)

C. Transmission Response: Advantages and Disadvantages
1) Advantages: Very fast one-step calibration procedure.
Only S21 needs to be measured in order to get its corrected
value, so a good option for unidirectional devices.
2) Disadvantages: Only for transmission (S21 or S12)
parameters. As Transmission Tracking error term is not
calculated correctly, this method is not very accurate with
lossy DUTs. On the other hand, it is recommended only for
insertable devices as in practice this method always
considers ideal Thru values as in (9).

V. 1-PORT + NORMALIZATION
This method performs a 1-Port calibration (at Port 1 or
Port 2) and, separately, a transmission response. This is
usually employed when only forward parameters (S11 and
S21) or reverse parameters (S22 and S12) are required.
A. VNA Calibration
1) Port 1 (or Port 2) Calibration: Procedure is applied
in the same manner as in Section II A.1 (or section II A.2).
2) Calibration between Ports: Procedure is applied in
the same manner as in Section IV A.
B. DUT Forward (or Reverse) Parameters Measurement
As DUT reverse parameters are not measured, e22 and all
reverse error terms are not calculated, hence all correction
terms related to them in (24) and (25) are considered null
valued. S11 can be expressed as follows

eeDUTS
eDUTS
=S
∆−⋅
−
1111M
0011M
11 )(
)(
(42)
As OSM and transmission normalization calibrations are
performed separately, S21 corrected value remains the same
as in section IV B.

3210
21
21
)(
ee
DUTS
=S M (43)

Similar considerations are applied for reverse parameters

eeDUTS
eDUTS
=S
′∆−′⋅
′
−
2222M
3322M
22 )(
)(
(44)

0123
12
12
)(
ee
DUTS
=S M
′′
(45)

C. 1-Port + Normalization: Advantages and Disadvantages
1) Advantages: Corrects directivity, reflection tracking
and source match of Port 1 (or Port 2).
2) Disadvantages: Similar as in Transmission Response
method.


VI. ENHANCED RESPONSE
It is an improvement of the 1-P+N method for measuring
Forward (or Reverse) S-parameters. It needs the same four
steps as before to calibrate the VNA but, in this case, it also
calculates Load Match error term. This allows Transmission
Tracking error term to be correctly calculated.
A. VNA Calibration
1) Port 1 (or Port 2) Calibration: Procedure is applied in
the same manner as in Section II A.1 (or section II A.2).
2) Calibration between Ports: Procedure is applied in
the same manner as in Section II A.4.
B. DUT Forward (or Reverse) Parameters Measurement
Although e22 is calculated in this case, DUT reverse
parameters are not measured and none of the reverse error
terms is calculated. Hence, all correction terms related to
them in (24) and (25) are considered null valued and S11 and
S21 can be derived as follows

eeDUTS
eDUTS
=S
∆−⋅
−
1111M
0011M
11 )(
)(
(46)





∆−
⋅
eDUTSe
ee
ee
DUTS
=S )(
)(
11M11
1001
3210
21M
21
(47)

Similar considerations are applied for reverse parameters

eeDUTS
eDUTS
=S M
′∆−′⋅
′
−
2222M
3322
22 )(
)(
(48)





′∆−′
′′
⋅
′′ eDUTSe
ee
ee
DUTS
=S )(
)(
22M22
3223
0123
12M
12 (49)

C. Enhanced Response: Advantages and Disadvantages
1) Advantages: Calculates Transmission Tracking error
term correctly.
2) Disadvantages: As only Forward (or Reverse) S-
parameters are measured, Load Match value can not be used
for correcting DUT S-parameters.

VII. ONE-PATH 2-PORT
Originally named One-Path Full 2-Port, was introduced
to T/R VNAs in order to measure all four S-parameters.
However, DUT must be manually reversed to measure
Reverse S-parameters .
At present most VNAs have this calibration option, but
special care must be taken as some manufactures consider
ER method as 1-P 2-P.

A. VNA Calibration
This method considers Forward and Reverse models the
same as follows

3300 e=e ′ (50)
2211 e=e ′ (51)
32230110 ee=ee ′′ (52)
23013210 ee=ee ′′
(53)
1122 e=e ′ (54)
0330 e=e ′ (55)

Hence, it needs the same four steps as in the previous
methods to calibrate the VNA and only 6 forward error
terms are needed to be calculated using (10), (11), (12), (16),
(18) and (19).
B. DUT Parameters Measurement
When measuring DUT device, forward parameters are
measured first, and then DUT is connected backwards and
reverse parameters are measured. This allows equations (24)
to (27) to be used with no correction terms null valued.
C. One Path 2-Port: Advantages and Disadvantages
1) Advantages: All four DUT S-parameters can be
measured. As Forward and Reverse error terms have same
values, only a four-step procedure is needed to calibrate the
VNA.
2) Disadvantages: Not recommended for VNAs using
any combination of coaxial sexed port connectors due to the
necessity of adapters. A series of single sweep and DUT
manually change procedure must be performed in order to
get all four S-parameters. In practice, uncertainties may be
higher that Full 2-Port due to connector mechanical
repeatability or cable flexibility.

VIII. SIMULATIONS
A series of comparisons between incomplete calibrations
methods respect to TOSM were carried out. S11 and S21
measurements were simulated and maximal deviation
results are shown in figures 3 to 6.

A. S11 Deviation Results
Different maximal deviations of |S11| for 1-P+N and ER
methods respect to TOSM are shown in figure 3. As in both
incomplete methods, S11 has the same value (see equations
(42) and (46)), such deviations respect to TOSM are the
same. These deviations depend on Port 2 Load Match, i.e.
e22 value, and DUT´s attenuation, i.e. S21 value.
For example, if the DUT consists of a 6-dB attenuator
and |e22| = 0.1, then maximal deviation respect to TOSM
method will be 0.026.
If now the DUT consists of a coaxial cable with nominal
0 dB attenuation value, and |e22| remains in 0.1, then
maximal deviation respect to TOSM method arises to 0.100.



Fig. 3 |S11| maximal deviation for 1-Port + Normalization and Enhanced
Response with respect to TOSM method.
B. S21 Deviation Results
Different maximal deviations of |S21| for TR and ER
methods respect to TOSM are shown in figures 4 and 5
respectively for a DUT having a nominal attenuation value
of 0 dB.

Fig. 4 |S21|dB maximal deviation for Transmission Response with respect
to TOSM method when measuring a S21 value of 0 dB.

Fig. 5 |S21|dB maximal deviation for Enhanced Response with respect to
TOSM method when measuring a S21 value between 0 dB and 6 dB.

For example, if DUT´s parameters |S11| = |S22| = 0.1, and
VNA´s error terms |e11| = |e22| = 0.1, then maximal deviation
respect to TOSM method will be 0.17 dB for TR method
and 0.09 dB for ER method.
According to figures 5 and 6, if now the same DUT has
an attenuation value of 6 dB and all other values remain the
same, then maximal deviation respect to TOSM method
arises to 0.24 dB for TR method and remains in 0.09 dB for
ER method.

Fig. 6 |S21|dB maximal deviation for Transmission Response with respect
to TOSM method when measuring a S21 value of -6 dB.

IX. CONCLUSIONS

Different types of incomplete 2-Port VNA calibrations
methods are explained in this paper. Each one of them has
its own advantages and disadvantages respect to a complete
2-Port method as TOSM.
In practice, if VNA´s error terms and/or DUT´s
mismatches are quite low, there will be no significant
deviation between incomplete and complete calibration
methods when measuring S11 or S21. On the contrary, if
VNA´s source and load match error term values are
considerable and also DUT is lossy, then incomplete
methods are not suitable due to the significant deviations
they may have.

REFERENCES

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Zealand Lower Hutt, New Zealand, 2010.
[4] J. Dunsmore, “Handbook of microwave component measurement”,
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[6] G. Wübbeler, Clemens Elster, Thomas Reichel and Rolf Judaschke,
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