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ECE 451 – Jose Schutt‐Aine 1
ECE 451Automated Microwave Measurements
Jose E. Schutt-AineElectrical & Computer Engineering
University of Illinoisjschutt@emlab.uiuc.edu
TRL Calibration
ECE 451 – Jose Schutt‐Aine 2
Board with traces
L-shaped support
Center pin
screw
Flange-mountconnector
Coaxial‐Microstrip Transition
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L1CL1 CR2
L2CL2 CR1
TL1SMA SMA
In Out
Coaxial‐Microstrip Transition
TDR Plot
Equivalent Circuit
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With parasiticsNo parasitics
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DUT
microstrip microstrip
coaxial connector coaxial connector
TRL CALIBRATION SCHEME
Want to measure DUT only and need to remove the effect of coax-to-microstrip transitions. Use TRL calibration
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Error BoxA
Error BoxB
Port1
Port21 2
1 2
W1 W2Measurement
Planes
Error boxes A and B account for the transition parasitics and the electrical lengths of the microstrip.
Make three standards: Thru, Line and Reflect
A model for the different error boxes can be implemented
TRL Error Box Modeling
ECE 451 – Jose Schutt‐Aine 7
connect thru
A B
Ra Rb
Rt
t a bR R R
Step 1 - THRU Calibration
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LINE
connect line (Note: difference in length between thru and line)
A B
Ra Rb
Rd
LINE
RL
Step 2 - LINE Calibration
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REFLECT
connect reflect
Step 3 - REFLECT Calibration
A B
Ra Rb
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-5
0
5
1 1.5 2 2.5 3 3.5 4 4.5 5
Measured |S11| of Microstrip Unknown Relative to TOUCHSTONE Models
PORT EXT. calibrationTRL calibration
Rel
ativ
e M
agni
tude
, dB
Frequency, GHz
PORT EXT. data compared to L=.808 nH modelTRL data compared to L=.948 nH model
TRL – Measurement Comparison
ECE 451 – Jose Schutt‐Aine 11
-20
-15
-10
-5
0
1 1.5 2 2.5 3 3.5 4 4.5 5
Measured Data for Microstrip Unknown
with TRL calibrationwith 722 ps port ext. (inc. barrel)
|S11
| (d
B)
Frequency, GHz
Measured 10/18/94
TRL – Measurement Comparison
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TRL Derivation
- Obtain network parameters of error boxes A and B- Remove their effects in subsequent measurements
TRL Objectives
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S11A
a1R
b1R
S22A
S12A
S21A
R
S12B
S21B
S22BS11
B
b2R
a2R
R
R2
R1R1 a 0
ba
R2
R2R2 a 0
ba
Model for Reflect
2 Measurements
ECE 451 – Jose Schutt‐Aine 14
S11A
1
1
a1T
b1T
S22A
S12A
S21A
S12B
S21B
S22BS11
B
b2T
a2T
T2
T1T1 a 0
ba
T2
T2T1 a 0
ba
T1
T2T2 a 0
ba
T1
T1T2 a 0
ba
Model for Thru
4 Measurements
ECE 451 – Jose Schutt‐Aine 15
S11A
e-La1L
b1L
S22A
S12A
S21A
S12B
S21B
S22BS11
B
b2L
a2L
e-L
L2
L1R1 a 0
ba
L2
L2L1 a 0
ba
L1
L2L1 a 0
ba
L1
L1L2 a 0
ba
Model for Line
4 Measurements
ECE 451 – Jose Schutt‐Aine 16
Using R parameters (same as T transfer parameters), we can show that if
1 11 2
1 22 221
11
b S ba S aS
1 11 1 12 2b S a S a 2 21 1 22 2b S a S a
12 21 11 22S S S S
11 2
22 221
11
S bR
S aS
Use R (or T) Parameters
ECE 451 – Jose Schutt‐Aine 17
M A BR R RR
A B
1 1MR R R R
11 12A 22
21 22
r r a bR r
r r c 1
11 12B 22
21 22
R1
A
1
22
1 b1 1Rc ar a bc
The measurement matrix RM is just the product of the matrices of the error boxes and the unknown DUT
or
Let RA be written as
The inverse of RA is
RB is similarly written as
TRL Derivation
ECE 451 – Jose Schutt‐Aine 18
B
1
22
11 1R
M22 22
1 b 11 1 1 1R Rc c ar a 1 b 1a
T A BR R R
And the inverse of RB is
The matrix of the DUT is then found from
Note that although there are eight terms in the error boxes, only seven quantities are needed to find R. They are a, b, c, , , and r2222
From the measurement of the through and of the line, seven quantities will be found. They are b, c/a, , r2222, a and e2l
In addition to the seven quantities, if a were found, the solution would be complete. Let us first find the above seven quantities.
The ideal through has an R matrix which is the 2 x 2 unit matrix. The measured Rmatrix with the through connected will be denoted by RT and is given by
Where RA and RB are the R matrices of the error box A and B respectively. With the line connected, the measured R matrix will be denoted by RD and is equal to
TRL Derivation
ECE 451 – Jose Schutt‐Aine 19
A
1A LD TRR R R R
T AD A L1RR R R R
T
1DT R R
A A LTR R R
11 12
21 22
t tT
t t
l
L l
e 0R
0 e
AD L BRR R R
AB T1R R R
where RL is the R matrix of the line
Now
so that
Define Which when substituted into the above equations results in
The matrix T is known from measurements and will be written as
, since the line is non-reflecting
TRL DerivationNOTE: quantities shown in RED are known
ECE 451 – Jose Schutt‐Aine 20
11 12A 22
21 22
r r a bR r
r r c 1
11 12B 22
21 22
R1
A A LTR R R
11 12
21 22
l
l
a b a b e 0c 1 c 1 0 e
t tt t
RA is unknown and was written as
RB similarly was written as
Recalling and writing the matrices results in
Next, writing out the four equations gives:
TRL Derivation
ECE 451 – Jose Schutt‐Aine 21
11 12la ct et a
21 22la ct et c
11 12lb bt t e
21 22lb bt t e
11 1211 12
21 2221 22
aa c c c
aa c a
t tt tt t
ct t
21 22
2
11 12t ta a t 0c c
t
Dividing the first of the above equation by the second results in
which gives a quadratic equation for a/c
Dividing the third equation in the group by the fourth results in
TRL Derivation
ECE 451 – Jose Schutt‐Aine 22
11 12
21 22
b bb
t tt t
211 221 22 1t t tb b t 0
21 22 21 22
21 2
2 L
221 22
b bt t t tt t t t
e c aa cc
11 12 2111
21 22
r S Sa Sc r S
which gives the analogous quadratic equation for b as
Dividing the fourth equation in the group by the second results in
Since e2L is not equal to 1, b and c/a are distinct roots of the quadratic equation. The following discussion will enable the choice of the root. Now b=r12/r22=S11 and
TRL Derivation
ECE 451 – Jose Schutt‐Aine 23
abc
A A LTR R R
A A Ldet R det R dedet T t R
Ldet det T R 1
11 22 12 21t t t t 1
For a well designed transition between coax and the non-coax |S22|, |S11| <<1 which yields |b|<< 1and |a/c|>>1. Therefore,
which determines the choice of the root
Recalling
or
so that
which implies that there are only three independent Tij. Then there are only three independent results, e.g. b, a/c, and e2L.
TRL Derivation
ECE 451 – Jose Schutt‐Aine 24
22 22 A B T
b d ear R R
c 1 1R g
f 1
1a 11c 1 c
b ba b ac
22 22
1 br
1 c aa bcd egf 1
22 22
d bf e bgf
r1 a c a cda ebc
Now let us find four more quantities
Now
So that
or
TRL Derivation
ECE 451 – Jose Schutt‐Aine 25
22 22
c1 ee ag g cba cra 1
ac b
d bf e11 a c a ca
bf d eec
cf dac1 ea
e bd bf
TRL Derivation
and
We also have
from which we can extract
from which we obtain
ECE 451 – Jose Schutt‐Aine 26
d bfa c1 ea
R
R1
ac 1
bw
R
1
1
w bc1 wa
a
12 21 222 22
1
R
R R1 11
RS S S1
w SS S1
The additional four quantities found are , , r2222 and a. To complete the solution, one needs to find a. Let the reflection measurement through error box A be w1. Then
which may be solved for a in terms of the known b and a/c as
We need a method to determine a. Use the measurement for the reflect from through the error box B. Let w2 denote the measurement
TRL Derivationand
ECE 451 – Jose Schutt‐Aine 27
21 11R
22 22
12R
22
2w1
R2
R 1w
R
2
2
w
1 w
R
1
1
w bc1 wa
a
or
may be found in terms of and as
Recall
TRL Derivation
ECE 451 – Jose Schutt‐Aine 28
21
21
1 ww bacw 1 wa
d bfa c1 ea
22 1
21
1 ww b d bfa c cw 1 w 1 ea a
12
21
21
1 ww b d bfa c cw 1 w 1 ea a
so that
From earlier
so that
which determines a to within a sign.
TRL Derivation
or
ECE 451 – Jose Schutt‐Aine 29
1R
1
w bca 1 wa
So if R is known to within then a may be determined as well. Calibration is complete and we can now proceed to the measurement of the DUT.
TRL Derivation
M22 22
1 b 11 1 1 1R Rc c ar a 1 b 1a
From earlier, the matrix of the DUT is found from
in which all the terms have now been determined.
ECE 451 – Jose Schutt‐Aine 30
TRL Application
ECE 451 – Jose Schutt‐Aine 31
TRL Application
Thru
Reflect
Line
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TRL Application
ECE 451 – Jose Schutt‐Aine 33
TRL Application
ECE 451 – Jose Schutt‐Aine 34
TRL Application
ECE 451 – Jose Schutt‐Aine 35
ECE 451 – Jose Schutt‐Aine 36
Paul W. Klock, “The Theory of Reflectometers”, 1995
References
Agilent Network Analysis, "Applying the 8510 TRL Calibration for Non-Coaxial Measurements", Product Note 8510-8A
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