HP 54753A - Page 199

TDR Fundamentals
Instrument Configuration
9-25
higher than the slope of a line through the 10% and 90% risetime points. For
reflections less than 10%, the error resulting from this method is less than 3%,
not including measurement error of the TDR system.
For a series inductive discontinuity, the relationship between the reflected
signal and the inductor, L, is found as follows:
1Since ωL << 100 Ω for frequencies of interest.
i
L
~ v
step
/ 100
Ω
where i
L
is the current through L and v
step
is the open
circuit step amplitude
2 The voltage across the inductor therefore is:
where v
L
is the voltage across the inductor, and
3 As discussed above the max slope is
4 If the incident voltage at the inductor is v
iL
and the reflected voltage at
the inductor is v
rL
then
or
and
or
5 Combining steps 2, 3 4 above produces
v
L
L
di
L
dt
-------
L
100
---------
dv
step
dt
--------------
==
v
Lmax
L
100
---------
dv
step
dt
--------------


max
=
dv
step
dt
--------------


max
0.8
()
v
step
()
1.27
()
t
rL
--------------------------------------------
1.016v
step
t
rL
-------------------------==
v
iL
0.5v
step
=
v
step
2v
iL
=
v
rL
0.5v
L
=
v
L
2v
rL
=
v
Lmax
L
100
---------
v
step
dt
-----------


max
=
v
Lmax
L
100
---------
1.016v
step
t
rL
-------------------------
=
2v
rLmax
L
100
---------
2v
iL
t
rL
----------
=
L
100 v
rL
()
t
rL
()
1.016v
iL
---------------------------------=