TDR Fundamentals
Instrument Configuration
9-22
The distance or time resolution of a Time Domain Network Analysis (TDNA)
system is related to the system risetime. The distance to a discontinuity is given
by:
so that
where c is the speed of light, t
o
is the Delta time between the incident step and
the reflected signal, and ε
r
is the relative dielectric constant of the dielectric of
the transmission line. Therefore the distance that separates two discontinuities
is given by:
where t
1
is the two way travel time to one discontinuity and t
2
is the two way
travel time to second discontinuity. These two discontinuities become
indistinguishable when separated by a time (t
2
- t
1
) of less than half the system
risetime. Therefore the minimum distinguishable distance between two
discontinuities is given by:
This means that with the HP 54750 Series TDR system risetime of 45 ps, two
discontinuities merge together and become indistinguishable at 3.5 mm for an
air dielectric. For practical systems the HP 54750 Series TDR systems define
the distance resolution to be twice this number, or 7 mm in air.
An example of how risetime affects distance resolution is an airline with two
washers (capacitive discontinuities) placed 2 mm apart on the center
conductor. The risetime needed to distinguish these as separate discontinuities
is given by:
or
d
υ
t=
d
c
ε
r
--------
t
o
2
----
=
d
∆
c
ε
r
--------
t
2
t
1
–
2
--------------
=
d
min
c
ε
r
--------
t
r
4
---
=
d
min
c
ε
r
--------
t
r
4
---
=
t
r
4d
min
ε
r
c
----------------------- 2 6 . 7 ps==
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