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FliOW HEWLETT
~e.. PACKARD
DIFFERENTIAL TDR USING A SINGLE STEP GENERATOR
Interest has been on the rise for making differential TDR measurements on
balanced systems like twisted pair cables, both shielded and unshielded, on
dual trace micros trip lines, and on dual conductor stripline. Under certain
conditions, such balanced transmission paths offer improved performance over
unbalanced lines, particularly in terms of common mode noise rejection and
immunity to crosstalk.
The question arises on whether standard TDR can be used effectively to analyze
balanced systems, and if so, how? This note explores these questions and will
describe how differential TDR is easily accomplished using a standard TDR if a
few special considerations are made. These are different considerations than
those required with dual step source differential TDR. Equivalent circuits of
dual and single step source TDR's are compared along with SPICE model
simulation results to support this claim. Finally, actual measurements are
performed on a number of standard devices and on a twisted pair cable to verify
the technique. A view of the twisted pair cable using a dual pulse
differential TDR is compared to these results and shown to have very close
agreement, while standard TDR with no special considerations is shown to be
error.
Dual pulse generator method:
Differential TDR can be accomplished by using two step generators to stimulate
the DUT. One step generator outputs a pulse from 0 volts to some positive DC
level with a fast edge. The other step generator has opposite polarity, and
steps from 0 volts to a negative level. Each generator is single ended
coaxial, but a differential pulse exists between the center conductors of the
output cables of these generators. This differential signal is applied to the
differential inputs of the DUT, a scope channel is attached to each input, and
the difference of the channels is displayed on screen.
A block diagram of the differential stimulas is shown in Figure 1. This
technique relies on step generators being synchronized in time, and identical
in pulse shape.
50 OHM
CH 1
SAMPLER
BALANCED
LINE OUT
..lac/IL37
Figure 1. Dual generator differential stimulus
Single generator method:
Differential TDR is also possible using a single pulse generator and taking
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advantage of its common mode and differential mode components. Waveform math
in the oscilloscope can be used to subtract the common mode component to view
the differential mode reflections.
The HP 54l20T TDR step is produced by a current source attached to the scope
input sampler which is back terminated in 50 ohms. This can be represented
with a Thevanin equivalent circuit like shown in Figure 2 with a step generator
in channell and no step in channel 2. This can again be redrawn to show the
common mode and differential mode components of the step source. An equivalent
circuit, which contains the desired dual source differential generator pair is
shown in Figure 3. Notice it's similarity to the true differential source in
Figure 1.
50 OHM
CH 1
SAMPLER
50 OHM
CH 2
SAMPLER
wIIC/81ae
Figure 2. Single ended pUlse generator built into Ch 1, and Ch 2 input with no
step
50 OHM
+ 2. A
2
BALANCED
LINE OUT
WI8C/8l38
Figure 3. Equivalent circuit of TDR step and scope inputs represented by
common mode and differential mode step sources.
The single step generator has been redrawn into its common mode (CM) and
differential mode (DM) equivalents. In this equivalent circuit, both channels
1 and 2 are simultaneously stimulated by the common mode source. Channels 1
and 2 are also stimulated differentially by a positive going and negative going
pair of sources.
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To View Differential TDR
By applying the center conductor of channell and channel 2 to the inputs of a
balanced line OUT, and shield ground to the OUT ground (if one exists, such as
a shield around a twisted pair), and defining a Function in the Waveform Math
menu of the HP 54120T as channell - channel 2, a differential response appears
on screen. The common mode element of the channel I driving source and
associated reflections are subtracted out, except for reflections caused by any
imbalance effect in the line, or from common mode resonance where the line acts
as an antenna.
In the case of imbalance or resonance, reflections cause a slightly different
response depending on whether the channel I source is attached to one side of
the device or to the other. This effect can be very helpful to determine if
and where imbalance is present in a OUT. In the event it is not desired to see
such effects and desired to match results that would be obtained from a
differential TOR step source using two pulse generators, this can be easily
accomplished.
One must only view and store the Ch I - Ch 2 response with scope channell
attached to one side of the device, and then view and store the response with
the leads reversed. Adding these two responses yields the same result as when
using a differential step source. Required waveform math functions are
available in the HP 54120T.
SPICE modeling for differential TDR:
Hpspice simulations illustrate dual and single pulse generator methods of
differential TOR, and show theoretically that the single pulse generator method
is effective in viewing differential and common mode impedance of balanced
OUT's, and results compare exactly to that of the two pulse method. Further,
for systems with imbalance, Spice indicates the single pulse method is cabable
of identifying an imbalance and displaying the differential impedance as would
be seen with a dual pulse method by using waveform storage and math functions.
The simplest SPICE results are presented here for a balanced delay line with
different common mode and differential mode impedances and delays, and with a
balanced termination. More complicated SPICE results with imbalance effects
and their removal are included in the appendix, as well as additional SPICE
model circuit equations.
The SPICE T section model and resultant delay line model
The basic T line section model used consists of series inductors L with mutual
coupling k, a differential capacitance Cdiff, and common mode capacitances Ccm
with ground reference between each capacitance. This is shown in Figure 4. T
lines Xl and X2 are formed by cascading 20 of these T sections together,
resulting in a common mode impedance and delay for each Xl and X2 of 26.5 ohms
and 2.12 nsec. The differential impedance and delay for Xl and X2 is 83.27
ohms and 5 nsec respectively. Oerived calculations can be found in the
appendix. All simulations use the same delay line OUT; cases vary in the way
the line is driven and terminated.
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L
L=4NH
B
K=+0.3
~
Cdiff=1PF
Cdi ff Ccm =1PF
L Cem