Tektronix 1S2 User manual

Tektronix, Inc.
P.O. Box
500
Beaverton, Oregon 97077
070-0889-00
TEKTRONI»
INSTRUCTION MANUAL
Serial Number
568

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Type 152

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Type 152

TYPE SAMPLING UNIT
ANO T!ME DOMAIN REHECTOMETER
VERT GAIN .S
Fig. l -1. Type .1 S2 Sampling Unit.

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Type 152
SECTION 1
CHARACTERISTICS
Change information, if any, affecting this section will be found at the
rear of the manual.
Introduction
The Tektronix Type 1S2 Sampling Unit is a DC to 3900
MHz multiple purpose sampling plug-in unit. It will operate
in any Tektronix 500-series Oscilloscope that will accept 1-
series or letter-series plug-in units. The Type 1 S2 provides
both the vertical
and the horizontal information to the oscil-
loscope during equivalent-time sampling.
Normal signal sampling operation
or special coaxial cable
Time Domain Reflectometry
(TDR) testing are the main fea-
tures
of the Type 1S2. The sampler step-response 10% to
90% risetime is 90 picoseconds (ps) or less in a 50 a environ-
ment. The sampler
is a two-connector through-signal channel
for viewing signals within a 50 a transmission line,
or at the
end of a terminated 50 a transmission line. Unterminated
sampler through-channel
DC resistance is approximately
5000 a, useful during low frequency real-time sampling
operation.
The vertical channel
is calibrated for either volts or reflec-
tion coefficient
(p) in seven steps from 0.005 to 0.5 in a 1-2-5
sequence. A Variable control can either increase
or decrease
these deflection factors for complete
coverage between cali-
brated deflection factors. Minimum uncalibrated deflection
factors are: approximately 0.002 Volts/div
or 0.002 p/div.
The horizontal axis
of the display is calibrated for either
Time
or Distance in three major ranges and 21 steps from
100 ps/div to 1000 ns/div Time, and from 1 cm/div to 100
meters/div Distance. Time or Distance units/div are dis-
played by an illuminated readout panel for ease of interpret-
ing the display. The illuminated panel Units lamps
are turned
off whenever the Magnifier Variable control
is not at its
CAL detent position. Maximum uncalibrated sweep rates with
the Range control
at .111s-lO m and Magnifier at XlOO
are: ::::;28.75 ps/div Time and ::::;o.275 cm/div Distance.
Distance calibration.
is dependent upon the position of a
Dielectric switch
that provides correct horizontal deflection
factors for the different
propagation velocities of AIR, solid
TFE, or solid POLYETHYLENE dielectrics. Other dielectrics
that cause intermediate propagation velocities can be tested
after the operator adjusts the front panel variable PRESET
dielectric control so the horizontal units/div match the par-
ticular line being tested.
The horizontal units/div
are automatically set to Time
whenever the Type 152
is operated as a normal sampling
plug-in unit.
Two internal step-function pulse generators provide a
selectable test signal during
TDR operation. One provides
a 0.25-volt 50 ps 10% to 90% risetime pulse and the other
provides a 1.0-volt 1
ns 10% to 90% risetime pulse, each at
a source impedance of 50 a. Other TDR features include a
two-position
RESOLUTION switch, signal-related vertical
OFFSET (positioning) voltage and time related horizontal
POSITION control that indicates the Time or Distance Posi-
tion of the time window start as a percentage of the unmagni-
fied ten division time window. These controls
(OFFSET and
POSITION), allow accurate slide-back measurements of both
the magnitude
and location of TDR signals.
Critical analysis
of any TDR display is possible through the
use of either a
storage oscilloscope or a photograph. Stor-
age displays are obtained by using the Type 1 S2 in a Tek-
tronix Type 549 Storage Oscilloscope. Permanent record
photographs
of CRT displays are possible with any one of
several Tektronix Oscilloscope Cameras.
Modes of Operation
The two general operating modes of the Type 1 S2 are as
a Time Domain Reflectometer and as a normal signal sam-
pling oscilloscope. Four display modes perform for both
general operating modes.
(1) Normal repetitive sweeps for
general
CRT viewing. (2) Single Sweep, where the desired
display can be caused to traverse the
CRT horizontally once,
without repeating until required.
(3) Manual scan; the display
is converted to a single spot that can be moved horizontally
at a hand operated rate convenient to the operator. And
(4) External scan; the display is a single spot (as in Manual
Scan) that is caused to traverse the horizontal axis at a rate
set by
any external drive signal. (The oscilloscope main
frame time-base Sawtooth
Out signal can be connected to
the external input to sweep the display
at very slow rates.)
Vertical
and Horizontal output signals permit the Type
1S2 to drive X-Y or Y-T recorders. Or, the recorder can con-
trol the
CRT scan rate (through the EXT INPUT) and the Type
1
S2 Vertical output signal will then control the pen recorder
Y axis. Output signal jacks have a 10 kn output impedance.
ELECTRICAL CHARACTERISTICS
The following characteristics apply over an ambient tem-
perature range of
0° C to +50° C, except as otherwise
stated. These characteristics
apply only after the Type 1 S2
has been properly mated to the oscilloscope and after a
warm-up time of
at least 20 minutes. A procedure for mating
the Type 1
S2 to each oscilloscope can be found in the Oper-
ating Instructions (Section 3) of this manual.
1-1

Characteristics--Type 1 S2
VERTICAL SYSTEM
General Characteristics
Performance Requirement Supplemental Information
Risetime 10% to 90% (sampling
Not more than 90 ps from + 15• C to Internal ·adjustment may be required between
operation)
+35° c.
o· c to + 15° c and +35° c to +so· c.
Use Cal Procedure Step
34 using setup of
Step 26.
Risetime l
0% to 90%
(TDR
Not more than 140 ps from
+15° C to Measured tr of reflection from shorted end of
operation)
+35° c.
20 cm air line driven by 0.25 V Pulser. Adjust-
ment may
be required as above, ·
THRU SIGNAL CHANNEL 50 n Nominally 50 n
Loop Impedance (Zol
Input Signal Range Signals between +2 V and -2 V limits
may be displayed at any
deflection
factor (Vertical Units/Div switch set-
ting).
Safe overload is +3 V if Thru
Signal Channel is coupled directly to
the EXT TRIG INPUT connector; +5 V
if not.
Reflections from within
THRU
Not more than 1Q%. Displayed during first 500
ps after 0.25-V Pul-
SIGNAL CHANNEL ser incident step, during TDR operation.
Noise (tangential) (sampling
mode
Not more than 2 mV.
Ignores occasional
+5%
and
-5%
peaks.
operation)
RESOLUTION Sw at NORMAL.
Deflection Factors 0.005 to 0.5 units/div
in seven calibrated Steps in a 1-2-5 sequence, either VOLTS or p.
steps.
Accuracy Within
3% of indicated deflection when Viewed at CRT.
VARI ABLE control is at CAL detent posi-
tion.
Variable units/div Counterclockwise rotation from
CAL posi- Counterclockwise rotation increases deflection
tion changes vertical deflection factor factor (decreases sensitivity); clockwise rotation
to
at least 2 times the units/div setting; decreases deflection factor (increases sensi-
clockwise rotation changes deflection tivity).
factor to
40% or less of the units/div
setting.
OFFSET Controls Voltage Range
Not less than -2 V to +2 V. Referred to the input.
Xl OFFSET OUTPUT Voltage
Not less than -2 V to +2 V.
Range
Xl OFFSET OUTPUT Voltage + l % of
full scale. Through l 0 kn. Accuracy valid into infinite
Accuracy (Referred to
any fixed vertical display
impedance voltmeter.
(l Mn meter causes
position).
-1 % error to Performance Requirement toler-
ance.)
VERT OUTPUT Jack voltage
ac- Input Signal =
VERT OUTPUT Maximum output,
+10 Volts. (Variable Units/
curacy (referred to input) UNITS/DIV Sw (volts) + l %.
Div control does not affect VERT OUTPUT sig-
nal referred to input).
Deflection Factor (referred to l volt
per displayed division when VARI ABLE
CRT display)
is at CAL.
Source resistance l0
kn, + l % resistor.
HORIZONTAL SYSTEM
POSITION Range Accuracy + l % of
full scale. Maximum
range is between 9.90 and 9.96.
Magnifier
VARIABLE Range
Not less than a 2.5:1 increase in sweep
rate
1 from the
CAL position.
HORIZ OUTPUT Jack Within
2%.
Relationship of time to
volts, not related to
l V/DIV Accuracy
CRT display.
Source resistance 10
kn, +5% resistor.
Horizontal Units/Div 1000 ns/div to 100
ps/div in 21
steps,
TIME in a 1-2-5 sequence.
Accuracy Within 3"/.;
except 100 ns ramp with Related to
CRT display when oscilloscope Ext
X50 and XlOO magnifier, within 5%.
Horiz set for l volt/div, +l %.
---
1-2

General
Characteristk:s
DISTANCE
Accuracy
DIELECTRIC Switch propagation
velocities and accuracy.
PRESET (Variable dielectric
range). "
EXT HORIZ Jack Input horizontal
deflection factor.
Maximum input
voltage
External Triggering
Trigger Jitter :
Sine Waves:
3SO kHz,·
SOOmV peak to
peak.
100 MHz,
SOOmV
peak
to
r peak.
Pulses:
1
ns risetime
80
mV step pulse
Sine Waves:
SGHz
Maximum input voltage
to
EXT
TRIG connector.
Pulse 10% to
90%
risetime
Display
aberrations
(Pulse Flatness Deviation)
Pulser source
impedance
Pulse amplitude into SO 0
Displayed jitter
Pulse 10% to
90% risetime
r
Display aberrations
(Pulse Flatness Deviation)
Characteristics-Type 1 S2
HORIZONTAL SYSTEM {cont)
Performance Requirement
Supplemental
Information
100 meters/div to 1 cm/div in 21 steps
Observed as not more than 140 ps risetime
in a 1-2-S sequence. from shorted
end of 20 cm air line while pulser
feeds
THRU SIGNAL Sampler through the 10
inch GR Connector
Cable.
Dependent upon dielectric material
In line
tested.
AIR: 1 X c, +3%.
Related to
speed of light, c,
where c -
Solid TFE: 0.69S X c, +3%.
30.0 cm/ns.
Solid
POLYETHYLENE:
0.6S9 x c,
+3%.
From 1 X
c, to between 0.6 and 0.6S
X G.
Variable from less than 2 volts/div to
more
than l S volts/div.
l SO volts combined DC plus AC peak.
SAMPLING MODE TRIGGERING
Not more thon 100 ns.
Not more than 100 ps.
Not more than 100 ps.
Not more than 30 ps.
+3 or -3 volts DC and combined AC
peak.
1.0 V, 1 ns, PULSE SOURCE
Not more than 1.1 ns from + 1S° C to
+3S
0
c.
Not more than + and -2.S% after
pulse
display reaches 100%.
From 0.9 to 1.0 volt.
Not more than 20 ps.
. 25 V, 50 ps, PULSE SOURCE
Not more than SS ps from + l S° C to
+3S
0
c.
EXT TRIG Operation.
EXT TRIG Operation.
EXT TRIG Operation, for both positive and
negative pulses.
UHF SYNC
Operation, tested according to
Step l S of the Performance Check procedure
in this manual.
Observed by terminated THRU SIGNAL Sam-
pier through the 10 inch GR Connector Cable.
.2S V, SO ps, PULSE SOURCE (Pulse 10% to
90% risetime)
When display system is as above and termina-
tion is GR 874-WSOB supplied with the Type
1S2.
Nominally SO 0, not tested.
When display system is as above.
Observed as not more than 140 ps risetime
from shorted
end of 20 cm air line while pulser
feeds
THRU SIGNAL Sampler through the 10
inch GR connector cable. Adjustments may
be
required to Vertical System per Step 34 of Cal
Procedure
between 0° C to +1S° C and
+3s
0 c
to +so
0
c.
Not more than + and - 7% in the first When displayed as above.
SOO ps after pulse display reaches 100%.
Not more than + and - 3% P-P after
the above SOO ps.
1-3

Characteristics-Type 152
.25
V, 50 ps, PULSE SOURCE Ccontl
General Characteristics Performance Requirement Supplemental Information
Pulser source impedance
Nominally 50 il. Not tested.
Pulse amplitude into 50 Q
From 230 to 260 mV.
Typically 250 mV.
Displayed jitter
Not more than 20 ps. When display system is as above.
POWER LINE VOLTAGE
Line voltage range Will operate over an RMS line voltage Does not apply when plug-in extenders are
range as stated for the Tektronix oscillo- used. May not operate correctly at low line
scope in which the Type 1 S2 is operated. voltage limits due to voltage drop in an ex-
ENVIRONMENTAL CHARACTERISTICS
Storage
Temperature- -40° C to +65° C.
Altitude-to 50,000 feet.
Operating
Operating temperature-0° C to +50° C.
0° C to + 15° C and +35° C to +50° C possible by
special adjustment.
Operating Altitude-Up to 15,000 feet.
1-4
tender.
MECHANICAL CHARACTERISTICS
Height
Dimensions-Width
Length
Weight-8 pounds.
7 inches
57/
8 inches
11 inches
Approximate
dimensions
including knobs
and connectors.
Construction-aluminum alloy chassis.
Finish-anodized and silk screened front panel.
Accessories
An illustrated list of the accessories supplied with the Type
1
S2 will be found at the end of the Mechanical Parts List
pullout pages following the schematic diagrams.

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Type 152
SECTION 2
TIME DOMAIN REF LECTOMETRY THEORY
AND THE TESTING Of
COAXIAL TRANSMISSION LINES
Change information, if any, affecting this section will be found at the
rear of the manual.
Introduction
This section of the manual contains general and detailed
descriptions of Time Domain Reflectometry (TDR) analysis of
coaxial transmission lines. The section begins with a com-
parison between two test methods, sine wave testing and step
function testing
of transmission lines. Sine wave testing is
known as frequency domain reflectometry (FDR) and step
function testing
is known as TDR. The FDR-TDR comparison is
followed by a basic description of TDR testing principles;
reflections from capacitors
and inductors; reflections from
resistive discontinuities; coaxial
cable response to a step
signal;
and finally special applications.
This section, combined with the Operating Instructions of
Section 3 should provide the experienced electronics tech-
nician with adequate information to effectively use the Tek-
tronix Type 1S2 Sampling Unit.
A TDR system can measure lumped resistance and reac-
tance as well as characteristic impedance within a transmis-
sion line. Measurement is by analysis of signals reflected
from a step function signal sent into the line.
TDR measure-
ments provide such information as a function of distance from
the transmission line input terminals,
and in particular, show
multiple discontinuities individually.
FDR-TOR Comparison
Frequency domain reflectometers, the slotted line and
bridges, drive and observe the input terminals of a transmis-
sion line as a function of frequency. They do. not locate dis-
continuities on a distance basis. As a result, measurement
techniques
and the unique advantages of such devices differ
from those
of TDR. ·
A pure resistance measured by either time domain or fre-
quency domain devices will appear as an infinitely long loss-
less transmission line. Thus, a perfectly terminated short
length of lossless line will yield the
same information to both
kinds of testing,
and neither test system can locate the ter-
mination. However, if the termination includes a small induc-
tive or capacitive reactance, both systems will indicate its
presence, but the TDR system will show where in the line the
reactance is located.
The following comparisons of
TDR and frequency domain
(FDR) devices are supported by four specific examples and
illustrations.
1. FDR measures Standing Wave Ratio directly, but a TDR
display can speed FDR testing by locating resonant fre-
quencies of resonant networks prior to FDR testing.
2.
TDR locates discrete discontinuities and permits analysis
of their value.
But FDR will indicate two different resonant
discontinuities which
may be located very close together
when TDR may not.
3.
FDR measures an antenna standing wave ratio directly
while
TDR will not. But TDR will locate faults more quickly
and identify the type of fault more rapidly than will FDR,
should a change in SWR indicate problems. The time domain
display will
validate a .transmission line to an antenna, while
frequency domain reflectometry cannot, unless the
antenna is
disconnected and the transmission line terminated.
4.
TDR can locate small changes in transmission line surge
impedance
{such as a too-tight clamp holding a flexible line)
while
FDR will show whether or not the standing wave ratio
is acceptable.
5. Both test systems will quantitatively evaluate single
discrete reactances, with a higher
degree of accuracy pos-
sible with FDR.
6. Both TDR and FDR have advantages, each being very
valuable in its own way. Thus, the two systems complement
each other and both aid where observations and measure-
ments are required.
TOR vs FDR Measurements
A one pF discrete capacitor inserted in parallel with a
transmission line will produce almost no
TDR indication if
the step pulse has a risetime of 1 nanosecond. The same
capacitor will produce a significant reflection if the step pulse
has a risetime of 150 picoseconds. A
FDR test will produce a
large standing
wave ratio at the series resonant frequency
determined by the
capitance and its lead inductance. Such
a discontinuity would require considerable time for proper
FDR testing due to the numerous frequency test points, but
with a fast rise
TDR system the capacitance and resonant fre-
quency can be quickly determined.
Fig.
2-1 shows waveforms and SWR curves of first a single
capacitor and then two capacitors inserted in parallel with a
transmission line. Note
that the FDR measurement on the
right side of the figure plainly shows the two resonant cir-
cuits of the two closely spaced small capacitors, while the
TDR display at the left shows two resonant frequencies, but
not in a manner to permit separation of the two capacitors.
2-1

TOR Theory-Type 152
8 1---1---1--+--+-+--+---ll---+---l--+--+-+--+-++--+---t-+---t
Iii=
:::::
"' 7 l--1---1-+-4-.f...--+--11--1---l-+--t-.f--l--H-1---l-+--I
I I
--+1300 ps I+-= 3.33 GHz
I I
Single Shunt Capa~or ----
Two Shunt Capacitors
0 2 3 4
Frequency GHz
2 3 4
Frequency GHz
Fig.
2-1. Two examples of discrete shunt capacitors.
The single capacitor of this example was made of 114 inch
wide strip copper, % inch long, with
one end soldered to the
side of a component insertion unit (Tektronix Part No. 017-
0030-00)
and the other end near the center conductor. The
insertion unit
was modified to have a continuous center con-
ductor using three inner transition pieces (Tektronix Part No.
2-2
358-0175-00). One of the inner transition pieces was short-
ened to fit between the two mounted end pieces, and then
soldered in place. The second capacitor (resonant at 2.1
GHz) was a 0.5 to 1.5 pF piston trimmer with a total lead
length of about
5/
16
inch, and it was adjusted to about 1.2 pf.
The piston capacitor was soldered in place in parallel with

I
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.+----Type 152
I
Air I
-Line--1
G)=
End View
of Line
JC:
z.
son
Electrical
Circuit
Fig. 2-2. Capacitors measured in Fig. 2-1.
Termination--~~
.::.
son
I2sn
I
-=-
Equivalent
Circuit
z.
the strip copper capacitor about
1
/8 inch
away. It is obvious
from both testing method.s that neither capacitor was crit-
ically damped by the characteristic impedance of the trans-
mission line. The physical
and equivalent circuit of the single
shunt capacitor is shown in Fig. 2-2. The single capacitor
test was made with a shield in place completely covering
both openings.
Fig. 2-3 shows the ability
of TDR to locate an off-imped-
ance point in a transmission line, and quickly resolve its
value. The same through-connected insertion unit used in
example number 1 was tested without any component
inserted in it. The shield was in place for both TDR and FDR
testing.
The
TDR display of Fig. 2-3 shows the increased surge
impedance due to the increased diameter of the outer con-
ductor at the two cutout access slots. Such a TDR display
will permit
rather rapid correction to be made to the center
conductor
diameter if one desires to make a truly constant
impedance through the length of the insertion unit.
TDR Theory~Type 152
~ r~~I Ulltt!tHi!Jtm
i.oi...::::'--L-J---'---'-'--'---'---'---'---'--L-'---'--....L...-'--'---'--.L......I
1 2 3 4
Frequency GHz
Connectors
/ ~
b-~~ ~---.,,. D DI--___,
I
'VS0.8 n -
son -
Fast
Pulser
Modified GR
Insertion Unit
500 ps/div 0.01 p/div
874-WSOB
Termination
Fig.
2-3. Modified lthrough-connectedl Tektronix Insertion unit
for testing small components in parallel with 50 n line.
The SWR curve shows some changes from a constant
impedance transmission line, but does not help to locate an
aberration if it is inside a continuous piece of cable. Either
FDR or TDR would help one to make the unit have a constant
impedance if such a unit were being designed.
Fig. 2-4 shows two TDR and two SWR plots of a simple
dipole
antenna. The TDR waveforms at the left were photo-
graphed first, quickly locating the two radiating resonant
frequencies
and permitting a saving in time for the FDR test-
ing. The SWR curves permit a direct
evaluation of the
t d.
t" · ( RL V max "f .
an enna ra 1a ion resistance -= -- 1 RL 1s purely re-
Zo Vmin
sistive), while the TDR display tells only the transmission line
quality
and the radiating resonant frequencies of the non-
shorting
type antenna. An antenna design engineer could
use the SWR data and FDR test equipment to test a com-
pensating network to
be located at the antenna to minimize
standing
waves in the transmission line. The TDR system can-
not
be used for such design assistance.
Fig. 2-5 shows both TDR and FDR tests of a General Radio
Type 874-K series blocking
capacitor. The upper TDR display
permits direct calculation of the series capacitance, in this
case approximately 6.2 nanofarads (0.0062 ,uF).
2-3

TOR Theory-Type 152
TOR shows open circuit
SWR shows acceptable
antenna radiation
resistance
son
..,_& _______ ___..( r-J.___, 435 MHz
I Dipole
1 ns/div
0.2 p/div
C0.25-V Pulser!
500 ps/div 0.1 p/div
Antenna resonant frequencies
seen by TOR:
!Fundamental! F -
2.3 x 10-
9
(Fourth Harmonic) F = 1
575 x 10-
12
435 MHz
1740 MHz
, ._ ...... ~ ...... __.~_.___,,____,_~...__..~_.___.~_.._~..__ ........ ~.__ ....
400
1
1.6
425
1.7
Frequency MHz
Frequency GHz
450 500
1.8
1.9
Fig. 2-4. Two plots of 435 MHz dipole antenna.
2-4

( 50 u o._87-5--K----D--~I 874-w5os
Q _ _ _ _ Termination
Air Line
10 cm/div
0.01 p/div = 1 % /div
1.0
I I I I I I
I I I I
Less than 0. 1
--
p 0.5 through 6 GHz _
~
..
I I I I I I
• I I I I I I
100
200
Frequency MHz
Fig.
2-5. Series blocking capacitor: General Radio Type 87 4-K.
The SWR curve shows that the series capacitor does not
upset the transmission line significantly except for low fre-
quencies. The middle TOR waveform shows the change in
surge impedance due to the physical shape of the series
capacitor. Note that the disc capacitor reduces the trans-
mission line surge impedance to approximately 49 ohms for
only a very short period of time. The same display also per-
mits the precise location of adjacent discontinuities that affect
the high frequency performance.
The combined TOR and
FDR data tells more about the series capacitor unit than
either testing method does alone.
TDR Theory~Type 152
Basic Approach to TDR.
Time Domain Reflectometry can be understood most easily
if its operation is first compared with a DC circuit.
DC Analogy
Fig. 2-6 shows three simple circuits that can be related to
transmission lines
an·d TOR. Fig. 2-6A is the diagram of an
ordinary resistance voltage divider, where the voltage across
Rz
Rz
is ER
2 =
Ri + Rz X E of the battery. (1)
Fig. 2-6B substitutes R1ine (or Z0) for R2, and substitutes R
9
(generator resistance) for R1. It is assumed the battery has
zero internal resistance
and that R9 is an inserted series gen-
erator resistance. If the battery is 1 volt and if R
9 = R1
;ne'
then a voltmeter across R1 ;ne will indicate 0.5 volt when the
switch
is closed.
Fig. 2-6( indicates a pair of zero resistance wires of same
length physically connecting R
1
;ne to the battery and switch.
A voltmeter across
R1ine will still indicate 0.5 volt when the
switch
is closed.
Adding the Time Dimension
Fig. 2-7 substitutes a step generator for the battery and
switch of Fig. 2-6. The generator has zero source resistance so
R
9
is again added in series with the generator. The generator
and R
9 drive a finite length transmission line
that has a char-
acteristic impedance of Z0• The transmission line has output
terminals that permit connecting a load
RL. An oscilloscope
voltmeter measures the voltage signal(s)
at the input end of
the transmission line.
Assume that
no load resistance is connected to the trans-
mission line output terminals (RL = oo) and that R
9 . Z0
(Z
0 acts exactly as
if it were the DC resistor Riine of Fig. 2-6).
As the zero impedance step generator applies its 1-volt step
signal to R
9, the oscilloscope voltmeter indicates
0.5 volt.
The oscilloscope voltmeter
will continue to indicate a 0.5 volt
signal
until the wave has traveled down the line to the open
end, doubled
in amplitude due to no current into RL . oo,
and reflected back to the generator end of the line. The
oscilloscope finally indicates a signal of 1 volt after the meas-
urable period of time required for the step signal to travel
down and back the finite length of open ended transmission
line.
Refledion Signal Amplitudes
Fig. 2-8 shows TOR oscilloscope (voltmeter) displays related
to the value of RL vs the value of the transmission line Z0•
Apply resistance values of 50 n to R
9
and Z0, and 75 0 to RL
of Fig. 2-7. By formula (1), the oscilloscope display of the
reflection amplitude will be 0.6 volt. The actual reflection,
however,
is only 0.1 volt added to the 0.5-volt incident step.
Reflection Coefficient
A somewhat more convenient method of handling signal
reflections than has just been suggested, is to consider the
reflection as having been
added to or subtracted from the
incident pulse. Thus the reflection amplitude is not measured
from zero volts, but is referenced to the incident signal ampli-
tude. This permits establishing a ratio between the incident
and reflected signals which is called the reflection coefficient,
rho
(p). The value of p is simply the reflected pulse ampli-
2-5

TOR Theory~Type 152
E
R1
R1ine
RJine
or
--i
or
Zo
Zo
R,
ER2
---1
IAI
(81 (Cl
Fig. 2-6. Circuits showing DC analogy of TDR.
1-Volt
Step
Generator
TOR
oscilloscope
voltmeter
Finite length of
transmission line
l
Zo
1
Fig. 2-7. Adding the time dimension to the circuit of Fig. 2-6.
Reflection
r-----
RL =oo; 1 V 0.5-Volt
Incident
Step
i----- RL > Zo
------------ - - - RL = Zo; 0.5 V
,__ - - - RL <Zo
- - - - - RL = O; 0 v
I 2 X
Propagation I
-- Time Once -+-
Through Line
Fig.
2-8. Oscilloscope voltmeter displays for circuit of Fig. 2-7,
dependent upon value of RL vs Zo.
tude (the display total amplitude minus the incident pulse
amplitude) divided by the incident pulse amplitude. Fig. 2-9
shows the two parts of the display appropriately labeled to
identify the incident and reflected signals.
When p = 0, the transmission line is terminated in a
resistance equal to its characteristic impedance l0• If the line
is terminated in RL > l0, then p is positive. If the line is
2-6
Incident {
Signal
TOR
Oscilloscope
R,
Fig. 2-9. TOR oscilloscope displays for various values of RL vs Zo.
terminated in RL < l
01
then p is negative. The dependence
of p on the transmission line load is
RL lo
p = RL + l0
(2)

f
If p is known, RL can be found by rearranging formula (2);
RL = Za (_!____±__e_)
1-p
(3)
Formula (3) applies to any display that results from a
purely resistive load. The load shown in Fig. 2-9 is assumed
to
be at the end of a lossless coaxial transmission line.
Substituting 50 O for Z0 in formula (3), calculations for
small values of p show that each division of reflected signal
is approximately equal to a certain number of ohms. Table
2-1 lists the ohms per division for vertical deflection factors
of 0.005 p, 0.01 p and 0.02 p. Or, for RL values near 50 0,
you may use the approximation forrriula
RL ~ 50 + 100 p.
This approximation formula has an error of S 2.2% for
absolute values of p S 0.1 and an error of S 8% for abso-
lute values of p S 0.2.
RL for reflections with p up to essentially +1 or -1 can
be quickly determined using the graph of Fig. 2-10. Fig. 2-10
is based upon a transmission line surge impedance of 50 0
just prior to the discontinuity that causes the reflection signal.
The graph of Fig. 2-10 may be photographically reproduced
without special permission from Tektronix.
TABLE 2-1
RL Approximations For Reflection
Coefficients of 0.005, 0.01 and 0.02
Related to a 50 O Transmission Line
p/div
O/div Error/div
0.005
112
~0.0160
0.01
1
,..:_,0.066 o
0.02 2
~0.20
TOR Theory~Type 152
REFLECTIONS FROM
CAPACITORS AND INDUCTORS
Contrary to frequency domain measurements, TDR response
to a
reactance is only momentary. Thus either an inductor or
a capacitor located in a transmission line will give only a
short duration response to the
TDR incident pulse. Analysis
of large reactances is relatively simple and makes use of
time constant information contained in the reflection display.
Small reactances are not so simple to evaluate quantitatively,
so will be treated separately.
Large Reactances
The difference between a "large" and a "small" reactance
is not a fixed value of capacitance or inductance, but is
instead related to the TDR display. If the displayed reflection
includes a definite exponential curve that lasts long enough
for one time constant tO be determined, the reactance is
considered "large".
Discrete (single) capacitors connected in series or parallel
with a transmission line start to charge at the instant the
incident pulse arrives. Inductors
start to conduct current at
the arrival of the incident pulse. Both forms of reactance
cause an exponentially changing reflection to be sent back
to the TDR unit. When a capacitor is fully charged, the TDR
unit indicates an open circuit. When an inductor is fully
"charged" (current through it has reached its stable state),
the TDR unit indicates a short circuit. The TDR unit will indi-
cate an inductor's series DC resistance if its value is signifi-
cant in relation to Z0• The general form of reflection and
long term effect upon the TDR display by both inductors and
capacitors is listed in Table 2-2 and Table 2-3.
TABLE 2-2
Single Capacitor or Inductor TDR Displays
Related to Terminated Transmission Lines
Reactance
In Series
with Line
CAPACITOR __r-
INDUCTOR
J--
Finding One Time Constant
In practice, TDR reactance displays usually contain aberr-
ations of the desired pure exponential reflection. Such aberr-
ations prevent finding the normal 63% one time-constant
point
of the curve accurately. (The aberrations are due to
either the environment
around the reactance, i.e. stray induc-
tance in series with a capacitor, or stray capacitance in
In Parallel
Line Impedance
with Line
at Reactance
SERIES: 2 Za
___rv--- PARALLEL: ~
0
SERIES: 2 Za
~
PARALLEL: ~
0
parallel with an inductor, or secondary system reflections.)
However,
accurate time constant information can be obtained
from less than a complete exponential curve. The principle
~used requires that a "clean" portion of the display must
exist. The
"clean" portion used must include the right-hand
"end" of the displayed curve (a capacitor is then fully
charged, or an inductor current has stopped changing). The
"end" of the curve will appear on the display to be parallel
2-7

TDR Theory-Type 152
"" .,,, 5000 •• RL
1mll
+0.980_~
-
3000
+0.961
2000
1000
+0.905~
·~
~~
soo,
"'I=
1=11
+0.818
~-~
400
300
+0.667.
200
~
'I
'"
100,
~"'
.. +0.333.
-1
so
~
ii
~ ~
~t-
-
... ~
Ii!' 40
30
0.333
.l '-
'.
20
, ..
.,
II'
I.I
0.667
10,
~ "'
"'fi
-
0.818 s
==
II
•
•
-
-
Ii m 3
t=c
0.905
2'
~.,
0.961
1'
~=
~-
TEKTRONIX, INC.
BEAVERTON, OREGON
Fig. 2-1 O. Values of RL vs reflection co-
efficient when reflection is compared to
...
0.980
0.5
50 n transmission line.
2-8

TABLE 2-3
Single Capacitor or Inductor TOR Displays
when Connected Across End of Transmission line
Reactance
CAPACITOR
INDUCTOR
Display Line
Impedance
at Reactance
to a horizontally scribed graticule line. Thus, aberrations
that exist
at the beginning of the curve can be ignored.
Fig. 2-11 shows the first example of obtaining valid time-
constant information
from less than a full 100% exponential
curve. The technique is to choose any "clean" portion of the
display that includes the "end" of the exponential curve and
find the half-amplitude point.
The time duration from the
beginning of any new 100% curve section
to its 50% ampli-
tude point is always equal to 69.3% of one time constant.
Thus, the time duration for a 50% change divided by 0.693
is equal to one time constant.
Fig. 2-11 shows the TDR displays of a capacitor placed in
series with a transmission line center conductor (2 Z0 environ-
ment). Fig. 2-11 A waveforms comprise a double exposure
with the left curve taken while the Type 1
S2 RESOLUTION
switch was at NORMAL and the right curve taken when the
switch was
at HIGH. Both curves give sufficient information
to measure one time constant. Note that the top of the inci-
dent pulse is indefinite (in the displays) due to the sweep rate
and short length of cable used between the Type 1
S2 and
the capacitor.
Such a display does not have a definite
beginning of the normal 100% exponential curve.
This pre-
vents
63 % of the total curve from being read directly from
the display. (It is also quite possible for lead. inductance to
cause a capacitor to ring. When a TDR display shows capaci-
tor ringing, the ringing can sometimes be reduced
by:
1. using the slower 1-Volt pulser, and/or 2. changing the
transmission line environment
to place a lower value Z0 in
parallel with the capacitor.)
The double exposure of Fig. 2-11 Bshows a full exponential
curve beginning in the vicinity of 1 division from the graticule
bottom. Then the same curve has been time-expanded for
easier reading. The indefinite beginning of the 500 ns/DIV
exponential curve prevents finding one time constant by
measuring the time of
63 % of the total curve amplitude. The
new arbitrarily chosen 100% amplitude portion of the curve
begins
at the graticule center horizontal line and extends
(off the right of the graticule) to the top graticule line. Three
divisions were chosen for the new 100% exponential curve,
with the 100% and 50% points marked. Then, dividing the
5 ns
152
'-----' RG213/U
1 ns
Pulser
Equivalent
Circuit
874-K Air Line
Termination
c
Fig. 2-11. Exponential curves and circuit of 6.5 nF capacitor in
series with terminated transmission line.
time for the 50% amplitude change by 0.693 gives a total
one time-constant time value of 650 ns. Since the equivalent
circuit shows 2 Z0 in series with the capacitor, its value is
found by formula (4) (Table 2-4) to be 6.5 nanofarads.
Large Capacitors
The difference between a "large" and a "small" capacitor
is not a fixed value of capacitance, but is instead related to
the TDR display. If the display includes a definite exponential
curve that lasts long enough to permit one RC time constant
to be determined, the capacitor value can be found by using
a normal RC time constant formula. The actual formula
varies according to the equivalent circuit in which the capaci-
tor
is located. Table 2-4 lists the possible configurations and
their related formulae.
2-9

TOR Theory~Type 152
TABLE 2-4
"Large" Capacitor Circuits and Formulae
Equivalent
Circuit
Circuit
Formula
Display
Series with
~fflf1]
C=3
C = 1 TC r
terminated
-=- -=- -= z.
141
line
0
c 2
Zo
--
~~1l]z.
~
fc
Parallel with
tz.
C = 1 TC
terminated
(5)
__nr-
line
Zo/2
--
~F[]~
VVv n
Across 0 1
line Z.o C = 1
TC
(6)
c
end
Zo
-
Where C = Farads; TC = Time Constant; Zo = Line Surge Impedance.
The first example of "large" capacitance measurement was
given under the previous heading Finding One Time Con-
stant. The large value of capacitor used is easy to measure
and usually causes only one aberration to the exponential
curve. That aberration is the indefinite curve beginning.
Moving A Reflection Aberration
When testing small capacitors that still produce a usable
exponential curve, it may be difficult to get accurate time
constant data when there are reflections within the system.
For
example, a 100 pf discap was soldered into a General
Radio Radiating Line section (Fig. 2-12). The 1-Volt pulser
was used; re-reflections from the pulser distort the exponential
curve at the arrow of Fig. 2-l 2A. The re-reflection is moved
to the right just outside the time window by placing a 20 ns
signal delay RG213/U cable between the pulser -and the
sampler. The acceptable waveform is shown in Fig. 2-128.
Fig. 2-l2C is a double exposure that shows first how the
"end" of the exponential curve is set to a graticule line. Then
the display is time expanded to 500 ps/DIV (leaving the
vertical position as adjusted} and the new arbitrary 100%
exponential curve is chosen and marked. The capacitor's
value taken from the time expanded curve of Fig. 2-l 2C
and using the formula (5) is 104 pF (1.8 X 10-9 /0.693 ...;.- 25 =
1.04 X 10-
10
= 104 pF}. Note that the vertical p factor was
changed for Fig. 2-12C in order to make the time constant
measurement from a clean section of the curve near its end.
Large Inductors
The difference between "large" and "small" inductors fol-
lows the same general display limits as large or small capaci-
tors. A "small" inductor in series with a transmission line
center conductor will give a display that does not permit
normal time-constant analysis. The same inductor in parallel
2-10
with a terminated transm1ss1on line may give a display that
does allow normal time-constant analysis.
Ringing in the exponential TDR display is often observed
when measuring inductors. It is usually caused by distributed
capacitance across the coil that has not been adequately
damped by transmission line surge impedance. Since an
inductor with stray capacitance will ring unless adequately
damped, and inductor in parallel with a transmission line
(Z
0
/2 environment} will be less likely to ring than the same
inductor in series with a line (2 Z0 environment}.
Fig. 2-13 shows waveforms taken of the reflections from a
seven turn % inch
diameter coil. The coil was connected
across the end of a 50 n transmission line (Z
0 environment}.
Fig. 2-13A
was made using the Type 1S2 0.25-Volt fast pulser
at High Resolution. The ringing makes it impossible to obtain
an accurate time constant measurement from the display.
Fig. 2-138 was made using the Type 1S2 1-Volt pulser at
Normal Resolution. Here the slower risetime incident pulse
does not excite the ringing, and in addition the time averag-
ing of fast changes by Normal Resolution operation permits
a time constant to be measured. Ringing could also have
been reduced by a Z0 /2 environment by placing a termina-
tion across the inductor, or placing the inductor at a con-
venient mid-point
of a long time.
The triple
exposure of Fig. 2-138 includes three curves:
#1, the total reflected signal at 10 ns/div and 0.5 p/div;
#2, increased vertical deflection and the exponential curve
end positioned one division below the graticule center hori-
zontal line; and #3, the ;#2 curve time expanded to 1
ns/div for measurement of the L/R time constant. The new
100% to 50% amplitude time duration of curve #3 is shown
as 3%ns. 3.75/0.693 = 5.41 ns for 1 time constant. Since the
coil is at the end of a 50 n transmission line, the inductance
is calculated by formula (9) of Table 2-5 to be 270.5 nH (L
= 50 X (5.41 X 10-9) = 2.705 X 10-1 = 270.5 nH}.

!Cl 500 ps/div. 0.1 p/div.
Fig. 2-12. Example of moving display reflection aberrations to
obtain a "clean" exponential curve.
Small Readances
"Small" reactances are here defined as series-connected
inductors
and shunt-connected capacitors that cause TDR
reflections without apparent time constant reaction to the
incident pulse. Some small reactances are capable of being
TDR Theory~Type 152
!BJ
65 ns
152
Cable
!Cl
Fig. 2-13. Seven turn coil across end of 50 n line.
"charged" (capacitor voltage is stable; inductor current is
stable) at a rate faster than the 0.25-Volt pulser-incident pulse
rate of rise. If the TDR display has no exponential section,
normal RC and L/R calculations cannot be made. All small
reactances generate TDR reflections with less than +1p or
-lp.
Small discrete capacitors with leads always include stray
series inductance of a significant amount. Fig. 2-1 and asso-
ciated discussion is an example of such a capacitor with
inductive
leads. Small shunt capacitors -without leads may
be produced by either an increase in a coaxial cable center
conductor diameter or a reduction of its outer conductor
diameter. Leadless capacitors are sometimes treated as a
small reduction in Z0 rather than as a capacitor. Usually,
such small capacitors are considered capacitance when the
section of reduced Z0 line is so short physically that no level
portion can be seen in the TDR display.
2-11

TOR Theory-Type 152
TABLE 2-5
"Large" Inductor Circuits and Formulae
Circuit Equivalent
Circuit Formula Display
Series with
~11Jz.
G[::J
(7)
~
terminated
L = 2
Zo X 1 TC
_J" Zo
line
-=
~z.
~
~L
tZo
Parallel with
(8)
terminated
L=
Zo
x 1 TC
_J\__
line
-2
-=
-
crr=oL
Across
line
end
-=
Small series inductors rarely have sufficient parallel (stray)
capacitance
to be significant in the TOR display. However,
the coaxial environment around
such a small inductor does
affect the
TOR display. Small series inductors without capaci-
tive strays are sometimes caused
by changes in diameter of
a coaxial cable: decreased center conductor diameter, or
increased outer conductor diameter.
This form of inductor is
usually treated as a small increase in Z0 rather than as an
inductor. Usually, such inductors
are considered to be induc-
tance when the section of increased Z0
line is so short physi-
cally that no level portion can be seen in the TOR display.
Assumptions that Permit Analysis of Small
Reactances
The usual TOR system does not have the required char-
acteristics for accurately measuring small reactances.
Yet
small reactances can be measured provided the following
assumptions are made regarding the TOR system:
1. That the actual TOR system may be adequately
described by a model having a simple ramp as the pulse
source and a lossless transmission
line with an ideal sampler;
2. That the rounded "corners" of the actual pulse source
may be ignored;
3. That the transmission
line high frequency losses classed
as "skin effect" or "dribble up" are not significant. ("Dribble
up"
is explained under Measuring Technique in connection
with
Fig. 2-17);
4. That the sampler is non-loading, non-distorting and of
infinitesimal risetime;
5. That parasitic (stray) reactances are insignificant.
The formula for small series inductance and small shunt
capacitance
in a transmission line contain factors for (1) the
system risetime
at the spatial location of the reactance, (2)
the observed reflection coefficient, and (3) the transmission
line surge impedance.
2-12
0
~L
A
(9)
L = Zo X 1
TC
The system risetime may be measured from the display by
placing either an open circuit or a short circuit
at the spatial
location of the reactance.
The value for a small series inductor can calculated using
the formula
L =
2.5 a Z0 t, (10)
where L is in henries, Z0 is in ohms, t, is the system 10% to
90% risetime in seconds, and a (as in formulas above and
below)
is a dimensionless coefficient related to the observed
reflection coefficient p by either the graph or
Fig. 2-14, or
formula (11 ).
- 1
p = a (1 -e a)
(11)
A small shunt capacitor's value can be calculated using
the formula
c 2.5 a t,
Zo
(12)
where C is in farads, and the other units are as in formula
(10).
Small Series Inductor
Fig. 2-15 is an example of TOR displays from a small induc-
tor
(1 % turn) placed in parallel with a 50 n line at (A), and
in series with the 50 n line at (B). Calculations were made on
Fig. 2-15A first because the display is a clean exponential
that permits
L/R time constant analysis. Waveforms #1 and
#2 of Fig. 2-15A show first the full exponential decay
through
five CRT divisions, then at #2 the waveform was
postioned vertically so the exponential end
is at -1 divi-
sion. Waveform
#3 used the same vertical calibration, but
was time expanded
to obtain the new 100% to 50% time
duration.