What Every Scope User Needs to
Know About Transmission Lines
Dr. Eric Bogatin, Signal Integrity Evangelist
Dean, Teledyne LeCroy Signal Integrity Academy www.beTheSignal.com
Director, Teledyne LeCroy Front Range Signal Integrity Lab
Adjunct Prof, Univ of Colorado, Boulder, ECEE
Editor, Signal Integrity Journal, www.SignalIntegrityJournal.com
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A Confusing Aspect of Scope Measurements
When you measure the rise time of the cal signal (really the compensation reference signal)
the rise time depends on the length of the cable.
How come? Are we seeing losses in the cable? Is it an RC charging effect?
How do we interpret the source features from this sort of measurement?
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Looks like longer cables have longer rise times
3 ft cable
6 ft cable
Cal out source is really RT = 5 nsec
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Outline
Five essential principles
1. All interconnects are transmission lines
2. Signals propagate
3. Signals see an instantaneous impedance
4. Signals reflect when they encounter a change in the instantaneous
impedance
5. ALL voltage sources have a Vth, Rth, 10-90 rise time
▪ Applied to interpreting scope measurements
▪ Common artifacts
▪ When to use 1 Meg input, when to use 50 Ohm input
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“A method is a trick that works more than once”- George Polya
Gary Larson:
We will encounter many trickssome more valuable than others
Pay attention to the more
valuable ones
“remember that spot”
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An important habit for ALL Engineers
Rule #9: Never do a measurement or simulation
without first anticipating what you expect to see.
If you are wrong, there is a reason- either the set up is wrong or your intuition is wrong. Either
way, by exploring the difference, you will learn something
If you are right, you get a nice warm feeling that you understand what is going on.
Corollary to rule #9:
There are so many ways of screwing up a measurement or
simulation, you can never do too many consistency checks
• Get in the habit of:
• Never passing an opportunity to apply rule #9.
• Evaluating every measurement with rule #9
• Practice thinking of new consistency tests you can perform, and doing them.
• “Put in the numbers” at every opportunity
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Essential Principle: All interconnects are transmission lines
Signal path
Vin
V
Return path
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GROUND
Essential Principle: Signals are Dynamic
All interconnects are transmission lines
A signal as a voltage difference
Signals propagate
Signal path
V
Vin
Return path
v
12 inches
n sec
Dk
In Coax cable
In FR4 traces


12 inches
n sec
4
GROUND
12 inches
n sec

 6 inches
n sec
2
12 inches
n sec
12 inches
n sec

 8 inches
n sec
1.5
2.2
TD for 1 foot coax = 1.5 nsec, 3 feet in 4.5 nsec ~ 5 nsec
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Dynamic Simulation of Propagating and Reflected Signals
Download this free animation tool from
www.beTheSignal.com
VRPW-30-16: Yoshi’s Animations of
Reflections
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Essential Principle: Signals see an instantaneous impedance
ALL Signals ALWAYS propagate
The edge has a spatial extent, where the dV/dt, dI/dt is
The edge sees an instantaneous impedance
Vsignal
V
Frozen in time
Signal path
Vin
V
Return path
The dV/dt
The dI/dt
V
I
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GROUND
Really Simple View of the Impedance of a Transmission Line
Z
Voltage applied
Current through
C = C L x
I = Qt
I
C
x
V
Q = CV,
x
every  t = v
v CL  x V

Q
= v C LV
I = t =
x
instantaneous impedance of the transmission line
V
V
1
Z 

I vCL V vCL
The characteristic impedance of a transmission line:
The one value of instantaneous impedance in a uniform transmission line
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Essential Principle: The Return Current is Just as Important
as the Signal Current
signal
+++
+++
I
=
---
displacement
current
+++
The current loop has two directions associated with it:
1. A direction of propagation
2. A direction of circulation
They are independent!
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Signals reflect when the instantaneous impedance changes
 If the instantaneous impedance changes some of the signal reflects
Most important distinction: signals are dynamic! Don’t confuse the signal that
propagates with the measured voltage at a node.
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Three Secrets to Understanding Scope Measurements
1. Keep track of all the reflections
2. Know your source impedance
3. Know the round trip time of the cable:
round trip time for a reflection to come
back to the scope is 2 x 1.5 nsec per foot of
cable.
• 2 foot cable, RT time ~ 6 nsec
• 1 m cable, RT time ~ 10 nsec
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Situational Awareness: ALWAYS be aware of your scope features
AND your DUT features
▪ Scope:
▪
▪
▪
▪
▪
▪
Sample rate
Time base
Number of samples in an acquisition
Vertical resolution
Analog bandwidth, instrument intrinsic rise time
Scope input impedance setting
▪ Cable (probe):
▪ BW (from losses)
▪ Z0, TD
▪ DUT (as a Thevenin Source)
▪ Unloaded voltage
▪ Source resistance
▪ Rise time
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The Scope We Are Using Today
▪ Teledyne LeCroy WavePro HD
▪ Main features
▪ 4 channels
▪ 8 GHz analog BW
▪ 12 bit vertical resolution
▪ 20 Gsamples/sec (50 psec interval)
▪ 60 fsec rms sample clock jitter
▪ 5 G samples acquisition memory
▪ Longest acquisition time at max sample rate = 5 G samples / 20 Gsamples/sec = 0.25
sec @ 50 psec resolution!
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Six important cases: what we expect to see depends on
the source impedance!
Source Impedance
Scope termination
50 Ohms
50 Ohms
50 Ohms
1 Meg
>> 50 Ohms
50 Ohms
>> 50 Ohms
1 Meg
<< 50 Ohms
50 Ohms
<< 50 Ohms
1 Meg
Expected behavior
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How to Reverse Engineer the DUT Figures of Merit
Measured voltage is the
unloaded, open circuit,
Thevenin voltage of source
Step 1: Measure the DUT output voltage with scope
at 1 Meg input
Step 2: Measure the DUT voltage with scope at 50
Ohms
(caution: make sure voltage is < 5 V rms!!)
Step 3: calculate the output source resistance
Vmeas  Vsource
Rscope
Rsource  Rscope
Rsource  Rscope
Measured voltage is the
voltage across a 50 Ohm load
to the Thevenin circuit
 Vsource  Vmeas 
Vmeas
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Example #1: LeCroy WaveStation 2052 50 MHz
Waveform Generator
Set up for 1 V P-P output
▪ On square wave output
▪ What is
✓Vsource
✓Rsource
✓10-90 rise time
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How to Understand the Voltages and Signals
50 Ohm source
2 v P-P
7 nsec rise time
When you set 1 V P-P, the Thevenin voltage is set to 2 V P-P
The source impedance is 50 Ohms. A 1 V P-P signal is launched into the 50 Ohm coax cable.
What you do with this 1 V P-P signal is up to you.
When scope is 50 Ohms, you measure the 1 V P-P signal
When scope is 1 Meg load, 1 V P-P enters 1 Meg resistor, 1 V P-P reflects. Scope measures sum of both waves
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The Cal Out Signal, 1 Meg Scope Input
Scope input: 1 Meg Ohm
Probe: 1 m long RG58 cable with gripper tips
V_source = 1 V
RT = 206 nsec
▪ On square wave output
▪ What is
✓ Vsource
✓ Rsource
✓ 10-90 rise time
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Source impedance of Cal signal
Rsource  Rscope
 Vsource  Vmeas 
Vmeas
V-measured, 1 Meg = 1 V
V-measured 50 Ohm load = 0.06 V
Rsource  50
1  0.06   780
0.06
780 Ohms >> 50 Ohms
Rule #9: What should we see?
3 ft cable, TD = 4.5 nsec, round trip = 9 nsec
With 50 Ohms
With 1 Meg input?
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Looks like longer cables have longer rise times
▪ It is an artifact of the reflections in the cable
▪ Eliminate the reflections (terminate at scope), you eliminate the artifacts
3 ft cable
6 ft cable
Cal out source is really RT = 5 nsec
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Summary
▪
▪
▪
▪
Always characterize your source: Know its Vth, Rth, RT
Eliminate cable reflections using 50 Ohm input to the scope
But this loads the source down
If you use 50 Ohm cable and 1 Meg input AND the source is
high output impedance
▪ Be aware that you will have cable reflections
▪ Rise time will look like it depends on the cable length
▪ Rise time will look like an RC charging, but it is due to
reflections
▪ If you do not want to load your source with 50 Ohms
▪ Use an active high bandwidth probe
▪ Use a 10x high impedance probe, but be aware of its
artifacts!!
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What Every Scope User Needs to
Know About Transmission Lines
Dr. Eric Bogatin, Signal Integrity Evangelist
Dean, Teledyne LeCroy Signal Integrity Academy www.beTheSignal.com
Director, Teledyne LeCroy Front Range Signal Integrity Lab
Adjunct Prof, Univ of Colorado, Boulder, ECEE
Editor, Signal Integrity Journal, www.SignalIntegrityJournal.com
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25