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What Every Scope User Needs to Know About Transmission Lines
Dr. Eric Bogatin, Signal Integrity EvangelistDean, Teledyne LeCroy Signal Integrity Academy
www.beTheSignal.comDirector, Teledyne LeCroy Front Range Signal Integrity Lab
Adjunct Prof, Univ of Colorado, Boulder, ECEEEditor, Signal Integrity Journal, www.SignalIntegrityJournal.com
Teledyne LeCroy Signal Integrity Academy
A Confusing Aspect of Scope Measurements
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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?
Teledyne LeCroy Signal Integrity Academy
Looks like longer cables have longer rise times
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3 ft cable 6 ft cable
Cal out source is really RT = 5 nsec
Teledyne LeCroy Signal Integrity Academy
Outline Two engineering principles to keep in mind Five essential principles
1. All interconnects are transmission lines2. Signals propagate3. Signals see an instantaneous impedance 4. Signals reflect when they encounter a change in the instantaneous
impedance5. 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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Teledyne LeCroy Signal Integrity Academy
“A method is a trick that works more than once”- George Polya
Gary Larson:
We will encounter many tricks- some more valuable than others
Pay attention to the more valuable ones
“remember that spot”
Teledyne LeCroy Signal Integrity Academy
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
An important habit for ALL Engineers
• 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
Teledyne LeCroy Signal Integrity Academy
Essential Principle: All interconnects are transmission lines
GROUND
Signal path
Return pathVVin
Teledyne LeCroy Signal Integrity Academy
Essential Principle: Signals are Dynamic
GROUND
Signal path
Return pathVVin
All interconnects are transmission linesA signal as a voltage differenceSignals propagate
Dk12v secn
inches
= secninchessecn
inchessecn
inches
62
124
12===In FR4 traces
inches inchesnsec nsec inches
nsec12 12 8
1.52.2= = =In Coax cable
TD for 1 foot coax = 1.5 nsec, 3 feet in 4.5 nsec ~ 5 nsec
Teledyne LeCroy Signal Integrity Academy
Dynamic Simulation of Propagating and Reflected Signals
Download this free animation tool fromwww.beTheSignal.com
VRPW-30-16: Yoshi’s Animations of Reflections
Teledyne LeCroy Signal Integrity Academy
VVsignal
Essential Principle: Signals see an instantaneous impedance
GROUND
Signal path
Return pathVVin
ALL Signals ALWAYS propagateThe edge has a spatial extent, where the dV/dt, dI/dt isThe edge sees an instantaneous impedance
The dV/dtThe dI/dt
Frozen in time
=ZIV
Teledyne LeCroy Signal Integrity Academy
Really Simple View of the Impedance of a Transmission Line
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throughCurrentappliedVoltageZ =
I
V
instantaneous impedance of the transmission line
∆x
C
C = CL ∆x
∆Q = CV,
every ∆t = ∆xv
I = ∆Q∆t =
vCL∆xV∆x = vCLV
I = ∆Q∆t
LL vC1
VvCV
IVZ ===
The characteristic impedance of a transmission line:The one value of instantaneous impedance in a uniform transmission line
Teledyne LeCroy Signal Integrity Academy
Essential Principle: The Return Current is Just as Important as the Signal Current
signal
The current loop has two directions associated with it:1. A direction of propagation2. A direction of circulation
They are independent!
+++
=+++
- - - +++
Idisplacement
current
Teledyne LeCroy Signal Integrity Academy
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
Teledyne LeCroy Signal Integrity Academy
Three Secrets to Understanding Scope Measurements
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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
Teledyne LeCroy Signal Integrity Academy
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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Teledyne LeCroy Signal Integrity Academy
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!
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Source Impedance Scope termination Expected behavior
50 Ohms 50 Ohms
50 Ohms 1 Meg
>> 50 Ohms 50 Ohms
>> 50 Ohms 1 Meg
<< 50 Ohms 50 Ohms
<< 50 Ohms 1 Meg
Teledyne LeCroy Signal Integrity Academy
How to Reverse Engineer the DUT Figures of Merit
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scopemeas source
source scope
RV V
R R=
+
( )source meassource scope
meas
V VR R
V−
=
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
Measured voltage is the unloaded, open circuit, Thevenin voltage of source
Measured voltage is the voltage across a 50 Ohm load to the Thevenin circuit
Teledyne LeCroy Signal Integrity Academy
Example #1: LeCroy WaveStation 2052 50 MHz Waveform Generator
On square wave output What is
Vsource Rsource 10-90 rise time
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Set up for 1 V P-P output
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How to Understand the Voltages and Signals
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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
2 v P-P
50 Ohm source
7 nsec rise time
Teledyne LeCroy Signal Integrity Academy
The Cal Out Signal, 1 Meg Scope Input
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Scope input: 1 Meg OhmProbe: 1 m long RG58 cable with gripper tips
V_source = 1 VRT = 206 nsec
On square wave output What is
Vsource Rsource 10-90 rise time
Teledyne LeCroy Signal Integrity Academy
Source impedance of Cal signal
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V-measured, 1 Meg = 1 V
V-measured 50 Ohm load = 0.06 V
( )source meassource scope
meas
V VR R
V−
=
( )source
1 0.06R 50 780
0.06−
= Ω = Ω
780 Ohms >> 50 Ohms
Rule #9: What should we see?3 ft cable, TD = 4.5 nsec, round trip = 9 nsecWith 50 OhmsWith 1 Meg input?
Teledyne LeCroy Signal Integrity Academy
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
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3 ft cable 6 ft cable
Cal out source is really RT = 5 nsec
Teledyne LeCroy Signal Integrity Academy
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 EvangelistDean, Teledyne LeCroy Signal Integrity Academy
www.beTheSignal.comDirector, Teledyne LeCroy Front Range Signal Integrity Lab
Adjunct Prof, Univ of Colorado, Boulder, ECEEEditor, Signal Integrity Journal, www.SignalIntegrityJournal.com