Using Transmission Lines III

1
Using Transmission Lines III class 7

• Purpose Consider finite transition time edges
  and GTL.

Acknowledgements Intel Bus Boot Camp Michael
Leddige
2
Agenda

• Source Matched transmission of signals with
  finite slew rate
• Real Edges
• Open and short transmission line analysis for
  source matched finite slew rates
• GTL
• Analyzing GTL on a transmission line
• Transmission line impedances
• DC measurements
• High Frequency measurements

3
Introduction to Advanced Transmission Line
Analysis

• Propagation of pulses with non-zero rise/fall
  times
• Introduction to GTL current mode analysis

Now the effect of rise time will be discussed
with the use of ramp functions to add more
realism to our analysis. Finally, we will wrap up
this class with an example from Intels main
processor bus and signaling technology.
4
Ramp into Source Matched T- line

• Ramp function is step function with finite rise
  time as shown in the graph.
• The amplitude is 0 before time t0
• At time t0 , it rises with straight-line with
  slope
• At time t1 , it reaches final amplitude VA
• Thus, the rise time (TR) is equal to t1 - t0 .
• The edge rate (or slew rate) is
• VA /(t1 - t0 )

T T0l
5
Ramp into Source Matched T- line
6
Ramp Function

• Ramp function is step function with finite rise
  time as shown in the graph.
• The amplitude is 0 before time t0
• At time t0 , it rises with straight-line with
  slope
• At time t1 , it reaches final amplitude VA
• Thus, the rise time (TR) is equal to t1 - t0 .
• The edge rate (or slew rate) is
• VA /(t1 - t0 )

7
Ramp Cases

• When dealing with ramps in transmission line
  networks, there are three general cases
• Long line (T gtgt TR)
• Short line (T ltlt TR)
• Intermediate (T TR)

8
Real Edges
Assignment Find sajf for a Gaussian and
capacitive edge
9
Short Circuit Case
Current
Voltage

• Next step
• Replace the step function response with one
  modified with a finite rise time
• The voltage settles before the reflected wave is
  encountered.

10
Open Circuit with Finite Slew Rate
Current
Voltage
11
Consider the Short Circuit Case

• Voltage and current waveforms are shown for the
  step function as a refresher
• Below that the ramp case is shown
• Both the voltages and currents waveforms are
  shown with the rise time effect
• For example I2 doubles at the load end
• in step case, instantaneously
• in the ramp case, it takesTR

12
Ramp into Source Matched Short T-line
I
I
2
1

• Very interesting case
• Interaction between rising edge and reflections
• Reflections arrive before the applied voltage
  reaches target amplitude
• Again, let us consider the short circuit case
• Let TR 4T
• The voltage at the source (V1) end is plotted
• showing comparison between ramp and step
• The result is a waveform with three distinct
  slopes
• The peak value is 0.25VA
• Solved with simple geometry and algebra

L, T
Short
V
S
13
Ramp into a Source Matched, Intermediate Length
T-Line

• For the intermediate length transmission line,
  let the TR 2T
• The reflected voltage arrives at the source end
  the instant the input voltage has reached target
  peak
• The voltage at the source (V1) end is plotted for
  two cases
• comparison between ramp and step
• Short circuit case
• Negative reflected voltage arrives and reduces
  the amplitude until zero
• The result is a sharp peak of value 0.5VA
• Open circuit case
• Positive reflected voltage arrives and increases
  the amplitude to VA
• The result is a continuous, linear line

Short Circuit Case
Open Circuit Case
14
Gunning Transistor Logic (GTL)
V
Chip (IC)
Chip (IC)

• Voltage source is outside of chip
• Reduces power pins and chip power dissipation
• Open Drain circuit
• Related to earlier open collector switching
• Can connect multiple device to same.
• Performs a wire-or function
• Can be used for multi-drop bus

15
Basics of GTL signaling current mode transitions
Low to High High to Low
Steady state low
Steady state high
Vtt
Vtt
Rtt
Rtt
Zo
Zo
R(n)
R(n)
Switch opens
Switch closes
Vtt
Vtt
Rtt
Rtt
Zo
Zo
R(n)
R(n)
16
Basics of current mode transitions - Example

1.6
1.5 V
1.4
V(a)
70 ohms
50 ohms
1.2
V(b)
12 Ohms
1.0
0.8
Volts
0.6
0.4
0.2
0.0
0
2
4
6
8
10
12
Time, ns
17
GTL, GTL BUS LOW to HIGH TRANSITION END AGENT
DRIVING - First reflection
IL Low steady state current VL Low steady
state voltage Vdelta The initial voltage step
launched onto the line Vinitial Initial voltage
at the driver T The transmission coefficient at
the stub
Notice termination was added at the source Why?
18
GTL, GTL BUS HIGH to LOW TRANSITION END AGENT
DRIVING - First reflection
R(n)
IL Low steady state current VL Low steady
state voltage Vdelta Initial voltage launched
onto the line Vinitial Initial voltage at the
driver T The transmission coefficient at the
stub
19
Transmission Line Modeling Assumptions

• All physical transmission have non-TEM
  characteristic at some sufficiently high
  frequency.
• Transmission line theory is only accurate for TEM
  and Quasi-TEM channels
• Transmission line assumption breaks down at
  certain physical junctions
• Transmission line to load
• Transmission line to transmission line
• Transmission line to connector.
• Assignment
• Electrically what is a connector (or package)?
• Electrically what is a via? I.e. via modeling
• PWB through vias
• Package blind and buried vias

20
Driving point impedance freq. domain

• Telegraphers formula
• Driving point impedance
• MathCAD and investigation

R, L, C, G per unit length
Zin
Rdie
Cdie
21
Driving Point Impedance Example
22
Measurement DC (low frequency)
2 Wire Method
Calibration Method Z(V_measure-V_short)/I
OhmMeter
Measure V
4 Wire or Kelvin measurement eliminates error
UNK
I
23
High Frequency Measurement

• At high frequencies 4 wires are impractical.
• The 2 wire reduces to a transmission line
• The Vshort calibration migrates to calibration
  with sweep of frequencies for selection of
  impedance loads.
• Because of the nature of transmission lines
  illustrated in earlier slides
• Vector Network Analyzers (VNAs) used this basic
  method but utilized s-parameters
• More later on s parameters.

24
Assignment

• Find driving point impedance vs. frequency of a
  short and open line
• (a) Derive the equation
• (b) given L10inch, Er4, L11 nH/in, C4.4
  pF/in, R0.2 Ohm/in, G10(-14) Mho/in, plot the
  driving point impedance vs freq for short open
  line. (Mathcad or Matlab)
• (c) Use Pspice to do the simulation and validate
  the result in (b)