Interconnect II

1
Interconnect II Class 22

Prerequisite Reading - Chapter 4
2
Effects of Frequency Domain Phenomena on Time
Domain Digital Signals

• Key Topics
• Frequency Content of Digital Waveforms
• Frequency Envelope
• Incorporating frequency domain effects into time
  domain signals

3
Decomposing a Digital Signal into Frequency
Components

• Digital signals are composed of an infinite
  number of sinusoidal functions the Fourier
  series
• The Fourier series is shown in its progression to
  approximate a square wave

1 2 3
1 2
1
1
0
-?
?
2?
3?
1 2 3 4 5
1 2 3 4
Square wave Y 0 for -? lt x lt 0 and Y1 for 0 lt
x lt ? Y 1/2 2/pi( sinx sin3x/3 sin5x/5
sin7x/7 sin(2m1)x/(2m1) ) 1
2 3 4
5 May do with sum of cosines too.
4
Frequency Content of Digital Signals

• The amplitude of the the sinusoid components are
  used to construct the frequency envelope
  Output of FT

5
Estimating the Frequency Content

• Where does that famous equation come from?
• It can be derived from the response of a step
  function into a filter with time constant tau

• Setting V0.1Vinput and V0.9Vinput allows the
  calculation of the 10-90 risetime in terms of
  the time constant

• The frequency response of a 1 pole network is

• Substituting into the step response yields

6
Estimating the Frequency Content
Edge time factor

• This equation says
• The frequency response of the network with time
  constant tau will degrade a step function to a
  risetime of t10-90
• The frequency response of the network determines
  the resulting rise time ( or transition time)
• The majority of the spectral energy will be
  contained below F3dB
• This is a good back of the envelope way to
  estimate the frequency response of a digital
  signal.
• Simple time constant estimate can take the form
  L/R, L/Z0, RC or Z0C.

7
Examining Frequency Content of Digital Signals

• The frequency dependent effects described earlier
  in this class can be applied to each sinusoidal
  function in the series
• Digital signal decomposed into its sinusoidal
  components
• Frequency domain transfer functions applied to
  each sinusoidal component
• Modified sinusoidal functions are then
  re-combined to construct the altered time digital
  signal
• There are several ways to determine this response
• Fourier series (just described)
• Fast Fourier transform (FFT)
• Widely available in tools such as excel,
  Mathematica, MathCad

8
3 Method of Generating a Square Wave

• Ramp pulses
• Use Heavy Side function
• Used for first pass simulations
• Power Exponential Pulses
• Realistic edge that can match silicon performance
• Used for behavioral simulation that match silicon
  performance.
• Sum of Cosines
• Text book identity.
• Used to get a quick feel for impact of frequency
  dependant phenomena on a wave.

9
Ramp Square Wave
10
Power Exponential Square Wave
11
Sum Cosine Square Wave
12
Applying Frequency Dependent Effects to Digital
Functions
13
Assignment

• Use MathCad to create a pulse wave with
• Sum of sine waves
• Sum of ramps
• Sum of realistic edge waveforms
• Exponential powers
• Use MathCad to determine edge time factor for
  exponential and Gaussian wave,
• 10 - 90
• 20 - 80

14
Edge Rate Degradation due to filtering
15
Additional Effects

• Key Topics
• Serpentine traces
• Bends
• ISI
• Topology

16
Effects of a Serpentine Trace

• Serpentine traces will exhibit 2 modes of
  propagation
• Typical straight line mode
• Coupled mode via the parallel sections
• Causes the signal to speed up because a portion
  of the signal will propagate perpendicular to the
  serpentine
• Speed up is dependent on the spacing and the
  length

17
Modeling Serpentines

• Assignment Find a the uncoupled trace length
  that matches the delay of the serpentine route
  below
• Use Maxwell Spice/2D modeling of serpentine vs.
  equal length wave.

Trace route on PWB

• 1 oz copper
• 5 mil space
• 5mil width
• 5 mil distance to ground plane
• Symmetric stripline
• Use 50 ohm V source w/ 1ns rise time (do for ramp
  and Gaussian)

1 2 port Tline model
5 mil 2 port Tline Model
10 port Transmission Line SpiceModel Couple
length2 inches
18
Rules of Thumb for Serpentine Trace

• The following suggestions will help minimize the
  effect of serpentine traces
• Make the minimum spacing between parallel section
  (s) at least 3-4H, this will minimize the
  coupling between parallel sections
• Minimize the length of the parallel sections (Lp)
  as much as possible
• Embedded microstrips and striplines exhibits less
  serpentine effects than normal m9ictrostirpsd

19
Effects of bends

• Virtually every PCB design will exhibit bends
• The excess area caused by a 90o bend will
  increase the self capacitance seen at the bend
• Empirically inspired model of a 90o bend is
  simply 1 square of excess capacitance

Capacitance of 1 extra square

• Measurements have shown increased delays due to
  the current components hugging the corner
  increasing the mean length

• 2 rights do not necessarily equal a left and a
  right, especially for wide traces
• 45o bends, round and chamfered bends exhibit
  reduced effects

20
Inter Symbol Interference

• Inter symbol interference (ISI) is reflection
  noise that effects both amplitude and timing
• The nature of this interference is cause by a
  signal not settling to a steady stated value
  before the next transition occurs.
• Can have an effect similar to crosstalk but has
  completely different physics

Volts
Ideal waveform beginning transition from low to
high with no reflections or losses
Timing difference
Waveform beginning transition from low to high
with unsettled noise cased by reflections.
Receiver switching threshold
Time
Different starting point due to ISI
21
Inter Symbol Interference

• ISI can dramatically affect the signal quality
• Depending on the switching rate/pattern,
  significant differences in waveform shape can be
  realized one or two patterns wont produce
  worst case
• If the designer does not account for this effect,
  switching patterns that are unaccounted for
  result in latent product defects.

22
Topology the Key to a sound design
23
Topology the Key to a sound design

• Now, consider the case where L2 and L3 are NOT
  Equal

Receiver 1
Zo2
RsZo
L2
L3
Zo1
0-2V
Vs
Zo3
Receiver 2
24
Topology the Key to a sound design
A
A
B
B
C
In J R1 R2