Title: Interconnect II Class 22
1Interconnect II Class 22
Prerequisite Reading - Chapter 4
2Effects 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
3Decomposing 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.
4Frequency Content of Digital Signals
- The amplitude of the the sinusoid components are
used to construct the frequency envelope
Output of FT
5Estimating 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
6Estimating 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.
7Examining 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
83 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.
9Ramp Square Wave
10Power Exponential Square Wave
11Sum Cosine Square Wave
12Applying Frequency Dependent Effects to Digital
Functions
13Assignment
- 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
14Edge Rate Degradation due to filtering
15Additional Effects
- Key Topics
- Serpentine traces
- Bends
- ISI
- Topology
16Effects 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
17Modeling 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
18Rules 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
19Effects 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
20Inter 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
21Inter 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.
22Topology the Key to a sound design
23Topology 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
24Topology the Key to a sound design
A
A
B
B
C
In J R1 R2