I am studying how IC routing is done in large chips. I am following advice I often give people that it is helpful
to learn how to do something by hand before using an automation tool. I was skeptical about this for
chip routing because the scale of the problem these routers solve (trillions of gates) is outside what can
be done by hand. As it turns out a few of the things I know about routing PCBs helped prepare me for learning
some of the conceptual
and strategic aspects of what these tools do.
These notes make some of these connections using examples of my most recent PCB project, the FingerPhone.
The FingerPhone board is moderately challenging as boards go. It doesn’t have any high speed (>10Mhz) or
very high speed (RF) requirements and it’s not handling high voltages or currents. However it is an audio
product so noise considerations are important.
Here are some of the general design constraints:
No parts on the bottom of the board
All surface mount parts on the top - no through hole parts
No parts to the left and right so Fingerphones can be tiled side by side to expand pitch range
No parts above the top C key so it could be snapped off when tiling
The device should slip into a laptop case
Two devices should be able to nest (component area smaller than keyboard height)
Audio and power I/O on top row
Control switches on the left and right
Mounting holes for a cover plate
Two sided board with ENIG plating (for the touch sensitive keyboard)
Complete the circuit design - it is expensive in time especially to reroute to accommodate changes
Exploit regularities: The processing of the 25 keys is mostly the same. Three chips (one custom)
do all the touch sensing and sound synthesis for 3 keys. Since the keyboard uses high resistance
sensing of currents through the fingers, it is a good to have short connections from the keys.
Separate the analog and digital circuits so they can have their own ground planes and power
In this project the key partitioning decision was to accept the analog limitations of the mixed signal
process available to me for the custom chips and just use that capability for the touch sensor conditioning.
One custom chip does top octave synthesis - dividing a master clock into 12 approximately equal tempered
square waves. The other (bottom 20-pin device in the picture) does digital synthesis
using Walsh functions and the touch sensing. Mixing, panning, frequency, shaping, amplitude modulation
are done with non-integrated analog op-amp circuits.
Floorplanning and Placement
The partitioning and ergonomic requirements mentioned above help with the floorplanning and component placement.
The synthesis chips are close to the keyboard and placed near the three keys they process. The vanilla companion chips
which do the amplitude modulation are placed above them and this group of three chips is tiled across the area
above the keyboard.
This cluster of three chips are spaced apart to make room for a surprisingly large number of resistors which sum the many
Walsh function pulse waves into summing buses. There are a lot of them so the outputs can be panned
into stereo and so that much of the timbre control can be providing using an organ-stop, additive-synthesis
style. I was somewhat comforted by the knowledge that an instrument Bob Moog made using this approach,
the PolyMoog, weighs 82 pound.
The summing buses and subsequent analog signals flow to the left, up to the output connectors and then to right
to the headphone and speaker amplifiers. Analog processing is completed at the right-most output connectors
with an envelope folllower and schmitt trigger for connection to eurorack synthesizers.
This is the heart of the problem and where most of the time went. Three different styles of routing were
The highly geometrically constrained maze patterning of the touch keys
The regularly tiled routing for the cluster of 3 chips doing the sensing and synthesis
The rest around the top edge and sides
Geometrically Constrained Maze
I invented an two-dimensional interdigitation pattern to address a couple of opportunities - only one of
which is important in this instrument - to lower the resistance being
sensed when you touch the instrument by providing multiple paths for the current
to flow. When you look closely you can see a continuous conductor pattern that flows
around and floods the “maze". This is the source of the current that will flow through
your finger and find the conductors patterned symmetrically around a central spine
conductor that flows to the top of each key. Notice there is a via at regular intervals
along this “spine”.
In other instrument controllers where I use the same pattern, this spine is not continuous - it
is a set of vertebra with separate bottom connections made using the vias. In this case mazes
for each “vertebra” interdigitate vertically. This affords position sensing and area (pressure)
The full keyboard involves resolving many different grid related-constraints
vertical, interdigitation rate
horizontal interdigitation rate
equal sized “white” keys for which there are 7/octave
equal sized “black” keys in the 2, skip, 3 pattern
equal sized “black” and white keys at 12/octave
the underlying design grid resolution (0.5mm)
The tensions between spacing coprime numbers of things (7 and 12) were an interesting and surprising
challenge of the project. I noticed quite a few ugly short cuts in other touch keyboard
products and decided to carefully measure how the piano, keyboards and organ in my house
expressed solutions - it would be arrogant to ignore 1000 years of keyboard design practice.
The final result is interesting and something I hadn’t really noticed before:
the black keys aren’t built to be half way between their surrounding white keys -except for the
G# key. Overall you end up with an equivalene class (combining lateral symmetries)
with 4 members: (C, F, B, E), (D), (G, A), (all the sharps).
If you have ever taken a piano keybed apart,
you may have noticed the keys are stamped with their pitch in case you make the mistake of losing track of where they go.
If you find an example when they are not stamped you should mark this on them with a wax crayon or pencil.
The conductor spacing is adjustable in the software via the trace width and flood spacing. With
the first instrument I built the spacing was too tight and you could activate chord clusters
by simply breathing over the the touch board. Coughing took you into stochastic music territory.
The interdigitation rates are determined by the size of finger you expect to be playing the instrument.
The one chosen works quite well for most kids and adults.
The actual layout was done by hand using the grid rounding built into Eagle in the form of tileable modules
which are simply pasted by hand into larger assemblies. Each tile is small enought that it is quick to build by hand and
in this kit of tiles has been amortized over 4 projects so far.
Routing for the Horizontally-Tiled Center
The tool I am using, Eagle, includes an essential features for this kind of project: the ability to
take subcircuits and store them along with their PCB layout. For these 3 chip tiles I was able to experiment
with the placement by looking at the results of running the autorouter. Like many affordable CAD programs
Eagle has an average-quality autorouter that is fast enough for these sorts of non-committed experiments.
There is one strategy I have found serves me rather often dealing with incomplete, congested, weird or
ugly routes. What I do is create “white space” around the board until there a set of successful or nearly-complete routes
offered. I study these to identify nets which were hard to route and ended up winding around the outside of the
placed objects, for example. If these are critical routes I consider hand routing and locking them in before letting the autorouter
loose again. Seeing this process dynamically as I reduce surrounding white space can reveal congestion points. These give me
hints as to how to change the placement. This may involve adding space around the parts and almost always involves rotating
parts. I used to rotate ICs as part of the placement optimization but this often causes questions from the fab. house and increases the chance of
erroneously hand installing parts backwards. It’s interesting that in chip placement situations you are constrained about the rotations
you can do - standard cells have to sit in tracks, but you can flip them horizontally. Vertical flips result in a track change as the power
rails are pre-established. With the FingerPhone most of the rotations were resistors and capacitors.
Because of the tight lead spacing of the ICs there isn’t enough room on the top layer to run all the summing buses. It became
clear these would have to run on the bottom and this produced another rather common approach in chip routing called
Manhattan routing where each routing layer has a preffered direction. This requires vias from the top to the bottom for every summing
resistor so it was necessary to create enough white space for these vias. Much of the top routing is vertical.
A nice feature of having untented vias in the prototypes
is that these buses were available for probing and by cutting traces on the bottom circuits could be isolated for debugging.
I would like to think this helps me think about DFT (Design For Test) strategies in chips.
It’s worth mentioning that I had some control over the pin assignment of the custom chips and some tuning of this
was informed by the placement and routing. This helped me appreciate that some standard cell libraries provide for more
via attachment points on their nets than others. It’s interesting because it suggests a high-density standard cell library is
more difficult to route because it provides for more functionality in a smaller area to route and also has to contend with less flexibility
as to where the vias attach.
Routing the Rest
If it wasn’t for analog circuit layout practice the rest of the board could have been autorouted. It’s hard to teach medium-quality
autorouters about guard rings, decoupling, ground plane management and other strategies to minimize noise and crosstalk.
Again I used the autorouter to give placement optimization hints but resorted to hand routing for the details.
Normally you would like to protect the input of opamps from stray signals. One of the main uncertainties of this design is
that this isn’t easy when the summing busses go 2/3rds the length of the board. To mitigate the problem and the need
to rev. the board to use fancier grounding (e.g. going to 4 layers), I lowered the impedance at the expense of higher
current. This is a two-edged sword because the higher currents may induce more noise. The final results were satisfyingly
quiet - better than traditional organ designs - presumably because the board is smaller and
voltage levels are so much lower and closer to the output
voltage levels. Old organs often ran with 10-30volt rails. Here I am using 3.3V and +- 3.3V
As I delve into the literature on IC routing, I see that what I have been improvising is similar to what a global router does. At the
least it will inform iterations necessary with placement and at best it also provides a viable seed route for the detail router.
In the PCB case - unless the board is small or has uncritical performance requirements, I am the detail router. I riff on the approximate
routing from the autorouter.
I remain skeptical of my own process. I was very influenced as a young computer scientist by a famous
paper on a small classical resource assignment problem. They asked the experts on this problem around the world to submit their
solution. None of them were better than random assignment. I develop theories and heuristics on how to proceed on a given project
but I have to remind myself they could be good be poor and a long way from optimal and also may not apply on the next project.
However I was encouraged to learn that some of these heuristics have been already discovered
and explored in professional routing tools. For example,
ripping up and rerouting is often necessary but when I do this by hand I try to use the knowledge from previous routes.
dont do this because of the cost of storing and using the prior information. Some routers are structured to be able to do this
and the history does indeed help.
The limitations of individual knowledge of routing problems are obvious - you don’t have enough
personal designs to say anything useful about how well algorithms work. Key progress in this area has come from pooling
large numbers of representative designs and benchmarking routers with them in annual competitions.
One of the things I enjoy about Jin Hu's 2013 dissertation is the careful account of how these benchmarks can be done
avoiding the classical gaming of recognizing the benchmark design and tweaking parameters. Their global router performers comparatively well
without expert tuning. They offer comparisons where they defeat the custom tuning of competitive routers in competition datasets.
"High-performance Global Routing for Trillion-gate Systems-on-Chips", Jin Hu, 2013, University of Michigan