Super-simplified: What is a topology

‘Super-simplified’ is my series of brief notes that summarizes what I have learned so I can pick it up at no time. That means summarizing an hour of lecture into a few takeaway points.

These lectures complemented my gap in understanding open sets in undergrad real analysis, which I understood it under the narrow world-view of the real line.


X: Universal set

Topology ≡ open + \left\{\varnothing, X\right\}

Open ≡ preserved under unions, and finite intersections.

Why finite needed for intersections only? Infinite intersections can squeeze open edge points to limit points, e.g. \bigcap^{\infty}_{n}(-\frac{1}{n},\frac{1}{n}) = \left\{0\right\}.

Never forget that \left\{\varnothing, X\right\} is always there because it might not have properties that the meat open set B doesn’t have. e.g. a discrete topology of \mathbb{Q} on (0,1) = B \subseteq universal set X=\mathbb{R} means for any irrational point, \mathbb{R} is the only open-neighborhood (despite it looks far away) because they cannot be ‘synthesized*’ from \mathbb{Q} using operation that preserves openness.

* ‘synthesized’ in here means constructed from union and/or finite intersections.


[Bonus] What I learned from real line topology in real analysis 101:

  1. Normal intuitive cases
  2. Null and universal set are clopen
  3. Look into rationals (countably infinite) and irrationals (uncountable)
  4. Blame Cantor (sets)!

 

 

 718 total views

韓国から愛をこめたカンチョー

ちょっとガキっぽいげど、この下ネタを見逃しません:

Kancho is LOVE. カンチョーはラブである。
Kancho from the back. 後ろ。
Contrary to common design, the bag is supposed to be opened from the middle. Exactly what Kancho does! もちろん、開け口は間中です。カンチョーですから。

中身は生チョッコだから、イメージはぴったりです。

 1,389 total views,  1 views today

EMC PCB Layout Notes

  • Implicit RLC (potentially filters) and antennas formed by traces
  • Large ground/voltage planes serves as EMI shield, low impedance path current sink
  • True differential signals can be generated by current sources
  • Decouple with ferrite beads if radiation inevitable by geometry/placement
  • Avoid / minimize large current swings on analog plane (e.g. buffer digital signals)
  • Star ground when splitting sections: don’t let heavy digital current sink through analog ground by cascading the grounds.
  • Don’t really need to split planes as long as large digital current’s preferred return paths are localized and far away from the analog section.
  • AGND/DGND refers to the grounds responsible for different sections of a mixed-signal IC. Has nothing to do with which actual ground to tie to. (e.g. DGND pin in ADC chips still goes to analog ground plane as it has low switching current)

 967 total views

Rick and Morty Quote: What people called love

From Rick and Morty Season 1, Episode 6:

Rick: Listen Morty, I hate to break it to you, but what people calls “love” is just a chemical reaction that compels animals to breed. It hits hard, Morty, then it slowly fades, leaving you stranded in a failing marriage. I (Morty’s grandpa) did it. Your parents are gonna do it. Break the cycle, Morty. Rise above. Focus on science.

A follow up from Episode 9:

With the writers Rick and Morty, universities can close down the philosophy department and move all the logicians to the math department:

A follow up from Episode 8:

Nobody exists on purpose 

 

 19,645 total views,  3 views today

Lepy LP-2024A+ Class T Amplifier Mod

My traditional Hi-Fi amplifier drains a lot of power and heats up my room when I’m not using it. The summer heat prompted me to look into Class-D amplifiers as they’re highly energy efficient.

I bought a Lepy LP-2024A+, a Class-T amplifier (It’s Tripath’s improvement over Class-D amplfiers) for $22 shipped. It sounded good over a narrow range of volume, as I can hear the background sound details on my ADS 200 speakers.

Unfortunately, strong bass components in certain music gets distorted, a sign that the amplifier cannot deliver fast energy impulses. To put it simply, I enjoyed the treble but not the bass with this amplifier.

I saw some mods reports on the older TA-2020A+ based units (like LP-2020A+), but as of now, only one Japanese blog site talk about switching out input stage op-amps without other changes. So I decided to do my own mod and post the results here.


First, the unit came with a dinky 2200uF capacitor for power smoothing. I upgraded it to 6800uF. I happen to have a 12uH inductor with thick wires, so I replaced the toroid inductor (as in the LC power smoothing pair) with it while I’m at it.

Then I replaced all the remaining white-label capacitors with decent brands (Wruth, Nichicon, Panasonic, CDE), all rated at 105 degC, sometimes with higher voltage ratings depends on which brand-name parts Newark has on sale when I order it.

Then I upgraded the 4 output stage inductors with Wruth 7447452100 rated 10uH 4.5A. Tripath’s datasheet says 2A, so I supposed the one populated on board would be less than that.

I also replaced the SMD (1206) ceramic capacitors at the output stage (very close to the speaker wire terminals) with Polyester Film (for the taller 0.47uF ceramic chips) and NP0/C0G (the thinner 0.1uF ceramic) to improve linearity. I suspect this change helped to reduce the listening fatigue for treble components of the music I’m listening to. Now I don’t have to tone down the treble gain (knob) that aggressively.

As prompted by the Japanese blog site, I ordered some LT1364, but the improvement isn’t that big since the NE5532 wasn’t bad in the first place:

The bass and drums are much more enjoyable after the mod, since the improved power handling reduced the bass distortion on bass impulses. The amplifier is still 15W (7.5W+7.5W) dictated by TA-2024A+, but I rarely want to crank the music up louder than that anyway.

As a bonus, I took a thermal image with my Seek Thermal Imager:

The input stage ICs LT1634 are 118 deg F:


Update [02/06/2018] I did some experiments with external capacitors and realized that the real problem is the crappy 13.5V@3A power supply that came with it. Yes, I tested it with a DC load and it can really do 3A, but it has a weird behavior: when there’s a huge power draw (like from a bass drum) that drops the voltage level below 11.5V, the power supply starts oscillating from 10V to 11.5V (never gets above that even when I stopped the music) with a regular hissing noise of around 1Hz physically from the power supply itself. I had to turn the unit off for it to ramp back to 13.5V.

Then I used my HP 6033A systems power supply (can do 30A, relatively clean power with fast transient recovery) and observed the rail voltage and compared it to when I power the LP-2024A+ with a big capacitor + original power supply. It’s clear that no capacitor is big enough to cover the flaw of that crappy power supply that came with the amp.

After the power supply issue is resolved, even loud music sounds smooth, expressing the 3D acoustic image crisply through my ADS 200 speakers: I felt like a person is talking/singing right in front of me than some loudspeaker generated sound. It’s so crisp that I can hear each individual string pluck. Bass is deep too after I added a ADS sub 6 subwoofer. I’ve been listening to “the Phantom Of the Opera” CDs ever since high school and I’m still rediscovering new musical details with this amplifier + ADS speakers! 

Before the mod, I would hesitate to make it my main amplifier and might want to go back to my Denon AVR-988 for serious listening. It took me quite a while to tune my Denon to sound good, but it works right out of the box on my modified Lepy LP-2024A+!


Update [08/21/2017]: Based on people’s comment (in audiokarma) on TA-2020A+ vs TPA3116, I decided to give it a shot and ordered Nobsound’s 50W model.

Actually before this LP-2024A+, I modded a Pyle TA-2020A and was disappointed at the clarity is totally lacking compared to the lower powered LP-2024A+. I thought it could be Pyle’s terrible implementation of TA-2020A+, but after hearing TPA3316, I observed these:

  • TPA3116 has less distortion than TA-2020A+ and it sounded slightly tighter at all frequencies, especially the low ones
  • Both TA-2020A+ and TPA3116 lack the clarity at vocal frequencies and above. TA-2024A+ beat them both hands down.
  • TA-2024A+ draws 0.15A when no music is played while TPA3116 draws 0.03A. The reading is from my HP 6032A (60V, 50A) power supply.

TPA3316 might have a tighter bass than TA-2024A+, but I wouldn’t trade the vocal and up for that. TA-2024A+ might be marginally OK for N.W.A., but certainly not for parties. It’s an amp for music, not for acting cool.

 

 3,421 total views,  3 views today

TDS 500 600 Series (and TDS 820) Monochrome CRT Horizontal Linearity

I have a batch of TDS 620A which everything looks shiny new, but the display will stretch vertically and eventually gone unstable after turning it on continuously for a long time.

Turns out there’s a specific batch of flyback transformer (120-1841-00) on the monochrome CRT driver board (640-0071-06) that has quite a bit of infant mortality. The newer the unit looks (of the CRT tube looks shiny new without burn-in), the more likely it’s a victim of the bad batch.

The transformer is almost impossible to source (other than getting another CRT driver board), but I was able to find a Chinese supplier who makes it. It was usable, but it’s a nightmare to get it on because it’s really done with the stereotypical Chinese (PRC) manufacturing caliber.  When I received the unit, it’s a WTF moment! Leave me a comment if you want me to write about it.

The replacement transformer is only pin and functionality compatible, but it’s not a drop in replacement (not even geometrically). The characteristics are different and I had to adjust the trimmers all over the place.

I was able to get the screen width I want by adjusting the variable inductor (L105, HOR SIZE) by nearly pulling ferrite rod out, but the horizontal linearity was way off (the left side is very squeezed):

I looked into the TDS520B Component Service Manual (Same CRT board circuit diagram) and found this:

But L100 looks like this, which doesn’t seems trimmable:

The right hand side is the same L100 choke I extracted from a CRT driver board (same model) that I’ve disposed of. I saw two suspicious pieces of metal-like objects strapped on the choke on the left (installed) which I haven’t seen in other identical boards. 

Thinking that by changing the magnetic property of the core, I can adjust the inductance of an otherwise non-adjustable inductor. I took a few bits of magnets sitting on my bench and swing it around the L100 choke, the horizontal display widens/narrows depending on which pole of the magnet is facing the L100 choke.

After a few trial and error, I picked the right amount of magnet discs to correct the horizontal linearity so the squares have roughly the same width:

I guess I cracked the code! Here’s the result of correction by magnet:

 

 2,160 total views,  1 views today

RTC / NVRAM in Test Equipment

HP Infiniium Series Atlas III Motherboard (Oldest generation Infinium oscilloscopes still branded as HP):

  • [RTC. There’s no exposed batteries] bq3287AMT = DS1288

Tektronix TDS Series (500, 600, 700, 800)

  • Older TDS (without alphabet suffix): Dallas DS1245Y
  • Model number that ends with ‘A’:  Dallas DS1650Y

The NVRAM in TDS series only contains the options data. Since I can reprogram the options, I can start with a blank NVRAM without reprogramming it). 

Will keep updating this page when I came across more test equipment.

 1,060 total views