I must have made a bad joint somewhere. I inspected whole board under the microscope and found a couple of joints that didn't really look so good, so I redid them. I also cleaned everything with alcohol and I now got results which are as good as my previously good results, except for the huge peaks. Smaller peaks are now gone. I'd attach an image of that, but I can't find it at the moment.
I got in touch with the other scope owner I know and it looks like that it will take a couple of weeks for us to find an empty time slot for inspection, since we both have exams starting real soon. My idea is to completely remove the PSU from the scope, fire it up from the battery and then poke around until I hopefully find something.
Rf-loop's idea is an improvement to what I was doing when probing and now I can reliably capture the problematic noise, but my problem now is that I can't pinpoint its location. It seems as if the whole scope is radiating the noise. I switched to my 150 MHz probes for this and I can pick up noise whenever I bring a probe within 1 cm of the Z-plate or the PSU and the whole plate seems to be radiating it with pretty even amplitude. I can see it very nicely when the probe is right next to the coil on the MC34063A, but I don't know how to decide if the noise is coming from there or if it just happens to be on that trace, just like it's everywhere else too.
The large peaks seem to be somewhat repetitive. I'm attaching an animation of how they look over a couple of "cycles". I made the shots using scope's waveform record feature. It seems quite complicated to me to export the whole recording and the manual plus scope's help don't seem to give me a good explanation. In the end, I played it back frame by frame and exported image of each frame. Pause between each frame is 100 ms (plus the time it takes the scope to trigger?).
Also note TomC's good advice. (and of course (as TomC advised) you can swap channels, which one you take trig and which one you look signal. (some times and/or for different peoples and light situations this yellow color may be better for use as "main" channel)
If source for this high peak is inside scope (and I believe it is) you can find source.
But you need perhaps change method/thinking how to probe/diagnose it.
In your animation there is aquire mode "peak" and speed 10ms/div. Signal is coming CH1 and you have level triggered to this peak using same channel CH1. Becouse this, only information what we have is that there is these level peaks what are about double level related to other noises level.
For detect where from it come and detect what is "inside" this one peak it may need some amount more.
How to localize this noise peak source.
You tell that you can pick up it "everywhere".
Connect CH1 probe using 10:1 setting in probe and scope to example probe comp out GND or other place of GND what exactly same place you can use also later (for keep same settings and get comparable information) Set vertical so that it is center of screen.
Do not now care about trigger anything. Only watch this TFT and there running noise (here you can use also slow speed and peak mode. Adjust level so that you can see these highest peaks highest level are peaking around 4th div up from vertical centerline (baseline).
And in all cases keep this CH1 probe connection and level settings.
Do not change anything in CH1. Remember where is highest peaks peak level around (not exatly of course).
Acquire mode normal (not Peak!)
Change horizontal speed first to example 100us or example 10us.
Memory so that with 2 channel mode it use 500MSa/s per channel what ever speed you use what need related to this problem. (this is important)
Connect other probe to CH2. (use also here now first 10:1 setting)
Change trigger source to channel CH1.
Trigger mode Normal.
Adjust CH2 level so that its base trace is around -2 - -3div down from center. ( is more easy if keep CH2 visible but so that it do not overlap CH1 on the upper half of screen.)
In this phase scope do not trig or it trigs depending what is on CH2 and how is trigger level set.
(and of course use trigger coupling DC and rising edge in this case now)
Now take CH2 probe hook out (hook is too big antenna) and take GND wire totally out from probe (no need at all now and it is danger for make short circuits inside scope probing and it is also antenna, so take away.)
Now there is GND area and center pin visible. Take small piece of some small isolating tube and put it over center pin and GND area. See picture attached, there is CH2 probe (but in this case I use Hewlett-Packard 300MHz probe)
Now it is perhaps enough unsensitive so that it give enough level only very near of source what we want find. Of course also need adjust CH2 vertical V/div so that CH2 is not too sensitive!
If you have not yet adjusted CH2 trigger level it is baseline of CH2. And you can see signal on the TFT if there is enough signal for produce trig. (becouse you are not in Auto trig mode, it do not generate automatic (unsync) trig in case there is not available real trig. (and THIS may lead many cases totally wrong findings... Auto trig is nice but it is also danger in some situations)
Now pick-up some signal to CH2, example move this "capasitive near field" probe head now near to main power flyback secondary (example near secondary diodes heatsink)
Adjust now CH2 level so that you get "something" around 2-3 div high yeallow signal on screen.
Now, start adjusting trigger level (CH2 is now trig source) until it trig these around highest signals in CH2. Now after you get steady trigger in CH2 keep it and look CH1 red trace. Some noise component is now there stopped and all other sources noise components are moving randomly.
What kind of signal there in CH1 is now sychronized. If it is not what we are finding, move probe CH2 position and pick up other suspected source. When you find what you have try find you see this level of signal locked what you remember when you first adjust CH1 level.
Now your CH2 probe is near this source. If you change some other position you see there is some other noise peak in CH1 locked to trigger time position. (look only this horizontal area where is CH2 trigger position horizontally)
Now you can look CH1 signal (and CH2 is just only for trig)
With this method you can go inside this very fat "noise" trace and if this trace noise level is example 6 div peak to peak you can easy find under 0.5div high sigle noise peak source there well under total noise noise level as long as CH2 lock this signal to trig position. (becouse this signal stay locked and others trawel over screen wildly your eyes do not need look these other noises, just this locked signal there is important and this is coming where is your CH2 probe. Now you can zoom in this peak, chnage CH1 better level etc. Now if you make changes in this noise source circuit you can also exactly see what change happend just in this noise signal level and other things (example its frequancy/risetime figure)
Keep care that CH2 is not too sensitive so that it pick up too much signals. If you put CH2 probe (insulated) to only Z-Plate and it give trig, your adjustment is far too sensitive in CH2. It need give trig only very close this noise peak real source.
After you get this highest noise peak (or what ever it is becouse from 10ms/div and peak mode showed peak we do not know "anything") locked in CH1 using this CH2 trigger pick-up method then adjust horizontal speed for better visibility. Your CH2 probe is now very very near this peak source circuit.
In image, this is example how to arrange this CH2 probe. And note agen, NO GND, only capasitive pick up with this around 5mm long probe own center pin what is there inside this red isolation tube. (black isolation is over probe GND area (this probe is more thin than Owon probe).
There can also use other kind of probe. (magnetic loop probe)
But this small capasitive pick-up is well enough for this case here now.
Probe hook out. From center pin to GND area around 1 - 2 turn round coil (just
without any extra leads), diameter around 6-8mm and this all inside isulation. This kind of probe is very unsensitive but if there is RF near this coil it pick up it. It need quite strong field. But, this is what many times need inside some equipment trouble shooting. But this do not need now here.
In this image is this "capasitive" pick-up probe for this Owon case now.
CH2 pic-up sensitivity need reduce so much that trig can do only from very very close signal source. Then it do not trig from "all" noises but just wanted source. What signal is now locked in CH1 trace is this noise what is generated in this circuit where CH2 probe get trigger. Yes it need some experiments and exercise. After can use this method, you really can go inside this total noise and find what fraction of noise is coming from this circuit where your CH2 probe is and what is this source noise "signature".
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