Hi,

I had a few miscellaneous comments:

(1)  There's something unusual in the code, there is a loop containing analogWrite, and it will repeatedly try to execute it forever. 

This may or may not be benign, and may even contribute to measured discrepancy or even jitter. It is down to the implementation of that analogWrite function, I have not checked, but it would be good to either check it before doing this, or (better) just do it in the setup() function, because that will be a more normal use of it. Often, functions can misbehave if used beyond what they were likely designed and tested for.

(2) The measurements from 'scopes are not necessarily accurate always. Despite it being (say) a 100 MHz 'scope, doesn't mean it is sampling with that granularity always, and it will also have it's own clock error too.

(3) The probe compensation should take less than a minute per probe and per channel, even if doing it manually. If it's not automated, then the probe should have a trimming tool adjustment.

(4) Not sure what you mean by a more accurate square wave, because the '555 output will almost certainly be less accurate than from the 'scope; the frequency will drift with temperature, and it's not a square wave anyway... I think from memory the 555 cannot generate a 50% duty cycle precisely due to the charge or discharge cycle having to use the same resistor (along with another), I have not checked in ages. One workaround for that is to do a divide-by-2 using logic gates, from the output of the 555 or whatever.

(5) STEM with 555 is a great idea.. for instance using it to generate sound effects and so on. Combining more than one 555 allows you to do siren-type effects, etc. There's a very good website with 50 projects entirely related to 555: http://talkingelectronics.com/projects/50%20-%20555%20Circuits/50%20-%20555%20Circuits.html?iframe=true&width=100%&height=100% 

I upgraded the scope firmware and also found the LED lights in the basement were throwing off noise that was causing the probe calibration to jump.   I put the scope into alternative mode so the end was on left side and beginning of the square wave was on the right side and was able to match them up more accurately.    I am considering a Tripp Lite Line Conditioner and put in 20A circuits to isolate the Siglent hardware from the soldering iron and other noisy components.   I worked with a Siglent engineer on getting it smoother.   The scope has some error too.   On one channel I should get 1 gigasample per second.  I think with the 1 kHz frequency, that won't be much error.   It will be interesting once I get to 100 kHz frequency.   I think a lot of the scope issue was not being familiar with how to use it.  

Arduino code loop was to keep it constantly running and not one time run.  I am planning on revisiting the Arduino and Pi solutions for PWM.  

I will have to check into your divider by 2 logic gate solution.  It would be interesting to build.   The next purchase is the Siglent 3 channel power supply.   The Siglent frequency generator is month down the line.   My son's tuition for preschool is coming up in a few months.   So my EE budget is the least priority.  

555 timer won't give a perfect 50% square wave.   I worked out the math for a 1 kHz frequency but the time high is 512 ms and time low is 488 ms.   This isn't that bad considering the error of 12 ms.   I played around with the common components that I have in capacitors and resistors.   Building it will be the test.   I will use my multimeter to get accurate readings on the components and redo the math.   I was hoping for 505 ms and 495 ms with 1 kHz frequency.    The new components are the sizes in between I was missing in caps and resistors.  So can use the multimeter to get the components closer to the actual math values. 

Scope is accurate.  The resistors and capacitors are 5%-10% variance.  So a 220 ohm resistor is usually 214-222 ohm.   So what is accurate on paper in the math isn't what the component is in reality. 

I was looking for a book on all the 555 projects I can build.   I have a good selection of op-amps and components from this months purchase to play with.   I wanted a decent scope to start out with.  All the reviews said this was a good choice. 

You can lookup several ways to make a 555 circuit that will get very close to 50% duty cycle. One simple way is to use a CMOS 555 and connect the output to the timing cap with a resistor.

The kit I bought has NE555 chips to start out with.  TLC555CPWR from Digikey are $0.95.   Maybe I will get some next time. 

A side project is getting LT Spice to simulate the 555 timer and my circuit accurately.   During my B.EE, we put the circuit on page.  Solved it with math.   Then, we put it into Spice and compared the results.   Last thing was acutally build it measing each component with a multimeter and recalculating everything with real values.   How can I get LT Spice to better simulate a NE555?  

I was looking for a book on all the 555 projects I can build

There's several used 555 projects books on Amazon etc., I don't think there are any new, since the 555 is quite a mature product. However the used books are sometimes pricey because they are out-of-print. The web link to the 555 projects mentioned earlier, is very good.

I have a paperback 555 project book by E.A. Parr, it is (was) great, but the web link content is (from my perspective) better.

 Many electronics books will have a section on the 555, sometimes focussed on how to use the 555, rather than projects, depending on the book. There's a thread on good electronics books here, and most will refer to the 555 for at least a few paragraphs if not more:

/members-area/personalblogs/b/john-wiltrout-s-blog/posts/i-want-to-do-electronics-where-do-i-start

Hi, I missed responding to this:

Arduino code loop was to keep it constantly running and not one time run

Sure, I understand that, however the approach to do that can be different, and it may improve the timing (can't guarantee that, since I don't know the Arduino function in detail, I've not checked the source code nor the microcontroller datasheet). In any case it's not normal to set the PWM configuration repeatedly, if the configuration has not changed.

This would be a 'normal' approach (in slightly pseudocode):

setup()
{
  analogWrite(PWM_IO, 64);
}

loop()
{
  delay(1000);
}

That code will simply do nothing in the loop() function, and do it forever. Meanwhile, the PWM hardware inside the chip will keep doing its thing (unless later instructed otherwise), based on the configuration that was done in the setup function.

I don't use Arduino often enough to be sure if this code structure will work once the syntax is sorted, but I'm fairly sure (95%).

#include <Wire.h>

void setup() {
  Serial.begin(9600);
  Wire.begin(0x4);                // join i2c bus with address #4
    pinMode(6, OUTPUT);
}

void loop() {
  analogWrite(6, 128);
 
}

set timer 0 divisor to    64 for PWM frequency of   976.56 Hz (The DEFAULT)

The measurements of the scope matches. 

10 kHz square wave.   I think this is fairly good specs.

Pin 5 : 10nF capacitor

Capacitor: 10nF
R2: 4.7k ohm + 2.2k ohm+ 100 ohm= 7k ohm
R1: 330 ohm

Frequency: 9.99kHz
Period: 100.141us

+ width: 49.4us
+ duty cycle: 49.34%

– width: 50.74us
– duty cycle: 50.66%

Still working on getting Eagle up and running with a 555 timer.