Hello, I will post later rest of analysis.

 

I take some real world measurement. I build this gen using CD4069 supply from 5V PSU and R1 = 100kΩ; R2 = 10kΩ ; C1 = 100nF.
And the results are
The Output voltage and V4 voltage (at R1,R2,C joint)



As we can see the Duty-cycle is not equal to 50% because the gate threshold voltage is not equal VDD/2 instead we have a threshold voltage around 3V also the "positive" and "negative" threshold voltage ar not equal (3.08V and 2.9V).
This is why the output frequency is out from ideal case Fo = 1/( 2*R2C*ln(3) ) = 1/( 2*10kΩ100nF*ln(3) ) = 455Hz but this do not include component tolernce.

And the V1 voltage, at the first gate input when we can see the protection diodes in action.



If I replace R1 resistor with a short circuit (R1 = 0Ω) the situation changes.



With R1 = 0Ω the output frequency goes up (435Hz) and some strange things happen with diode clamper.

 

Here is similar circuit:



How would this modification affect waveforms we already found for original circuit?

 

ps. I use simulation software Multisim for analog electronics but I have problems using it for digital electronics. If someone here uses Multisim, please post here simulation of this circuit (or original one).

 

How would this modification affect waveforms we already found for original circuit?

Not much. Notice that this additional RD network will come into play only if V4 > VDD.