# Fundamental CMOS astable multivibrator

So i need to perform analysis of simple astable multivibrator circuit shown in the following picture: These Vdd and GND are just the power rails of those CMOS inverters.

Now, i need to perform analysis, so i have three characteristic points here: point 1) input to first not gate point 2) output of 1st not gate (input to the 2nd not gate at the same time) point 3) output of 2nd not gate

We want to determine the period of oscillation

Assume that we have high state at the 2nd point, then we have the following circuit (I've neglected the effect of output resistances of inverters since i consider them too small comparing to R1) Now, well known expression for voltage of point 1) which can be derived from solution of differential equation of this circuit is:

$$V_1(t)= V_1(\infty) - (V_1(\infty) - V_1(0)) e^{-\frac{t}{R_1C_1}}$$ Now, i am supposed to know the starting value of V_1, but i determine what it should be, at the infnity, it should be Vdd since it cant go beyond that, but i cannot determine the starting value of V1, so any help is appreciated!

• Note that when you use the CircuitLab button on the editor toolbar an editable schematic is saved in your post. That makes it easy for us to copy and edit in our answers. You don't need a CircuitLab account, no screengrabs, no image uploads, no background grid. Jul 7, 2019 at 14:30
• @Transistor I didn't knew that, i'll keep that in mind though, thanks for the heads up! Jul 7, 2019 at 14:31
The capacitor is trying to charge to 1.5 times above the supply voltage and 0.5 times below the supply voltage, but it can't due to the input protection diodes clamping the capacitor voltage, because your oscillator circuit is too simple and is missing an input resistor. 