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The output starts to resemble a triangle wave, of the same frequency as the input signal.
To fix it you need to use a faster device.
The usual advice is to have your signal pull the input to either zero V or supply V, as rapidly as possible. It may cause the internal switching to happen slightly faster.
If you need an inverter to run faster, normally you choose a family of CMOS or ECL that runs faster. GaAs runs fastest at GHz speeds. For normal HCT CMOS, you may read about the reasons for speed differences (**broken link removed**)
If you have more specific question , then ask with more details.
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