Frequency of an Trigger Schmitt RC oscillator

Hi everybody!
I'm making a RC relaxation oscillator with the 74**14 Trigger Schmitt inverter. I have found out that the frequency of the circuit depends on the technology of the logic family (LS, HC, HCT...),that is, it depends not only on the values of R and C but also on the parameters of the chip; Ioh,Iol,Iih,Iil,Voh...

I need to find out the formula and all i've got is this information from the Philips 74HC14 datasheet that says:
HC--> f= 1/0.8RC
HCT--> f= 1/0.67RC

(Datasheet: http://www.farnell.com/datasheets/5029.pdf)

Can any of you help me and tell me how they get to these values??? What do 0.8 and 0.67 stand for?

Thanks in advance for your time!

 

The so-called RC time is used as a measure of the rate at which charge may be placed onto a capacitor. It is a crude measure, as it describes a linear transfer, and the actual accumulation of charge is an exponential function. The approximation to full charge is 5RC. When we speak of frequency response of circuits with a resistance and a capacitor, we speak of RC time.

So, if we want to quantify it, by multiplying R times C (Resistance in ohms times capacitance in Farads) we obtain a time for that transfer of charge. For instance, a 1 microfarad capacitor and a 100,000 ohm resistor gives us a charge time of .1 second. Eight tenths (.8) of that time is .08 second. Two thirds of that RC time (.67) is .067 seconds.

The significance of these measures is in the trip points for voltage levels in the HC and HCT logic families.

Most logic senses change from one logical state to the other by rate of change. That is, it is edge-triggered. A slower rate of change may not be correctly sensed.

The Schmitt trigger is a way around this difficulty. Rather than rate sensitive, the input circuit is level sensitive, and will respond to a definite voltage level regardless of the rate of change.

So, when constructing an RC oscillator using a 74XX14 inverter, it is significant to pay attention to the logic family. In every case, the RC product is invariant. But, we see that the 74HC14 will sense a transition from a low to a high when the charge on the capacitor has reached four fifths of what it will be in the full RC time. The oscillator will run faster than would be predicted by the full RC period.

Likewise, a 74HCT14 will sense a transition from low to high in two thirds of the time predicted by the RC product. It will also run significantly faster than the RC product would predict.