This thread has been locked.

If you have a related question, please click the "Ask a related question" button in the top right corner. The newly created question will be automatically linked to this question.

AUP Logic Inverter for Crystal Circuit?

Other Parts Discussed in Thread: SN74AUP2G04

Background:
I inherited a design using a 74AUP2G04 (buffered inverter) as the gain element in a standard Pierce oscillator circuit running at 3.6864MHz.
I know an unbuffered part would be better in this situation and I have built perfectly working crystal circuits with the AUP2GU04 from NXP and even VLCGU04 from TI.
However, they have used the other half of the 74AUP2G04 to drive across a connector to another board and the unbuffered parts really start to draw too much current when you ask them to drive this line.

The Circuit:
Rf across the inverter input and output is 1M ohm.  Rseries = 1K ohm from inverter output to crystal and cap to ground which is 33pF.
Cap to ground and at input to inverter is 27pF.  (This gives me, about 1ppm frequency accuracy at 25C.)  The SN74AUP2G04 inverter is running at 2.5V Vcc.
The crystal is a fundamental mode, parallel resonant, AT cut, 18pF Cload, HC49 surface mount crystal with an ESR max = 200 ohms from Citizen/Fintech.
It is Digikey PN 300-6102-1-ND  (30ppm @ 25C, 50ppm over -10 to 60C, 5ppm year).
The caps are both surface mount 0603 ceramic NPO parts of 5% tolerance. 
The resistors are both 1% tolerance surface mount 0603 thick film chip resistors with 100ppm tempco.

The problem:
When I touch the input pin of the inverter with probes, fingers, etc.  The inverter output which normally looks like a nice sine wave, becomes a sawtooth and doesn't have nearly the voltage swing of the sine wave.  The frequency shifts significantly lower, also, to about half the fundamental frequency.  We have also seen this circuit jump to higher frequencies, but I have not been able to scope the circuit in the higher frequency mode.

The question:
Does the 74AUP2G04 have switching/stepped output drive (or output impedance)?  Can it go into a mode where it can no longer drive the crystal circuit it was previous driving when a little disturbance is put on the input pin?  Or, is this a function of the input structure of the 74AUP2G04?  Perhaps the schmitt trigger inputs are a problem?  Or is this frequency shift possibly related to a very narrow range of "linear" operation of the buffered inverter which is set by Rf?

Some of the checks specified in application notes for Pierce crystal circuits do not work with this circuit; the one that bothers me most of all is that the circuit should not oscillate with the crystal replaced by its equivalent ESR.  With just Rf and the inverter, I cannot make this circuit stop oscillating, with square wave output, at all (freq about 33MHz).  If I add only the capacitor to ground at the input, the circuit still creates beautiful square wave but at much lower frequencies, in the < 50kHz range depending on the value of Cin.  With the whole circuit, minus the crystal replaced by about 200 ohms, the square wave is about equivalent.  Increasing the Rseries doesn't seem to stop the oscillations, either, though maybe decreasing it would which I haven't tried.

I'd really like to know that this gate can be used in this circuit or if it is not recommended. 
We have very stringent power consumption requirements and the LVC part previously used drew too much current. 
Almost any other family of parts would seem to be too much additional current.