Using 4049 hex inverters

[PBE6]

I haven't played with these for a while, but I have a few lying around so thought I might in the near future. I remember being a bit confused by these in the past, so I thought I'd jot down some things I know and ask a few questions:


Calculating gain

Gain for 4049 hex inverters is calculated in essentially the same way as with an standard inverting opamp gain stage, except that the open loop gain is much lower than usual and therefore needs to be considered. This approach gives:

G = -(Rf/Ri) * (G(OL) / (G(OL) + Rf/Ri + 1))

(It's interesting to note that "Rf/Ri + 1" term in the denominator is the expression for gain from a non-inverting opamp gain stage - I'm not sure what that means, but it's interesting nonetheless!)

Basically the gain will be less than what you expect, and gets worse as the G(OL) value goes down.

As far as tone shaping goes, it seems as though capacitors can be added to either the Ri or Rf paths to cut bass/treble as required. In that case, Ri and Rf would be replaced by Zi and Zf (impedance a of the resistor/capacitor combinations) and calculated the same way. Is that correct?


Impedance

Hex inverters have a large input impedance, but a large output impedance as well. Is it always advisable to buffer the hex output with very-high input impedance buffer (like a JFET, or JFET-based opamp like the TL072) if you plan to run additional filters/stages after the hex output? Are there any issues with noise/oscillation using this method?


Miller effect

I basically don't know enough about this to ask a reasonable question, I just know it can be an issue if preceding stages have large output impedances. Any general advice or explanations here?


Any other tidbits/thoughts on working with these inverters would be appreciated too!

[PRR]

> G = -(Rf/Ri) * (G(OL) / (G(OL) + Rf/Ri + 1))

Oh, fah.

If naked amp gain is infinite, gain is just Rf/Ri.

If amp gain is barely 10 times higher than what the resistors impose, gain falls about 10% shy of what the resistors imply.

If amp gain is about what the resistors impose, gain falls about about half of what the resistors imply.

Say the naked amp gain is 10. Use 100K+1Meg. Actual gain is about 9.

In general if you NEED to know the final gain, do not use CMOS "linear" tricks. The not-high gain varies wildly with supply voltage, loading, and frequency.

Also CMOS traditionally hisses. And the inverting configuration adds all that resistor hiss on top.

If you need to KNOW gain, use an Op-Amp. Gain may be "infinite enough" for all practical audio purposes. Hiss may be low or very-low. Diff-input allows non-inverting configuration for high input impedance and low hiss resistance.

> seems as though capacitors can be added

Yes. Main gotcha is that shunting Rin with a cap gives a falling input impedance, but the gain will rise less than you'd guess because the CMOS gain is falling.

> Miller effect

Simple. With NFB, the input pin of the amp (the Rin-Rfb node) will be "zero" impedance. For low CMOS gain and high value resistors, maybe more like 1K; but that's "almost zero" compared to 1meg zone resistances.

[anotherjim]

The famous, unique and historical AN-88...
https://www.fairchildsemi.com/application-notes/AN/AN-88.pdf
...suggests that 3 inverters can be used in series with a single overall feedback resistor. Open loop gain could get to around x1000?

Despite having played with CMOS inverters in linear mode quite a bit, I've never tried this, probably because it uses half the chip for just one function.

Use them for fun & effect - it won't be hi-fi.
If AC coupled input, you can terminate Rin to ground. Do this for a deliberately asymmetric clip.
You can do without an Rin completely in some AC coupled cases, it will bias purely from Rf.
Similarly if the input is DC coupled from something that is Vcc/2 DC bias, you can do without an Rf (but not if you have a Cf or it'll just wander off and hit a rail).
Remember the chip current is high when in linear bias, so feed V+ via some resistance or begin experiments with a lower voltage supply.

[PBE6]

Awesome! Thanks.