Sine wave CMOS buffer from inverters with or without feedback

Question

Is it possible to buffer a sine wave using inverters alone or with some kind of feedback?

I've been browsing google for minimalistic (I'm in 3.3-12 V domain) sine wave buffers and this thought stuck in my mind.

The idea was there, because I came upon High Speed Digital CMOS Input Buffer Design by Krishna Duvvada, and I already asked a question with this in reference but of a different kind, so I don't think I'm breaking any rules with this one.

I realized, a bit later, that in that master thesis, that's actually not how you would wire the output of the first stage, the rail to rail input stage. Do you agree? So it's some kind of inverters structure basically.

I don't have enough knowledge to contribute my thoughts, and my thoughts are currently very tangled, hence the question.

Answer 1

Assumptions:

I'm assuming you need to preserve the amplitude and frequency information of your signal. Therefore, you need a linear amplifier, which means, you need negative feedback. I also assume you don't mind inverting the signal as long as the gain=1.

The Simplified Amplifier Circuit Architecture

CMOS inverters lend themselves easily for inverting amplifier implementations, as we can readily use the 1st stage inverter gate as the virtual ground. See the circuit below:

^{simulate this circuit – Schematic created using CircuitLab}

You can only do this with an odd number of stages, otherwise you don't have negative feedback. However, 1 stage only might provide too low of a loop gain (thus, poor distortion) and 5 stages will probably be a nightmare to frequency compensate. 3 stages should be the sweet spot.

Problem: Inverter's sensitivity with respect to supply voltage

Unfortunately, an inverter's transconductance can vary significantly over temperature and process corners and supply voltage. The process variation you can't avoid, the temperature and voltage variations you can with the solution below.

Solution: Dedicated Voltage Regulators for the stages

One way to overcome this is to bias your inverters such that they have a dedicated current through them, and have them track over temperature. To this end, you can design a regulator that provides a replica voltage to your inverters supply, like this:

^{simulate this circuit}

(BTW, I'm just drawing schematics to illustrate my ideas, I didn't simulate any of these.)

The nice thing about this regulator is that, say, if your "model/replica" inverters (M2 and M3) are of size \$W/L\$, and have a current \$I_b\$, then, in your actual stage, you can scale up your size as \$k\times W/L\$ and your current will be scaled up accordingly as well (it's a replica/model-based kind of biasing, so it'll never be super accurate, but you get the idea).

Extra Suggestion

As an extra, there might be a possibility of distorted currents from the 2nd stage coupling via the supply to the 3rd stage, which dominates distortion. That means it can have more distortion than usual. A way around this could be isolate the supply by putting dedicated regulators for 2nd and 3rd stage. Perhaps 1st stage can share the regulator with the 2nd. You have to experiment.

Answer 2

CMOS inverters can be used, to some extent, as linear amplifiers, and they have been used.

You need an unbuffered inverter for it to work, as standard inverters are buffered, i.e. they have three inverters in a chain between input and output.

As an example, CMOS inverters are used as inverting amplifiers (or buffers) in crystal oscillators, input amplifiers for converting low-amplitude signals to digital logic levels, or even simply as audio amplifier (Nintendo Entertainment System).

Answer 3

Is it possible to buffer a sinewave using inverters alone or with some kind of feedback?

Two things are needed: -

• The inverter needs to be an unbuffered type
• A high value resistor (typically 100 kΩ to 10 MΩ) is used for feedback

It converts the unbuffered inverter into a reasonable linear amplifier but, because feedback is used you have to think of the input to the inverter being like a virtual ground (as in an op-amp) so, don't mess with the DC levels at this point or the output could easily crash into a supply rail.

Think of the feedback resistor as automatically setting the right bias level for the gate's input.

Use it for AC signal amplification (just like an unbuffered logic gate that is turned into a Pierce oscillator when used with a crystal.