The cascode circuit is a "common-source stage" with a source follower (top transistor J1) inserted between the drain of the bottom transistor (J2) and the drain resistor Rd. The follower only fixes the drain voltage of J2 but freely passes its current. So there is no particular difference in establishing the Q-point of the cascode circuit; use an usual bias technique.

@Circuitfantasist I'd disagree, the gate of cascode is at AC ground as it's typically connected to a bias voltage. The best description, IMHO, is a common-gate stage working as a current buffer for J2. The whole point of the cascode is that the drain J2 sees now a very low impedance -> low swings at the drain side of the gate-to-drain capacitor will mean this capacitor will not appear bigger due to the intrinsic gain of J2.

@ErnestoG, I think there is no contradiction between our points of view. I agree that the circuit can be represented as a common-gate current-driven stage (current buffer as you say)... also that the goal is to eliminate the Miller effect. I'm just looking for more functional explanations of the circuit that allow it to be intuitively understood. But what the OP is interested in is setting the Q-point. I hope you will agree that it is done in the same way as the ordinary common-source stage - through biasing J2 (not through the J1's gate).

Is it a goal to reduce component count? You can AC-couple J1 to J2, optimizing DC bias for both. OTOH, direct coupling allows you to use gate DC bias on J1 to perform AGC: ka7exm.net/hycas/hycas_200712_qst.pdf ... For maximum gain, you want roughly 6V on J2's drain - you'd like to have a few more DC volts for the direct-coupled cascode supply.

@Circuitfantasist does your last comment mean that I would only need to set the \$V_{GS}\$ for J2 instead of J1 like I would for the common source amplifier?

@normal chemist, Exactly! Set a bias voltage to J2 as if J1 is not there (J1 has only the auxiliary function of fixing the J2's drain voltage). In fact, J2 is self-biased by Rs and there is nothing else to do there; you only need to set a fixed voltage to J1's gate. I am preparing a detailed answer to your question to explain the basic idea of ​​this famous circuit configuration.

I agree with @ErnestoG. There's nothing common source about the isolation transistor. Its gate (or base when talking about BJT) is grounded, which makes it a common gate.

@Bart, I have not said this; look at my first comment above: "The cascode circuit is a "common-source stage" with a source follower (top transistor J1) inserted between the drain of the bottom transistor (J2) and the drain resistor Rd". So, the bottom transistor J2 forms a "common source" but the top transistor J1 forms a voltage follower driven by a constant gate voltage, which if you want you, can call it "common gate".

@Circuitfantasist of course I should have said source follower, not common source. But that is still not what it is. The small signal input for the isolation transistor is at the source, which makes it a common gate configuration.

@Bart, That's right... But presented like this - a "common-base stage" controlled by current, it looks strange and incomprehensible. The point of this configuration is not visible because there is no gain. Meaning is seen when it is controlled by voltage. So, it is more understandable if it is presented as a source follower with a constant gate voltage (that is, as a voltage stabilizer).

The upper cascode transistor doesn't need to be identical. It could even be a cheap NPN.

@Circuitfantasist the way I usually visualize this is as the top transistor as a low impedance load to the bottom half. Because it is so low impedance, it takes most of the current, so only a small amount goes in the parasitic capacitance, thereby reducing the Miller effect. One could also say that because of the low load impedance, the amplification at the drain is virtually zero. At the same time, almost the full current comes out of the drain of the top transistor. It's as if the top stage isolates the bottom stage from its output voltage, hence my using the moniker "isolation transistor".

@tobalt, Exactly! Its role is not vitally important...

@Bart, I like your explanations, especially the "isolation transistor"! Don't you think its source behaves as a virtual ground?

@Circuitfantasist "Don't you think its source behaves as a virtual ground?" Almost, but not quiet. It has a low impedance, but unequal to a short nonetheless. There will still be some voltage which feeds back into the parasitic capacitance, albeit at a much higher cutoff frequency due to the smaller RC time constant. But as an approximation, yes, I think it could be.

@Bart, I remembered that years ago I asked such a question on ResearchGate - Is there any relation between the common-base amplifier and op-amp inverting amplifier?. You might be interested in seeing it...

@normalchemist if you want to limit your amplifier to just an inverting cascode stage (I also hope your load is in the order of 10kohms or more; otherwise, it'll considerably change your gain as it'll be in parallel with Rd), then the choices of Rd and Rs are simply dictated by the gain you want to achieve. Now, Rs fixes the current through both transistors (assuming they are in saturation) how much should Rd be? that depends on the output swing you're looking for. If you make it very large, you'll increase the quiescent voltage drop across Rd and the cascode will have less saturation margin.

@normalchemist by saturation margin, I mean, when you have a downward swing at the drain of the cascode, its vds will reduce; you have to make sure this will not go down as much as Vgs-Vpinchoff.

as you can see, there are many free independent variables that dictate the design. Hence my questions about more specs from your design.

@ErnestoG I added a small bit in my question about the specifics for the design; namely, I think I need something low noise given that the signal I am amplifying is in the nanovolt-microvolt range, which is why I am more determined to make this work with JFETs as opposed to another transistor species. I think I just need to get it to a high enough level to send through an op-amp that can handle the majority of the gain.

@ErnestoG After thinking about this for a bit, it sounds like a cascode cascade with incremental stages of smaller gain up to a level that an op amp can reliably amplify would be a more robust architecture?

@ErnestoG 38kHz was a somewhat arbitrary choice, I actually plan on using this as an amplifier for a spectrometer operating in the MHz regime, but I think the only difference at that point would be the choice of op amp. I figured the cascode was the correct choice to reduce distortion due to input capacitance at those frequencies, but I will certainly take a look at the articles you have linked.

*disturbances at AC

That being said, I'd strongly suggest implementing JFETs input stages as they appear in the articles I sent. Since you are amplifying a voltage, you would want a large loop gain with shunt feedback at the output and series feedback the input (basically, the type of a feedback of a non-inverting voltage amplifier). It can also be that an inverting type of op-amp amplifier might better, and it also will simplify the implementation of your input stage as you can simply use a single-ended one.