Feedback MOSFET circuit anaylsis

Question

I am having difficulty calculating the gain and input resistance of the circuit below.

Neglecting ro, capacitance, and considering Ibias as ideal (infinite resistance), would this mean that the current from M1 is 0 (gm1Vgs)?

And further, indicating that the output voltage is 0?

Regarding the input resistance, I am not sure how to treat small-signal vo. I found a similar case regarding a common source with source degeneration, where the author (Razavi) was calculating the output impedance, and he shorted the small-signal input. I am not sure if this applies to the circuit below. Also, similar to the case above, since gm1Vx = 0, would this mean the input resistance in 0?

M1 is causing me lots of problems. If the input resistance is 0 this would imply that the noise figure would be 0. If you consider a source with resistance Rs, the alpha value (Rin/(Rin+Rs)) is 0, thus the noise from Rs is zero. Meaning the total noise figure would be each noise contribution divided by 0.

Answer 1

Not an answer yet, a few hints though

^{simulate this circuit – Schematic created using CircuitLab}

If you consider just your M1 MOS and its bias source small signal model you may consider \$g_\mathrm{m}v_\mathrm{i}\$ current dependant generator.

It's open circuit, so the only consistent operation point can be "zero output current" i.e.

$$i_\mathrm{o}=g_\mathrm{m}v_\mathrm{i}=0\quad\Rightarrow\quad v_\mathrm{i}=0$$

So, looking at the input port we have \$(v_\mathrm{i}=0\,;\,i_\mathrm{i}=0)\$

---

In these conditions output voltage could be written as output current over output conductance (zero since it's open circuit)

$$v_\mathrm{o}=-\frac{i_\mathrm{o}}{g_\mathrm{o}}=\frac{0}{0}\;\rightarrow\;\mathrm{undefined}$$

Undefined just means that \$v_\mathrm{o}\$ could be any value.

---

Toghether they form one circuit which exhibits zero input voltage and current (sometimes called virtual ground in english speaking countries) and whatever output voltage.

This is similar to an ideal opamp, the only difference is that our circuit output current has to be zero. All the above is similar to a nullor

So now @user367640, any idea??