Figure is the small signal equivalent circuit of the MOSFET active load. The signal voltages Vsg1 and Vsg2 are zero, since there is no ac excitation in this part of the circuit. This means that gm.Vsg2 = 0 and Ro = ro2.

A simple MOSFET amplifier with an active load, and a load resistor RL capacitively coupled to the output. is shown in the figure below.

Figure below shows the small signal equivalent circuit in which the load Rl, the active load resistance ro2 and the output resistance ro of the transistor Mo are included.

The output voltage is Vo = -gm.Vgs (ro || RL || ro2) and since Vgs = V1 where V1 is the ac volatge, the small signal volatge gain is

$$ A_v = \frac{V_0}{V_i} = -g_m (R_0 \space || \space R_l \space || \space r_{o2} ) = \frac{-g_m}{g_0 + g_L + g_{02}}$$

The parameters go and go2 are the output conductances of M0 and M2, and gL is the load conductance.