DC Analysis of MOSFET Active Load Circuit:-

Transistors M1 and M2 form a PMOS active load circuit, and M2 is the active load device. We will consider the voltage transfer function of Vo versus V1 for this circuit.

The reference current may be written in the form

$I_{REF}=K_{pl}(V_{SG}+V_{TP1})^2(1+\lambda_1V_{SD1})$

The drain current I2 is

$l_2=K_{p2}(V_{SG}+V_{TP2})^2(1+\lambda_2 V_{SD2})$

If we assume that M1 and M2 are identical, then $\lambda_1 = \lambda_2 = \lambda_p$, VTP1 = VTP2 and Kp1 = Kp2 = Kp. Combining equations, we find the output voltage as

$V_O=\frac{[1+\lambda_p(V^+-V_{SG})]}{\lambda_n+\lambda_p}-\frac{K_n(V_1-V_{TN})^2}{I_{REF}(\lambda_n+\lambda_p)}$ - (1)

The above equations describes the Vo versus V1 characteristics of the circuit, provided that both M0 and M2 remain biased in their saturation regions.

Figure shows a sketch of the voltage transfer characteristics. If the circuit is to be used as a small-signal amplifier, then a Q-point must be established, as indicated in the figure, for maximum symmetrical swing.. As before, the input transition region in which both M0 and M2 are biased in the saturation region is quite narrow. A sinusoidal variation in the input voltage produces a sinusoidal variation in the output voltage as shown in the figure.

Voltage gain of MOSFET Active Load Circuit:-

The small-signal voltage gain of a MOSFET circuit with an active load is also the slope of the voltage transfer function curve at the Q-point. Taking the derivative of equation (1) with respect to V1, we obtain

$A_v=\frac{dV_O}{dV_1}=\frac{-2K_n(V_t-V_{TN})}{I_{REF}(\lambda_n+\lambda_p)}$ - (2)

The transconductance of the driver transistor is gm = 2kn( V1 - Vtn ). Since M1 and M2 are assumed to be identical, then Io = Iref and the small signal transistor resistances are

$r_{on}=1/\lambda_{n}I_{REF}$ and $r_{op}=1/\lambda_p I_{REF}$

From equation (2), the small signal open circuit voltage gain can now be written as

$A_v = \frac{-g_m}{(\frac{1}{r_{on}}+\frac{1}{r_{op}})} = -g_m(r_{on} \parallel r_{op})$