Q$1.$ For the circuits given in Figure $1,$ solve the questions Q$1.$a$-$d$.$ Assume output resistances $(r_o)$ of all transistors are $50k$ and the transconductances of the MOSFETs are $4m\frac{A}{V}.$ The PMOS transistors M$3$ and M$4$ have the same W$/$L ratio. The $$ of the Q$1$ transistor is $100.$

Q$1.$a$.(21$ pts$.)$ Calculate the small$-$signal resistances $R_u,R_d$ and $R_{in}$ as shown in Fig. $1.$a$.$

$R_u=,R_d=,R_{in}=$

Q$1.$b$.(14$ pts$.)$ Calculate the open circuit voltage gain $A_{v0}=\frac{v_0}{v_{in}}$ of the circuit in Fig. $1.$a$.$

$A_{v_0}=$