Using a computer simulation, verify the results of Example $11\mathrm{.}12.$

EXAMPLE $11\mathrm{.}12$

Objective: Calculate the differential$-$mode voltage gain of a MOSFET diff$-$amp with a cascode active load.

Consider the diff$-$amp shown in Figure $11\mathrm{.}36.$ Assume the circuit and transistor parameters are the same as in Example $11\mathrm{.}11.$

Solution: The transistor transconductance is

$g_m=2\sqrt[\phantom{2}]{K_n{I}_{DQ}}=2\sqrt[\phantom{2}]{(\frac{0\mathrm{.}08}{2})(10)(0\mathrm{.}1)}=0\mathrm{.}40m\frac{A}{V}$

The output resistance of the individual transistors is

$r_o=\frac{1}{I_{DQ}}=\frac{1}{(0\mathrm{.}02)(0\mathrm{.}1)}=500k$

The output resistance of the cascode active load is then

$R_o=r_{o4}+r_{o6}(1+g_m{r}_{o4})=0\mathrm{.}5+0\mathrm{.}5[1+(0\mathrm{.}40)(500)]=101M$

The differential$-$mode voltage gain is then found to be

$A_d=g_m(r_{o2}||R_o)=(0\mathrm{.}40)(500||101000)=200$

Comment: Since $R_o{r}_{o2},$ the voltage gain is now essentially equal to $A_d=g_m{r}_{o2}$ which is twice as large as the gain calculated in Example $11\mathrm{.}11.$