$20.$ A certain operational amplifier has an open$-$loop response curve as shown in Figure $7-32.$ A particular application requires a $30$ dB closed$-$loop midrange gain. In order to achieve a $30$ dB gain, compensation must be added because the $30$ dB line intersects the uncompensated openloop gain on the $\backslash (-40\backslash$mathrm$\{$~dB$\}/\backslash )$ decade slope and, therefore, stability is not assured.

$($a$)$ Find the critical frequency of the compensating network such that the $-20$ dB $/$decade slope is lowered to a point where it intersects the $30$ dB gain line.

$($b$)$ Sketch the ideal response curve for the compensating network.

$($c$)$ Sketch the total ideal compensated open$-$loop response.

FIGURE $7-32$