The op amp differentiator of Problem 7.54 can be stabilized by inserting a series resistance Rc, as in Fig. P7.59, to create a LHP transmission zero at fz 5 1y(2RcC). As we know, a LHP zero...

The op amp differentiator of Problem 7.54 can be stabilized by inserting a series resistance Rc, as in Fig. P7.59, to create a LHP transmission zero at fz 5 1y(2RcC). As we know, a LHP zero contributes phase lead, and as such it can be positioned so as to raise m. (a) Assuming the component values of Problem 7.54, sketch and label the linearized Bode plots of uav( jf )u and u1yv( jf )u before compensation (i.e. with Rc 5 0). Locate the frequency fx at which the two curves intersect and fi nd the value of Rc that makes fz 5 fx (this will result in m > 458). How does the u1yv( jf )u curve look after compensation? Hint: the presence of Rc results in the highfrequency asymptote 1yv` 5 1 1 RyRc. (b) Obtain an expression for v( jf ) 5 VnyVo with Vi 5 0, and then use trial and error to fi nd the actual values of fx, x, and m.