Show that when an opamp has a finite gain of , the transfer function for the discrete-time integrator of Fig. 14.5 is given by                             Vo( ) z Vi ( ) z XXXXXXXXXXC1 C2 ----- ⎝ ⎠ ⎛...

Show that when an opamp has a finite gain of , the transfer function for the discrete-time integrator of Fig. 14.5 is given by

                            Vo( ) z Vi ( ) z ------------ C1 C2 ----- ⎝ ⎠ ⎛ ⎞ 1 z 1 C1 C2A + ---------- ⎝ ⎠ ⎛ ⎞ – 1 ------------------------------------- ⎝ ⎠ ⎜ ⎟

Also show that this transfer function has a dc gain of and a pole that is located slightly to the left of by an amount approximately equal to .