Problem 6.4 By cascading the Sallen-Key circuit, we can create higher-order filters. Figure P6.4 shows an example of a fourth-order filter. Using Equations (P6.3a) and (P6.3b), write a system of four first-order differ- ential equations to describe the fourth-order Sallen-Key circuit. Remember that v of the first stage will be equal to v of the second stage. 1. Solve for vusing MATLAB's ode45 function. Assume that the input to the circuit v,n is a step voltage that changes from 0 Vto 1 Vat time t0*. Assume the following values for the circuit elements: Ri-R,-R,=R,-5000 G-18000 pF, C2-15000 pF, C3-4.7 F, and C4-10 pF. Use a time interval of t= [0, 0.005] sec and assume uo (0) = ul (0)-U2 (0) = u3 (0) = 0 2. Plot v and vin with respect to t on the same set of axes out Figure P6.4 Fourth-order filter using cascaded Sallen-Key circuits (P6.3a) di olut Wm (P6.3b) 1n Problem 6.4 By cascading the Sallen-Key circuit, we can create higher-order filters. Figure P6.4 shows an example of a fourth-order filter. Using Equations (P6.3a) and (P6.3b), write a system of four first-order differ- ential equations to describe the fourth-order Sallen-Key circuit. Remember that v of the first stage will be equal to v of the second stage. 1. Solve for vusing MATLAB's ode45 function. Assume that the input to the circuit v,n is a step voltage that changes from 0 Vto 1 Vat time t0*. Assume the following values for the circuit elements: Ri-R,-R,=R,-5000 G-18000 pF, C2-15000 pF, C3-4.7 F, and C4-10 pF. Use a time interval of t= [0, 0.005] sec and assume uo (0) = ul (0)-U2 (0) = u3 (0) = 0 2. Plot v and vin with respect to t on the same set of axes out Figure P6.4 Fourth-order filter using cascaded Sallen-Key circuits (P6.3a) di olut Wm (P6.3b) 1n