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Please solve the following problem in MATLAB Problem 6.4 By cascading the Sallen-Key circuit, we can create higher-order filters. Figure P6.4 shows an example of
Please solve the following problem in MATLAB
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 Vout of the first stage will be equal to Vin of the second stage. duout-1 dv, RC (P6.3a) otut 7 di dtRC RC Vout + v1 + RC (P6.3b) 12 Solve for out, using MATLAB's ode45 function. Assume that the input to the circuit vn is a step voltage that changes from 0 V to 1 Vat time t 0.Assume the following values for the circuit elements: R-R2 R R4 G-18000 pF, C2-15000 pF, G-4.7 F, and C4-10 pF. Use a time interval oft= [0, 0.005] o (O) = ui (0)-U2(0)-y(0) = 0 Plot vo, and vn with respect to ton the same set of axes. Sec and assume z C1 V2 4 out 4 Figure P6.4 Fourth-order filter using cascaded Sallen-Key circuits. 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 Vout of the first stage will be equal to Vin of the second stage. duout-1 dv, RC (P6.3a) otut 7 di dtRC RC Vout + v1 + RC (P6.3b) 12 Solve for out, using MATLAB's ode45 function. Assume that the input to the circuit vn is a step voltage that changes from 0 V to 1 Vat time t 0.Assume the following values for the circuit elements: R-R2 R R4 G-18000 pF, C2-15000 pF, G-4.7 F, and C4-10 pF. Use a time interval oft= [0, 0.005] o (O) = ui (0)-U2(0)-y(0) = 0 Plot vo, and vn with respect to ton the same set of axes. Sec and assume z C1 V2 4 out 4 Figure P6.4 Fourth-order filter using cascaded Sallen-Key circuitsStep by Step Solution
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