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HI EVERYONE

the circuit and my solution are (as attachment)

the qustion is

Consider the Wien-Bridge oscillator circuit in the figure.

(a) Write down the circuit equations in state-space in terms of the capacitor voltages 1 and 2.

(b) Obtain the second order differential equations that describe the behaviors of 1 and 2.

(c) Determine the value of =/ for which the voltages will show perfectly sinusoidal variations when they have nonzero initial values. Find the period of oscillation.

(d) Assume that the condition derived in the previous part is satisfied and derive the solutions for voltages 1 and 2 in terms of the initial voltages.

(f) Choose the resistors and the capacitors among the standard values in such a way that the oscillation condition is satisfied and the oscillation frequency is as close as possible to a value that is obtained as follows: =The Month You were Born+611 =The Standard Frequency that is Closest to The list of standard frequencies: {697,770,852,941,1209,1336,1477,1633} Hz The list of standard resistances: {1,1.2,1.5,1.8,2.2,2.7,3.3,3.9,4.7,5.6,6.8,8.2} ×10 Ω The list of standard capacitances: {1,1.5,2.2,3.3,4.7} ×10 F

thanks

the circuit and my solution are (as attachment)

the qustion is

Consider the Wien-Bridge oscillator circuit in the figure.

(a) Write down the circuit equations in state-space in terms of the capacitor voltages 1 and 2.

(b) Obtain the second order differential equations that describe the behaviors of 1 and 2.

(c) Determine the value of =/ for which the voltages will show perfectly sinusoidal variations when they have nonzero initial values. Find the period of oscillation.

(d) Assume that the condition derived in the previous part is satisfied and derive the solutions for voltages 1 and 2 in terms of the initial voltages.

(f) Choose the resistors and the capacitors among the standard values in such a way that the oscillation condition is satisfied and the oscillation frequency is as close as possible to a value that is obtained as follows: =The Month You were Born+611 =The Standard Frequency that is Closest to The list of standard frequencies: {697,770,852,941,1209,1336,1477,1633} Hz The list of standard resistances: {1,1.2,1.5,1.8,2.2,2.7,3.3,3.9,4.7,5.6,6.8,8.2} ×10 Ω The list of standard capacitances: {1,1.5,2.2,3.3,4.7} ×10 F

thanks