Answer to Question #246878 in Mechanical Engineering for MDS

Question #246878

QUESTION 3 Figure 2 depicts the schematic diagram of a phase shift oscillator . Figure 2 Phase shift oscillator for Question 3 The circuit will oscillate if it is designed to have poles on the jv-axis. 3.1Show that the transfer function for the passive network in the circuit is given by 𝑉2(𝑠) 𝑉1(𝑠) = βˆ’1 (1 + 1 𝑠𝑅𝐢) (2 + 1 𝑠𝑅𝐢) 2 βˆ’ 3 βˆ’ 2 𝑠𝑅𝐢 (10) 3.2Show that the oscillator’s characteristic equation is given by 1 βˆ’ 𝐾 1 (1 + 1 𝑠𝑅𝐢) (2 + 1 𝑠𝑅𝐢) 2 βˆ’ 3 βˆ’ 2 𝑠𝑅𝐢 = 0 (10) [20]


1
Expert's answer
2021-10-06T00:30:51-0400

3.1)

We know that;

"\\frac{V_f(s)}{V_2(s)}=\\frac{1}{1+\\frac{6}{sCR}+\\frac{5}{s^{2}C^{2}R^{2}}+\\frac{1}{s^{3}C^{3}R^{3}}}"

"V_1(s)=\\frac{R}{R+\\frac{1}{Cs}}V_f(s)"

"\\frac{RCs+1}{RCs}V_1(s)=V_f(s)"

"\\frac{V_2(s)}{V_1(s)}=\\frac{-1}{(1+1sRC)(2+1sRC)^{2}}-3-2sRC"


3.2)

1+AB=0

"1+(\\frac{R_1}{R_2})\\frac{1}{1+\\frac{6}{sRC}+\\frac{5}{s^{2}R^{2}C^{2}}+\\frac{1}{s^{3}R^{3}C^{3}}}"


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