Problem $1)$ Design the following $$Phase shift" oscillator for a $10$kHz sine wave output. Note that since the op amp acts as an inverting amplifier $,$a $3-$section R$-$C feedback network is used to provide the necessary $180$ phase shift to affect positive feedback $!$ a$)$Analyze the circuit by writing the appropriate circuit equations, and derive the oscillations conditions: i$)$ oscillations frequency fosc in terms of the time constant TERC. ii$)$ the minimum required Rf in terms of R$.$ NOTE: Recall that for a set of homogeneous' simultaneous algebraic equations to have a non$-$ trivial solution, the system determinant must equal zero $1$ Rf b$)$ Design the circuit $($ R $,$Rt$=?)$ using C$=1$ nf$.410$ c$)$The above oscillator can also work with $($ Ans. Yes $/$no$)$: RS i$)$ more than x$3$ R$-$C sections ii$)$ less than x$3$ R$-$C sections nin ideal