how to get or derive this function in the red from this circ

how to get or derive this function (in the red) from this circuit ? and how to derive the break or pole frequency.wp1,wp2 and wp3? and what do they mean?

Solution

The transfer function provides a basis for determining important system response characteristics without solving the complete differential equation. As defined, the transfer function is a rational function in the complex variable s = + j, that is H(s) = bmsm + bm1sm1 + ... + b1s + b0 ansn + an1sn1 + ... + a1s + a0 (1) It is often convenient to factor the polynomials in the numerator and denominator, and to write the transfer function in terms of those factors: H(s) = N(s) D(s) = K (s z1)(s z2)...(s zm1)(s zm) (s p1)(s p2)...(s pn1)(s pn) , (2) where the numerator and denominator polynomials, N(s) and D(s), have real coefficients defined by the system’s differential equation and K = bm/an. As written in Eq. (2) the zi’s are the roots of the equation N(s)=0, (3) and are defined to be the system zeros, and the pi’s are the roots of the equation D(s)=0, (4) and are defined to be the system poles. In Eq. (2) the factors in the numerator and denominator are written so that when s = zi the numerator N(s) = 0 and the transfer function vanishes, that is limszi H(s)=0. and similarly when s = pi the denominator polynomial D(s) = 0 and the value of the transfer function becomes unbounded, limspi H(s) =