A circuit has the following transfer function:

\[
T(s)=\frac{s+10^{6}}{s^{2}+B s+10^{6}}
\]

\(B\) is a constant multiplier that can change the behavior of the circuit. With \(B=50\), use MATLAB to plot the Bode magnitude diagram of the transfer function. Repeat for \(B=500\) and \(B=\) 5000. From the plot determine the following:

(a) The nature of the filter, that is, LP, HP, BP, BR. Does changing \(B\) alter the nature of the circuit?

(b) The cutoff frequency in radians. Does changing \(B\) alter the cutoff frequency of the circuit?

(c) In the case where \(B=50\), at what frequency does the peak value of the transfer function occur? Is it at the cutoff frequency?

(d) Is an OP AMP required to achieve this transfer function? Explain.