2. In the above circuit, the
initial conditions are all zero and the op-amp is ideal. (15
pts)
A. Determine the transfer function, 𝐻(𝑠)=𝑉𝑂(𝑠)𝑉𝐼(𝑠) in one of the
following forms:
i) 𝐻(𝑠)=𝑘𝑐𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants;
ii) 𝐻(𝑠)=𝑘𝑠2𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants;
iii) 𝐻(𝑠)=𝑘𝑏𝑠𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants;
iv) 𝐻(𝑠)=𝑘𝑠2+𝑐𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants.
B. Determine the type of filter implemented by the circuit.
C. If the circuit is a low-pass or high-pass filter, do Parts i and
ii. If the circuit is a band-pass or band-reject filter, do Parts
iii.
i) Determine the order of the filter.
ii) Find the values for the relevant components that will yield a
gain of 8 under the requirement that ALL resistors must have a
resistance greater than or equal to 1kΩ.
iii) Find the values for the relevant components that will yield a
bandwidth of
𝛽=12500 rad/s and a gain of 8 at the resonance frequency under the
requirement that ALL resistors must have a resistance greater than
or equal to 1kΩ.
с RO R + V;(t) + Vo(t) bs 2. In the above circuit, the initial conditions are all zero and the op-amp is ideal. (15 pts) A. Determine the transfer function, H(S) Vo(s) in one of the following forms: V;(s) i) H(S) =k Sa+bs+c' where k, b and c are constants; s2 ii) H(S) = k where k, b and c are constants; 52+bs+c' iii) H(S) = k where k, b and c are constants; $2+bs+c' Sa+C iv) H(S) = k where k, b and c are constants. $2+bs+c' B. Determine the type of filter implemented by the circuit. C. If the circuit is a low-pass or high-pass filter, do Parts i and ii. If the circuit is a band- pass or band-reject filter, do Parts iii. i) Determine the order of the filter. ii) Find the values for the relevant components that will yield a gain of 8 under the requirement that ALL resistors must have a resistance greater than or equal to 1kl. iii) Find the values for the relevant components that will yield a bandwidth of B = 12500 rad/s and a gain of 8 at the resonance frequency under the requirement that ALL resistors must have a resistance greater than or equal to 1kN.