$[12$ pts$]$ Given: You have the transfer functions shown below:

$H_1()=\frac{18,000}{j+9,000},H_2()=\frac{j15}{j+2,500}$

$H_3()=\frac{j120,000}{(j+40,000)(j+500)},H_4()=(\frac{j3}{j+20,000}+\frac{600}{j+200})$

Find: Determine $1)$ the type of filter; $2)$ the passband gain; and $3)$ the cut$-$off frequency or frequencies

Solution:

Filter $1$ type

Filter $2$ type

Filter $3$ type

Filter $4$ type

Filter $1$ gain

Filter $2$ gain

Filter $3$ gain

Filter $4$ gain

Filter $1$ freq$($s$)$

Filter $2$ freq$($s$)$

Filter $3$ freq$($s$)$

Filter $4$ freq$($s$)$