11.10 Exercises

1. The circuit of Figure 11.39 is a VCVS second-order high-pass filter whose transfer function is

   
   

   
   Figure 11.39: Circuit for Exercise 1

   and for given values of a, b, and desired cutoff frequency ? _C, we can calculate the values of C ₁, C ₂, R ₁, R ₂, R ₃, and R ₄ to achieve the desired cutoff frequency ? _C.

   For this circuit,

   
   

   and the gain K is

   
   

   Using these relations, compute the appropriate values of the resistors to achieve the cutoff frequency f _C = 1 KHz. Choose the capacitors as C ₁ = 10/ f _C ? F and C ₂ = C ₁. Plot G( s) versus frequency.

   Solution using MATLAB is highly recommended.

2. The circuit of Figure 11.40 is a VCVS second-order band-pass filter whose transfer function is

   
   

   
   Figure 11.40: Circuit for Exercise 2

   Let ? ₀ = center frequency, ? ₂ = upper cutoff frequency, ? ₁ = lower cutoff frequency, Bandwidth BW = ? ₂ ? ? ₁, and Quality Factor Q = ? ₀/ BW

   We can calculate the values of C ₁, C ₂, R ₁, R ₂, R ₃, and R ₄ to achieve the desired centered frequency ? ₀ and bandwidth BW. For this circuit,

   
   

   Using these relations, compute the...