Question

Design a basic band pass filter comprising of a series combination of a T-section high pass filter and a T-section low pass filter to pass the frequencies between 10 kHz and 100 kHz. Take K = 100 for HPF and K = 400 for LPF

Answer 1

Please see a simple design for a series combination. Actually there should be some isolation or matching of impedance (load ) between the two filters.

We could also do a design of a band pass filter (constant K) with T-network of L and C.

For the simple design as shown:

HPF:

   K = √(Z1 Z2) = √[L₂ / C₂] = 100
      =>  L₂ = 10,000 * C₂
   f₀ = cut of frequency = 10 kHz
   ω₀ = 2 π * 10 kHz = 1 / [ 2√(L₂ C₂) ]
      =>  L₂ C₂ = 1 / (16 π² f₀²) = 63.325 * 10⁻¹²

   Solving for C₂ and L₂, we get   C₂ = 0.0795 μF  and  L₂ = 795 μH

LPF:  design:

    K = 400 = √(L/C)
         => L₁ = 160,000 * C₁
    f₀ = cut of frequency =100 kHz
    ω₀ = 2 π * 100 kHz = 2 /√(L₁ C₁)
         =>  L₁ C₁ = 10.13 * 10⁻¹²
  Solving for  C₁ we get  7.95  pF 
                   L₁ = 1.273 mH