What is Approximation?

Approximation refers to a value or quantity that is nearly but not exactly correct. Approximation of analog filter is required because the practical characteristic of a filter is not identical to ideal characteristics. So, in order to realize ideal filters, we need infinite number of components which might be impracticable. Hence, an approximation of practical filter is realized.

fig: Ideal LPF and Non-Ideal LPF

Signals become contaminated with high frequency signal. It is evident that low pass filter is required to remove such unwanted signals from the useful one. For a normalize frequency i.e., 0 = 1, the amplitude T(jw) is constant and above this frequency it is zero. Pass band and stop band are clearly separated at wo = 1. Since the ideal response cannot be achieved. We make the approximation based on the ideal response. The idea is to make the magnitude T(jw) nearly constant in passband and with a sharp roll off (n-pole roll –off). Where ‘n’ will be large no if abrupt transition from PB to SB is desired.

fig: Response of LPF (Gain and Attenuation Relationship)

Desirable features of low pass Approximation (Requirements) 

• • Should have minimum pass band attenuation αp

  • Should have maximum stop band attenuation αs

  • Should be small pass band variation (small ripples)

  • Should have a low transition band ratio (( wswp ) nearly equal to 1)

  • Should be a simple network

There are no networks that satisfies all the above points, so a tradeoff is needed between circuit complexity and response. So based on it, there are different approximations.

• • Butterworth

  • Chebyshev

  • Inverse Chebyshev

  • Ellipse (Cauer)

  • Bessel-Thompson