1000 characters left

IIR and Analog Filters - Basic Types

IIR and Analog Filters Passive, Active, Distributed Element and Digital IIR and FIR filters are all supported in FilterSolutions. (See the page:  FIR filters). Analog and IIR filters may all be quickly and easily delay equalized with FilterSolutions real-time updates through all-pass pole/zero manipulation. Passive and active filters may be quickly and easily modified and reanalyzed using the real-time analysis feature. Finite Q factors may be included in the analysis. Digital filters may be modified and analyzed in real time using finite precision analysis.

The following table lists the type of analog and IIR filters supported in FilterSolutions with are Analog and IIR Filter Types:

  • Basic Filters    
  • Advanced Filters          
  • Bessel
  • Chebyshev II
  • Butterworth
  • Delay
  • Chebyshev I
  • Elliptic
  • Gaussian
  • Hourglass
  • Legendre
  • Matched 
  • Custom
  • Raised Cosine

Bessel and Linear Phase Filters

The distinguishing characteristic of Bessel Filters and Linear Phase Filters is the near constant group delay throughout the pass-band of the low-pass filter. FilterSolutions normalizes Bessel and Linear Phase filters such that the prototype high frequency attenuation matches the Butterworth filter. The passband attenuation of the Bessel Filter increases with the order of the filter when this normalization is applied. However, FilterSolutions allows the user the option of selecting the desired passband attenuation in dB. Bessel Filters, modified for equiripple group delay, are frequently referred to as Linear Phase filters.  The equiripple group delay adds efficiency: it remains flat further into the stop band.  (Refer the description of Delay Filters for more on equiripple group delay). Bessel and Linear Phase filters may be further modified to have a stop-band with transmission zeros.

The following is an example of Bessel and Linear Phase low-pass and step responses.

  • Bessel Low Pass filter, 10KR/S Pass Band Frequency 
  • Linear Phase With Equiripple Group Delay, Period=2.0
  • Linear Phase With Equiripple Group Delay, Period=2.6
  • Bessel Modified With Stop Band
  • Linear Phase With Stop Band and Equiripple Group Delay
  • Bessel Low Pass Filter Step Response 

Butterworth Filters

Butterworth Filters result in the flattest pass band and has moderate group delay. A standard Butterworth Filter's pass-band attenuation is: -3.01dB. However, FilterSolutions allows the option of selecting any passband attenuation, in dB, that defines the filters cut-off frequency. FilterSolutions also offers the option of placing user-defined zeros in the stop-band. A filter with stop band zeros is no long a true Butterworth Filter, but is still in the maximally flat filter family. 

Following are examples of Butterworth low-pass, high-pass, band-pass and band-stop filters and the low-pass step response:

  • Butterworth Low Pass filter, 10KHz Pass Band Frequency 
  • Butterworth High Pass filter, 10KHz Pass Band Frequency 
  • Butterworth Band Pass filter, 10KHz Center Frequency, 10KHz Pass Band Width 
  • Butterworth Band Stop filter, 10KHz Center Frequency, 10KHz Pass Band Width 
  • Butterworth Low Pass Step Response 

Chebyshev Type I Filters

The Chebyshev Type I Filter results in the sharpest passband cut-off and contains the largest group delay. The most notable feature of this filter is the magnitude of the ripple in the pass band. The passband attenuation in a standard Chebyshev Type I Filter is defined to be the same value as the passband ripple amplitude.  However, FilterSolutions allows the user the option of selecting any passband attenuation, in dB, that will define the filter’s cut-off frequency. FilterSolutions also offers the user the option of placing user-defined zeros in the stop band, and/or constricting the ripple to a percentage of the passband The following examples are Chebyshev Type I low pass, high pass, band pass and band stop filters and the low-pass step response.

  • Chebyshev Type I Low Pass filter, 1MHz Pass Band Frequency 
  • Chebyshev Type I High Pass filter, 1MHz Pass Band Frequency 
  • Chebyshev Type I Band Pass filter, 1MHz Center Frequency, 1MHz Pass Band Width 
  • Chebyshev Type I Band Stop filter, 1MHz Center Frequency, 1MHz Pass Band Width 
  • Chebyshev Type I Low Pass Step Response 

Gaussian

Gaussian Filters have the most gradual passband roll-off and the lowest group delay. The step response of the Gaussian filter NEVER overshoots the steady state value. As the name states, the Gaussian Filter is derived from the same basic equations used to derive the Gaussian Distribution. The significant characteristic of the Gaussian Filter is that the step response contains no overshoot at all. FilterSolutions normalizes the Gaussian filter such that the prototype high frequency attenuation matches the Butterworth filter. The passband attenuation of the Gaussian Filter increases with the order of the filter when this normalization is applied. However, FilterSolutions allows the user the option of selecting the desired passband attenuation in dB. 

Gaussian Transitional Filters

It is occasionally desirable to transition from a Gaussian frequency response to a steeper roll-off response at a user-defined attenuation point. FilterSolutions provides 3, 6, 9, 12, and 15 dB Transitional Filters. Passband attenuation is always set to 3.01 dB for Gaussian Transitional Filters.

Below are examples of Gaussian, and Gaussian Transitional, low-pass frequency responses and a Gaussian low-pass step response.

  • Gaussian Low Pass filter, 100Hz Pass Band Frequency 
  • Gaussian With -3.01dB Pass Band Attenuation
  • Gaussian With 6dB Transition
  • Gaussian With 15dB Transition
  • Gaussian Step Response 

Legendre

The Legendre filter is a monotonic all-pole filter in that the passband slope is always zero or downward, never upward. The response is optimized for the greatest slope at the pass band edge. Legendre filters are useful in applications which require a steep cutoff at the pass band edge without passband ripple, or in cases where a Chebyshev I filter produces too much group delay at the passband edge.

The following are examples of Legendre low-pass and step responses:

  • Legendre Low Pass filter, 10MHz Pass Band Frequency 
  • Legendre Low Pass filter Pass Band
  • Legendre Band Pass Filter
  • Legendre Time Response

Inverse Legendre

Legendre filter may also be inverted so that the maximum monotonic response is in the stop-band.  This inversion can only be implemented for Active, Switched Capacitor, or Digital Filters. Inverse Legendre Low Pass filter, 10MHz Pass Band Frequency Basic Custom Filters. FilterSolutions supports filters designed from user entered poles and zeros, Biquads, or polynomials, in the program’s Custom windows. Using the transfer function pages one may export transfer functions to the Custom windows, in which one may add, delete, or modify the transfer function. It is possible to create filters composed of a combination of active and passive filters, or filters composed of Elliptic and Butterworth filters.

More in this category: FIR Filters »