FILTERS & THEIR PARAMETERS

Rachit Manchalwar | D063

WHAT ARE FILTERS? Filters are circuits which separate and allow only signals of specific frequencies to pass through.

4 categories – • Low Pass• High Pass• Band Pass• Band Stop

LOW FREQUENCY FILTERS• Frequency range in kHz

• Plot of Gain v/s. Frequency

LOW FREQUENCY FILTERS

HIGH FREQUENCY FILTERS• Frequency Range of GHz• Plot of Attenuation (α) v/s. Frequency

HIGH FREQUENCY FILTERS

FILTER CIRCUITS

FILTERS TO BE DISCUSSED1. Butterworth (Binomial) Filter

2. Chebyshev Filter

TYPES OF FILTERS

BUTTERWORTH FILTERS Also called as Maximally Flat Filter. No ripple permitted in attenuation profile Insertion Loss can be determined from the loss factor;

N = Order of the filterΩ = Normalized frequency

BUTTERWORTH FILTERS

ATTENUATION PROFILE FOR BUTTERWORTH FILTER FOR VARIOUS FILTER ORDERS

CHEBYSHEV FILTERS Also called as Equiripple Filter.

Insertion Loss will be as folllows;

IL = , where•TN(Ω) = , for |Ω|≤1•TN(Ω) = , for |Ω|≥1

CHEBYSHEV FILTERS

ATTENUATION RESPONSE FOR CHEBYSHEV

COMPARISON

CONCLUSION Chebyshev filter has the steepest slope of the attenuation profile.

Linear phase filter exhibits lowest roll-off.

Thus, Chebyshev is selected when:1. If a sharp transition from PB to SB is required2. Ripples can be tolerated

Also, its Attenuation at cut-off frequency is equal to the ripple size in PB.

Linear phase can be used for modulation and mixer circuits.

A COMPARISON BETWEEN BUTTERWORTH AND CHEBYSHEV

Butterworth Filter

• Magnitude response decreases with increase in frequency (from 0 - ∞)

• Width of Transition band is more.

• The order of filter is more, for same specifications, as compared to chebyshev. Hence no. of components required to construct a filter are less.

Chebyshev Filter

• Magnitude response fluctuates or shows ripples in PB and SB depending on the type of filter.

• Width of Transition band is comparatively less.

• The order of filter is less, for same specifications, as compared to chebyshev. Hence no. of components required to construct a filter are more.

PARAMETERS OF FILTERS Insertion Loss: Power Loss in PassbandIL =

WherePIN = Input PowerPL = Load Power = Reflection Coefficient

PARAMETERS OF FILTERS Ripple: Difference between maximum and minimum amplitude response in dB or nepers. We can control the amplitude of the ripple in Chebyshev Filters

PARAMETERS OF FILTERS Bandwidth: Difference between the upper and lower cut-off frequencies in Band Pass FiltersRecorded at 3dB attenuation points above the passband.BW3dB =

PARAMETERS OF FILTERS Shape Factor: Sharpness of filter responseRatio of 60dB and 3dB bandwidths SF =

PARAMETERS OF FILTERS Rejection:

Rejection is the finite attenuation level in practical filtersDue to limited number of filter componentsUsually 60dB (since can be readily combined with shape factor)

PARAMETERS OF FILTERS Quality Factor: Ratio of average stored energy to energy loss per cycle at resonant frequency.

ATTENUATION PROFILE OF BPF

ATTENUATION AND ORDER - IDEAL

ATTENUATION AND ORDER - PRACTICAL

ATTENUATION AND ORDER Ideally, there should infinite attenuation from cut-off frequency

Practically not attainable

Steep transition from PB to SB can be achieved by increasing order of filter.

Steeper transition to stopband comes at a price – higher ripple in passband

THANK YOU