Post on 19-Dec-2015
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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