Filters Flashcards
What are 5 types of filters? What do they block?
> Low-pass: Blocks all high frequency signals
High-pass: Blocks all low frequency signals
Band-pass: Blocks all frequencies above one threshold and below another threshold
Band-stop: Blocks all frequencies between two thresholds
All-pass: Doesn’t block any frequencies but changes the phase of the signal:
What is a brick wall filter?
This is an ideal filter where all frequencies that are supposed to be blocked are fully attenuated.
What are the 3 phases of a frequency response of a filter?
> Passband: The range of a filters frequency response where signals are unchanged in amplitude (less than -3dB amplitude change)
Transition band: The range of frequencies where the amplitude is decreasing/increasing between the passband and stop band
Stopband: The range of frequencies where the amplitude of the signals at the corresponding frequencies is 0.
Define ‘cut-off’
Frequency at which the power of that frequency is half the value it has in the passband. (-3dB point)
Define ‘transfer function’
Mathematical description of how the output signal responds relative to the input signal
Define ‘poles’
The number of frequency dependent elements
Define ‘Roll-off’
The steepness of the initial transition between the passband and the stopband
Define ‘Ripple’
The amount of variation in the passband and stopband attenuation.
Define ‘Phase linearity’
The amount of distortion to the phase of the signals in the passband
Define ‘Active filter’
Adds power to the signal (op-amp filters are therefore active filters)
What is the relationship between roll off and ripple?
Accepting a bit of ripple improves the roll-off of the transition band
Why do filters affect phase?
For any filter, it takes a finite amount of time for the signal to pass through. If this time delay is equal for all frequencies, then the phase shift will be a linear function of frequency.
What are the 4 types of filter characteristics?
> Bessel
Butterworth
Chebyshev
Elliptic
What are the frequency response features and applications (2) of a Bessel Filter?
Frequency response features:
> Initial roll-off: Poor
> Ripple: No passband ripple
> Phase linearity: Excellent
Applications:
> Use when minimum distortion to wide-band signals is required
> Audio applications
What are the frequency response features and applications (4) of a Butterworth Filter?
Frequency response features:
> Initial roll-off: Moderate
> Ripple: No passband ripple
> Phase linearity: Moderate
Applications: > When you need minimum distortion of passband frequencies > Easier to design > Reconstruction for DACs > Audio applications
What are the frequency response features and applications (3) of a Chebyshev Filter?
Frequency response features:
> Initial roll-off: Steep
> Ripple: Ripple in either passband or stopband
> Phase linearity: Poor
Applications:
> Good when closely spaced adjacent signals need to be blocked
> Anti-aliasing for ADCs
> Reconstruction for DACs
What are the frequency response features an Elliptic Filter?
> Initial roll-off: Very steep
> Ripple: Ripple in both the passband and stopband
What is an RC filter?
A filter formed from a capacitor and a resistor.
What is the circuit for an RC low-pass filter?
[Picture23]
What is the circuit for an RC high-pass filter?
[Picture24]
How many poles is an RC filter?
> 1 pole
> only the capacitor is frequency dependent
What is the roll off of an RC filter?
> 6dB / octave
> 20dB / decade
What happens if you cascade RC filters?
Does not improve the roll-off because each stage is loaded by the previous stage
What happens if you cascade RC filters with buffers in between?
Does not improve the roll-off much but buffers can alleviate the loading effect, but the improvement is only moderate.
What is an LC filter?
A filter formed from a capacitor and an inductor.
What is the circuit for an LC low-pass filter?
[Picture25]
What is the circuit for an LC high-pass filter?
[Picture26]
How many poles is an LC filter?
> 2 pole filter
> because both the capacitor and inductor are frequency dependent
What is the roll off of an LC filter?
> 12dB / octave
> 40dB / decade
What of the frequency filter characteristics can an LC filter have?
> Butterworth
> Chebychev filter
What is the problem with using LC filters in circuits?
For low frequencies (< 100kHz), the inductor needs to be physically large which is problematic for small portable circuits.
What is a Sallen-key filter?
This is an active filter that has the overall transfer functions that is equivalent to a high-pass or low-pass LC filter.
What is the general tropology of a Sallen-Key filter?
[Picture27]
What is the transfer function of a Sallen-key filter?
[Picture28]
What is the low-pass tropology of a Sallen-Key filter?
[Picture29]
What is the high-pass tropology of a Sallen-Key filter?
[Picture30]
What is equal component design for a Sallen-Key filter?
> R1 = R2 = R
> C1 = C2 = C
What is the equation for the cut off frequency for a Sallen-Key filter?
ω0 = 1 / RC
What is the equation for the gain resistors for a Sallen-Key filter?
R_An = R_Bn(K_n - 1)
What is the equation for the gain resistors for a Sallen-Key Chebyshev filter?
ω_0 = 1 / (R×C×c_n)
What is K for the gain resistor equation?
> This is a value of the gain of each stage.
> The value needs to be looked up in a table
What is the narrow band-pass tropology of a Sallen-Key filter?
[Picture31]
What defines a wide-band or narrow-band filter? What is the equation?
> Wideband is when Q < 10 > Q = ω0 / (ω2 - ω1) - ω0 = Centre frequency - ω1 = Lower cut off - ω2 = Upper cut off
What is the equation for Q in terms of fractional bandwidth?
Q = 1 / fractional_bandwidth
What is another method of forming a wideband-pass filter?
By cascading high-pass and low-pass filters.
