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ELEC2130 - Circuit Design > Filters > Flashcards

Filters Flashcards

1
Q

What are 5 types of filters? What do they block?

A

> 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:

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2
Q

What is a brick wall filter?

A

This is an ideal filter where all frequencies that are supposed to be blocked are fully attenuated.

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3
Q

What are the 3 phases of a frequency response of a filter?

A

> 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.

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4
Q

Define ‘cut-off’

A

Frequency at which the power of that frequency is half the value it has in the passband. (-3dB point)

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5
Q

Define ‘transfer function’

A

Mathematical description of how the output signal responds relative to the input signal

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6
Q

Define ‘poles’

A

The number of frequency dependent elements

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7
Q

Define ‘Roll-off’

A

The steepness of the initial transition between the passband and the stopband

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8
Q

Define ‘Ripple’

A

The amount of variation in the passband and stopband attenuation.

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9
Q

Define ‘Phase linearity’

A

The amount of distortion to the phase of the signals in the passband

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10
Q

Define ‘Active filter’

A

Adds power to the signal (op-amp filters are therefore active filters)

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11
Q

What is the relationship between roll off and ripple?

A

Accepting a bit of ripple improves the roll-off of the transition band

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12
Q

Why do filters affect phase?

A

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.

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13
Q

What are the 4 types of filter characteristics?

A

> Bessel
Butterworth
Chebyshev
Elliptic

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14
Q

What are the frequency response features and applications (2) of a Bessel Filter?

A

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

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15
Q

What are the frequency response features and applications (4) of a Butterworth Filter?

A

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
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16
Q

What are the frequency response features and applications (3) of a Chebyshev Filter?

A

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

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17
Q

What are the frequency response features an Elliptic Filter?

A

> Initial roll-off: Very steep

> Ripple: Ripple in both the passband and stopband

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18
Q

What is an RC filter?

A

A filter formed from a capacitor and a resistor.

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19
Q

What is the circuit for an RC low-pass filter?

A

[Picture23]

20
Q

What is the circuit for an RC high-pass filter?

A

[Picture24]

21
Q

How many poles is an RC filter?

A

> 1 pole

> only the capacitor is frequency dependent

22
Q

What is the roll off of an RC filter?

A

> 6dB / octave

> 20dB / decade

23
Q

What happens if you cascade RC filters?

A

Does not improve the roll-off because each stage is loaded by the previous stage

24
Q

What happens if you cascade RC filters with buffers in between?

A

Does not improve the roll-off much but buffers can alleviate the loading effect, but the improvement is only moderate.

25
Q

What is an LC filter?

A

A filter formed from a capacitor and an inductor.

26
Q

What is the circuit for an LC low-pass filter?

A

[Picture25]

27
Q

What is the circuit for an LC high-pass filter?

A

[Picture26]

28
Q

How many poles is an LC filter?

A

> 2 pole filter

> because both the capacitor and inductor are frequency dependent

29
Q

What is the roll off of an LC filter?

A

> 12dB / octave

> 40dB / decade

30
Q

What of the frequency filter characteristics can an LC filter have?

A

> Butterworth

> Chebychev filter

31
Q

What is the problem with using LC filters in circuits?

A

For low frequencies (< 100kHz), the inductor needs to be physically large which is problematic for small portable circuits.

32
Q

What is a Sallen-key filter?

A

This is an active filter that has the overall transfer functions that is equivalent to a high-pass or low-pass LC filter.

33
Q

What is the general tropology of a Sallen-Key filter?

A

[Picture27]

34
Q

What is the transfer function of a Sallen-key filter?

A

[Picture28]

35
Q

What is the low-pass tropology of a Sallen-Key filter?

A

[Picture29]

36
Q

What is the high-pass tropology of a Sallen-Key filter?

A

[Picture30]

37
Q

What is equal component design for a Sallen-Key filter?

A

> R1 = R2 = R

> C1 = C2 = C

38
Q

What is the equation for the cut off frequency for a Sallen-Key filter?

A

ω0 = 1 / RC

39
Q

What is the equation for the gain resistors for a Sallen-Key filter?

A

R_An = R_Bn(K_n - 1)

40
Q

What is the equation for the gain resistors for a Sallen-Key Chebyshev filter?

A

ω_0 = 1 / (R×C×c_n)

41
Q

What is K for the gain resistor equation?

A

> This is a value of the gain of each stage.

> The value needs to be looked up in a table

42
Q

What is the narrow band-pass tropology of a Sallen-Key filter?

A

[Picture31]

43
Q

What defines a wide-band or narrow-band filter? What is the equation?

A 
> Wideband is when Q < 10
> Q = ω0 / (ω2 - ω1)
- ω0 = Centre frequency
- ω1 = Lower cut off
- ω2 = Upper cut off
44
Q

What is the equation for Q in terms of fractional bandwidth?

A

Q = 1 / fractional_bandwidth

45
Q

What is another method of forming a wideband-pass filter?

A

By cascading high-pass and low-pass filters.

ELEC2130 - Circuit Design (15 decks)

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