Understanding Analog Filters: Types, Designs, and Frequency Response Characteristics
Introduction
Electronic filters are used everywhere inside the electronic system. Its primary purpose is signal conditioning. Signal conditioning is based on performance requirements. In this article, we will go over basic four types of filter and filter examples.
Background
Filter Type
Low Pass Filter (LPF)
LPF passes low frequency part of the signal while attenuates high frequency part of the signal.
1st Order Analog Filter
Series R Shunt C
|--- R ---|---
| |
| --- C
| ---
| |
|---------|---
Series L Shunt R
|--- L ---|---
| |
| R
|
|---------|---
2nd Order Analog Filter
Series R+ L Shunt C
|--- R + L ---|---
| |
| --- C
| ---
| |
|-------------|---
Cascade two first order filter (RC->RC or LR->LR)
High Pass Filter (HPF)
HPF passes high frequency part of the signal while attenuates the low frequency of the signal.
1st Order Analog Filter
Series C Shunt R
|--- C ---|---
| |
| R
|
|---------|---
Series R Shunt L
|--- R ---|---
| |
| L
|
|---------|---
2nd Order Analog Filter
Series R+C Shunt L
|--- R + C ---|---
| |
| L
|
|-------------|---
Cascade two first order filter (CR->CR or RL->RL)
Band Pass Filter
BPF passes a band of frequency of the signal while attenuates left and right parts outside of the band of the signal.
It's an inherently a 2nd order filter due to a minimum two reactive components
Cascade a LPF and HPF forms a bandpass filter where bandwidth of lower cutoff point is defined by HPF and higher cutoff point is defined by LPF
Note: the above statement would be the transfer function H(s) would be Hhpf(s)*Hlpf(s) if there is a buffer between two circuits to eliminate any loading effect.
Series LC bandpass
Series L+C and Shunt R where bandwidth is determined by the resonance point of L+C, where impedance of C is high and dominate at lower frequency forming an effective series C shunt R HPF defining the lower cutoff point, and impedance of L is high and dominates at higher frequency forming an effective series R shunt R LPF defining the higher cutoff point.
|--- L + C ---|---
| |
| R
|
|-------------|---
Parallel LC Bandpass
Series R and Shunt L||C where bandwidth is determined by the resonance point of L+C, where impedance of L is low and dominate at lower frequency forming an effective series R shunt L HPF defining the lower cutoff point, and impedance of C is low and dominates at higher frequency forming an effective series R shunt C LPF defining the higher cutoff point
|--- R ---|---
| |
| L || C
|
|---------|---
Band Stop Filter
BSP filter attenuates a band of frequency of the signal (stopband) while passes signal to the left and right parts outside of the stopband.
It's inherently the same design as that of Bandpass filter where LPF cutoff point is used for low frequency cutoff and HPF cutoff is used for high frequency cutoff.
Note: however the transfer H(s) function needs to be summed
Series LC bandStop
Series R and Shunt L+C where bandwidth is determined by the resonance point of L+C, where impedance of C is high and dominate at lower frequency forming an effective series R shunt C LPF, and impedance of L is high and dominates at higher frequency forming an effective series R shunt L HPF.
|--- R ---|---
| |
| L + C
|
|---------|---
Parallel LC Bandpass
Series L||C shunt R where bandwidth is determined by the resonance point of L+C, where impedance of L is low and dominate at lower frequency forming an effective series L shunt R LPF, and impedance of C is low and dominates at higher frequency forming an effective series C shunt R HPF.
|--- L || C ---|---
| |
| R
|
|-------------|---
Filter Characteristics
Bode Plot
Amplitude vs frequency
it's a plot of the gain equation where absolute gain magnitude is the amplitude
Phase vs frequency
It's a plot of the gain equation where the phase information of gain is plotted as the phase.
3dB cut off frequency
the frequency at which the filter' amplitude is -3dB of the pass band
A filter is characterized by its 3dB cut off point
Roll off rate
Roll off rate determines the sharpness/steepness of the filter edge. Ideally, the filter has perfect brick wall like edge; however, real filter has different roll off at different attenuation rates.
Example, 1st order analog signal is 20 dB/decade
with each higher order, 20 more dB/decade roll off is added (i.e 2nd order LC filter has 40 db/decade roll off)
Passband
It's a region of frequency range of the filter where the amplitude is unaltered.
Frequency range is determined by the 3dB cuff of frequency
Stopband
It's a region of frequency range of the filter where the amplitude is heavily attenuated
Frequency range is determined by the 3dB cuff of frequency
Below is depiction for for filter characteristics:
Here's how the key characteristics of a filter are represented in these plots:
3dB cutoff: The red dashed line marks the -3dB point. For the LPF and HPF, frequencies at which the magnitude response crosses this line are the 3dB cutoff points. For the BPF and BSF, the band of frequencies between the two points where the magnitude response crosses this line is the passband (for BPF) or stopband (for BSF). The 3dB cutoff frequencies are marked with arrows and labels.
Roll-off rate: The roll-off rate is the slope of the magnitude response in the stopband. For a first order filter, this is typically -20dB per decade. For a second order filter, it's -40dB per decade. In the plots, you can see how quickly the magnitude response decreases beyond the 3dB cutoff points.
Passband: The passband is the frequency range where the filter does not significantly attenuate the signal. On the plots, it's the flat area of the magnitude response before the roll-off begins. For the BPF, it's the "bump" in the middle of the plot.
Stopband: The stopband is the frequency range where the filter significantly attenuates the signal. On the plots, it's where the magnitude response has dropped off after the roll-off point. For the BSF, it's the "dip" in the middle of the plot.
Analog Filter
Passive Filter
Passive filter contains or resistor, inductor, and capacitors.
Active Filter
Active filter contains an operation Op-Amp.
Pros are
Provide amplification
a 2nd order filter design can be achieved without an inductor
Cons
Filter upper boundary is band limited by Op-Amp's limited gain product bandwidth.
Digital Filter
Finite Impulse Response (FIR)
Uses only only multiple accumulate computation
Delay is the same for all frequencies which has no group delay distortion
Infinite Impulse Response (IIR)
Uses feedback and feedforward network as part of filtering algorithm
Inherently unstable hence careful feedback design must be utilized
uses less coefficient to generate similar frequency response.
Computation friendly due to smaller length of convolution
Design Analysis
Digital Circuit
a RC LPF with low cutoff is used at a digital input to filter out unwanted noise from miss-trigger the digital input
a RC LPF is used to slow the edge of the low speed interface to reduce unwanted signal reflection due to sharp edges of the signal.
Note: sharp edges of a signal contains high frequency content which as a results, the trace exhibits transmission line effect, which causes signal reflection due to high input impedance of the receiver for a low speed interface.
Power Circuit
a ferrite bead (essentially a low pass filter) in series of power rail is used to filter power noise on supply rails
a ferrite bead has high impedance at high frequencies hence stop any high frequency noises from going in through.
RF Desense Circuit
a shunt RF capacitor (modeled by a series RLC) is used to provide bandstand filtering for radiated emission because the RF capacitor impedance is low at resonance for a series LC circuit (LC impedance becomes 0 at resonance leaving R), hence shunting RF noise energy to ground in the vicinity of RF capacitor self resonance frequency.
Selecting this self resonance frequency point to match where the noise frequency makes the filter most useful.
Audio Processing
FIR filter is used to preserve linear phase of an audio signal when computation power and group delay is not an issue to prevent any distortion.
It's common to see FIR filter used in linear audio post processing such as a equalizer, cross-over filter ,etc.
IIR Filter
It's commonly used in simple digital IC that has limited or no DSP computation hardware for fast computation and low delay.
It's common to see FIR filter is used digital amplifiers where the filter response is limited to few frequency bands and limited frequency response tuning, but sufficient for the application.
Q&A
What is the most commonly used filter for electronic system design for digital designers?
Low Pass filter!
RC low pass filter is widely used for stabilizing digital signals such as enable pin, reset pin, and interrupt pints of a digital circuit.
RC low pass filter is also used for circuit delay for turning on specific chip such as power regulator output.
RC low pass filter is used to filter differential noise and common mode noise for differential input of an op-amp
More complex noise filtering uses different materials such as ferrite bead and common mode chokes as low pass filters but uses magnetic materials.
Summary & Conclusion
Analog filter can be think as voltage resistor divider using capacitor or inductor where its reactive nature causes its impedance vary with frequency. Hence the resultant voltage varies across different frequency due to different resistor divider ratio.
Low Pass Filter (LPF) attenuates high frequency signal
HPF filter attenuates low frequency signal.
Combination of LPF and HPF filter and arrangement of respective filter cutoff points forms shape of band-pass or band-stop filters
Higher order filtering (i.e sharper roll off) can be achieved using more reactive components (either L or C)
LC resonance behavior sets the cutoff points of the filter
Digital filters are easier to design but at much higher cost and complexity due to special hardware needed.
Filter is widely used to conditioning signal transmissio within the electronic system. Understanding basic filter type and different real world filter components and application enables electronic system engineers to break down any filter design into its basics four types. We omitted more complex filter design used in RF world such as Chebychev, Butterworth, Ellipication,etc but provided link for anyone to play around with.
Further Reading/Practice
"Analog Filters", https://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdf
"Filter Design and Tool", http://sim.okawa-denshi.jp/en/Fkeisan.htm
"RF LC RF Design Tool", https://rf-tools.com/lc-filter/