Understanding Analog Filters: Types, Designs, and Frequency Response Characteristics

Introduction

In this article, we explore the critical role of electronic filters in signal conditioning. Categorized into active and passive types, these filters serve as essential components in any electronic system. Their primary function is to permit useful signals to pass through with minimal attenuation, while effectively blocking or reflecting unwanted signals. Based on specific performance requirements, signal conditioning shapes the characteristics of these signals for optimized system performance. We will delve into the four fundamental types of filters and provide real-world examples to illustrate their applications 

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

First Order Filter Bode Plots

Second Order Filter Bode Plots

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/