Hello, friends welcome to another interesting post. In this post, we will have a detailed look at Three Types of Filter Response Characteristics. Every category of filter response either low pass, bandpass, or high pass can be treated through the circuitry element parameters to maintain Butterworth, Chebyshev, or Bessel parameters or characteristics.
Every one of these features is defined through the structure response graphical representation and every one has its benefit in a specific type of application. In this post, we will discuss different circuitry and parameters for understanding the filter response characteristic. So let’s get started with Describe Three Types of Filter Response Characteristics.
Three Types of Filter Response Characteristics
- The Butterworth, Chebyshev, or Bessel response features can be analyzed through the active filter circuitry arrangments through proper usage of specific elements parameters.
- The general comparison of these 3 response characteristics in case of a low pass filter response curvature is can be seen in the below figure.
- High pass and band filter circuitry configuration can also be used to get any one of these parameters.
Butterworth Characteristic
- The Butterworth features offer a flat amplitude response in the passband and roll-off rate of value having -20db/decade/pole.
- The phase response is not straight line though the phase shift of signal moving in the filter changes in a nonlinear fashion with respect to frequency.
- So a pulse given to the filter through a Butterworth response will become overshoot at the output side since every frequency element of the pulse increase and decreasing edges beares a different time delay.
- A filter having the Butterworth response generally works when all types of frequency in the passband should have the saim value of gain.
- The Butterworth response is generally denoted as an extremely flat response.
Chebyshev Characteristic
- Filter configuration with the Chebyshev response characteristic are beneficial in the case of a roll of is needed since it offers a roll-off rate larger than -20db/decade/pole.
- It is a larger rate than the Butterworth. therefore can be used with the Chebyshev response with small working people and small size complicated circuit for a certain roll-off rate.
- This category of filter response is measured through the overshoot or ripples in passband and in case small linear phase response than the Butterworth.
What is Bessel Characteristic
- The Bessel response shows the linear phase features which means that the phase shift rises in a linear fashion according to frequency.
- The output is close to no overshooting at the output with respect to pulse input.
- Due to this cause filter with the Bessel response used for filtering pulse wave by reducing the disturbing the shape of the wave.
What is Damping Factor
- As discussed that an active filter can be created with the Butterworth Chebyshev or through the Bessel response characteristic irrespective of either it is low pass, high pass band pass or band stop type.
- The damping factor of the active filter circuitry configuration finds the response that characteristic the filter show.
- For discussion of the general behavior a general active filter is can be seen in the below figure.
- It comprises of amplifier negative feedback circuitry and filter part.
- The amplifier and feedback are linked in noninverting arrangments.
- The damping factor is found through the negative feedback circuitry and is explained through the given equation.
DF=2-R1/R2
- Generally, the damping factor has an influence on the filter response through negative feedback action.
- Any increment or decrement in the output voltage is offset through the restricting factor of the negative feedback.
- This fashion to create the response curvature flat in the passband of the filter if the parameter for the damping factor is accurately adjusted.
- With the use of modern mat different values for the damping, the factor is calculated for numerous categories of filter to obtain the extremely flat response of Butterworth characteristic.
- The value of the damping factor needed to generate a resultant response feature relies on the number of poles existing in the filter.
- The pole used in for our benefit is generally a circuitry having one resistance and a single capacitor.
- The more poles exist in the filter there will be its high speed of roll-off rate.
- To obtain the 2nd order Butterworth response for instance the damping factor should have a value of 1.414.
- For implemnetiaon this damping factor the feedback resistance ration value should be
R1/R2=2 – DF = 2 – 1.414 = 0.586
- This ration value provides the closed-loop gain of the noninverting amplifier part of the filter Acl(NI) the value of 1.586, is measured as follows:
Acl(NI) =1/B == 1/R2 /(R1 + R2)=(R1 + R2)/R2=R1/R2+1= 0.586 + 1 = 1.586
What is Critical Frequency and Roll-Off Rate
- The value of critical frequency is measured through the value of resistance and capacitor in the frequency-selective RC circuitry as shown in the figure below.
- In the case of a single-pole filter that is shown in the below figure the critical frequency value is given as.
fc = 1/2πRC
- Though we can indicate that low pass arrangement a similar formula is used for the one pole high pass filter configuration.
- The quantity of poles finds the role of rate of the filter. The Butterworth response generates -20dB/decade/pole. The second-order filter comprises a roll-off rate of -40dB/decade and third-order filer has a roll-off rate of -60dB/decade.
- Normally for getting a filter with the 3 poles or great single or 2 pole filters are used as you can see in the below figure.
- To get 3rd filter for instance cascade a 2nd order and ist order filter to get a 4rth order filter cascade 2-second order filter and continue.
- Every filter in a cascaded configuration is known a state.
- since it is an extremely flat response the Butterworth feature is the most commonly used. So we will restrict our point to the Butterworth response to define basic filter structure.
- The below table shows the roll-off rates damping factor and feedback resistance rations to the 6th order Butterworth filter.
- Resistance configuration related to the gain setting resistance is shown in the below figure.
That is all about the Types of Filter Response Characteristics i have mentioned each and every parameter. If you have any further query ask in comments. Thanks for reading
