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Band-Pass Active Filter Designer
by Martin E. Meserve

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Introduction

Description

Requirements

R Standard

R Custom

Introduction

This web page deals with the design of low frequency active Band-Pass filters. A Band-Pass filter is intended to pass a narrow band of frequencies, F_Max-F_Min, centered around a center frequency, F0. Signals outside of this band are to be attenuated at a rate of about 6db per octave. This means that a signal that is twice the center frequency, but equal in strength on the input to the filter, will be 6db down (~25%) at the output of the filter. Better out of band attenuation can be obtained by cascading filter sections.

In order to keep the filter stable the user should try not to specify a Gain (K) greater than 10 or a Q greater than 10. If higher gains or greater out of band attenuation is required, cascade two or more filter sections.

Two types of Second-Order Band-Pass filters are described on this web page, the Multiple Feedback (MFB) type, and the Voltage Controlled Voltage Source (VCVS) type, both shown below. They both have very similar characteristics in that they both have low parts counts and is capable of values of Q up to about 10, for moderate gains. The main difference is that the MFB type has inverted gain and the VCVS has non-inverted gain. At high Q and Gains the VCVS type may not be very stable.

Note that in both the MFB and VCVS case, I am assuming that both capacitors are equal in value. This is normally the case with VCVS filters, however, MFB filters can have different value capacitors, but then the equations become much more complicated. Choosing incorrect values for the capacitors can cause the resistor calculations to go to zero. I may include this capability in the future, but for now, if you want to know more about using different value capacitors in a MFB band pass filter, please refer to Reference Data for Radio Engineers by Howard W. Sams & Co., Inc.

Also note that this web page does not deal with the operation and selection of operational amplifiers for these filters. Nor does it deal with proper power biasing. For a little more insight on these areas refer to the page on Operation Amplifier Operation and Operation Amplifier Power Biasing (when I get around to creating them).

Below is the diagram of the MFB type of filter and the equations necessary to determine the resistor values. In the equations, K = Stage Gain, F0 = Center Frequency (Hz), and Capacitors are in Farads. FMIN and FMAX are the frequencies at which the output amplitude equals 1/sqrt(2) times its maximum output value and defines the Band Width.

Below is the diagram of the VCVS type of filter and the equations necessary to determine the resistor values. In the equations, K = Stage Gain, F0 = Center Frequency (Hz), and Capacitors are in Farads. FMIN and FMAX are the frequencies at which the output amplitude equals 1/sqrt(2) times its maximum output value and define the Band Width.

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Introduction

Description

Requirements

R Standard

R Custom

Program Description

Scattered throughout this page is a button that says, . This will open a window with the design based on the design entry data. You can use it any time to view your design or you can leave it up while you are developing. It won't update itself automatically, however, each time you hit the button, the window will refresh and show you the latest information. When you are done you will have everything ready for printing.

A Band-Pass Filter is designed in several steps. First, the designer defines the initial specifications, i.e. Filter Type, Center Frequency, Gain, Q, and a Standard Value Capacitor. These values are then run through a series of equations to yield resistor values. These values are accurate but probably not very useful, because, resistors come in a range of standard values that may not match the calculated values. The web page gives you three choices to resolve the problem:

  1. Attempt to purchase high precision resistors for the calculated values.

  2. Select standard value resistors that are close to the calculated values. The web page will list the eight possible combinations and then calculate the filter properties in reverse, allowing you to see the effects.

  3. Create your own high precision resistors using two standard value resitors for each calculated value. Again the filter properties will be calculated in reverse so you can see the results.

Below are a few things that you need to consider when designing a Band-Pass filter.

  • The Standard Value Capacitor should be limited to between 500 and 2000 pF. Note in the schematic that C1 and C2 are equal and should be of high quality. Silver Mica, Polystyrene, etc. are the most desirable types. Low quality capacitors will cause the filter properties to change with time and temperature.

  • The Center Frequency can be based on several things. You may have a required Bandwidth, in which case, your Center Frequency would be the arithmetic mean between Fmax and Fmin. Or, you may have a specific Center Frequency in mind and want to experiment with different Bandwidths.

  • This would bring Q into the picture. In the context of a band pass filter, High Q means Narrow Bandwidth, Low Q means Wide Bandwidth. A user has the ability of allowing Bandwidth to be calculated from a specified Q or you can specify the upper and lower frequencies and let the program calculate the Q.

Note: When you choose to have Q calculated, from a specified Fmax and Fmin, it is up to the user to insure that the specified Center Frequency is the arithmetic mean between Fmax and Fmin.

Page Top

Introduction

Description

Requirements

R Standard

R Custom

Defining Requirements

In the table below enter your filter requirements. The table is set up to give you flexibility in defining your needs.

There are a lot of calculations behind this web page, and every time you change any piece of data the entire page is recalculated. This may cause a brief pause in operation of 1-2 seconds.

1

Choose the type of filter (MFB or VCVS)

2

Enter a Filter Gain (K) that greater 0, but less than 10.

3

Use the check boxes on the right to select how you want to define your input data. The web page will automatically fill in the text boxes for the other choices.

F0
Hz

Q

FMax
Hz

FMin
Hz

F0
Hz

BW
Hz

4

It is assumed that C1 and C2 are equal. For a Center Frequency of x you should choose a standard value capacitor around x.

C1 and C2


The text box to the right lists your filter specifications and the part values necessary to achieve them. In your requirements you specified standard value capacitors, but the the resistor values are calculated precisely and are probably not common values.

You have a couple of choices here. You can simply select resistors that are close the calculated values. This is a viable choice if your specifications are not very stringent and you can live with the filter being slightly off.

The other choice is to obtain precision resistors. There are several sources of precision (1%) resistors but these can get expensive. An option to purchasing percision resistors it to make your own using two parallel resistors. It is possible to calculate the values of two standard resistor values that, when they are connected in parallel, produce a resistance very close to the value that you need.

Second-Order x Band-Pass Active Filter.

Specifications

x

x

x

x

x

x

Components

x

x

x

x

 

 

 

 



That's what the next two sections are all about. The first one shows you various filter alternatives using standard resistors that are close to the calculated values. Because there are three resistors involved in the determination of the filter parameters, there are eight possibilities.

The second section performs the necessary calculation for determining two parallel resistors for each of the resistors that are involved in the determination of the filter parameters. The resistors are listed followed by the effect they will have on the filter parameters.

Page Top

Introduction

Description

Requirements

R Standard

R Custom

Select Standard Resistors

As I mentioned above, you could just simply select standard resistors that are close to the required values, and accept a filter that is going to be slightly different than initially specified. This is a good choice when the filter specifications are not critical. In fact, you can get quite close to your required specifications.

For each resistor you can choose the closest value above or below the calculated value. For a 3 resistor system, this means that there are 8 possible resistor combinations. One of the combinations listed below, sorted by frequency, may meet your needs without resorting to other methods.

Note that the Q and Gain also change and may influence your decision. This is especially true for VCVS type filters because the Gain and Q are very sensitive to component variations. For VCVS type filters, any resistor combination that shows very high Gain and Q will be a very poor choice.

For VCVS type filters, you may not be able to create a filter that is reasonably close to the initial specifications, if you use 10 percent resistors. You may find one that is reasonably close in center frequency, but it will probably be way off in Q, Gain, or Bandwidth. 5 percent resistors are always a better choice. Select the resistor tolerance you wish to use.

Tolerance


Standard Resistor Table

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Introduction

Description

Requirements

R Standard

R Custom

Calculate Precision Resistors Using Two Standard Values

Each calculated resistor could be replaced by two standard value resistors Ra and Rb which, when connected in parallel, will result in a net resistance R that will be within very close tolerances of almost any value you want.

The text area below shows the parallel resistor values, Ra and Rb, that would be necessary to create precision resistors for R1, R2, and R3. The Delta value is the deviation percentage from the required value.

Use the selector on the right to define the parallel resistor tolerances. The text area below will then show the precision resistors, constructed from two parallel resistors, for each of the calculated values.

For VCVS filters, precision resistors will be calculated for R4 and R5. However, these resistors are for biasing purposes and do not have any effect on the filter specifications. You can use the precision resistors or just use the resistors defined in section above.

images_actfil/prec_res.gif

Tolerance




Custom Resistor Table