Band-Pass Active Filter Designer
by Martin E. Meserve
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Filters | Band-Pass Active Filter
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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
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
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.
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:
Attempt to purchase high precision resistors
for the calculated values.
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.
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.
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.
Choose the type of filter (MFB or VCVS)
Enter a Filter Gain (K) that greater 0,
but less than 10.
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.
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.
Band-Pass Active Filter.
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.
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.
Standard Resistor Table
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.
Custom Resistor Table