Javascript Electronic Notebook Low-Pass Active Filter Designer by Martin E. Meserve

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Introduction

Description

Requirements

R Standard

R Custom

A Low-Pass Filter is a frequency selective device which passes low frequencies and blocks high frequencies. It has a single passband and a single stopband. W_{C} is defined as the frequency that separates the two bands. This is also known as the cutoff frequency and is the point at which the amplitude is 3 dB below its maximum value. This web page is intended to aid you in designing Second-Order and/or Fourth-Order Multiple Feedback (MFB) and Voltage Controlled Voltage Source (VCVS) Low-Pass Active Filter.

One of the simplest active filters which realizes the second-order low-pass filter is the MFB network shown below. In the equations, the coefficients a and b are determined by the response characteristics, Butterworth or Chebishev, and the filter order, Second-Order or Fourth-Order. See the table at the end of this section.

Some of the advantages of the MFB configuration are, minimal number of circuit elements, low output resistance, convenient for cascading with other stages, and good stability characteristics. One of the disadvantages is that high gains are not possible.

Another common filter configuration, which realizes the second-order low-pass filter, is the VCVS network shown below. As with the MFB filter, the coefficients a and b are determined by the response characteristics, Butterworth or Chebishev, and the filter order, Second-Order or Fourth-Order. See the table at the end of this section.

Some of the advantages of the VCVS configuration are, minimal number of circuit elements, low output resistance, convenient for cascading with other stages, capable of relatively high gains, and relative ease of adjustment of characteristics. One of the disadvantages is that, it is not as stable as the MFB filter.

The table below only lists the coefficients for second and fourth order filters. Orders beyond fourth are practical, but are beyond the scope of this web page.

Low-Pass Coefficients for Second-Order and Fourth-Order Designs

Butterworth

Chebishev

n

0.1 dB

0.5 dB

1.0 dB

a

1.41421

2.37209

1.42562

1.09773

b

1.00000

3.31329

1.51620

1.10251

a1

0.76537

0.52827

0.35071

0.27907

b1

1.32981

1.06352

0.98650

a2

1.84776

1.27536

0.84668

0.67374

b2

0.62282

0.35641

0.27940

Program Description

I have tried to make the data input and output as user friendly as possible. Pretty much, once you define your requirements the rest is automatic. As you enter data all calculations are performed. This allows you to make small incremental changes and realize the changes in the design immediately. 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.

Depending on your design, there will be some limitations on the capacitor values. You have a pretty wide leeway in your choice of capacitors, so you aren't restricted heavily. The web page will warn you if you get to fare off the mark.

When you are designing a Second-Order filter, the entries area for Fourth-Order filter are grayed out and disabled. I do this to help eliminate any confusion in the required input data.

The calculated resistor 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 give 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.

Defining Requirements

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

Note that, 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

Select the filter -3 dB Cutoff Frequency, F_{C}

Hz

3

Select the Filter Order, Second-Order = 1 Stage, Fourth-Order = 2 Stages.

4

Select the Response Characteristics, Cheb = Chebishev

5

For the Second-Order Filter, or the first stage of a Fourth-Order Filter, select the stage gain, K. For multi-section filters restrict K to 1 or 2.

For unity gain (K=1) VCVS filters, short R_{4} and omit R_{3}.

6

For the Second-Order Filter, or the first stage of a Fourth-Order Filter, select a standard value for C_{1} near and C_{2} such that .

uF pF

7

For the Fourth-Order Filter, select the stage gain, K. For multi-section filters restrict K to 1 or 2.

1 2 3 4 5 6 7 8 9 . 00 10 20 25 30 40 50 60 70 75 80 90

8

For the Fourth-Order Filter, select a standard value for C_{1} near and C_{2} such that .

You are given a lot of latituded in selecting the capacitors for the filter, however, it is possible to go to far. Choosing capacitors that are out of range will cause the output of some of the equations to go negative. If, in the text box below, some of the resistor values show up at "NaN", the most probable cause is that C_{1} is specified to large. When C_{2} is specified incorrectly the text area, in the entry areas above, will turn red.

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. See the section on Selecting Standard Resistors.

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. See the section on Calculating Precision Resistors Using Two Standard Values.

Component specification for a x-Order x Low-Pass Active Filter with x response and a -3 db Cutoff Frequency (Fc) of x. x.

x

Selecting 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. This means that for a 3 resistor system (MFB), there are 8 possible resistor combinations. For a 4 resistor system (VCVS), there will be 16 possible resistor combinations. One of the combinations listed below, sorted by frequency, may meet your needs without resorting to other methods.

Also note that, with VCVS type filters, you will not be able to create a filter that is reasonably close to the initial specifications, if you use 10 percent resistors. 5 percent resistors would be a better choice. Select the resistor tolerance you wish to use.

Tolerance 5 Percent 10 Percent

Standard Resistor Table

Calculate Precision Resistors Using Two Standard Values

Each calculated resistor could be replaced by two standard value resistors R_{a} and R_{b} 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, R_{a} and R_{b}, that would be necessary to create precision resistors for R_{1}, R_{2}, and R_{3}. 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 R3 and R4. 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