This page is from a Texas Instrument's Application Report (SLOA093 – December 2001) written by Bruce Carter. It is an introduction to active filters and presents a very simple method to design a filter. All I am doing in this page is automating this already simple method.

I have made some changes to how a circuit is drawn and in some cases, modified the reference designators. I understand why the original author drew some of the circuits but things like reusing reference designators only cause confusion.

When this page is refreshed, all of the filters will revert to their default input paramaters. The default parameters are simply examples and can be changed by the user.

I will be including some of the verbiage used in the original document. However, all of the drawings and scripting are my own. You can always read the original document yourself: Filter Design in Thirty Seconds

The Resistor Tolerances in each filter design area will select the closest resistor, based on the tolerance specified. While the default tolerance is 5%, it would be best to use 1% resistors. It's also possible for higher tolerance resistors to be graded and the closest values selected.

Introduction

This document is intended for designers that do not have the time to check filter theory in old college textbooks and try to translate transfer equations into something that can be put into production. This is like looking at the back of the textbook for the answer. Speaking of the back of the book, Appendix B contains a brief introduction to the filter circuits given here, and the limitations of this quickie approach to design.

To design a filter, four things must be known in advance:

  • The power supplies available: positive/negative (± Supply) or only positive (Single Supply)
  • The frequencies that need to be passed, and those that need to be rejected.
  • A transition frequency, the point at which the filter starts to work or a center frequency around which the filter is symmetrical.
  • An initial capacitor value. Pick one somewhere from 100 pF for high frequencies to 0.1 µF for low frequencies. If the resulting resistor values are too large or too small, pick another capacitor value.

Low-Pass Filter
-3db Freq.
Hz 		C1:
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
750 Hz Low-Pass Filter
VIn
−
+
U1
LM741CN
V+
V-
7
4
2
3
6
VOut
-Supply
+Supply
R1
1.5 KΩ
R2
1.5 KΩ
C1
0.1 uF
C2
0.2 uF
C1 = 0.1 uF, C2 = C1×2 = 0.2 uF
R1 = R2 = 1/(2×√2×PI×C1×F) = 1501 => 1.5 KΩ, 5%

This filter is a unity gain Sallen-Key filter, with a Butterworth response characteristic.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on the Op-Amp is tied to ground and the reference changes to +Supply/2. R3 and R4 form a voltage divider to obtain +Supply/2. CIn and COut are then added to provide input and output isolation.

High-Pass Filter
-3db Freq.
Hz 		C1:
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
750 Hz High-Pass Filter
VIn
−
+
U1
LM741CN
V+
V-
7
4
2
3
6
VOut
-Supply
+Supply
R1
3.0 KΩ
R2
1.5 KΩ
C1
0.1 uF
C2
0.1 uF
C1 = C2 = 0.1 uF
R1 = 1/(√2×PI×C1×F) = 3001 Ω => 3.0 KΩ, 5%
R2 = 1/(2×√2×PI×C1×F) = 1501 Ω => 1.5 KΩ, 5%

This filter is a unity gain Sallen-Key filter, with a Butterworth response characteristic.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on the Op-Amp is tied to ground and the bottom of R1 is tied to +Supply/2, adjusting the reference to 1/2 the Supply voltage. COut is then added to provide output isolation. The input is already capacitor isolated and doesn't need further isolation.

Band-Pass Filter, Narrow
Center Freq.
Hz 		C1:
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
750 Hz Narrow
Band-Pass Filter
VIn
−
+
U1
LM741CN
V+
V-
7
4
2
3
6
VOut
+Supply
R1
2.2 KΩ
R2
110 Ω
-Supply
R3
39 KΩ
R4
2.2 KΩ
C1
0.1 uF
C2
0.1 uF
C1 = C2 = 0.1 uF
R1 = R4 = 1/(2×PI×C1×F) =
2122Ω => 2.2 KΩ, 5%
R3 = 19×R1 = 40318 Ω => 39 KΩ, 5%
R2 = R1 / 19 = 112 Ω => 110 Ω, 5%

This circuit includes a gain of 10 (20 dB) at the center frequency

This filter is a modified Deliyannis filter. A Deliyannis filter is a special case of the MFB bandpass configuration, one that is very stable and relatively insensitive to component variation. The Q is set at 10, which also locks the gain at 10, as the two are related by the expression:

(R3+R4)/(2*R1) = Q = Gain

A higher Q was not selected, because the op amp gain bandwidth product can be easily reached, even with a gain of 20 dB. At least 40 dB of headroom should be allowed above the center frequency peak. The op amp slew rate should also be sufficient to allow the waveform at the center frequency to swing to the amplitude required.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on the Op-Amp and the bottom of R2 is tied to +Supply/2, adjusting the reference to 1/2 the Supply voltage. CIn and COut are then added to provide Input and Output isolation.

Band-Pass Filter, Wide
Hi-Pass Freq.
Hz
C1 and C2
 Lo-Pass Freq.
Hz
C3 (C4=C3×2)
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
500 Hz High-Pass Filter
VIn
−
+
U1
LM741CN
V+
V-
7
4
2
3
6
+Supply
-Supply
R1
4.7 KΩ
R2
2.2 KΩ
C1
0.1 uF
C2
0.1 uF
C1 = C2 = 0.1 uF
R1 = 4502 Ω => 4.7 KΩ, 5%
R2 = 4502 Ω => 2.2 KΩ, 5%
2.5 KHz Low-Pass Filter
−
+
U2
LM741CN
V+
V-
7
4
2
3
6
VOut
-Supply
+Supply
R3
430 Ω
R4
430 Ω
C3
0.1 uF
C4
0.2 uF
C3 = 0.1 uF, C4 = C3×2 = 0.2 uF
R3 = R4 = 450 Ω => 430 Ω, 5%

This filter consists of a cascaded Sallen-Key High-Pass and Low-Pass filter. First you design a High-Pass filter for the low end of the band. This is so that energy from it, that stretches to infinite frequency, will be Low-Passed.

NOTE: The start (High-Pass Freq.) and ending (Low-Pass Freq.) frequencies of the pass-band should be at least five times different.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on Op-Amp U1 and U2 are tied to ground. The bottom of R1 is tied to +Supply/2, adjusting the reference of U1 to 1/2 the Supply voltage. The input is already capacitor isolated so only COut is needed to provide Output isolation.

Notch Filter
Notch Freq.
Hz 		C1 & C2
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
VIn
−
+
U1
LM741CN
V+
V-
7
4
3
2
6
+Supply
-Supply
C1
0.1 uF
R1
68 KΩ
R2
68 KΩ
R3
3.3 KΩ
R4
3.3 KΩ
R5
100 KΩ
R6
100 KΩ
VOut
−
+
U2
LM741CN
V+
V-
7
4
3
2
6
+Supply
-Supply
C2
0.1 uF
C1 = C2 = 0.1 uF
R3 = R4 = 1/(2×PI×C1×F) = 3183 Ω => 3.3 KΩ, 5%
R1 = R2 = 20 × R3 = 63660 Ω => 68 KΩ, 5%
R5 = R6 = 100 KΩ, 5%

This is the Fliege Filter topology, set to a Q of 10. The Q can be adjusted independently from the center frequency by changing R1 and R2. Q is related to the center frequency set resistor by the following: R1 = R2 = 2 *Q*R3

The Fliege filter topology has a fixed gain of 1.

The only real possibility of a problem is the common mode range of amplifier U2, in the single supply case. For this particular topology, you might want to read this document on High-Speed Notch Filters. The document shows how other Q values can be handled. The calculations here, and the ones in the document, match up very nicely.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on Op-Amp U1 and U2 are tied to ground. The bottom of R1 is tied to +Supply/2, adjusting the reference of U1 to 1/2 the Supply voltage. CIn and COut are then added to provide Input and Output isolation.

Band Reject Filter
Start Freq.
Hz
C1 (C2=C1×2)
 End Freq.
Hz
C3 & C4
 PS Type:
± Supplies
Single Supply
Res. Tol.
1% | 2%
5% | 10%
Texas Instruments, Inc.
500 Hz LPF
VIn
−
+
U1
LM741CN
V+
V-
7
4
2
3
6
+Supply
-Supply
R1
2.2 KΩ
R2
2.2 KΩ
R6
100 KΩ
C1
0.1 uF
C2
0.2 uF
2.5 KHz HPF
−
+
U2
LM741CN
V+
V-
7
4
2
3
6
+Supply
-Supply
R3
910 Ω
R4
430 Ω
R5
100 KΩ
C3
0.1 uF
C4
0.1 uF
−
+
U3
LM741CN
V+
V-
7
4
2
3
6
VOut
+Supply
-Supply
R7
100 KΩ
C1 = 0.1 uF, C2 = C1×2 = 0.2 uF
R1 = R2 = 2251 => 2.2 KΩ, 5%
C3 = C4 = 0.1 uF
R3 = 900 => 910 Ω, 5%
R4 = 450 => 430 Ω, 5%
R5 = R6 = R7 = 100 KΩ 5%

This filter is made up of a Sallen-Key high pass and low pass filter. The outputs of which are summed. They cannot be cascaded, because their responses do not overlap as in the wide band pass filter case.

NOTE: The start and ending frequencies of the band to be rejected should be at least fifty times different.

With a ±Supplies, the input (VIn) and output (VOut) are assumed to be referenced to Ground ("0V") allowing for ± excursions on the input (VIn) and output (VOut).

With a Single Supply, V- on Op-Amp U1, U2, and U3 are tied to ground. The bottom of R3, and the + input of V3, are tied to +Supply/2, adjusting the reference to 1/2 the Supply voltage. CIn is added to isolate the Low-Pass Filter (U1). COut is added to provide isolation for the Summing Amplifier U3.