Categories: Electronics

Easy low-pass filters tunable with a single potentiometer

A scheme of straightforward band-pass RC- and LR- filters on operational amplifiers containing just one capacitor or inductor and three resistors is proposed. A comparability is manufactured from the amplitude-frequency traits of the proposed filters, in addition to the RC filter of Robert Allen Pease and its modified LR- variant.

Wow the engineering world together with your distinctive design: Design Concepts Submission Information

From the entire set of straightforward low-frequency filters, one can spotlight the Sallen-Key filters [1, 2]. Regardless of their enticing exterior simplicity, these filters are removed from simple to arrange and require the usage of coordinated components.

The RC filter, proposed in 1971 by an engineer of George A. Philbrick Analysis—Robert Pease—Determine 1 [3, 4], has a number of distinctive properties. This can be very easy, and its resonant frequency is managed by just one potentiometer R2, and the transmission coefficient of the filter virtually doesn’t rely upon the resistance worth of this potentiometer. The amplitude-frequency traits of this filter when adjusting the potentiometer R2 are proven in Determine 1 [5].

Determine 1 Electrical diagram of the Pease RC-filter and its amplitude-frequency traits when R2: 1) 10.0 kΩ; 2) 3.0 kΩ; 3) 1.0 kΩ; 4) 0.3 kΩ; 5) 0.1 kΩ; 6) 0.03 kΩ.

By barely modifying Pease’s circuit, particularly, by changing capacitors with inductors, we get a modified filter circuit. The amplitude-frequency traits of the modified LR-filter throughout the adjustment of the R2 potentiometer are proven in Determine 2 [5].

Determine 2 Electrical diagram of the modified LR-filter and its amplitude-frequency traits when R2: 1) 0.03 kΩ; 2) 0.1 kΩ; 3) 0.3 kΩ; 4) 1.0 kΩ; 5) 3.0 kΩ; 6) 10.0 kΩ. L1=L2=20 mH.

Along with the op-amp, the filters mentioned above include 5 elements every. Nonetheless, it’s doable to supply even easier filters that include solely 4 the place the weather R3 + R4 could be changed with one potentiometer.

The “resonant” frequency of the RC filter, Determine 3, is decided from the expression:

the place f₀ is in Hz, R is in Ω, C is in F, a is a continuing relying on the mannequin of the op-amp.

So, for instance, for LM324 a ≈ 426. The equal Q-issue of the filter Q is proportional to the expression:

the place b is a continuing (b ≈ 110).

Within the calculations: C = C1; R = R3 + R4. Thus, the “resonant” frequency of the filter relies upon solely on the nominal values of the weather R = R3 + R4 and C = C1. The ratio R2/R1 doesn’t have an effect on the frequency of the “resonance”, however impacts solely the worth of the equal high quality issue of the filter and the transmission coefficient of the filter on the frequency of the “resonance”.

Determine 3 Electrical diagram of the RC-filter with the adjustment of the “resonance” place by the potentiometer R4.

The amplitude-frequency traits of the RC-filter are proven in Determine 4.

Determine 4 Amplitude-frequency traits of the RC-filter with the adjustment of the “resonance” place when the resistance worth R = R3 + R4 varies.

Changing the capacitor C1 with the inductor L1 and swapping the frequency-determining elements R and L, we get the LR-version of the filter, Determine 5. Its amplitude-frequency traits with various values of R are proven in Determine 6.

The “resonant” frequency of the LR-filter, Determine 3, is decided from the expression:

the place f₀ is in Hz, R is in Ω, L is in H, and a is a continuing. The ratio R2/R1 impacts the identical parameters as earlier than.

Determine 5 Electrical diagram of the LR-filter with the adjustment of the “resonance” place by the potentiometer R4.

Determine 6 Amplitude-frequency traits of the LR-filter with the adjustment of the “resonance” place when the resistance worth R = R3 + R4 varies.

Michael A. Shustov is a physician of technical sciences, candidate of chemical sciences and the creator of over 800 printed works within the area of electronics, chemistry, physics, geology, drugs, and historical past.

Associated Content material

References

Sallen R.P., Key E.L. “A Sensible Technique of Designing RC Lively Filters”. IRE Transactions on Circuit Concept, 1955, Vol. 2, № 1 (March), pp. 74–85.
Tietze U., Schenk Ch. “Halbleiter-Schaltungstechnik”, 12. Auflage, Berlin-Heidelberg, Springer Verlag, 2002, 1606 S.
Pease R. “An simply tunable notch-pass filter”. Digital Engineering, December 1971, p. 50.
Hickman I. “Notches, High”. Electronics World Incorporating Wi-fi World, 2000, V. 106, No. 2 (1766), pp. 120–125.
Shustov M.A. “Circuit Engineering. 500 gadgets on analog chips”. St. Petersburg: Science and Expertise, 2013, 352 p.

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