Analog Integrated Circuits

Active Filters

32 questions By Tony R. Kuphaldt

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Question 22 of 32

Choose appropriate values for this Sallen-Key high-pass filter circuit to give it a cutoff frequency of 7 kHz with a “Butterworth” response:

f_−3dB = √2
2 πR C

A good guideline to follow is to make sure no component impedance (Z_R or Z_C) at the cutoff frequency is less than 1 kΩ or greater than 100 kΩ.

Reveal answer

Bear in mind that this is just one possible set of component values:

C = 3.3 nF

R = 9.744 kΩ

^R/₂ = 4.872 kΩ

Follow-up question: how would you suggest we obtain the precise resistance values necessary to build this circuit?

Notes:
In order for students to solve for R, they must algebraically manipulate the cutoff frequency formula. Ask them why we might choose a standard value for capacitance and then calculate a non-standard value for resistance. Why not the other way around (first choose R, then calculate C)?
Question 23 of 32

Choose appropriate values for this Sallen-Key low-pass filter circuit to give it a cutoff frequency of 4.2 kHz with a “Butterworth” response:

f_−3dB = 1
2 √2 πR C

A good guideline to follow is to make sure no component impedance (Z_R or Z_C) at the cutoff frequency is less than 1 kΩ or greater than 100 kΩ.

Reveal answer

Bear in mind that this is just one possible set of component values:

C = 0.0047 μF

2C = 0.0094 μF

R = 5.701 kΩ

2R = 11.402 kΩ

Follow-up question: while 0.0047 μF is a common capacitor size, 0.0094 μF is not. Explain how you could obtain this precise value of capacitance needed to build this circuit.

Notes:
In order for students to solve for R, they must algebraically manipulate the cutoff frequency formula. Ask them why we might choose a standard value for capacitance and then calculate a non-standard value for resistance. Why not the other way around (first choose R, then calculate C)?
Question 24 of 32

A popular passive filtering network called the twin-tee is often coupled with an operational amplifier to produce an active filter circuit. Two examples are shown here:

Identify which of these circuits is band-pass, and which is band-stop. Also, identify the type of response typically provided by the twin-tee network alone, and how that response is exploited to make two different types of active filter responses.

Reveal answer

The first filter shown is a band-stop, while the second filter shown is a band-pass.

Notes:
Like all the other active filter circuits, the fundamental characteristic of each filter may be determined by qualitative analysis at f = 0 and f = ∞.

An interesting concept at work here is the inversion of a function by placement inside the feedback loop of a negative-feedback opamp circuit. What is a band-stop filter all by itself forces the opamp to be a band-pass if placed within the negative feedback signal path. Discuss this very important concept with your students, as this is most definitely not the only application for it!