# Understand low-pass, high-pass, band-pass, band-stop, state-tunable filters at once!

The second-order voltage-controlled low-pass filter circuit is shown in the figure. Two first-order low-pass filters are formed by R1, C1, R2, and C2, respectively. However, C1 is connected to the output terminal, and positive voltage feedback is introduced to form a voltage-controlled filter.

1 Second-order voltage-controlled low-pass filter

The second-order voltage-controlled low-pass filter circuit is shown in the figure. Two first-order low-pass filters are formed by R1, C1, R2, and C2, respectively. However, C1 is connected to the output terminal, and positive voltage feedback is introduced to form a voltage-controlled filter.

(1) Transfer function

(2) Frequency characteristics

It can be seen that the characteristic of this low-pass filter is that the damping coefficient ζ is determined by the ratio of the resistors R1, R2, C1, and C2; while the natural frequency ω0 is related to the specific values ​​of R1, R2, C1, and C2, that is, ω0 and ζ are independently adjustable and independent of each other. influence.

(3) Parameter selection

In order to facilitate parameter matching, considering that there are few types of nominal capacitors, generally choose C1=C2=C. The specific natural frequencies ω0 and ζ can be satisfied by choosing different R1 and R2.

2 Unity Gain Second Order Voltage Controlled Low Pass Filter

For the second-order voltage-controlled low-pass filter, when the passband amplification factor Aup =1 (unity gain), the circuit shown in the figure becomes as shown in the figure, where RF=R1+R2.

(1) Basic relationship

(4) Parameter selection

When the natural frequency ω0 and the damping coefficient ζ are known, the design steps are as follows:

3 second order low pass filter

(1) Transfer function

(2) Frequency characteristics

4 Infinite Gain Multiple Feedback Low Pass Filters

(1) Transfer function

(2) Frequency characteristics