# Sallen-Key Filter : Circuit, Working, Advantages, Disadvantages & Its Applications

Filters play a key role in the communication field because they remove noise & help in optimizing performance. The applications of filters within telecommunication systems will differ from high to very low frequency. The selection of channels within telephone services is a main task for high-frequency BPFs; while data acquisition depends on anti-aliasing LPFs. For the performance of the low-pass filter circuit & active low-pass filter, it is very important to know the cutoff frequency of the circuit and high-frequency performance for designing of active filter, passive low-pass filter, and RC low-pass filter. Low-pass filters which are identified simply with active and passive components are known as active low-pass filters. This article provides brief information on the Sallen-Key Filter, circuit, and its applications.

## What is the Sallen-Key Filter?

The most popular active second-order analogue filter topology is a Sallen Key Filter which is also called voltage control voltage source. These are very popular because their configuration will show that it does not depend very much on the op-amp performance. This is mainly because the operational amplifier is connected as an amplifier which reduces the gain-bandwidth necessities of the operational amplifier. The Sallen-Key filter has low component spread, high input impedance & low output impedance, which allows various filters to be connected devoid of intermediary buffers.

### Sallen Key Filter Circuit

A Sallen key filter is an electronic circuit, used to filter unnecessary frequencies from an audio signal. This circuit is simply designed with two resistors, an op-amp & two capacitors which form a feedback loop. Based on the values of the components, this circuit can act as a low-pass filter and a high-pass filter. Here Sallen key low-pass filter circuit is discussed below.

#### Sallen Key Low Pass Filter

In the Sallen-Key LPF, better filter performance can be achieved by properly selecting the RC components. The main features of this filter are; voltage amplification & voltage gain control with stable filter operation. The Sallen Key low pass filter schematic diagram for the unity gain is shown below. This circuit has two RC filter sections effectively in series; however, with the first stage capacitor is bootstrapped through the output.

The general transfer function (T.F) for a second-order LPS is

**H(s) = Kω ^{2}0/S^{2}+ (ω0/Q)S+ ω^{2}0 —–(1)**

Where:

‘K’ is the gain factor,

‘ω0’ is the characteristic frequency within radians/s.

‘Q’ is the quality factor.

S = jω.

The 2nd-order Sallen-Key low pass filter transfer function can be written in the same form as the above general equation.

**H(s) = (K/ R1R2 C1C2)/ S ^{2}+[( 1/R1+1/R2) 1/ C1 +(1- K/ R2C2]S + 1/ R1R2C1C2 —–(2)**

By equating the above two equations, we can get the cut-off frequency & quality factor equations.

The cutoff frequency of the Sallen key filter equation is fc = 1/2π√ R1R2 C1C2.

The Q factor of Sallen Key Filter ‘Q’ is √R1R2 C1C2/ R1C1+R2C1+ R1C2 (1-K).

The gain equation is similar to a non-inverting amplifier.

K = 1+ R3/R4

Similarly, a sallen key high-pass filter can be designed by replacing capacitors in place of resistors.

### How Does a Sallen Key Filter Work?

The Sallen–Key topology works by implementing second-order active filters for enhancing the Q factor of the filter with controlled positive feedback. This topology is very simple compared to other active filter topologies. This is an active filter design based on a single non-inverting op-amp with two resistors.

### Sallen-Key Filter Advantages

The advantages of the Sallen Key Filter include the following.

- The Sallen-Key filter design is very simple including single op-amp & RC components.
- These filters are capable of increasing the output voltage higher than the input voltage.
- The high input & low output impedance makes the Sallen-Key filters cascading much easier.
- The op-amp in the Sallen-Key filter assists in conquering the RC component’s effect on filter characteristics.
- These filter’s frequency range is wide.
- The op-amp within this filter can be arranged either as a non-inverting amplifier or a unity gain buffer.
- These filters have various stages & different gains.
- The Sallen-Key filter stability is good.
- Understanding this filter design is simple.
- The utilization of a non-inverting amplifier can increase voltage gain.
- Both the first & second-order based filters can be cascaded easily together.
- Every RC stage can include a different voltage gain.

The **disadvantages of the Sallen Key Filter** include the following.

- The Sallen-Key filter is not easily tuned because of the interaction of the component values on F0 & Q.
- The low maximum ‘Q’ value is obtainable.
- Sallen key filter is very sensitive to component variations & tolerances which means the actual resistors & capacitors values will be different from the ideal values & they can change eventually because of different factors like aging, humidity & temperature. This can affect the stability & accuracy of the filter.
- It is susceptible to distortion & noise from the operational amplifier. So the characteristics & quality of the operational amplifier can affect the performance as well as output of the Sallen key filter.
- In the design of the Sallen-key filter, the voltage gain & magnification factor are closely related because of the use of an op-amp in this design.
- Almost any Quality factor value larger than 0.5 can be realized because utilizing a configuration of non-inverting op-amp, the voltage gain will be greater always than 1 but must be below 3, or else it will turn unstable.

### Sallen-Key Filter Applications

The applications of the Sallen Key Filter include the following.

- A Sallen-Key filter is preferred usually whenever a small Q factor is required, noise rejection is prioritized, & filter stage’s non-inverting gain is necessary.
- This filter is used as the basic building block used to implement higher-order filter circuits like LPF, HPF, and BPF circuits.
- This filter can be utilized for different applications within audio signal processing like tone control, equalization, synthesis, modulation, and noise reduction.
- This filter is used for modulating/synthesizing an audio signal by simply changing the Q factor or cutoff frequency dynamically through an additional signal like an envelope, a control voltage, or an oscillator.

Thus, this is an overview of the Sallen-Key Filter (Sallen key topology) or Sallen and Key filter which is one of the very popular active second-order LPFs that can be configured as an LPS, HPS, BPS, and BSF. This Sallen-Key topology helps in implementing various filter tunings like Butterworth, Chebyshev & Bessel. This filter is similar to VCVS (voltage-controlled voltage source) including filter characteristics like; good stability, low output impedance & high input impedance. The Sallen-Key low pass filter is used for many reasons like; simple design, filter cascading, a wide range of frequency, voltage gain control, multiple stages, high-order filter design, stability & different gains. Here is a question for you, what is the function of a low-pass filter?