Sallen-Key Low Pass Filters: Second-Order Active Filters with Voltage Amplification and Gain Control

Updated in 2022. 

Key Takeaways

• The Sallen-Key low pass filter and the multiple feedback low-pass filter are the two topologies of second-order active low pass filters.

• The Sallen-Key low pass filter is the most popular second-order active low pass filter. The design of Sallen-Key filters is similar to voltage-controlled voltage-source (VCVS), with filter characteristics such as high input impedance, good stability, and low output impedance. 

• The merits of the Sallen-Key low pass filter are a simple design, voltage gain control, cascading of filters, wide frequency range, high-order filter design, multiple stages, different gains, and stability.

Filter circuits are essential in telecommunication systems 

Filters are vital in communication circuits, as they eliminate noise and help optimize  performance. Filter applications in telecommunication systems vary from high frequency to very low-frequency. The channel selection in telephone services is a task of high-frequency band-pass filters, whereas data acquisition relies on anti-aliasing low pass filters.  For active low pass filter and low pass filter circuit performance, it is vital to understand circuit cutoff frequency, and high frequency performance whether looking at RC low pass filter, active filter, or passive low pass filter design. 

The function of high pass and low pass filters are diametrically opposite and so is their hardware realization. High-frequency filters operate on signal frequencies greater than 1 MHz and they are usually realized using passive components such as resistors (R), capacitors (C), and inductors (L). The frequency of operation of low pass filters is within 1Hz to 1MHz, making the size of L and C components used in passive filter designs bulky. Usually, low pass filters are realized using active and passive components and collectively called active low pass filters. 

Important Features of Active Filters

The most commonly used active component in filters is the operational amplifier, or op-amp. Advantages such as its lighter weight, high sensitivity, and better response at low frequency make an active low pass filter a constant in communication systems. It is also possible to amplify the output in active filters. 

Gain control is the next important feature of any active filter. The active low pass filter is always attached to the word ‘order’. The number of passive components present in the filter determines the order of the active filter. The first order active low pass filters are commonly seen in speaker, equalizer, and amplifier circuits. The second-order filters are used as anti-aliasing filters, hissing sound filters, and echo elimination filters. The Sallen-Key low pass filter and multiple feedback low-pass filters are the two topologies of second-order active low pass filters. 

Sallen-Key Low Pass Filters

The Sallen-Key low pass filter consists of an active component—an op-amp—as well as passive components such as resistors and capacitors. RC components control the frequency response characteristics, whereas the op-amp is responsible for the voltage amplification and gain control.  The figure above shows a Sallen-Key low pass filter. The op-amp in the amplifier can be used either as a unity gain buffer or a non-inverting amplifier.

Sallen-Key low pass filters are the most popular second-order active low pass filter. The design of Sallen-Key filters is similar to voltage-controlled voltage-source (VCVS), with filter characteristics such as high input impedance, good stability, and low output impedance. 

When the op-amp is used as a non-inverting amplifier, the output voltage amplitude can be varied by controlling the gain of the op-amp. The voltage gain of the Sallen-Key low pass filter is always greater than unity, with a non-inverting amplifier op-amp configuration. In a non-inverting amplifier configuration, the gain of the Sallen-Key filter is given by the equation:

Gain, Av = 

However, the gain of the op-amp amplifier should be maintained less than 3, as Av greater than 3 makes the Sallen-Key filters unstable.

The RC networks control the frequency response of the Sallen-Key low pass filter. By varying the resistor and capacitor values, the frequency response of the filter can be controlled. The cut-off frequency of the filter can be given by equation:

Cut-off frequency, fc= 

The four components R₁, R₂, C₁, and C₂ of the filter can be chosen according to the required frequency response. The high value of the resistors prevent performance degradation of the filters at high frequencies. The DC performance, bias currents, and the impact of the capacitors can be enhanced by choosing low resistor values. 

If your objective is to only filter the input, then the solution is a Sallen-Key low pass filter, with the op-amp configured as a unity gain amplifier. 

Merits of Sallen-Key Low Pass Filters

The merits of Sallen-Key filters can be summarized as:

• Simple design- The Sallen-Key design is simple, with one op-amp and RC component.

• Voltage gain control- By using Sallen-Key filters, it is possible to increase the output voltage greater than the input voltage. The input voltage is given to the non-inverting op-amp amplifier and the voltage gain control of the op-amp is comparatively easy.

• Cascading of filters- The high input impedance and low output impedance make the cascading of the Sallen-Key filters much easier. The low-pass and high-pass stages of Sallen-Key filters can be cascaded together.

• Attenuator to an amplifier- The incorporation of the op-amp in the Sallen-Key filter helps to overcome the effect of RC components on filter characteristics. 

• Wide frequency range- The impedance characteristic of these filters reduces the external loading of the filter. It possesses the property of adjusting to a wide frequency range without altering the designed frequency response.

• Different configurations- The op-amp in the Sallen-Key filter can be configured either as a unity gain buffer or non-inverting amplifier

• High-order filter design- The Sallen-Key filters can be cascaded with RC components to increase the order of the filter. The number of capacitors in the design determines the order of the filter and orders greater than 2 are possible. 

• Multiple stages and different gains- The multiple filter stages built using RC components in a Sallen-Key topology can have different voltage gains and cut-off frequencies.

• Stability- The good stability of Sallen-Key filters is a factor enabling the cascading. The filter stability is dependent on voltage gain, which in turn is controlled by the resistors in the op-amp amplifier circuit.

Sallen-Key low pass filters give us so much freedom during the filter design process. The aim to achieve better filter performance can be fulfilled by appropriately choosing the RC components in the Sallen-Key low pass filter. The voltage amplification and voltage gain control features with stable filter operation are the USP of Sallen-Key low pass filters. Next time you are designing anti-aliasing filters or low pass noise filters, try the Sallen-Key topology for improved performance.

Op amp and op amp filter design, chebyshev filter, active high pass filter, butterworth filter, active band pass filter, and more low pass filter circuit design techniques require a robust understanding of cut off frequency and high frequency or high frequency signal interactions, as well as power supply challenges with transfer function. For your next low pass filter circuit, rest easy regardless of low frequency signal, capacitor usage, corner frequency, and input signal or output signal. Your circuit can move ahead comfortably.