A low pass Sallen Key filter is an active second-order RC filter topology that uses an operational amplifier to provide a sharp -40 dB/decade roll-off without the insertion loss or loading effects inherent to passive designs. When you insert this circuit into a signal path, it strips away high-frequency noise, switching ripple, and aliasing artifacts while passing your DC or low-frequency baseline intact, all without attenuating the passband amplitude. Unlike passive LC filters that require bulky inductors, or first-order RC filters that roll off too slowly to protect sensitive ADCs, the Sallen-Key topology leverages the high input impedance and low output impedance of an op-amp to isolate the filter stages from the rest of your circuit.
The Core Topology and What It Changes in a Circuit
The standard unity-gain low pass Sallen Key filter consists of two cascaded RC networks feeding into the non-inverting input of an op-amp configured as a voltage follower. The first RC stage (R1 and C1) is connected to the input signal, while the second stage (R2 and C2) connects to the op-amp input. The critical magic of this topology is the feedback capacitor (C1), which is tied not to ground, but to the output of the op-amp. This creates a controlled positive feedback loop at high frequencies, which boosts the Q-factor (quality factor) and sharpens the filter's 'knee' right at the cutoff frequency, achieving a true second-order response (-40 dB/decade) using only resistors, capacitors, and a single active device.
Designers frequently confuse the Sallen-Key topology with the Multiple Feedback (MFB) low-pass filter. The easiest way to tell them apart on a schematic is the op-amp configuration. The Sallen-Key uses a non-inverting configuration (signal enters the '+' terminal), meaning the output signal is in-phase with the input. The MFB filter uses an inverting configuration (signal enters the '-' terminal), which flips the signal phase by 180 degrees. While MFB is less sensitive to the op-amp's Gain-Bandwidth Product (GBW) at high Q values, the Sallen-Key is vastly preferred for audio and sensor applications because it is easier to tune, requires fewer precise component ratios for unity-gain alignments, and avoids the noise-gain peaking issues of MFB circuits.
Component Ratios for Standard Filter Alignments
To design a low pass Sallen Key filter, you must first choose your alignment. The alignment dictates the shape of the filter's transition band and its phase response. The three most common alignments are Butterworth (maximally flat passband), Bessel (linear phase/best step response), and Chebyshev (steepest roll-off at the cost of passband ripple). The table below provides the exact component ratios required to achieve these alignments in a unity-gain Sallen-Key topology.
| Filter Alignment | Damping / Q Factor | R1/R2 Ratio (if C1=C2) | C1/C2 Ratio (if R1=R2) | Primary Use Case |
|---|---|---|---|---|
| Critical Damping | Q = 0.500 | R1/R2 = 1.0 | C1/C2 = 4.0 | Slow roll-off, zero overshoot in time domain |
| Bessel | Q = 0.577 | R1/R2 = 1.36 | C1/C2 = 2.72 | Audio crossovers, preserving square wave edges |
| Butterworth | Q = 0.707 | R1/R2 = 1.0 | C1/C2 = 2.0 | General purpose, flat passband amplitude |
| Chebyshev (0.5dB) | Q = 0.864 | R1/R2 = 1.0 | C1/C2 = 1.45 | Anti-aliasing where steep roll-off is critical |
| Chebyshev (2.0dB) | Q = 1.126 | R1/R2 = 1.0 | C1/C2 = 1.15 | Extreme noise rejection, high passband ripple |
For a comprehensive interactive design experience, the Texas Instruments Filter Designer Tool is an excellent resource for simulating these alignments and generating exact BOMs. As the table shows, if you force the resistors to be equal ($R_1 = R_2$), you must adjust the capacitor ratios to achieve the desired Q. Conversely, if you use equal capacitors ($C_1 = C_2$), you must adjust the resistor ratios—except for the Butterworth alignment, which elegantly allows both $R_1=R_2$ and $C_1=C_2$ in a unity-gain configuration.
Worked Numeric Example: Designing a 1 kHz Butterworth Filter
Let's design a unity-gain Butterworth low pass Sallen Key filter with a cutoff frequency ($f_c$) of 1 kHz. We will use the equal-component variant ($R_1 = R_2 = R$ and $C_1 = C_2 = C$) for simplicity.
Step 1: Select the Capacitor Value
Capacitors come in fewer standard values than resistors, so we always pick the capacitor first. For a 1 kHz audio-range filter, 10 nF (0.01 µF) is an ideal starting point. It is large enough to swamp PCB parasitic stray capacitance (usually 2-5 pF) but small enough to avoid bulky, expensive film capacitors.
Step 2: Calculate the Resistor Value
The cutoff frequency formula for the equal-component Sallen-Key topology is:
f_c = 1 / (2 * π * R * C)
Rearranging to solve for R:
R = 1 / (2 * π * f_c * C)
Plugging in our target values ($f_c = 1000$ Hz, $C = 10 \times 10^{-9}$ F):
R = 1 / (2 * 3.14159 * 1000 * 0.00000001) = 15,915.5 Ω
Step 3: Select Standard Components
The exact calculated value is 15.915 kΩ. Looking at the standard 1% tolerance E96 resistor series, the closest value is 15.8 kΩ. If you are restricted to the 5% E24 series, use 16 kΩ. Using 15.8 kΩ shifts our actual cutoff frequency slightly to 1,007 Hz, which is well within acceptable tolerances for audio and sensor conditioning.
Step 4: Verify Op-Amp Gain-Bandwidth Product (GBW)
A common failure mode in active filters is selecting an op-amp with insufficient bandwidth, causing the filter to peak or oscillate. The rule of thumb for a Sallen-Key filter is that the op-amp's GBW must be at least 100 times the product of the cutoff frequency and the Q factor:
GBW_min = 100 * f_c * Q
For our 1 kHz Butterworth filter ($Q = 0.707$):
GBW_min = 100 * 1000 * 0.707 = 70.7 kHz
A basic LM358 op-amp has a GBW of roughly 1 MHz, so it passes the mathematical threshold. However, for audio applications, the LM358 introduces severe crossover distortion and high noise. A much better choice is the TL072 (3 MHz GBW, JFET input, low noise) or the OPA2134 (8 MHz GBW, FET input, audiophile grade) for high-fidelity signal paths.
Where You Meet This in Practice (and Edge Cases)
You will encounter the low pass Sallen Key filter in three primary domains: audio DAC reconstruction, ADC anti-aliasing, and DC sensor signal conditioning.
The Capacitor Dielectric Trap
The most frequent real-world mistake when building this filter on a breadboard or PCB is using the wrong capacitor dielectric. If you grab a handful of 10 nF capacitors from your bin, they are likely X7R or Y5V Class II ceramics. These dielectrics exhibit a massive voltage coefficient—meaning their actual capacitance drops by up to 50% when a DC bias voltage is applied across them. Furthermore, X7R capacitors are piezoelectric; they act as microphones, converting mechanical vibrations into electrical noise (microphonics).
The Fix: Always specify C0G (also known as NP0) dielectric capacitors for the C1 and C2 positions in a Sallen-Key filter. C0G is a Class I ceramic with near-zero voltage coefficient, zero piezoelectric effect, and excellent temperature stability. If C0G is unavailable in your target value, use polypropylene or polyester film capacitors.
In ADC anti-aliasing, the Sallen-Key filter is placed directly before a Successive Approximation Register (SAR) or Sigma-Delta ADC. The -40 dB/decade roll-off ensures that high-frequency switching noise from the environment or the ADC's own internal charge-pump is attenuated below the noise floor before it can fold back into the baseband during sampling. According to Electronics Tutorials, cascading two of these second-order stages yields a 4th-order (-80 dB/decade) filter, which is the gold standard for protecting 16-bit and 24-bit ADCs.
In DC sensor conditioning (like load cells or thermocouples), the cutoff frequency is often set very low (e.g., 10 Hz to 50 Hz) to reject 50/60 Hz mains hum and RF interference. At these low frequencies, the required resistor values become massive (often >1 MΩ). When using megaohm resistors, the input bias current of the op-amp creates a significant DC offset voltage. In these low-frequency edge cases, you must select an op-amp with ultra-low input bias current, such as a CMOS device like the TLV2371 or an LMC6482, rather than a bipolar or standard JFET part.
Frequently Asked Questions
Can I use the exact same Sallen-Key topology for a high-pass filter?
Yes. To convert a low pass Sallen Key filter into a high pass Sallen Key filter, you simply swap the positions of the resistors and capacitors. The resistors go in the series signal path, and the capacitors go to ground. The math and alignment tables remain identical, though the practical component selection changes (you now pick the resistor value first and calculate the capacitor).
Why is my Sallen-Key filter output oscillating or ringing?
Oscillation in a unity-gain Sallen-Key filter usually stems from two issues. First, the op-amp's GBW is too low for the desired Q and cutoff frequency, causing the phase margin to collapse. Second, you have a highly capacitive load (like a long coaxial cable or a large bulk capacitor) connected directly to the op-amp's output. The output impedance of the op-amp interacting with the load capacitance creates a pole that destroys stability. Fix this by adding a small series isolation resistor (e.g., 22Ω to 47Ω) between the op-amp output and the capacitive load.
Does the Sallen-Key filter invert the signal?
No. In its standard configuration, the signal is applied to the non-inverting (+) input of the operational amplifier. The output signal will be exactly in-phase with the input signal, just with the high-frequency components attenuated. If you require signal inversion, you should look into the Multiple Feedback (MFB) topology instead.
