A Sallen filter (formally the Sallen-Key topology) is a second-order active analog filter that uses a single operational amplifier, two resistors, and two capacitors to shape frequency response without the signal degradation and loading issues inherent to passive RC networks. In a real circuit, it changes a sloppy -20 dB/decade passive roll-off into a sharp -40 dB/decade active attenuation while providing a low-impedance output that can drive an ADC or audio line without the load impedance altering the cutoff frequency. Beginners commonly confuse it with cascaded passive RC stages (which interact and fail to achieve a true -40 dB/decade slope without interstage buffers) or the Multiple Feedback (MFB) topology (which inverts the phase and requires tighter op-amp gain-bandwidth margins).
The Core Anatomy of a Sallen-Key Network
The standard unity-gain Sallen-Key low-pass filter routes the input signal through a two-stage RC network directly into the high-impedance non-inverting input of an op-amp. The op-amp is configured as a voltage follower (output tied directly to the inverting input). Because the op-amp draws virtually zero input bias current, it isolates the delicate RC voltage divider from whatever load is connected to the output.
The magic of the Sallen topology lies in the feedback capacitor (C1) connected from the op-amp output back to the node between the two resistors. At high frequencies, the op-amp output drops to zero, pulling that intermediate node to ground through C1 and accelerating the attenuation rate to -40 dB/decade. By adjusting the ratio of the resistors and capacitors, or by adding gain to the non-inverting amplifier stage, you can tune the filter's Q factor to achieve Butterworth (maximally flat), Chebyshev (steeper roll-off with passband ripple), or Bessel (linear phase) response curves.
While both are second-order active topologies, the Sallen-Key filter is non-inverting and highly stable at unity gain, making it ideal for audio and sensor buffering. The MFB topology inverts the signal, requires the op-amp to have a much higher Gain-Bandwidth Product (GBW) to maintain the same Q factor, and is generally reserved for high-gain or high-Q bandpass applications where component spread needs to be minimized.
Worked Numeric Example: 1 kHz Butterworth Low-Pass
Let us design a unity-gain ($K=1$) 1 kHz Butterworth low-pass Sallen filter to act as an anti-aliasing front-end for a 3.3V microcontroller ADC sampling at 4 kSPS. For a Butterworth response, the damping factor requires $Q = 0.707$. At unity gain, this simplifies the math significantly if we set $C_1 = C_2 = C$ and $R_1 = R_2 = R$.
The cutoff frequency formula simplifies to:
$f_c = \frac{1}{2 \pi R C}$
Step 1: Select the Capacitors
Always start with capacitors, as standard values are sparser than resistors. We need a 1 kHz cutoff, so 10 nF is an excellent starting point. Crucially, you must use C0G/NP0 dielectric capacitors. X7R or Y5V ceramics exhibit severe capacitance loss under DC bias and introduce piezoelectric microphonics that will inject noise into your signal path. We will specify a Kemet C315C103J1G5TA (10 nF, 50V, C0G, 5% tolerance).
Step 2: Calculate the Resistors
Rearranging the formula for R:
$R = \frac{1}{2 \pi \times 1000 \text{ Hz} \times 10 \times 10^{-9} \text{ F}} \approx 15,915 \Omega$
The closest standard 1% (E96 series) resistor value is 15.8 kΩ. Using a Yageo RC0603FR-0715K8L gives us an actual cutoff frequency of roughly 1,008 Hz, which is well within the acceptable margin for ADC anti-aliasing.
Step 3: Select the Op-Amp
For a 3.3V rail-to-rail system driving a SAR ADC, the Texas Instruments TLV2372 is a robust choice. It offers rail-to-rail I/O, a GBW of 3 MHz (more than enough for a 1 kHz filter), and low quiescent current.
| Component | Designator | Value | Specification / Part Number |
|---|---|---|---|
| Resistor | R1, R2 | 15.8 kΩ | 1%, 0603, Metal Film (Yageo RC0603FR-0715K8L) |
| Capacitor | C1, C2 | 10 nF | C0G/NP0, 50V, 5% (Kemet C315C103J1G5TA) |
| Op-Amp | U1 | Unity-Gain Buffer | TLV2372 (Dual, RRIO, 3 MHz GBW) |
For automated component selection and Bode plot verification, analog engineers heavily rely on the Texas Instruments Filter Designer or the Analog Devices Filter Wizard. These tools account for real-world op-amp non-idealities like finite open-loop gain and phase margin degradation at high frequencies.
Where You Meet This in Practice
You will rarely see a Sallen filter used for high-frequency RF work, but it dominates the sub-100 kHz analog signal chain. Here is where it earns its keep on the bench:
- DAC Reconstruction (Audio): In hi-fi audio DACs, a Sallen-Key low-pass filter removes the high-frequency quantization steps and switching noise generated by the digital-to-analog converter, leaving only the clean 20 Hz - 20 kHz audio band. The non-inverting nature of the Sallen-Key topology preserves the absolute phase of the audio signal.
- ADC Anti-Aliasing (Industrial Sensors): When sampling a 4-20mA pressure transducer with a microcontroller, a Sallen filter is placed directly before the ADC sample-and-hold circuit. It strips out 50/60 Hz mains hum and high-frequency EMI, preventing those signals from folding back into your baseband measurement and corrupting your data.
- Biomedical Baseline Wander Removal: In ECG (electrocardiogram) front-ends, high-pass Sallen-Key filters are used to block the DC offset and low-frequency baseline wander caused by patient respiration and sweat, while passing the 1 Hz to 40 Hz QRS complex.
A critical layout rule for all these applications: keep the feedback capacitor (C1) physically adjacent to the op-amp's output and non-inverting input pins. Any parasitic trace capacitance added to the high-impedance summing node will alter the Q factor and can cause peaking or even high-frequency oscillation.
Sallen Filter FAQ
Why use a Sallen filter instead of a passive RC filter?
A single passive RC filter only provides a -20 dB/decade roll-off, which is too gradual for most anti-aliasing or noise-rejection tasks. If you cascade two passive RC stages to get -40 dB/decade, the second stage loads down the first stage, shifting the cutoff frequency and destroying the Q factor (resulting in a sagging, poorly defined knee). A Sallen filter uses an op-amp to buffer the stages and actively drive the feedback capacitor, yielding a precise, mathematically predictable -40 dB/decade slope with a low-impedance output that can drive cables and ADC inputs directly.
What is the difference between Sallen-Key and Multiple Feedback (MFB) filters?
The primary differences are phase, gain sensitivity, and component spread. The Sallen-Key topology is non-inverting and can be configured for unity gain, making it highly stable and easy to tune. However, at high Q factors (Q > 3) or high gains, the Sallen-Key topology becomes extremely sensitive to the op-amp's Gain-Bandwidth Product (GBW). The MFB topology inverts the signal phase but handles high-Q and high-gain requirements much more gracefully, requiring less GBW from the op-amp and allowing for a tighter spread of capacitor values. For general-purpose low-pass and high-pass filtering below Q=1, Sallen-Key is the default choice.
How do I choose the right op-amp for a Sallen-Key filter?
Selection hinges on three datasheet parameters: Gain-Bandwidth Product (GBW), Slew Rate, and Input Bias Current. As a strict rule of thumb, your op-amp's GBW must be at least $100 \times f_c \times Q$ to prevent the finite open-loop gain from degrading your filter's stopband attenuation. For a 1 kHz filter with a Q of 0.707, you need a minimum GBW of ~70 kHz (though 1 MHz+ is preferred for clean transient response). If your filter handles large voltage swings at high frequencies, verify that the op-amp's Slew Rate (V/μs) exceeds $2 \pi \times f_{max} \times V_{peak}$ to avoid slew-induced distortion. Finally, if you are using high-value resistors (e.g., >100 kΩ) to minimize capacitor size, choose a CMOS or JFET-input op-amp with picoamp-level input bias currents to prevent DC offset errors. For a deeper dive into active filter component selection, Electronics Tutorials provides excellent foundational math on op-amp limitations in active networks.
