Aren KhachaturianElectrical Engineering
Projects / Sallen-Key Filter

1 kHz Sallen-Key
Low-Pass Filter

I designed and simulated a second-order, unity-gain active low-pass filter targeting a 1 kHz cutoff, then checked it with an AC sweep and an automated measurement.

Target1.000 kHz
Calculated1.02 kHz
Simulated (−3 dB)1.023 kHz
ToolsLTspice

Why I built it

I wanted practice turning a target frequency response into component values, and then proving the circuit behaves the way the calculation predicts.

Circuit design

LTspice schematic: R1, R2 10k; C1 22n; C2 11n; op-amp U1 with ±5 V supplies
Figure 1. LTspice schematic with component values and op-amp supply connections.

The math

With R1 = R2 = 10 kΩ, C1 = 22 nF and C2 = 11 nF, the cutoff frequency is

fc=12πR1R2C1C2=12π(10,000)(10,000)(22×10−9)(11×10−9)≈1,023 Hz≈1.02 kHz\begin{aligned} f_c &= \frac{1}{2\pi\sqrt{R_1 R_2 C_1 C_2}} \\[12pt] &= \frac{1}{2\pi\sqrt{(10{,}000)(10{,}000)(22\times10^{-9})(11\times10^{-9})}} \\[12pt] &\approx 1{,}023\ \mathrm{Hz} \approx 1.02\ \mathrm{kHz} \end{aligned}

Verification

An AC sweep shows the classic low-pass shape: flat through the passband, then rolling off above 1 kHz. The close-up view makes the −3 dB region easier to see.

Full frequency response
Figure 2. Full frequency response.
Zoomed frequency response near 1 kHz
Figure 3. Close-up near the cutoff (100 Hz – 10 kHz).

Cutoff-frequency measurement

Reading a cutoff off a graph is imprecise, so I used a .meas command to find the frequency where the output magnitude reaches 0.7071 (−3.01 dB).

1,023.06 Hz

LTspice-measured cutoff. That matches my hand calculation (≈1,023 Hz) and is 2.3% above the 1 kHz design target.

cutoff: mag(V(out))=0.70710678 AT 1023.05854255
Figure 4. LTspice output log.

What I learned

  • How to pick component values from a target cutoff frequency.
  • How to build and sweep a circuit in LTspice and read the frequency response.
  • How to use .meas for exact results so I'm not estimating from a plot.
  • How to compare simulation against hand analysis to check my design.