Notch Filter Calculator
This calculator designs and analyzes balanced passive Twin-T notch filters and standard second-order notch references. It handles 50 Hz and 60 Hz rejection targets, component ratios, tolerance envelope, ideal response, Q, bandwidth, and sweep tables.
V1 deliberately avoids unverified active-notch synthesis and arbitrary unbalanced Twin-T notch-depth claims. Ideal mathematical nulls are labeled as ideal states because real notch depth is finite.
Engineering tool
Notch Filter Calculator
Design balanced Twin-T notch filters, estimate notch frequency, check ratios, evaluate ideal response, and use second-order notch Q/BW references.
Balanced Twin-T target frequency.
Series resistor value used when solving C.
Series capacitor value used when solving R.
Result console
- Series resistor 1
- 15.91549431kΩ
- Series resistor 2
- 15.91549431kΩ
- Shunt resistor
- 7.95774715kΩ
- Series capacitor 1
- 10nF
- Series capacitor 2
- 10nF
- Shunt capacitor
- 20nF
- Calculated notch frequency
- 1,000Hz
- Resistor ratio
- R, R, R/2
- Capacitor ratio
- C, C, 2C
This is an ideal balanced Twin-T target. Real notch depth depends on matching, source impedance, load impedance, and parasitics.
Formula reference
Twin-T Notch Formulas
Adopted topology: Balanced passive Twin-T notch filter. Assumptions: Ideal low source impedance.; High load impedance or buffered load..
Balanced Twin-T: Rseries = R, RBalanced Twin-T: Rshunt = R / 2Balanced Twin-T: Cseries = C, CBalanced Twin-T: Cshunt = 2Cf0 = 1 / (2πRC)R = 1 / (2πf0C)C = 1 / (2πf0R)H(s) = (s² + ω0²) / (s² + 4ω0s + ω0²), where ω0 = 1/(RC)Standard notch reference: H(s) = (s² + ω0²) / (s² + (ω0/Q)s + ω0²)|H| = |1 - x²| / sqrt((1 - x²)² + (x/Q)²), where x = f/f0BW = f0 / QGain dB = 20log10(|H|)Attenuation dB = -Gain dBVariable definitions
- The low-pass T branch uses two equal series resistors
- R and R.
- The high-pass T branch midpoint uses a shunt resistor of R/2 to ground.
- The high-pass T branch uses two equal series capacitors
- C and C.
- The low-pass T branch midpoint uses a shunt capacitor of 2C to ground.
- R
- base series resistor value
- C
- base series capacitor value
- f0
- ideal notch frequency
- Q
- standard second-order notch selectivity reference
- BW
- bandwidth reference
Twin-T Formula Audit
| Adopted Topology | Balanced passive Twin-T notch filter |
|---|---|
| Series Resistor Definition | The low-pass T branch uses two equal series resistors: R and R. |
| Shunt Resistor Definition | The high-pass T branch midpoint uses a shunt resistor of R/2 to ground. |
| Series Capacitor Definition | The high-pass T branch uses two equal series capacitors: C and C. |
| Shunt Capacitor Definition | The low-pass T branch midpoint uses a shunt capacitor of 2C to ground. |
| Ideal Source Assumption | Ideal low source impedance. |
| Load Assumption | High load impedance or buffered load. |
| Notch-Frequency Formula | f0 = 1/(2πRC) |
| Transfer Function | H(s) = (s² + ω0²) / (s² + 4ω0s + ω0²), where ω0 = 1/(RC) |
| Low-Frequency Limit | |H| approaches 1 in the ideal reference response. |
| High-Frequency Limit | |H| approaches 1 in the ideal reference response. |
| At-Notch Behavior | Perfectly balanced ideal network reaches a mathematical null. |
| Mismatch Limitation | Unbalanced exact notch depth is not claimed in V1; mismatch is reported as balance error and warning. |
Worked Examples
1 kHz design
Known: Target f0 = 1 kHz, C = 10 nF
R = 1/(2πf0C) ≈ 15.9155 kΩ.
Shunt resistor
Known: R ≈ 15.9155 kΩ
Balanced shunt resistor is R/2 ≈ 7.95775 kΩ.
Shunt capacitor
Known: C = 10 nF
Balanced shunt capacitor is 2C = 20 nF.
50 Hz hum notch
Known: Target f0 = 50 Hz, C = 100 nF
R ≈ 31.831 kΩ.
60 Hz hum notch
Known: Target f0 = 60 Hz, C = 100 nF
R ≈ 26.5258 kΩ.
Known R/C
Known: R = 10 kΩ, C = 10 nF
f0 ≈ 1591.55 Hz.
At f0
Known: Balanced ideal Twin-T
The ideal response is an Ideal Mathematical Null.
Far below f0
Known: f << f0
Ideal notch reference response approaches passband gain.
Far above f0
Known: f >> f0
Ideal notch reference response approaches passband gain.
Tolerance envelope
Known: R ±1%, C ±5%
Frequency range uses Rmax/Cmax for fmin and Rmin/Cmin for fmax.
R shift
Known: +1% R only
Notch frequency decreases because f0 is inversely proportional to R.
C shift
Known: +5% C only
Notch frequency decreases because f0 is inversely proportional to C.
Q reference
Known: f0 = 1 kHz, Q = 10
BW = 100 Hz.
Generic notch null
Known: Second-order notch at f0
The numerator is zero, so display uses Ideal Mathematical Null.
Frequency units
Known: 1000 Hz and 1 kHz
Both evaluate to the same notch point.
Log sweep
Known: 50 points
The table returns finite ordered rows and null states without raw Infinity.
Unbalanced ratios
Known: Rshunt not equal to R/2
The calculator reports Unbalanced Twin-T and warns that notch depth can degrade.
Round-trip solver
Known: f0 + C → R → calculated f0
The recovered frequency returns to the target within numerical tolerance.
Notch Filter
A notch filter rejects a narrow frequency band around a target frequency.
Band-Stop Filter
Band-stop and band-reject are broader terms for filters that attenuate a frequency band.
Twin-T Network
Balanced Twin-T networks rely on accurate R/R/R2 and C/C/2C relationships.
Notch Frequency
For the adopted balanced topology, f0 = 1/(2πRC).
Notch Depth
Ideal networks can reach a mathematical null, but real notch depth is finite.
Q Factor
Q is a second-order reference for selectivity and bandwidth, not an exact arbitrary Twin-T loading model.
50/60 Hz Hum
Hum rejection needs frequency tolerance review because mains frequency and components can shift.
Source Impedance
Passive Twin-T response assumes low source impedance.
Load Impedance
A high load impedance or buffer prevents the load from disturbing the RC ratios.
Active Buffering
Buffering helps isolate the Twin-T network but does not eliminate matching requirements.
Common Mistakes
Support reference
FAQ
What is a notch filter?
A notch filter, also called a band-stop or band-reject filter, attenuates a narrow band around a target frequency while passing lower and higher frequencies.
What is a Twin-T notch filter?
A Twin-T notch filter is a passive notch topology made from a low-pass T network and a high-pass T network connected in parallel.
How do I calculate Twin-T notch frequency?
For the adopted balanced Twin-T topology, the ideal notch frequency is f0 = 1/(2πRC), where the series resistors are R and the series capacitors are C.
What resistor and capacitor ratios are used in a balanced Twin-T?
The low-pass T branch uses two series resistors R and R with a shunt capacitor 2C. The high-pass T branch uses two series capacitors C and C with a shunt resistor R/2.
How do I design a 50 Hz notch filter?
Choose either R or C, set the target frequency to 50 Hz, and solve the other value using R = 1/(2πf0C) or C = 1/(2πf0R). Component tolerance should be reviewed carefully.
How do I design a 60 Hz notch filter?
Use 60 Hz as the target notch frequency and solve the balanced Twin-T base R or C value. Real mains frequency, tolerance, and loading can shift the effective notch.
Why is my notch not very deep?
Real notch depth is limited by resistor and capacitor matching, source impedance, load impedance, parasitics, layout, and active-buffer implementation.
How do component tolerances affect notch depth?
Tolerance shifts the notch frequency and unbalances the Twin-T ratio. This calculator reports frequency tolerance envelope and ratio warnings, but does not invent an unverified exact notch-depth estimate.
How does source impedance affect a Twin-T filter?
Passive Twin-T response assumes low source impedance. A large source impedance can change the effective network ratios and degrade the notch.
Why is buffering useful?
A buffer can isolate the Twin-T network from source and load impedance. Buffering improves practical repeatability but does not remove tolerance or parasitic limits.
What is Q in a notch filter?
Q is a selectivity reference. In the standard second-order notch model, Q = f0/BW, where BW is the selected stopband or reference bandwidth.
What is the difference between notch frequency and bandwidth?
Notch frequency is the center of rejection. Bandwidth describes how wide the rejected band is around that frequency.
Is a passive Twin-T the same as an active notch filter?
No. A passive Twin-T is the RC network itself. Active notch filters may buffer the network or place it inside an op-amp feedback loop, which changes practical behavior.
Planned Engineering Guides
Planned guide
Twin-T Notch Filters Explained
Planned guide
How to Design 50 Hz and 60 Hz Notch Filters
Planned guide
Notch Filter Q and Bandwidth
Planned guide
Component Tolerance in Notch Filters
Planned guide
Passive vs Active Notch Filters
Planned Filter Calculators
Butterworth Filter Calculator
Multiple-Feedback Low-Pass Filter Calculator
Pi Filter Calculator
Related Calculators
Filter Q Factor & Bandwidth Calculator
Analyze Q, bandwidth, fractional bandwidth, and exact reference frequencies.
AvailableSallen-Key Low-Pass Filter Calculator
Design and analyze second-order Sallen-Key low-pass active filters.
AvailableSallen-Key High-Pass Filter Calculator
Design and analyze second-order Sallen-Key high-pass active filters.
AvailableMultiple-Feedback Band-Pass Filter Calculator
Design and analyze second-order MFB active band-pass filters.
AvailableGain Bandwidth Product Calculator
Review op-amp bandwidth constraints for active or buffered notch implementations.
AvailableFrequency / Period Converter
Convert 50 Hz, 60 Hz, and other interference frequencies to periods.
Engineering Disclaimer
This calculator uses ideal balanced Twin-T and standard second-order notch reference models. It does not model exact unbalanced notch depth, real source impedance, real load impedance, op-amp non-idealities, PCB parasitics, capacitor ESR, leakage, or EMI certification behavior. Validate critical notch filters with SPICE, tolerance analysis, and bench measurement.