Wien Bridge Oscillator Calculator
Calculate and audit the classic op-amp Wien Bridge oscillator using the series RC plus parallel RC positive-feedback network. The tool supports equal-component frequency design, unequal network analysis, amplifier gain, non-inverting gain resistors, loop-gain startup margin, component tolerance range, and a sine-wave slew-rate reference.
The results are intended for first-pass analog oscillator design. Real circuits still require amplitude stabilization, op-amp bandwidth and phase checks, slew-rate margin, distortion analysis, component tolerance review, and bench validation.
Engineering tool
Wien Bridge Oscillator Calculator
Analyze and design the classic op-amp Wien bridge oscillator using the series RC plus parallel RC positive-feedback network.
Mode
Parameter panel
Optional. Leave blank to evaluate phase at the zero-phase frequency.
Result console
- Zero-Phase Frequency
- 1.59155 kHz
- Period
- 628.319 µs
- Feedback β0
- 0.333333V/V
- Required Gain
- 3V/V
- Actual Gain
- 3V/V
- Loop Gain
- 1Aβ
- Startup Margin
- 0%
- Phase at Selected f
- 0deg
- β at Selected f
- 0.333333V/V
Loop gain is close to 1; real startup may need slightly more initial gain.
Wien Formula Audit
- Adopted Network Topology
- Positive-feedback Wien network with a series RC arm and a parallel RC arm.
- Series RC Definition
- Zs = R1 + 1/(sC1).
- Parallel RC Definition
- Zp = R2 || 1/(sC2).
- Feedback Transfer Function
- β(s) = Zp / (Zs + Zp).
- Equal-Component Frequency
- For R1 = R2 = R and C1 = C2 = C, f0 = 1 / (2πRC).
- General Zero-Phase Frequency
- For the adopted topology, f0 = 1 / [2π sqrt(R1R2C1C2)].
- Equal-Component Beta
- For equal R and C, β0 = 1/3.
- General Beta
- β0 is calculated from the same complex transfer function; it is not forced to 1/3.
- Required Gain
- Arequired = 1 / β0.
- Loop Gain Definition
- L = Aβ.
- Startup Margin Definition
- Margin = L - 1, displayed also as percent above threshold.
- Gain Resistor Formula
- Non-inverting gain A = 1 + Rf/Rg.
- Tolerance Model
- Equal-RC worst-case fmin uses Rmax and Cmax; fmax uses Rmin and Cmin.
- Slew-Rate Reference
- SRmin ≈ 2π f Vpeak for a sine wave.
- Op-Amp Non-Ideal Boundary
- GBW, phase shift, slew rate, output swing, amplitude control, and nonlinearities are not fully modeled.
- Formula Used
- 1.59155 kHz and β0 0.333333.
Formula reference
Wien Bridge Oscillator Formulas
The calculator uses the positive-feedback Wien network with a series RC arm feeding a parallel RC arm. Equal-component mode reduces to the familiar f0 = 1 / (2πRC) and required gain of 3.
Zs = R1 + 1/(sC1)Zp = R2 || 1/(sC2)β(s) = Zp / (Zs + Zp)f0 = 1 / [2π sqrt(R1R2C1C2)]Equal RC: f0 = 1 / (2πRC)Equal RC: β0 = 1/3Arequired = 1 / β0A = 1 + Rf/RgRf = (A - 1)RgRg = Rf/(A - 1)L = AβStartup margin = L - 1SRmin ≈ 2πfVpeakVariable definitions
- R1
- resistor in the series RC arm
- C1
- capacitor in the series RC arm
- R2
- resistor in the parallel RC arm
- C2
- capacitor in the parallel RC arm
- β
- feedback network transfer magnitude
- A
- non-inverting amplifier gain
- Rf
- feedback resistor in the non-inverting amplifier
- Rg
- ground resistor in the non-inverting amplifier
Wien Bridge Formula Audit
| Adopted Topology | Positive-feedback Wien network with a series RC arm and a parallel RC arm. |
|---|---|
| Series Arm | Zs = R1 + 1/(sC1). |
| Parallel Arm | Zp = R2 || 1/(sC2). |
| Feedback Transfer | β(s) = Zp / (Zs + Zp). |
| Equal-Component Frequency | For R1 = R2 = R and C1 = C2 = C, f0 = 1 / (2πRC). |
| General Frequency | For the adopted unequal network, f0 = 1 / [2π sqrt(R1R2C1C2)]. |
| Equal-Component Beta | At f0 with equal components, β0 = 1/3. |
| Unequal Beta | β0 is calculated from the complex network transfer function and is not forced to 1/3. |
| Required Gain | Arequired = 1 / β0. |
| Non-Inverting Gain | A = 1 + Rf/Rg. |
| Gain Resistor Solver | Rf = (A - 1)Rg and Rg = Rf/(A - 1). |
| Loop Gain | L = Aβ. |
| Startup Margin | Margin = L - 1, displayed as (L - 1) x 100%. |
| Tolerance Range | Equal-RC fmin uses Rmax and Cmax; fmax uses Rmin and Cmin. |
| Slew-Rate Reference | SRmin ≈ 2πfVpeak, with Vpeak = Vpp/2. |
| Non-Ideal Boundary | Amplitude stabilization, op-amp phase shift, GBW, output swing, distortion, noise, and layout are outside the ideal calculator model. |
Worked Examples
Equal RC frequency
Known: R = 10 kΩ, C = 10 nF
f0 = 1 / (2πRC) ≈ 1.59155 kHz.
Equal RC beta
Known: R1 = R2, C1 = C2
At f0, β0 = 1/3 and Arequired = 3.
Required gain
Known: β0 = 0.333333
Arequired = 1/β0 = 3 V/V.
Loop gain at threshold
Known: A = 3, β = 1/3
L = Aβ = 1 and startup margin = 0% in the ideal model.
Startup margin
Known: A = 3.1, β = 1/3
L ≈ 1.03333 and startup margin ≈ 3.333%.
Insufficient gain
Known: A = 2.9, β = 1/3
L ≈ 0.966667, so the ideal small-signal model predicts no startup.
Solve equal R
Known: Target f = 1 kHz, C = 10 nF
R = 1 / (2πfC) ≈ 15.9155 kΩ.
Solve equal C
Known: Target f = 10 kHz, R = 10 kΩ
C = 1 / (2πfR) ≈ 1.59155 nF.
Feedback resistor
Known: A = 3, Rg = 10 kΩ
Rf = (A - 1)Rg = 20 kΩ.
Ground resistor
Known: A = 3, Rf = 20 kΩ
Rg = Rf/(A - 1) = 10 kΩ.
Unequal network frequency
Known: R1 = 8.2 kΩ, R2 = 12 kΩ, C1 = 15 nF, C2 = 8.2 nF
f0 = 1 / [2π sqrt(R1R2C1C2)], then β0 is evaluated from β(s).
Phase below f0
Known: Evaluate the same network at f0 / 2
The feedback phase is positive, so it is not the zero-phase operating point.
Phase above f0
Known: Evaluate the same network at 2f0
The feedback phase is negative, again outside the zero-phase condition.
Tolerance minimum
Known: R and C at their maximum tolerance limits
Frequency is lowest because f is inversely proportional to RC.
Tolerance maximum
Known: R and C at their minimum tolerance limits
Frequency is highest because the RC product is smallest.
Slew-rate reference
Known: f = 10 kHz, output = 10 Vpp
Vpeak = 5 V and SRmin ≈ 0.314 V/µs.
Unit round trip
Known: 10 nF and 0.01 µF
Both entries produce the same frequency when the unit conversion is correct.
Design boundary
Known: Aβ > 1
This supports startup in the ideal small-signal model but does not guarantee a clean real oscillator.
Engineering Notes
Ideal model
The calculator assumes an ideal RC feedback network and an ideal non-inverting amplifier unless warnings indicate otherwise.
Amplitude stabilization
Real Wien oscillators need gain reduction after startup to avoid clipping and distortion.
Gain margin
A small gain excess can help startup, but too much excess can produce a square-looking output.
Op-amp bandwidth
Choose an op-amp with sufficient gain-bandwidth and phase margin at the target oscillator frequency.
Slew rate
Large sine-wave amplitude at higher frequency can require more slew rate than the small-signal bandwidth estimate suggests.
Component matching
Matched R and C values help keep beta predictable and reduce sensitivity to imbalance.
Capacitor type
C0G/NP0 ceramic, film, or other stable capacitors are preferred for low distortion and frequency stability.
Layout
Keep the high-impedance feedback node compact and away from noisy switching traces.
Startup noise
Oscillation begins from noise or a transient, so a perfectly quiet mathematical model is not a full startup simulation.
Simulation
Use SPICE transient analysis for amplitude control, distortion, clipping, startup time, and op-amp non-ideal effects.
Common Mistakes
Support reference
FAQ
What is a Wien Bridge oscillator?
A Wien Bridge oscillator is an RC sine-wave oscillator that uses a lead-lag positive-feedback network and a non-inverting amplifier to satisfy the zero-phase and loop-gain startup conditions.
What is the Wien Bridge oscillator frequency formula?
For equal components, f0 = 1 / (2πRC). For the adopted unequal series-RC and parallel-RC topology, the zero-phase frequency is f0 = 1 / [2π sqrt(R1R2C1C2)].
Why is the required gain 3 for equal components?
At the equal-component zero-phase frequency, the Wien feedback network has β = 1/3, so the ideal non-inverting amplifier gain required for unity loop gain is A = 1/β = 3.
Does this calculator force beta to 1/3 for unequal components?
No. For unequal R and C values, beta is calculated from β(s) = Zp / (Zs + Zp) at the same zero-phase frequency instead of being forced to 1/3.
What topology does the calculator use?
It uses a series RC arm Zs = R1 + 1/(sC1) and a parallel RC arm Zp = R2 || 1/(sC2), with feedback β(s) = Zp / (Zs + Zp).
What does startup margin mean?
Startup margin is based on loop gain L = Aβ. The margin is L - 1, or (L - 1) x 100% when shown as a percentage.
Does Aβ greater than 1 guarantee a clean oscillator?
No. Aβ above 1 only indicates small-signal startup margin in the ideal model. Real oscillation also depends on op-amp phase shift, bandwidth, slew rate, output swing, nonlinear amplitude control, noise, layout, and component tolerances.
How are Rf and Rg calculated for the amplifier?
The calculator uses the non-inverting gain formula A = 1 + Rf/Rg. Therefore Rf = (A - 1)Rg and Rg = Rf/(A - 1).
What is the tolerance mode?
Tolerance mode estimates the nominal, minimum, and maximum equal-RC oscillation frequency. Minimum frequency uses maximum R and C values; maximum frequency uses minimum R and C values.
Why does a Wien oscillator need amplitude stabilization?
If the gain stays above the steady-state value, the sine wave grows until the amplifier clips. Practical circuits use lamps, diodes, JFETs, AGC loops, or other nonlinear controls to reduce gain after startup.
Can this calculator choose an op-amp?
No. It provides a sine-wave slew-rate reference, but op-amp choice still requires datasheet checks for gain-bandwidth product, phase shift, output swing, noise, distortion, and load drive.
What is the slew-rate formula used?
For a sine wave, SRmin is approximately 2πfVpeak. When output amplitude is entered as Vpp, Vpeak is Vpp/2 and the displayed result is in V/µs.
Can I use mismatched R and C values?
Yes, but the feedback magnitude and required gain change. Matching also affects distortion, frequency accuracy, and startup behavior.
Is this a simulation of a real Wien oscillator?
No. It is an engineering calculator for first-pass frequency, feedback, gain, and tolerance estimates. Verify any final design with circuit simulation, prototype measurements, and the selected op-amp datasheet.
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Engineering Disclaimer
This calculator uses ideal Wien Bridge equations for first-pass engineering estimates. It does not guarantee real oscillator startup, low distortion, amplitude stability, op-amp suitability, or production performance. Validate the final design with simulation, component datasheets, tolerance analysis, and measured prototypes.