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A resistor pair in a Wien-bridge oscillator influences both frequency selection and the feedback attenuation that the amplifier must overcome. These two outcomes do not respond identically to resistor variation. A pair can preserve frequency closely while changing the gain requirement, or track perfectly while moving frequency. Specify the printed network from both relationships and include the capacitors and amplifier rather than treating resistance matching alone as an oscillator specification.
For a drawing-specific part, review the Custom printed resistor network construction, product evidence and quotation inputs alongside this method. Prepare the resistance and tolerance tool with your operating conditions.
Key design decisions
- Evaluate the resistor product for frequency and the resistor ratio for feedback attenuation as separate quantities.
- Use actual capacitor relationships alongside the printed resistor requirements.
- Keep passive-network calculations separate from startup, amplitude regulation, distortion and complete-circuit verification.
Name the series and shunt branches unambiguously
Define the frequency-selective branch from amplifier output to its positive-feedback node as series R1 and C1. From that node to the small-signal reference, place R2 in parallel with C2. The following calculation assumes a low-impedance source, negligible loading of the feedback node and ideal passive elements within the modeled frequency range.
The amplifier's negative-feedback resistors are a different part of the circuit. Keep their labels and required gain separate from the two frequency-selective resistors. A custom printed network may include some or all of these resistors, but external capacitors, active-device behavior and the reference connection remain part of the implemented oscillator. State which elements the requested network actually contains.
Calculate the passive transfer before closing the loop
Write the series impedance as Zs = R1 + 1/(sC1) and the shunt impedance as Zp = R2/(1 + sR2C2). Their divider transfer is beta(s) = Zp/(Zs + Zp). Expanding gives a denominator containing both the resistor product and the resistor-to-capacitor relationships. Keeping the elements unequal exposes requirements hidden by the familiar equal-component case.
At sinusoidal frequency, the passive phase crosses zero when omega0 squared times R1R2C1C2 equals one. At that frequency, the passive gain is 1/(1 + R1/R2 + C2/C1). Equal resistors and equal capacitors reduce it to one third, but equality is not required for the general zero-phase expression to exist.
f0 = 1/[2 pi sqrt(R1 R2 C1 C2)]; beta0 = 1/(1 + R1/R2 + C2/C1)
- f0 is the passive network's zero-phase frequency in hertz.
- R values are in ohms and C values in farads.
- beta0 is the dimensionless passive transfer at f0 under the stated branch definition.
Ideal series-RC and shunt-RC network with negligible receiver loading and low source impedance. Amplifier phase and parasitic elements can shift the actual closed-loop oscillation frequency.
Establish an independent nominal comparison
Assume both frequency-selective resistors are 15 kilohms and both capacitors are 22 nanofarads. The passive zero-phase frequency is approximately 482.288 Hz and beta0 is one third. An ideal noninverting amplifier would require a gain magnitude of three for unity loop-gain magnitude at that passive frequency, if its own phase contribution were negligible.
This does not establish a practical startup or stable-amplitude condition. It provides a nominal point around which to allocate passive variations. Retain the absolute resistance values as well as their ratio, because the bridge loading and interaction with nonideal active circuitry depend on impedance. Do not substitute a ratio-only acceptance report for the full circuit values.
Recognize the frequency effect of common resistor movement
If both resistors increase by the same one-percent factor while capacitors remain unchanged, R1/R2 stays equal to one. The passive attenuation remains one third, but the resistor product increases by 1.01 squared. Frequency therefore decreases by a factor of 1/1.01 to approximately 477.513 Hz.
This is a 0.9901-percent frequency reduction despite perfect resistor tracking. A network can consequently meet a tight ratio requirement while missing an absolute frequency allocation. The appropriate corrective action is not automatically tighter matching; the common resistance scale and the capacitor product must be considered. The same distinction applies to correlated changes after thermal exposure or adjustment.
Recognize the gain effect of opposing resistor movement
Now let R1 increase one percent and R2 decrease one percent. Their product is only 0.9999 of nominal, so frequency rises by approximately 50.004 parts per million to 482.312 Hz. Yet R1/R2 becomes 1.020202 rather than one. The ideal reciprocal feedback factor becomes 3.020202 instead of three.
The required gain has increased approximately 0.6734 percent while frequency barely changes. Measuring only oscillator frequency would therefore provide weak evidence that the resistor relationship supports the intended loop behavior. It could miss a change that consumes available startup margin or shifts the operating point of an amplitude-control system.
| Resistor condition | Passive frequency | Reciprocal passive gain | Main allocation exposed |
|---|---|---|---|
| Both nominal | 482.288 Hz | 3.000000 | Nominal comparison |
| Both +1% | 477.513 Hz | 3.000000 | Common impedance scale |
| R1 +1%; R2 −1% | 482.312 Hz | 3.020202 | Differential ratio change |
| R1 −1%; R2 +1% | 482.312 Hz | 2.980198 | Opposite attenuation change at the same frequency |
Include capacitor ratio and product in the same review
The capacitor product enters frequency in the same multiplicative way as the resistor product, while C2/C1 appears separately in the attenuation denominator. Improving only resistor matching cannot remove capacitor mismatch. Request capacitor values and their relevant operating dependencies when evaluating a printed network intended for this circuit.
For example, with nominal equal resistors but C1 two percent high and C2 two percent low, the capacitor product is 0.9996 of nominal. Frequency rises by approximately 200.06 parts per million, while reciprocal passive gain becomes 1 + 1 + 0.98/1.02 = 2.960784. These calculations describe the selected mismatch, not a recommended capacitor tolerance or a prediction of measured output distortion.
Keep startup and amplitude control outside the passive equality
An ideal unity loop-gain equality identifies a sustaining condition, not a guarantee that a real circuit starts reliably and settles to the required amplitude. The amplifier introduces frequency-dependent gain and phase, and practical amplitude regulation changes the effective loop behavior as the signal develops. Excess gain without controlled limiting can drive clipping rather than a useful clean waveform.
Evaluate the complete circuit's startup, stable amplitude and distortion at the intended supply, temperature and load. Do not adjust the printed pair solely until one room-temperature frequency reading looks correct. That operation can alter attenuation and place more demand on the amplitude-control range. Frequency trim and loop-gain allocation must be coordinated, including the physically reachable direction of any resistor adjustment.
Specify two passive outcomes and verify the complete circuit
A useful network requirement identifies the allowed resistor product or resulting passive frequency contribution separately from the allowed resistor ratio or attenuation contribution. Include measured capacitors if the network will be adjusted to a particular assembled set. Preserve the association between that set and the final calibration rather than treating an adjusted network as interchangeable with any nominal capacitor pair.
Measure the passive branch response where practical without letting the measurement instrument add a material load. Then verify the complete oscillator under its required operating states. Keep the reported passive zero-phase frequency distinct from the actual oscillation frequency, and preserve startup and amplitude observations separately. This turns matching into a circuit-linked specification without claiming that the passive printed network alone establishes oscillator performance.
Provide the frequency-selective and gain-setting circuit
Send both branches and the intended adjustment strategy so resistor requirements can be assigned to the correct oscillator behavior.
- Series R1–C1 and parallel R2–C2 connections, nominal values, actual capacitor data and the small-signal reference.
- Required frequency range and the allocated common and differential resistor variation.
- Amplifier and negative-feedback circuit, startup requirement, amplitude-control arrangement and operating load.
- Permitted trim elements and adjustment direction, with any capacitor-pair association used during calibration.
- Passive frequency-response measurements and complete-circuit startup, amplitude and distortion observations across the intended states.
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