Crystal Oscillator Negative Resistance Calculator
Declared idealPierce small signal negative resistance−gm/(ω²C1C2), transistor/parasitic limits omitted, no oscillation startup safety inferred. Actual matched units/topology and independently established parameters; not a safe device/electrical design or verified manufacturer rating.
Description
An ideal Pierce small-signal negative-resistance relation depends on transconductance, angular frequency and load capacitances.
An ideal Pierce small-signal negative-resistance relation depends on transconductance, angular frequency and load capacitances.1
This tool calculates that restricted signed value without determining oscillator startup or parasitic limits.
When to use Crystal Oscillator Negative Resistance Calculator
Use this tool to calculate that restricted signed value without determining oscillator startup or parasitic limits.
How to use Crystal Oscillator Negative Resistance Calculator and how it works
- Prepare callerActualTransconductanceSiemens, actualAngularFrequencyPerSecond, actualFirstLoadCapacitanceFarads, actualSecondLoadCapacitanceFarads, with the units, conventions and assumptions below.
- Enter the required fields and run Crystal Oscillator Negative Resistance Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| callerActualTransconductanceSiemens | Caller Actual Transconductance Siemens. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualAngularFrequencyPerSecond | Actual Angular Frequency Per Second. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualFirstLoadCapacitanceFarads | Actual First Load Capacitance Farads. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualSecondLoadCapacitanceFarads | Actual Second Load Capacitance Farads. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Supply positive transconductance in siemens, angular frequency in radians per second and two positive capacitances in farads. Return -gm/(omega^2*C1*C2) in ohms. The negative sign is retained; no startup margin, crystal drive or complete oscillator stability assessment is performed.
negativeResistanceOhms=-transconductance/(angularFrequency^2*C1*C2) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Signed negative resistance in ohms. | number |
{
"input": {
"callerActualTransconductanceSiemens": 2,
"actualAngularFrequencyPerSecond": 2,
"actualFirstLoadCapacitanceFarads": 1,
"actualSecondLoadCapacitanceFarads": 1
},
"output": {
"result": {
"value": -0.5
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Pcb Via Inductance Calculator for a complementary operation: An isolated via partial-inductance estimate omits its return-path coupling.
Use Pcb Trace Inductance Per Length Calculator for a complementary operation: A trace partial inductance per length depends on a stated isolated long-conductor approximation.
References
Similar or alternative tools
- Pcb Via Inductance Calculator
An isolated via partial-inductance estimate omits its return-path coupling.
- Pcb Trace Inductance Per Length Calculator
A trace partial inductance per length depends on a stated isolated long-conductor approximation.