Hartley Oscillator Calculator
Calculate and design an ideal Hartley oscillator tank using L1, L2, tank capacitance, and optional coupling orientation. The tool solves equivalent inductance, frequency, mutual inductance, inductive divider references, reactance, capacitance, and tolerance range.
This is topology-specific. It extends a generic LC resonance calculation with tapped-inductor behavior, mutual inductance sign, winding polarity boundaries, and startup limitations.
Engineering tool
Hartley Oscillator Calculator
Analyze and design the ideal Hartley oscillator tank using split inductors, capacitance, and optional coupling orientation.
Mode
Parameter panel
Optional. Leave blank to evaluate reactance at ideal f0.
Result console
- Oscillation Frequency
- 3.558813 MHz
- Equivalent Inductance
- 20 µH
- Mutual Inductance M
- 0 nH
- Coupling Contribution
- 0 nH
- Period
- 280.992589 ns
- L1:L2 Ratio
- 1
- L2:L1 Ratio
- 1
- Turns Ratio Ref
- 1N1/N2
- XLeq
- 447.213595 Ω
- XC
- 447.213595 Ω
- Tank Status
- Near Tank Resonance
Hartley Formula Audit
- Adopted Tank Topology
- Ideal Hartley LC tank with split inductors L1/L2 and one tank capacitor C.
- L1 Definition
- L1 is one section of the tapped inductor or one coupled inductor segment.
- L2 Definition
- L2 is the second tapped or coupled inductor segment.
- Coupling Convention
- Uncoupled uses M = 0; aiding adds +2M; opposing subtracts -2M.
- Mutual Inductance Formula
- M = k√(L1L2) in the ideal two-coupled-inductor model.
- Aiding Leq
- Leq = L1 + L2 + 2M.
- Opposing Leq
- Leq = L1 + L2 - 2M; Leq must remain positive.
- Oscillation Frequency
- f0 = 1 / (2π√(LeqC)).
- Reactance Identity
- At ideal f0, XLeq = XC.
- Inductive Divider Definition
- The calculator reports L1:L2, L2:L1, and turns-ratio references.
- Feedback Ratio Boundary
- A universal loop beta cannot be stated without active-device topology, winding polarity, and node definitions.
- Component Solvers
- C solver supports coupling; L1/L2 solvers are intentionally limited to uncoupled mode in V1.
- Tolerance Model
- Tolerance mode uses uncoupled worst-case L1/L2/C corners.
- Startup Boundary
- Tank resonance does not guarantee oscillation startup or amplitude stability.
- Formula Used
- 3.558813 MHz with Leq 20 µH.
Formula reference
Hartley Oscillator Formulas
The ideal Hartley tank uses split inductance and one capacitance. Mutual inductance must include orientation.
M = k√(L1L2)Uncoupled: Leq = L1 + L2Series aiding: Leq = L1 + L2 + 2MSeries opposing: Leq = L1 + L2 - 2Mf0 = 1 / (2π√(LeqC))XL,eq = 2πfLeqXC = 1 / (2πfC)At f0: XL,eq = XCC = 1 / [(2πf0)^2Leq]Variable definitions
- L1
- first inductor segment
- L2
- second inductor segment
- C
- tank capacitance
- k
- coupling coefficient
- M
- mutual inductance
- Leq
- equivalent tank inductance
- f0
- ideal tank resonant frequency
Hartley Formula Audit
| Adopted Tank Topology | Ideal Hartley LC tank using split inductance L1/L2 and tank capacitance C. |
|---|---|
| L1 Definition | One tapped-inductor segment or one coupled-inductor section. |
| L2 Definition | The second tapped-inductor segment or coupled-inductor section. |
| Coupling Convention | Uncoupled uses M = 0; series aiding adds +2M; series opposing subtracts -2M. |
| Mutual Inductance Formula | M = k√(L1L2), where 0 <= k <= 1. |
| Aiding Leq | Leq = L1 + L2 + 2M. |
| Opposing Leq | Leq = L1 + L2 - 2M, requiring positive Leq. |
| Oscillation Frequency | f0 = 1/(2π√(LeqC)). |
| Reactance Identity | At ideal f0, XLeq = XC. |
| Inductive Divider Definition | L1:L2, L2:L1, and turns-ratio references are reported. |
| Feedback Ratio Boundary | Loop beta depends on active circuit, winding polarity, tap node, and loading. |
| Component Solvers | Capacitance solver supports coupling; L1/L2 solvers are uncoupled in V1. |
| Tolerance Model | Uncoupled worst-case corners recompute Leq from L1/L2 corners. |
| Startup Boundary | Tank resonance does not guarantee oscillator startup. |
Worked Examples
Uncoupled Leq
Known: L1 = 10 µH, L2 = 10 µH
Leq = 20 µH.
Oscillation frequency
Known: Leq = 20 µH, C = 100 pF
f0 ≈ 3.55881 MHz.
Reactance identity
Known: At f0
XLeq and XC are equal in the ideal tank.
Inductive ratio
Known: L1 = 10 µH, L2 = 40 µH
L1:L2 = 1:4 and turns ratio reference N1:N2 ≈ 1:2.
Mutual inductance
Known: L1 = L2 = 10 µH, k = 0.5
M = 5 µH.
Series aiding
Known: L1 = L2 = 10 µH, k = 0.5
Leq = 30 µH.
Series opposing
Known: L1 = L2 = 10 µH, k = 0.5
Leq = 10 µH.
Aiding frequency shift
Known: Aiding coupling increases Leq
Frequency is lower than the uncoupled case.
Opposing frequency shift
Known: Opposing coupling reduces Leq
Frequency is higher as long as Leq remains positive.
Solve capacitance
Known: Target f with known L1 and L2
C is solved from C = 1/[(2πf0)^2Leq] and round-trips through analysis.
Solve L2
Known: Target f, C, known L1, uncoupled
L2 = Leq,target - L1, requiring a positive result.
Invalid solved L
Known: Target Leq less than known L1
The solver rejects the design instead of returning negative inductance.
k = 0
Known: Aiding or opposing with k = 0
The result is identical to uncoupled.
Cancellation boundary
Known: L1 = L2, k = 1, opposing
Leq = 0 ideal cancellation boundary, so resonance is invalid.
Tolerance range
Known: L1/L2 ±5%, C ±5%
fmin < fnominal < fmax using worst-case corners.
Unit equivalence
Known: 1000 nH = 1 µH
Equivalent unit inputs produce the same result.
Frequency units
Known: 1 MHz = 1000 kHz
Target-design outputs match after unit conversion.
Design round trip
Known: Solve C or L, then analyze
The analyzer recovers the target frequency within numerical tolerance.
Engineering Notes
Hartley oscillator
A Hartley oscillator uses an inductive divider in its LC tank.
Hartley vs Colpitts
Hartley uses an inductive divider; Colpitts uses a capacitive divider.
Mutual coupling
Coupled inductors require M = k√(L1L2) and a defined orientation.
Winding polarity
Wrong polarity can reduce Leq, reverse feedback phase, or prevent oscillation.
Feedback boundary
The calculator does not claim a universal loop beta because the active circuit defines feedback.
Tank Q
Winding resistance, core loss, load resistance, and capacitor ESR reduce Q and startup margin.
Startup
Frequency selection is not enough; the active device must overcome tank loss.
Core saturation
Large-signal operation can shift inductance and increase distortion.
Parasitics
Winding capacitance, transistor capacitance, PCB capacitance, and probe loading shift high-frequency tanks.
Verification
Critical RF Hartley designs need device models, SPICE, layout review, and measured validation.
Common Mistakes
- Always using L1 + L2 while ignoring coupling.
- Using +2M without checking winding polarity.
- Treating k as mutual inductance instead of a dimensionless coefficient.
- Forgetting M = k√(L1L2).
- Calling L1/L2 a universal feedback beta.
- Confusing Hartley inductive divider with Colpitts capacitive divider.
- Allowing negative solved inductance.
- Continuing calculation when opposing coupling makes Leq <= 0.
- Assuming resonance guarantees startup.
- Ignoring winding resistance and tank Q.
- Ignoring parasitic capacitance at RF.
- Ignoring core saturation.
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Support reference
FAQ
What is a Hartley oscillator?
A Hartley oscillator is an LC oscillator that uses an inductive divider, often a tapped inductor or two coupled inductors, with a tank capacitor.
How do I calculate Hartley oscillator frequency?
Calculate the equivalent inductance Leq from L1, L2, and any mutual coupling, then use f0 = 1/(2π√(LeqC)).
How do I calculate the equivalent inductance?
For uncoupled inductors Leq = L1 + L2. For ideal coupled inductors, series-aiding uses L1 + L2 + 2M and series-opposing uses L1 + L2 - 2M.
When can I use L1 + L2?
Use L1 + L2 when the split inductors are effectively uncoupled or when the tapped-inductor coupling contribution is intentionally ignored as a first-order estimate.
What is mutual inductance?
Mutual inductance M represents magnetic coupling between L1 and L2. In the ideal coupling model, M = k√(L1L2), where k is the coupling coefficient.
How does coupling coefficient affect Hartley frequency?
Series-aiding coupling increases Leq and lowers frequency. Series-opposing coupling reduces Leq and raises frequency, as long as Leq remains positive.
What is the difference between series-aiding and series-opposing inductance?
Aiding orientation adds the mutual contribution +2M. Opposing orientation subtracts it as -2M and can approach cancellation if coupling is very strong.
How does the L1/L2 ratio affect feedback?
The inductance ratio affects the tank divider reference, but the actual loop feedback factor depends on topology, winding polarity, tap node, loading, and active device.
What is the feedback ratio of a Hartley oscillator?
There is no universal feedback beta that is safe without defining the circuit connection. This calculator reports inductance and turns-ratio references instead.
Why does winding polarity matter?
Winding polarity determines whether mutual inductance is aiding or opposing and whether the feedback phase supports oscillation.
How do I solve the capacitor for a target frequency?
After calculating Leq from the selected coupling model, use C = 1/[(2πf0)^2Leq].
How do component tolerances affect frequency?
In the uncoupled tolerance model, low frequency occurs with maximum L1, L2, and C. High frequency occurs with minimum L1, L2, and C.
Does LC resonance guarantee oscillation?
No. Resonance selects the frequency, but startup still requires loop gain or negative resistance sufficient to overcome tank losses.
What is the difference between Hartley and Colpitts oscillators?
A Hartley oscillator uses an inductive divider. A Colpitts oscillator uses a capacitive divider. Both are LC feedback oscillators, but the feedback network differs.