Hartley Oscillator
The Hartley oscillator, patented by Ralph Hartley in 1915, is the oldest and one of the most widely built LC oscillator circuits. Where the Colpitts uses a capacitive voltage divider (two capacitors, one inductor) to produce feedback, the Hartley does the reverse — it uses an inductive voltage divider, implemented as a tapped inductor (two inductor sections, one capacitor). The result is a simple, robust oscillator that is especially easy to tune over a wide frequency range.
The Hartley Topology — Inductive Voltage Divider
In the Hartley oscillator, the tank circuit consists of a single capacitor C and two inductors L1 and L2, typically wound as a tapped coil on a single former. The capacitor connects from one end of the combined inductor to the other (across the whole inductor), while the tap between L1 and L2 is the feedback point.
The transistor is usually connected in common-emitter configuration (unlike the Colpitts, which is often common-base). The collector connects to the top of the tank (one end of the inductor), the emitter connects to the junction of L1/L2 (the tap), and the base is connected to the emitter through a feedback network. Alternatively, in the grounded-collector (common-collector) form, the circuit is slightly rearranged but the inductive feedback principle remains the same.
The most common practical arrangement is: capacitor C connected across the full inductor (from collector to ground), the tap providing feedback from a point part-way along the inductor. The transistor's emitter connects to ground and the tap connects to the transistor base through a coupling capacitor. The phase relationships work out such that the total loop phase is 360° (= 0°), satisfying the Barkhausen phase condition.
Hartley oscillator schematic. The tank circuit is capacitor C in parallel with the series combination of L1 and L2. The tap between L1 and L2 feeds back a fraction of the tank voltage to the transistor base, sustaining oscillation.
View LargerHow the Tapped Inductor Produces Feedback
To understand the feedback mechanism, think of the tapped inductor as an RF transformer or auto-transformer. The full inductor (L1 + L2) has a voltage across it equal to the full tank voltage. The smaller section L1 (between the collector connection and the tap) has a smaller voltage across it, proportional to L1/(L1+L2). Similarly, L2 (from the tap to ground) has a voltage of L2/(L1+L2) times the tank voltage across it.
The feedback voltage returned to the base is the voltage across L2 (or L1, depending on which end connects to ground). This voltage is in the correct phase to provide positive feedback because an inductor's voltage is 180° out of phase with the current through it, and the two inductor sections produce opposite phase relationships at the tap — the combination works out to sustain oscillation.
The Hartley tapped inductor. Voltage distributes across L1 and L2 in proportion to their inductances. The feedback fraction is L2/(L1+L2) or L1/(L1+L2) depending on the circuit orientation. The tap acts as an inductive voltage divider.
View LargerThe feedback fraction in the Hartley oscillator is:
β = L2 / (L1 + L2) (where L2 is the inductor section connected between the tap and the base)
Typical values: L1 about 20–30% of total, L2 about 70–80% of total, giving β ≈ 0.7 — but the amplifier gain is effectively reduced by the transistor's emitter bypass, so total loop gain is still manageable. In many Hartley designs, L2 is 10–25% of total to give a feedback fraction of 0.1–0.25 (10%–25%).
The Frequency Formula
The oscillation frequency is set by the resonant frequency of the tank. In the tank, capacitor C is in parallel with the series combination of L1 and L2. When the two inductor sections are wound on separate, non-coupled formers (no mutual inductance between them), the total inductance is simply their sum:
Ltotal = L1 + L2
f = 1 / (2π × √(Ltotal × C))
f = 1 / (2π × √((L1 + L2) × C))
This formula is identical in structure to the basic LC resonance formula, with Ltotal being the sum of the two inductor sections and C being the single tank capacitor. Compare this with the Colpitts: the same formula applies, but with Cseries (the series combination of C1 and C2) in place of C, and a single L.
Mutual Inductance and Its Effect
When L1 and L2 are wound on the same former (as a tapped coil), the magnetic fields of the two sections interact — this is mutual inductance (M). Mutual inductance increases the effective total inductance by 2M (where M is the mutual inductance between the sections), giving:
Ltotal = L1 + L2 + 2M
f = 1 / (2π × √((L1 + L2 + 2M) × C))
The mutual inductance M equals k × √(L1 × L2), where k is the coupling coefficient (0 for no coupling, 1 for perfect coupling). For a tightly wound coil with both sections on the same former and wound in the same direction, k is typically 0.5 to 0.9. For two separate, well-separated coils, k approaches 0 and M is negligible.
In practical Hartley oscillator design for HF radio work, the two coil sections are usually wound on the same toroidal or air-wound former, so mutual inductance is significant. If you measure L1 and L2 separately and calculate Ltotal = L1 + L2, the actual oscillation frequency will be lower than calculated because the real Ltotal is higher due to mutual coupling. To get the correct frequency, either measure the total inductance of the complete tapped coil (which automatically includes mutual coupling), or use a shorter tap to reduce coupling effects.
Worked Examples at Ham Radio Frequencies
Design a Hartley oscillator for the 20-meter band (14.0–14.35 MHz). Target centre frequency 14.175 MHz.
Choose the tuning capacitor: Use a 100 pF variable capacitor (35–100 pF range gives tuning across the band).
For 14.175 MHz with C = 100 pF:
Ltotal = 1 / (4π² × f² × C)
= 1 / (4 × 9.87 × (14.175 × 106)² × 100 × 10-12)
= 1 / (4 × 9.87 × 200.93 × 1012 × 10-10)
= 1 / (793.3 × 102)
= 1 / (79,330) ≈ 0.886 μH
Design the tapped coil:
Wind 9 turns of #24 enamelled wire on a T50-6 core (6 is the mix for 10–50 MHz).
Approximate inductance: ≈ 1.0 μH (close to needed 0.886 μH).
Place the tap at turn 2 from the grounded end. L2 ≈ 2/9 × 1.0 μH = 0.22 μH, L1 ≈ 0.78 μH.
Feedback fraction: β ≈ L2/Ltotal = 0.22/1.0 = 0.22 (22%) — suitable.
Check frequency:
f = 1 / (2π × √(1.0 × 10-6 × 100 × 10-12))
= 1 / (2π × 10 × 10-9)
= 1 / (62.83 × 10-9) = 15.92 MHz
Slightly high — increase turns to 10 (≈1.23 μH) for centre frequency near 14.3 MHz. Fine-tune by adjusting the core depth in an air-wound version, or by using a ferrite slug for adjustment in a commercial design.
For 28.4 MHz using a 47 pF fixed capacitor and variable series capacitor for tuning.
Ltotal needed = 1 / (4π² × (28.4 × 106)² × 47 × 10-12)
= 1 / (4 × 9.87 × 806.56 × 1012 × 4.7 × 10-11)
= 1 / (150.0 × 103) = 666 nH ≈ 0.67 μH
Wind 6 turns on T50-6 (≈0.4 μH each for this core). Increase to 8 turns (≈0.7 μH) for a closer match. Tap at turn 2 from grounded end for 25% feedback.
Hartley Oscillator Frequency Calculator
Hartley Oscillator Frequency Calculator
Enter the two inductor values and the tank capacitance. The total inductance is L1 + L2 (assuming negligible mutual coupling between the sections). If the sections are on the same former, add the measured mutual inductance correction manually.
Hartley vs Colpitts — Comparison and Selection
The Hartley and Colpitts are the two most common LC oscillator types and are often interchangeable for a given application, but each has advantages that make it preferred in certain situations.
| Feature | Hartley | Colpitts |
|---|---|---|
| Feedback element | Tapped inductor (inductive divider) | Two capacitors (capacitive divider) |
| Number of reactive components | 2 inductors + 1 capacitor | 1 inductor + 2 capacitors |
| Tuning method | Variable capacitor across the full tank | Variable capacitor (often in series with L) |
| Wide-range tuning | Excellent — single variable cap tunes frequency without changing feedback ratio | Good — but must ensure feedback ratio stays acceptable across range |
| Frequency stability | Moderate — inductor is large and physically sensitive | Good to very good — especially with Clapp variant |
| Harmonic output | Moderate | Similar to Hartley; Clapp produces cleaner output |
| VHF suitability | Less suitable above 100 MHz (inductor lead inductance is significant) | Better at VHF — small chip capacitors easy to use |
| Circuit complexity | Simple — fewer components to specify | Simple — slightly easier capacitor selection |
| Typical ham use | HF VFOs (1–30 MHz), broadcast receivers | HF VFOs, VHF oscillators, crystal oscillators |
The key practical advantage of the Hartley at HF is tuning: when you turn a variable capacitor connected across the full tank, you change the resonant frequency without changing the feedback ratio (β = L2/Ltotal stays constant as long as L1 and L2 are fixed). In a Colpitts, a variable capacitor that is part of C1 or C2 changes both the frequency and the feedback fraction simultaneously, which can alter the oscillation amplitude across the tuning range.
For fixed-frequency or narrow-range tuning, the Colpitts (especially the Clapp variant) generally gives better frequency stability and lower drift. For wide-range tuning VFOs at HF, the Hartley is often the more practical choice.
Practical Design Notes
Tap position: The tap at 1/5 to 1/4 of the total turns from the grounded end is a typical starting point. This gives L2 ≈ (1/5)² = 4% to (1/4)² = 6% of total inductance — actually, for a uniformly wound coil, inductance is proportional to turns squared, so a tap at 1/4 of turns gives L2 = (0.25)² / (1)² × Ltotal only if the entire inductor is uniformly wound. In practice, wind the coil, measure Ltotal, then experiment with tap position to find the ratio that gives clean oscillation without excessive distortion.
Component rating: At HF (3–30 MHz), the peak voltage across the tank can be several times the DC supply voltage. Capacitors must be rated for this. Use capacitors with at least twice the supply voltage rating. At QRP power levels (1 W), a 50 V-rated capacitor is usually adequate.
Grounding the tap: In the most common Hartley circuit, the tap goes to the transistor base, and the emitter is grounded. For best stability, keep the RF ground (emitter bypass capacitor) as short as possible — use a short, direct connection from emitter to the copper ground plane.
Wide-range tuning: To tune across an entire amateur band (e.g., 7.0–7.3 MHz, about 4% tuning range), you need about 8% capacitance variation (since f ∝ 1/√C). A 10–100 pF variable capacitor (10:1 range) gives over an octave of tuning — far more than needed for a single band. For a single amateur band, a 2:1 capacitance ratio is typically sufficient.
Frequently Asked Questions
Do the two inductor sections in a Hartley have to be wound on the same coil?
No. They can be two separate inductors in series, with no mutual coupling. When wound separately on separate formers and positioned at right angles to each other (to minimise coupling), M ≈ 0 and Ltotal = L1 + L2. This approach gives predictable frequency calculation since mutual inductance is negligible. However, two separate coils take up more space and may have lower Q than a single tapped coil of the same total inductance, because the single coil uses the core material more efficiently.
Why is the Hartley less common at VHF compared to HF?
At VHF (above 30 MHz), inductance values are very small — typically 10–100 nH. Making a reliable tap on such a tiny inductor is mechanically difficult. Additionally, the lead length between the tap point and the transistor contributes its own parasitic inductance (about 1 nH per mm of wire), which becomes a significant fraction of the total and shifts the frequency unpredictably. The Colpitts avoids this problem: its feedback comes from two capacitors, which are easy to solder directly to the circuit board without long leads.
Can the same inductor be used as both the tank and the coupling transformer to the antenna?
Yes — this is the principle of the MOPA (Master Oscillator Power Amplifier) transmitter and some simple transmitter designs. A link winding — a few turns wound over the main tank coil — magnetically couples RF power out of the tank to the antenna or the next stage. The link winding typically has 3–5 turns for a 50 Ω load. However, coupling the load directly to the tank coil (even through a link) does affect the tank Q and can pull the frequency, so this technique is mainly used in simple or low-power transmitters where perfect frequency stability is not critical.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.