Hartley Oscillator

BJT Hartley oscillator design calculator – step-by-step with all formulas shown

This calculator designs a BJT Hartley oscillator in either of two topologies: a tapped-coil common-base variant (single autotransformer winding split into L_c/L_e with feedback to the emitter) or a transformer-coupled common-emitter variant (separate primary/secondary coils on a shared core with feedback to the base). It computes the tank inductance/capacitance for the target frequency, the coupling ratio, DC bias point, loop gain against the Barkhausen criterion, and an estimate of the output amplitude.

0Select oscillator variant

Variant A – Tapped coil on shared core (Common-Base)
Autotransformer topology, feedback to emitter, CB configuration
  • Transistor Q1 in common-base configuration – base is RF ground
  • Single tapped coil wound on a shared core (or two tightly coupled halves)
  • L_c – upper portion: collector → tap point
  • L_e – lower portion: tap point → GND
  • Tank capacitor C connected in parallel with the entire coil (L_c + L_e)
  • RF choke (RFC) supplies DC to the collector, blocks RF from the supply rail
  • The tap point drives the emitter – this is the feedback input
  • Base bypassed to RF ground via capacitor C_b
  • Output taken from the collector via coupling capacitor C_out
  • Coupling factor k ≈ 1.0 for a single continuous winding
Variant B – Transformer-coupled Hartley (Common-Emitter)
Two separate coils on shared core, feedback to base, CE configuration
  • Transistor Q1 in common-emitter configuration
  • Primary coil L_p is in the collector circuit and resonates with tank capacitor C
  • L_p connected: collector → L_p → GND, with C in parallel
  • Secondary coil L_s wound on the same core, magnetically coupled with factor k
  • L_s feeds the base of Q1 via coupling capacitor C_k – this is the feedback path
  • Mutual inductance: M = k · √(L_p · L_s)
  • Emitter resistor R_E provides DC stability; bypassed by C_E for RF signals
  • Output taken from the collector (or optionally from a tertiary winding)
  • Typical coupling factor: k = 0.5 – 0.95

1Input parameters

Transistor and power supply
Collector bias current
Recommended ≈ VCC/2
Air / ferrite core: 50–200
Variant A – Tapped coil (autotransformer)
Collector → tap point
Tap point → GND
1.0 = single winding
Note on effective inductance: L_eff = L_c + L_e + 2·M, where M = k·√(L_c·L_e)
Single winding (k≈1): M ≈ √(L_c·L_e) → L_eff ≈ (√L_c + √L_e)²
Uncoupled coils (k=0): M = 0 → L_eff = L_c + L_e

Formula Reference

Thomson's formula (LC resonance):
f₀ = 1 / (2π · √(L · C))
ω₀ = 2π · f₀ = 1 / √(L · C)
Solving for C given f₀ and L:
C = 1 / ((2π · f₀)² · L)
Effective inductance (Variant A, shared core):
M = k · √(L_c · L_e) ← mutual inductance
L_eff = L_c + L_e + 2M ← series-aiding connection
For k=1: L_eff = (√L_c + √L_e)²
Effective inductance (Variant B, transformer):
L_eff = L_p (tank resonates on primary only)
Secondary L_s does not significantly affect f₀

Variant A – Tapped coil:
M = k · √(L_c · L_e)
n = (L_e + M) / (L_c + L_e + 2M) = (L_e + M) / L_eff
Limiting cases:
  k=0: n = L_e / (L_c + L_e) [simple inductive divider]
  k=1: n = √(L_e / L_eff) [autotransformer ratio]
Variant B – Transformer:
M = k · √(L_p · L_s)
n = M / L_p = k · √(L_s / L_p) [voltage transformation ratio]
Physical meaning:
n = V_feedback / V_tank
V_fb = n · V_tank (voltage applied to the transistor input)

Barkhausen criterion:
|A · β_fb| ≥ 1 (amplitude condition)
arg(A · β_fb) = 0° (phase condition – satisfied by circuit topology)
Transistor transconductance:
g_m = I_C / V_T, where V_T = 26 mV at 25 °C
g_m [mS] = I_C [mA] / 26
Dynamic (parallel) resistance of LC tank:
X_L = ω₀ · L = 2π · f₀ · L [coil reactance]
R_p = Q_L · X_L [parallel equivalent resistance]
Loop gain:
A_v = g_m · R_p [transistor voltage gain across tank]
T = g_m · R_p · n [total loop gain]
Oscillation condition: T ≥ 1
Minimum transistor β (practical rule of thumb):
Var A: β_min ≈ L_c / L_e
Var B: β_min ≈ 1/n = L_p / M

Bias operating point:
V_E = max(1.0 V, 0.1 · V_CC) [emitter stabilisation]
V_B = V_E + 0.65 V
I_E ≈ I_C · (1 + 1/β)
I_B = I_C / β
I_div = 10 · I_B [stiff voltage divider]
Base voltage divider:
R₁ = (V_CC − V_B) / I_div
R₂ = V_B / I_div
Emitter resistor:
R_E = V_E / I_E
RF choke (RFC) – collector supply:
X_RFC ≥ 10 · R_p (must not load the tank)
L_RFC = X_RFC / (2π · f₀)
Typical: 10–100 μH (HF), 0.1–10 μH (VHF)
Collector resistor R_C (inferior alternative to RFC):
R_C = (V_CC − V_CE − V_E) / I_C
Loads the tank → reduces Q → lower output voltage
For oscillators: use RFC whenever possible!

Maximum tank voltage swing (small-signal upper bound):
V_tank,pk = I_C · R_p
Limit from transistor saturation:
V_swing,max = V_CE,Q − V_CE,sat ≈ V_CE,Q − 0.2 V
Practical output amplitude estimate:
V_out,pk = min(V_tank,pk, V_swing,max) · 0.9
(factor 0.9 = safety margin before saturation)
RMS value and feedback voltage:
V_out,rms = V_out,pk / √2
V_fb,pk = V_out,pk · n
Note:
Actual amplitude depends on the limiting mechanism (soft transistor
nonlinearity, AGC, or hard saturation). These are approximate upper bounds.