Franklin oscillator is a radio frequency oscillator with some interesting properties. No coil taps or capacitive dividers are needed.
Franklin oscillator uses two active devices to provide 360 degrees phase shift necessary for the positive feedback and oscillations. LC circuit is very loosely coupled to this dual amplifier, permitting very good sinewave waveform. No coil taps or capacitive dividers are needed.
In this particular case, 420 kHz - 780 kHz frequency range was achieved on the protoboard. High end frequency was limited by large parasitic capacitances of protoboard wiring. Positive feedback amount can be changed with C1, C2 and R5. Smaller values of C1 and C2 should be used on higher frequencies (to reduce LC tank loading). R5 value should be experimented with to achieve adequate feedback for oscillation, and to prevent waveform distortion.
Coil used was wound on a ferrite stick covered with tight cardboard tube, so that ferrite stick can be taken in and out of the coil. Ferrite diameter was about 10 mm. Cardboard tube diameter is about 12 mm, and wire wound on top of that is about 13 mm in diameter. 100 turns with 0.4 mm diameter enameled wire were used, turns being wound tight next to each other. This coil (cylinder of wound wire) ended up being 43 mm long.
Variable capacitor is standard small variable capacitor from transistor radio receiver. Oscillator and input circuit sections are shorted together, increasing the maximum capacitance. When ferrite stick was taken out of the coil, maximum frequency of 3800 kHz was recorded, without any other changes in the circuit.
Q1 and Q2 are 2N4401, but any silicon small signal transistor can be used, like 2N3904, BC548, BC108, etc.
All components are non-critical, and the circuit will work with significant changes, as long as C1 and C2 are kept large enough for oscillations to commence.
RF output should be applied to a buffer stage (grounded collector or similar).
Modulation was tried successfully: collector of Q1 was connected to the collector of modulator transistor through the resistor of 2.2 - 10 K in value.