Editing Hartley oscillator (section)

==Operation==

[[Image:Hartley osc.svg|framed|Hartley oscillator using a [[common-drain]] n-channel [[JFET]] instead of a tube.]]

The Hartley oscillator is distinguished by a [[tank circuit]] consisting of two series-connected [[inductor|coils]] (or, often, a [[coil tap|tapped]] coil) in parallel with a capacitor, with an amplifier between the relatively [[high impedance]] across the entire LC tank and the relatively low voltage/high current point between the coils. The original 1915 version used a [[triode]] as the amplifying device in [[common cathode]] configuration, with three batteries, and separate adjustable coils. The simplified [[common-drain]] [[Junction FET|JFET]] circuit diagram uses an [[LC tank]] (here the single winding is tapped) and a single battery, but is otherwise essentially the same as the patent drawing. The circuit illustrates the Hartley oscillator operation:{{dubious|Circuit operation|reason=Many subtle problems with description such as JFET gm, Q killing, and lossless elements "absorbing" signals off resonance|date=August 2015}}

* the output from the JFET's ''source'' (''emitter'', if a [[Bipolar Junction Transistor|BJT]] had been used; ''cathode'' for a triode) has the same [[phase (waves)|phase]] as the signal at its gate (or base) and roughly the same voltage as its input (which is the voltage across the entire tank circuit), but the ''current is amplified'', i.e. it is acting as a [[Buffer amplifier#Current buffer|current buffer]] or [[VCVS|voltage-controlled voltage-source]].
* this low impedance output is then fed into the coil tapping, effectively into an [[autotransformer]] that will step up the voltage, requiring a relatively high current (compared with that available at the top of the coil).
* with the capacitor-coil [[resonance]], all frequencies other than the tuned frequency will tend to be absorbed  (the tank will appear as nearly 0Ω near DC due to the inductor's low [[Electrical reactance|reactance]] at low frequencies, and low again at very high frequencies due to the capacitor); they will also shift the phase of the feedback from the 0° needed for oscillation at all but the tuned frequency.

Variations on the simple circuit often include ways to [[Automatic gain control|automatically]] reduce the amplifier gain to maintain a constant output voltage at a level below overload; the simple circuit above will limit the output voltage due to the gate conducting on positive peaks, effectively damping oscillations but not before significant distortion ([[Spurious tone|spurious]] [[harmonics]]) may result. Changing the tapped coil to two separate coils, as in the original patent schematic, still results in a working oscillator but now that the two coils are not [[magnetically coupled]] the inductance, and so frequency, calculation has to be modified (see below), and the explanation of the voltage increase mechanism is more complicated than the autotransformer scenario.

A quite different implementation using a tapped coil in an LC tank feedback arrangement is to employ a common-grid (or common-gate or common-base) amplifier stage,<ref>{{cite web|last1=Coates|first1=Eric|title=The Hartley Oscillator|url=http://www.learnabout-electronics.org/Oscillators/osc21.php|website=Learnabout electronics|access-date=22 March 2016}}</ref> which is still [[non-inverting]] but provides ''voltage gain'' instead of ''current gain''; the coil tapping is still connected to the cathode (or source or emitter), but this is now the (low impedance) input to the amplifier; the split tank circuit is now dropping the impedance from the relatively high output impedance of the plate (or drain or collector).

[[File:Oscillator comparison.svg|thumb|Comparison of Hartley and Colpitts oscillator]]
The Hartley oscillator is the [[Duality (electrical circuits)|dual]] of the [[Colpitts oscillator]], which uses two capacitors rather than two inductors for its [[voltage divider]]. Although there is no requirement for [[Mutual Inductance|mutual coupling]] between the two coil segments, the circuit is usually implemented using a tapped coil, with the feedback taken from the tap, as shown here. The optimal tapping point (or ratio of coil inductances) depends on the amplifying device used, which may be a [[bipolar junction transistor]], [[FET]], triode, or amplifier of almost any type (non-inverting in this case, although variations of the circuit with an earthed centre-point and feedback from an [[inverting amplifier]] or the collector/drain of a transistor are also common), but a [[junction FET]] (shown) or triode is often employed as a good degree of amplitude stability (and thus [[distortion]] reduction) can be achieved with a simple [[grid leak]] <!-- is grid-leak confusing here? Hope not --> resistor-capacitor combination in series with the gate or grid (see the Scott circuit below) thanks to [[diode]] conduction on signal peaks building up enough [[reverse bias|negative bias]] to limit amplification.

The frequency of oscillation is approximately the [[resonant frequency]] of the tank circuit.  If the capacitance of the tank capacitor is ''C'' and the total [[inductance]] of the tapped coil is ''L'' then
:<math>f =  {1 \over 2 \pi \sqrt {LC}} \,</math>
If two ''uncoupled'' coils of inductance ''L''<sub>1</sub> and ''L''<sub>2</sub> are used then 
:<math>L = L_1 + L_2 \,</math>
However, if the two coils are magnetically coupled the total inductance will be greater because of [[mutual inductance]] ''k''<ref>Jim McLucas, Hartley oscillator requires no coupled inductors, EDN October 26, 2006 {{cite web |url=http://www.edn.com/article/CA6343253.html |title=Hartley oscillator requires no coupled inductors - 10/26/2006 - EDN |access-date=2008-12-10 |url-status=dead |archive-url=https://web.archive.org/web/20080704153045/http://www.edn.com/article/CA6343253.html |archive-date=2008-07-04 }}</ref>
:<math>L = L_1 + L_2 + k \sqrt{L_1 L_2} \,</math>
The actual oscillation frequency will be slightly lower than given above, because of [[parasitic capacitance]] in the coil and loading by the transistor.

The Hartley oscillator has several advantages:

* The frequency may be adjusted using a single [[variable capacitor]], one side of which can be earthed
* The output amplitude remains constant over the frequency range
* Either a tapped coil or two fixed inductors are needed, and very few other components
* Easy to create an accurate fixed-frequency [[crystal oscillator]] variation by replacing the capacitor with a (parallel-resonant) [[quartz crystal]] or replacing the top half of the [[tank circuit]] with a crystal and grid-leak resistor (as in the [[Tri-tet oscillator]]).

The output is harmonic-rich if taken from the amplifier and not directly from the LC circuit (unless amplitude-stabilisation circuitry is employed). This may be considered an advantage or a disadvantage.

===Practical example===
[[File:Hartley Osz JFET Drain.gif|framed|Practical common-drain Hartley oscillator with an oscillation frequency of ~10&nbsp;MHz]]

The schematic shows an example with component values.<ref>{{cite book   
  | last = Hayward
  | first = Wes
  | title = Introduction to Radio Frequency Design
  | chapter = Figure 7.16 A practical JFET Hartley oscillator
  | publisher = ARRL
  | year = 1994
  | location = US
  | page = 285
  | url = https://archive.org/details/isbn_9780872594920
  | doi = 
  | id = 
  | isbn = 0-87259-492-0}}</ref> Instead of [[field-effect transistors]], other active components such as [[bipolar junction transistor]]s or [[vacuum tube]]s, capable of producing gain at the desired frequency, could be used.

The [[common-drain|common drain amplifier]] has a high input impedance and a low output impedance. Therefore the amplifier input is connected to the high impedance top of the LC circuit C1, L1, L2 and the amplifier output is connected to the low impedance tap of the LC circuit. The [[grid leak]] C2 and R1 sets the [[operating point]] automatically through [[Biasing#Grid_leak_bias|grid leak bias]]. A smaller value of C2 gives less [[Distortion#Harmonic_distortion|harmonic distortion]], but requires a larger load resistor. The load resistor RL is part of the simulation, not part of the circuit.