# Voltage amplitude of Hartley oscillator

I am trying to follow these videos to learn about oscillator circuits; Hartley, Colpitts, and Clapp oscillators and they're all helpful to understand the LC relationship for frequency.

I am concerned with selecting a Vin and different R1/R2 and Rfc's to get a desired amplitude on the vout of the circuit.

Pictured is the Khan Academy video I used to build my circuit in LTspice and my current LTspice model which I can get to produce a sine wave.

I would like to figure out the best way to control my Vout amplitudes ideally to keep the Vout pk-pk amplitude around 10mV but capable of as large f0 range as possible?

• Try making the inductors smaller, while keeping the capacitor the same, e.g. 0.22u (BTW, even if units are discarded, the inductors are still meant to be Henry, unless the world is up-side down). Commented Jul 14, 2022 at 18:41
• Just a possibly useful site. A lot of good info there.
– jonk
Commented Jul 14, 2022 at 19:39

While conceptually useful (oscillations are possible) component values chosen make this "Hartley" unlikely to oscillate over a wide frequency range.
A summary of design goals:

• oscillate over a wide frequency range
• sine wave out
• output voltage amplitude constant at all frequencies.

The components that most-affect frequency are L1, L2, C2.
The stated equation is a good start to determine oscillation frequency: $$\ f_r={1}\over{2\times\pi\times \sqrt{(L1+L2)\times C_2}}\$$, in this case 75.87kHz.
LTspice settles at a frequency near 75.5 kHz.
However, those 2.2uh inductors must be very high quality, above 200 Q factor at this frequency, else their resistive losses kill oscillations. Furthermore, taking an output voltage from transistor collector (a high-impedance point) will also tend to kill oscillations, because amplifier gain is dependent on a high impedance here...a breadboard attempt is unlikely to oscillate.

Decreasing C2 improves the critical Q required of those two L's. For example,
with C2=0.1uf, inductor Q near 60 results in LTspice oscillation.
With C2=0.01uf, inductor Q of 26 is adequate for oscillations , however the oscillator now squeggs because C5 is now too large and/or feedback too robust.

Sinusoidal waveshape is often achieved by choosing resonator components so that L's and C2 trade a great deal of energy back and forth during the oscillation cycle. Only a little energy is extracted to the load, and the amplifier is only required to replenish energy lost to the load, plus a little more to account for component Q.
In other words, the resonator runs at a high Q - perhaps half of unloaded Q.
Even though the amplifier has very non-sinusoidal currents, resonator Q smooths currents into something much more sinusoidal. An inductive link or tap might be a good way to extract resonator energy. Buffer stages having high input impedance and low output impedance work too.

Achieving constant amplitude over a wide frequency range is difficult for a few reasons:

• amplifier gain and impedances are frequency-dependent
• resonator Q often varies with frequency when C2 or L's are variable.

In these type LC oscillators, gain must always be high enough to ensure that oscillations start. Excess gain can be dialed-back by using an automatic-gain-control (AGC) mechanism, which re-biases the amplifier at some lower collector current. Doing so often requires extra circuitry. The extra complexity gives you more freedom to optimize other oscillator qualities, like spectral purity or noise floor.

Apart from AGC, an oscillator can be biased so the collector current bottoms out to zero current on one peak of the oscillator cycle. This will put an end to exponential amplitude growth, eventually settling to constant oscillator amplitude. Many one-transistor oscillators use this method (see below).

One of the strongest amplitude control methods for a single-transistor LC oscillator uses the base-to-collector diode junction to clamp the collector's most negative peak.
I have re-arranged the OP's oscillator to show how this mechanism works. Collector starts at Vcc voltage of +10V. Base bias has been raised from OP's 1V up to 5V. L1, L2 ratio has been changed so that collector impedance is higher than base impedance, and inductor Q is (unreasonably) near infinite:
Note that V(collector) bottoms-out near 5V when the base-collector diode becomes forward-biased for a moment, a real gain-killer. You can see that collector current reverses direction for this moment, then immediately after, pulses up in the other direction to maintain oscillations. Collector peak voltage is limited to near 5V - a very well-defined upper limit to amplitude. Be aware that this mechanism also limits resonator loaded Q as well - something not often desired.
When C2 is returned to 1uf, with near-infinite inductor Q's, amplitude of V(collector) almost reaches the 5V-clamp limit as above, so the oscillator reverts to the other gain-control mechanism where collector current bottoms-out at zero for most of the oscillation cycle:
In this last case, those very non-linear collector current pulses still result in a collector voltage of a clean sinusoidal shape. Harmonic content of this collector voltage is suppressed by about -70 dB...easy to do with infinite-Q components!

I am concerned with selecting a Vin and different R1/R2 and Rfc's to get the desired amplitude on the out of the circuit.

I guess that "Vin" is the supply voltage (?) ...
For such a goal, you need to know the whole "transfer" function ...

Here is a picture to begin studying ... In this case, L1 & L2 are not coupled.
Just to know "how" oscillation starts (search for Laplace function).
Note the "non-linearity" of the "oscillation" ...
Note also that at the very start, there is also a special "start", which is not "seen" in this picture.

Zoom in the "start" but note the time logarithmic scale.
(perhaps simulation "artifact", power supply "step").

Quote: "I am concerned with selecting a Vin and different R1/R2 and Rfc's to get a desired amplitude on the vout of the circuit."

Why do you ask for Vin? An oscillator provided an output without any input signal.

Regarding the output amplitude: Because the oscillator must start at zero amplitude the gain must be large enough to cause a continuous increase of the amplitude. Therefore, when the circuit does not contain a special provision for limiting the amplitude, the signal will grow until it reaches the upper limit (supply voltage). In such a case, the signal is "clipped" and it is not sinusoidal anymore.

For this reason, it is best to include a "soft-limiting device" (for example a diode circuit) for determining the amplitude without a hard clipping effect. So it is possible that the user determines the amplitude he wants.