# Op Amp based Hartley oscillator

I would like to build an oscillator that will satisfy a few requirements. The main requirement is to have exactly one capacitor. Another one is to have high Q and sine wave output.

I am considering Hartley's oscillator design. Since it has only one cap. I don't what to built the biasing network and select a transistor that will suit the oscillator's needs, so I figured that there must be a way to build Hartley's oscillator around an operational amplifier as shown on the figure below.

I have made the simulation as shown above, and I believe it should oscillate, since the gain of the Op Amp negative feedback loop is greater than $\frac{L1}{L2}$ ratio. But the oscillations start and die. I can see that the frequency of the decaying oscillations is correct, but they would not sustain. I event tried to crack the gain up to some unreasonable number, but this doesn't help at all.

Can anyone advise me as to what I'm overlooking and how to make this circuit oscillate?

PS. The simulation uses 741. If is is not the best op-amp for the job, then what would be a good replacement?

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## 2 Answers

I think you have a few issues that you need to address.

The primary issue is that the Q of your tank is very low. The Q of a parallel RLC circuit is:

$$Q=R\sqrt{\frac{C}{L}}$$

Considering that your resistive feedback is effectively in parallel with the tank, we can calculate Q:

$$1500\Omega \sqrt{\frac{1nF}{15\mu H}}=Q= 12$$

The Q of 12 is VERY low, so this is probably your main issue. Increasing the magnitude of R1 and R2 should be sufficient for your circuit to oscillate properly. See my example simulation here. If your Q is too low, you will need more gain to compensate for the losses.

A second potential problem is that the op-amp you selected, the 741, has a bandwidth that is a bit low for the frequency you selected. The datasheet indicates a bandwidth of 1.5 MHz, and your oscillator frequency is 1.3 MHz. This may result in your op-amp not providing enough gain for the oscillator to function properly. There are MANY op-amps that would provide an improvement over a 741.

Another possible issue is that oscillators are a bit tricky to get working in simulators. While it sounds like this is not an issue for you, it is a potential pitfall. Often, the random noise that usually starts oscillators in reality does not occur in a simulator. Often a noise source or impulse is required to kick-start the oscillator.

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Thanks for the advice. Will try. What's the purpose of the 100Ohm resistor at the Op-Amp output in your simulation? – udushu Nov 29 '11 at 17:49
I've changed the circuit to oscillate at 100kHz with the Q of 7800. The feedback resistors R1 and R2 are 25k and 100k respectively. The oscillations now sustain for approx. 2ms but then die. Is there any other pitfalls that might contribute? – udushu Nov 29 '11 at 18:06
@udushu The 100 ohm resistor on the output is to simulate a finite output resistance. I tried building the circuit in PSPICE, and I got similar results as you. I had to significantly decrease the frequency to maintain stable oscillation. – W5VO Nov 30 '11 at 4:26
@udushu Given the behavior of the oscillations, it looks like there is significant loss in the system. I suspect the op-amp is the culpret, as the phase starts to roll off before 100kHz - well before the gain becomes an issue. This topology may be unsuitable for any frequency << the bandwidth of the op-amp. – W5VO Nov 30 '11 at 4:29
I've tried to replace the 741 with an ideal op-amp but I am still getting the same results. This is funny, because, I got the Hartly's working on a single BJT and it is working like a charm. But the op-amp just would not give up. – udushu Nov 30 '11 at 4:44

W5VO has explained things well, oscillators in SPICE can be really tricky, and sometimes just don't work correctly at all.
The opamp model you are using can sometimes stop things working (sometimes they are not accurate), lack of real world noise makes it difficult to start etc.

Follow W5V)'s advice (e.g. about resistors), plus here's a few extra thoughts on making it work with the 741.

Tips for getting oscillation to start:

You can use .startup to start the supply rails at 0V

You can set initial conditions e.g. `.ic I(L1) = 10mA, or V(n001) = 2V and so on.

You can apply a voltage source in series e.g. a sine wave at the expected frequency of oscillation for e.g. 100 cycles to get it started. It will not affect the circuit when it's completed N cycles as long as you don't set the source series resistance > 0 ohms.

The 741 is a very old opamp with a low GBP. You would need to lower you frequency of oscillation. Try setting C1 to 100nF, and using .startup. If that doesn't work include a voltage source in series between C1 and opamp out of 1V for 100 cycles at ~129kHz.

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I used the 741 because it is an OpAmp I am familiar with. I agree that something more modern should be selected. Thanks for the advice with the frequency. I definitely should lower it. As for the initial conditions, I used to use the starter circuit, but then I realized that oscillations start even without it, but decay very fast. – udushu Nov 29 '11 at 17:44
@udushu - the initial ringing may not even be enough to start if it's lower than say, 100mV. I would maybe try using the series voltage source to have the best chance of it working. If you have no other opamps in your SPICE to try, look on manufacturers sites (e.g. TI, LT, AD etc) for spice models. Alternatively, LTSpice has a decent selection of opamps included. – Oli Glaser Nov 29 '11 at 18:00