Op Amp based Hartley oscillator

Question

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?

Answer 1

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.

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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.

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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.

Answer 2

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.

Answer 3

The circuit cannot work because the opamp has a voltage output in contrast to a transistor which provides a current output at the collector node. Therefore, an additional resistor Ro is neessary between node (6) and the upper node of L2.

In this case, we have 3rd-order highpass in ladder topology (Ro-L2-C1-L1) which can provide a 180 deg phase shift for feeding the inverting path through R1. This is the principle of an opamp based Hartley oscillator.

In addition, I like to recommend somewhat larger resistor values for R1 and R2 (just the ratio is important). This can avoid heavy loading of the RLC highpass.

Answer 4

One important factor is that the input impedance of your OPAMP is getting very low because of 500 ohms. if you take it to be some 10k or so, your oscillations may sustain. also your loss of signal due to low Q can be compensated. as input impedance falls, loading effects the opamp and hence your oscillations are damping.

Answer 5

you may want to try LF347 4mhz bandwidth quad jfet input amp.# focQs200 kHz

• 10V peak sinusoidal output swing without slew limiting to 200 kHz
• See LM148 data sheet for design equations