Thank you dear Dr. Muhammed.

In ordinary LC oscillators, there are already some important issues which may sometimes be difficult to cope with. Honestly speaking, I am not totally self-confident when designing an LC oscillator. That is why, when it comes to designing an (-L)(-C) oscillator, I feel hesitation in many regards, for which I cannot be sure whether prepare my guard or be relaxed.

This is the reason I asked this question.

I am sure there are other experts out there who can write other helpful comments.

A negative inductor ?.

v = -L di/dt

v = -jwLi

I guess you can create it with a couple of gyrators.

- Take a capacitor C, voltage over the capacitor V1, current into the capacitor I1.

- Take 2 gm-elements, so that I1 = gm1*v2, and i2=gm2*v1

- We also have i1 = C dv1/dt

- This then becomes : gm1 *v2 = C/gm2 *di2/dt

- or v2 = C/(gm1*gm2) * di2/dt

a. If gm1 or gm2 are negative (and the other positive), this emulates a negative inductor.

b. The noise is the noise produced by the gm-elements gm1 and gm2. (there is a minimum.)

c. From stability perspective, it behaves as an impedance -jwL. Dont see any issue with that.

d. There are of course other ways to emulate. Narrowband you can eg emulate with a capacitor,

and that, of course, is noisefree.

Best Regards,.

Henri.

Dear Ali Zeki

Hope you are well!

What are the causes to use synthetic negative inductors and capacitors to realize LC oscillators. The conventional LC oscillators were realized and built using one active device and an L-C circuit since long time. The L-C oscillators are named after their inventors such as the Hartley oscillator, the Colpitts oscillator, the Meissner oscillator and others. They are based on positive feedback of amplifiers.

The other basic building block of the oscillator is to use negative resistance instead of the amplifier with positive feedback in addition to a parallel L-C network.

Would you use a negative capacitance instead of a negative resistance to build the oscillator such that the LC oscillator will be built from a negative capacitance shunted by conventional inductor? You will use active devices to build the negative capacitance then why not suing them directly to build the oscillators? Then what will be the merits of such a technique?

Best wishes

Dear Abdelhalim

This is of course very true.

- It is indeed true you can built an oscillator using a NEGATIVE inductor AND a NEGATIVE capacitor,

and then you dont need a negative resistor (amplifier.)

- From a realization point of view, this makes little sense, as the normal inductor and capacitor are noise-free, while the gm-elements in the gyrators used to create the negative inductors/capacitors do create noise.

- I considered it as a thought experiment with no practical value.

Best Regards,

Henri.

Dear Henri Cloetens ,

hope you are well!

I think when one uses a negative capacitance one must shunt it by a negative inductance such that energy transfer between the two will be feasible. If one invert the charging and discharging cycles of the capacitor one must do the same for the inductor such that one makes the oscillations possible.

That is when one makes dv/dt negative one has to make di/dt negative also.

In this case the frequency of oscillations will be positive

Since w= 1/sqr LC so if one changes the sign of L one has to change the sign of C.

This will require both active L and active C.

This will consume larger power.

It will be much more complex.

It may be used at extremely low frequencies as in the active filter as Muhammad Hamza El-Saba

Best wishes

Dear Muhammad Hamza El-Saba

Thank you for your answer.

Of course, even when one of the devices is synthetic, the effects you mentioned will cause several oscillator performance issues. That is, it will be a problem not only for (-L)(-C) but for any LC oscillator using at least one synthetic L or C (including some capacitance multiplier based designs). Many of such problems have already been investigated in the literature for LC oscillators/filters with at least one synthetic L or C.

My question is specific to (-L)(-C), but I felt obliged to emphasize that they will be synthetic, since these devices are not practically available, unlike ordinary L and C devices.

Thanks again.

Dear Abdelhalim abdelnaby Zekry

Thank you for your answers.

You really pointed out several issues that I was expecting to be clarified. Actually I was already aware of some of them, but some others provided a better insight to understand the potential problems of such an oscillator better.

As a response to your ideas and questions, I want to write two things.

1. Synthetic L or C devices are used in ordinary LC oscillators (synthetic L, like inductance simulators; or synthetic C, like capacitance multipliers), especially for integrated circuit implementation. So, some problems you mentioned also exist in those designs (and of course, you are right that their performances and frequency of operation are rather limited). I actually wanted to know the problems specific to (-L)(-C) oscillators, which the other theoretical comments of yours have already answered many of them.

2. You asked: "What's the merit of using it if it has this much problems?". Unfortunately I don't have an answer to this. Our discussions will help to decide whether it may or may not have an advantage in any similar application. There are no significant differences (in terms of design techniques or used active devices) of synthetic realization of positive and negative inductors (or capacitors). Therefore, if (-L)(-C) realization of LC oscillator has at least one advantage, it would be good to point it out. In fact, I personally don't feel like it has an important advantage. However, since just a "feeling" is not scientifically informative enough, I wanted the topic to be discussed by researchers.

Best regards...

Dear Henri Cloetens ,

Thank you for your answers, which really clarified some issues that I was curious about. Actually I already knew some of them, but some others provided a better understanding, not only for me, but probably for some others who follow this discussion.

You wrote "I considered it as a thought experiment with no practical value".

This is largely correct.

However, although I don't feel like (-L)(-C) oscillator might have any significant advantage, there is a possibility of getting a practical value out of this discussion if we can i) find at least one significant advantage of a synthetic (-L)(-C) oscillator over an LC oscillator based on synthetic L and/or C devices, ii) find out that (-L)(-C) oscillator has such critical problems/disadvantages that a designer would better not consider it at all.

Maybe some researchers who read this question and the answers are already somehow completely aware of the 2nd one ("practical value" (ii) - if is valid), so they see no point of even discussing it. :) After all, as you said, the question can be regarded as an item of a "thought experiment".

Thanks again for your valuable comments.

Best regards...

I am a bit late with my response - nevertheless, I like to mention an oscillator topology that is based on a frequency-dependent negative resistance (FDNR).

This type has excellent characteristics and can be used without any means for amplitude stabilization due to inherent high-Q filtering .

Article GIC resonator has inherent amplitude control

Data A novel harmonic Oscillator: GIC Resonator

Thank you dear Lutz von Wangenheim .

Dear Ali Zeki

If we attempt to design an LC oscillator using synthetic negative inductor and negative capacitor (-L & -C), what might be the main issues faced?

My understanding as below:

Since we are going to design LC oscillator, the major concern is about the performance, regardless negative or not, we are going to use L/-L C/-C to form LC tank for good phase noise, low power consumption etc.

We are talking about active inductor for Q enhancement for better phase noise but it is at expense of increase of power consumption

Dear K. MA ,

Thank you for your contribution.

Best regards...

A.Z.