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Design >> Analog Design >> Question about negative impedance
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Message started by James Bond on May 4^th, 2008, 11:07am

Title: Question about negative impedance
Post by James Bond on May 4^th, 2008, 11:07am

Hi, all,

I am designing an oscillator, I have a question regarding the negative impedance. The oscillator is supposed to oscillate around 22MHz, for the following two curves about negative impedance, which one is better ? Why? (I am not sure about the impedance at low frequency, should it be more negative or flat ? if we only consider the negative impedance.)

Thank you very much

james

Title: Re: Question about negative impedance
Post by buddypoor on May 4^th, 2008, 11:10pm

Hi James ,

the answer to your question is easy: Of course the curve with the highest slope is best. The other one has a frequency dependence (slope) which is nearly zero and, therefore, cannot be used . The reason is: (a) the oscillation condition should be fulfilled at one frequency only and (b) at all other frequencies the loop gain Ao should be far away (as far as possible) from the point of oscillation (Ao=1). The latter condition (b) is connected with frequency accuracy requirements.
Regards
Lutz

Title: Re: Question about negative impedance
Post by buddypoor on May 4^th, 2008, 11:38pm

James, here is an important addendum to my answer:

My comments are valid only for an oscillator structure in which the negative resistance is used to create a resonance effect in conjunction with an ohmic resistor (GIC resonator structure).
There is another principle in which the oscillation frequency is determined by an LC-tank circuit. In this case it is the task of the negative resistance to compensate for all (more or less constant) losses within the circuit. In this case you can, of course, use also the flat resistance curve.
Which topology do you use ?
Regards
Lutz

Title: Re: Question about negative impedance
Post by James Bond on May 5^th, 2008, 12:50am

it's not a standard topology, it is a novel circuit. It is used to connect a crystal. The problem is I have seen some problems with the black impedance curve but not for the red curve. With black curve, the chip sometimes oscillate at another frequency, this wrong freq is not any harmonic of crystal frequency. The design with red curve impedance is very good actually. I don't know why .

Title: Re: Question about negative impedance
Post by buddypoor on May 5^th, 2008, 1:23am

In this case, I think, the arguments as contained in my first reply are valid: The oscillation condition is fulfilled at one frequency only - determined by the correct value of the negative resistance (red curve with great slope).

But in any case, it would be helpful if you could provide a block diagram of the oscillator circuit. This is really necessary to reveal the task of the negative resistance.

Title: Re: Question about negative impedance
Post by James Bond on May 5^th, 2008, 5:55am

(a) the oscillation condition should be fulfilled at one frequency only and (b) at all other frequencies the loop gain Ao should be far away (as far as possible) from the point of oscillation (Ao=1).

Hi,

Regarding to the reason above:

At intercept point of black and red curve, they both fulfil (a). What about (b), could you please explain (b) a bit more?

Thank you very much
james

Title: Re: Question about negative impedance
Post by buddypoor on May 5^th, 2008, 6:34am

OK, here are some explanations.
In general, there are two different oscillation principles:
(1) Four-pole-oscillators: Closed loop consisting of a passive frequency-dependent network and an amplifier; oscillation condition: Loop gain Ao=1.
(2) Two-pole-oscillators: A circuit with the ability to exhibit resonance (tank circuit) is shunted with a negative resistance to compensate for the damping of the tank circuit; oscillation condition: Ohmic part of the tank resistance equal to the neg. resistance.

Requirements:
(a) In both cases the oscillation condition should be met at one frequency only.
(b) In order to make sure that the whole circuit is not too sensible upon design uncertainties, the oscillation condition should die out as quick as possible for frequencies lower as well as higher than the wanted frequency.

Conclusion:
Depending on the topologie chosen it can be advantageous to have a resistance vs. frequency function with a big slope (red curve), because this can support requirement (b).

I hope this helps a bit.
Lutz

Title: Re: Question about negative impedance
Post by James Bond on May 5^th, 2008, 11:05am

Hi,

I think the explaination about (b) is very reasonable, but if there is too high slope at low frequency(red curve), how could it die out at lower frequency? It will be sensitive at lower frequency, right ? This problem confuses me quite a while.

james

Title: Re: Question about negative impedance
Post by buddypoor on May 6^th, 2008, 12:27am

Introduction: "Linear" oscillators are non-linear circuits !

This funny statement is illustrating the problem. In fact, it is not easy in each case to explain why a circuit produces a signal as wanted resp. why NOT !
As far as your problem is concerned: It would be interesting to know what kind of negative resistance (impedance ?) you are using. That means, for instance, if some frequency dependent phase deviations are connected with the changing resistance value. And - as mentioned earlier - a circuit diagram (at least a functional block arrangement) would be necessary to try to explain the effects.
Therefore, you may be right that the big slope of the resistance function within the lower frequency region could govern the whole circuit behaviour, but as stated above: what is the chosen oscillator principle ?

Lutz

Title: Re: Question about negative impedance
Post by James Bond on May 6^th, 2008, 11:47am

HI,

Thank you for the patient and excellent explaination. Regarding to the slope of the negative impedance, do you know some papers or documents giving the detail proof that the slope of the negative impedance should be at least above some certain value? Because it's really hard to tell which slope is good enough and which is not good enough?

Thanks

james

Title: Re: Question about negative impedance
Post by buddypoor on May 6^th, 2008, 1:52pm

James, I am really sorry, but I cannot answer your question.
The reason is that a circuit will probably oscillate at the designed frequency if (and only if) both conditions (a) and (b) – as mentioned earlier – are fulfilled. More than that, at the beginning of the whole process condition (a) must be “over-fulfilled” in order to safely start oscillations.

Since both conditions are determined by the whole circuit – especially by the frequency dependent part of the circuitry – one cannot specify resp. evaluate one single component (in your case: neg. resistance) without knowing the behaviour of the rest of the circuit.
In this context, especially the phase relationships are very important and, therefore, my question if the neg. resistance circuit contributes to the phase of the whole network.

Did you try circuit simulation already ?
“Linear” oscillators are probably the most “suspicious/malicious” circuits in analog electronics and many textbooks are in this context afraid of exact explanations.
Regards
Lutz