There is hardly so controversial, misunderstood and denied phenomenon in circuitry as negative impedance (resistance). Many questions can be asked about the mystical phenomenon: What is it? Is it possible at all? Does it violate natural laws? Does it exist at all? If so, how do we make it? What is the use of the true negative impedance? What is the difference and what is the common between the positive and negative impedance?
Actually, this is an extremely simple, clear and intuitive idea... but I needed years of time to grasp it. I began thinking about the negative impedance phenomenon in the early 90s... but I completely realized the simple truth about it in 2008! Why are the simplest things in this world the most incomprehensible? Here are my insights about the great phenomenon.
Strictly speaking, there are not true negative resistors exactly as there are not true energy sources; if there were, they would violate thermodynamics laws (energy from nothing). There are only energy converters - constant voltage/current sources and dynamic voltage/current sources (negative impedance devices). We may think of the (true) negative impedance element as of a "mirror copy" of the equivalent "positive" impedance element (resistor, capacitor or inductor) since the negative element adds the same energy (voltage, current) that the corresponding positive element would consume. For example, if the same current I flows through a positive resistor and through an S-shaped negative resistor with the same resistance R, the positive resistor subtracts a voltage drop V = R.I from the circuit
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#Series-connected_.22positive.22_impedance_elements
while the negative resistor adds a voltage V = R.I to the circuit
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#Current-driven_negative_impedance_elements
Thus the positive resistor acts as a two-terminal (1-port) "current-to-voltage drop converter" while the equivalent true negative resistor acts as a "current-to-voltage converter" (as Lutz said as well). But, in contrast to ordinary constant sources, true negative resistors are dynamic sources whose voltage depends linearly on the current flowing through them or whose current depends linearly on the voltage across them. They are auxiliary sources that cannot operate independently; they begin operating only after the main source begins operating.
Usually, the negative resistance is not used independently but together with a portion of "positive" resistance. The amazing feature of this arrangement is that negative resistance "neutralizes" the same positive resistance. Depending on the proportion between the two ingredients of this "mixture", the result of this neutralization can be positive, zero, infinite or negative resistance. Most frequently, two equivalent (positive and negative) resistances are mixed to obtain virtual zero or infinite resistance. Thus, if a current-controlled negative resistor is connected in series with an equivalent "positive resistor", the result is zero resistance; if a voltage-controlled negative resistor is connected in parallel to an equivalent "positive" resistor, the result is infinite resistance.
Negative resistors are wonderful... but there is only one small problem with them - there are not such magical active elements in nature; there are only ordinary, passive ohmic resistors. So, we have to make them... and this is discussed in the question below as an interesting continuation of our discussion:
https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_negative_impedance_converter_How_is_it_implemented_How_does_it_operate_What_does_the_op-amp_do_in_this_circuit
I wasted five years of my life struggling with orthodox wikipedians and trying to tell the truth about the negative impedance in the respective Wikipedia article... but I could not... Here are a short history of these "epic battles" and some disputes (I joined them under the user names Circuit-fantasist and Circuit dreamer)
https://en.wikipedia.org/wiki/User:Circuit-fantasist/Negative_resistance#Some_history_in_retrospective
https://en.wikipedia.org/wiki/Talk:Negative_resistance/Archive_2#Another_fresh_viewpoint_at_negative_resistance (September, 2006) is my first insertion to Negative resistance talk page
https://en.wikipedia.org/wiki/Talk:Negative_resistance/Archive_4#What_negative_impedance_is is an old discussion where I have explained that there is and what is negative impedance
https://en.wikipedia.org/w/index.php?title=Negative_resistance&oldid=91831382 (December 3, 2006) is my first naive but enthusiastic version of the Wikipedia page about the negative resistance.
https://en.wikipedia.org/w/index.php?title=Negative_resistance&oldid=268968353 (February 6, 2009) is an improved and very well developed story about the negative resistance
https://en.wikipedia.org/w/index.php?title=Negative_resistance&oldid=442011666 (July 29, 2011) is my last version, almost completely removed...
I did it later in Wikibooks... and this story is listed by Google immediately after the Wikipedia article:
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance, see also
https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Resistance
But I have still managed to generalize the negative impedance idea in the Wikipedia page about Miller theorem
https://en.wikipedia.org/wiki/Miller_theorem#Applications
You can see also my stories about negative resistance uploaded on circuit-fantasia.com:
http://www.circuit-fantasia.com/circuit_stories/inventing_circuits/ser_nr_comp/ser_neg_res_comp.htm
http://www.circuit-fantasia.com/circuit_stories/inventing_circuits/decreased_resistance/decreased_resistance.htm
http://www.circuit-fantasia.com/my_work/conferences/cs_2006/paper.htm
We have discussed this topic also in the RG questions below:
https://www.researchgate.net/post/Why_are_there_no_practical_applications_of_negative_impedance
https://www.researchgate.net/post/Is_the_Barkhausen_criterion_about_the_loop_gain_right_in_the_case_of_the_Wien_bridge_oscillator1
https://www.researchgate.net/post/What_is_the_basic_idea_of_Wien_bridge_oscillator_How_does_it_operate#share
It is also interesting to compare the true with differential negative resistance:
https://www.researchgate.net/post/What_is_negative_differential_resistance_How_is_it_implemented_How_does_it_operate_What_is_its_relationship_with_the_true_negative_resistance#share
So, what does "negative impedance" mean? I am waiting for your responses...
OK - let`s start the discussion.
Cyril - I didn`t go through all the links provided by you.
Thus, it is certainly not a new statement to say:
An active negative resistor is nothing else than a (quasi-)linear voltage controlled current source whereby the current flows through the controlling voltage source.
Remark : Based on the same principle also a negative capacitance can be realized, for example.
Talking about passive components, a sensitive resistor NTC is able to offer negative resistance in a certain range of its V-I behaviour. But if we look at its composition, is difficult to be classified as passive. This is in relation with the reverse Ohms law. By other side, plenty of logic circuits mantain a direct voltage at the same time they emit reverse current, as seen in TTL multiemitter devices. While an output gate is sending a voltage signal to the next stage input this latter part is feeding the output with a current signal.
As another consideration, it is necessary to add that the classical active opamp implementation (NIC) allows two alternatives:
NIC that is
* short-circuit stable, or
* open-circuit stable..
More than that, one could add that there is another active implementation of a negative resistor with a value which is frequency dependent :
FDNR (Frequency-dependent negative resistor).
It is interesting to note that such an FDNR element - together with a classic ohmic resistor - can create a resonant effect (similar to an LC circuit).
Thank you for the instant response! Great circuit phenomena deserve great responses...
First at all, I would like to dispel the doubt, perhaps due to the many text and links above, that I can not briefly explain what the negative impedance is. Here is my attempt to explain it, like Lutz above, in only one sentence:
A true negative impedance element is nothing else than a dynamic voltage source mimicking a corresponding "positive" element.
If it mimics a resistor, we obtain a negative resistor; diode - negative diode, capacitor - negative capacitor, etc...
Lutz: "An active negative resistor is nothing else than a (quasi-)linear voltage controlled current source whereby the current flows through the controlling voltage source." I would only make it more clear:
Voltage-inversion negative impedance converter (VNIC) is a current-controlled voltage source (linear, in the case of a negative S-shaped resistor).
Current-inversion negative impedance converter (INIC) is a voltage-controlled current source (linear, in the case of a negative N-shaped resistor).
Manuel, the NTC sensitive resistor (thermistor) exhibits a negative differential resistance. I intend to devote a special question to this great phenomenon. The present question is about the true (absolute) negative impedance (devices containing their own sources).
Your insertion about TTL gates: "By other side, plenty of logic circuits mantain a direct voltage at the same time they emit reverse current, as seen in TTL multiemitter devices. While an output gate is sending a voltage signal to the next stage input this latter part is feeding the output with a current signal", is extremely interesting since this phenomenon resembles true negative resistance...
But I doubt that this is really a negative resistance since this phenomenon is not only a simple current reversal as it is made in TTL by the internal pull-up base resistor of the input multiemitter transistor. The problem is that the upper terminal of the base resistor is fixed to the steady Vcc; so, when the input voltage of the previous gate increases, the contrary current (exiting the next gate) decreases. If there was a negative resistance, when the input voltage increases, Vcc should increase as well; accordingly, the contrary current will increase (see the attached picture below).
(BTW, a few years ago, I wrote the section about the gate implementation and operation in the Wikipedia page about TTL; it may be interesting for you):
https://en.wikipedia.org/w/index.php?title=Transistor%E2%80%93transistor_logic&oldid=394474156#Implementation
Mechkov, you're certainly right. So, apart from academic definitions technology has made us to think in certain phenomena as something subjective. Very Interesting observations from you.
Finally, I have asked the extremely interesting question about how to create virtual electrical elements in electronics:
https://www.researchgate.net/post/How_do_we_create_virtual_electrical_elements_in_electronics_Are_they_really_elements_or_circuits
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