Negative impedance (my RG questions and answers) 1
Last updated December 25, 2013
In this material, I have collected my answers to questions so far related to the negative impedance phenomenon. I do not arrange them systematically but chronologically. I will periodically update the content of the material by adding the new posts. To see and join the full discussions, click on the respective questions. You can see also the lists of my questions and answers.
Negative impedance
Cyril Mechkov: What is negative impedance? Does it exist? If so, how can elements with negative impedance be implemented? Are they passive or active?
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
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
So, what does "negative impedance" mean? I am waiting for your responses...
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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...
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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).
Cyril Mechkov: 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?
We have already seen that negative impedance elements are amazing and extremely useful electronic devices (circuits)
https://www.researchgate.net/post/What_is_negative_impedance_Does_can_it_exist_If_so_how_can_elements_with_negative_impedance_be_implemented_Are_they_passive_or_active
But there is only one small problem:) - there are not such elements in nature; there are only humble passive elements with "positive" impedance (resistors, capacitors, inductors and memristors:( So, we have to make them... and maybe this is the most interesting part of our discussion about the negative impedance phenomenon. Then, how do we create negative impedance elements (named "negative impedance converters", shortly NIC)?
IMO they are ones of the most interesting, odd, "mystic" and still unexplained electronic circuits... a real nightmare for students... and their teachers:) I have not still met some "human-friendly" explanations of this legendary circuit (if you find, let me know). Even the famous Mr. Horovitz has not explained (although mentioned) the NIC in his bestseller The Art of Electronics (see page 251). Instead, he has afforded this opportunity to his students; maybe, he had hoped they would help him:)?
For me, as a "circuit thinker", the understanding of this clever circuit (in its two versions) was crucial for understanding the phenomenon of negative impedance. It was interesting that I first figured out what the op-amp was doing in this circuit to create a negative impedance and this gave me a chance to figure out what the phenomenon of negative impedance was. Here are my insights.
"REVERSING" THE RESISTANCE. The idea is simple but powerful - we can make negative impedance by "inverting" some initial positive impedance. Thus the original positive elements will serve as shaping elements for creating "mirror" negative elements. But how do we invert the positive impedance (e.g., the positive resistance)?
The answer is simple (but a bit formal) and requires only to know the Ohm's law (how wonderful it sounds!) As we know, it presents the resistance as a ratio between the voltage and the current (R = V/I); so when the two variables are positive, the resistance is positive as well. To make negative resistance, we have to invert one of them - the voltage or the current:
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#How_to_create_negative_impedance_.28compare_with_NDR.29
* INVERTING THE VOLTAGE POLARITY. In the case of the S-shaped negative resistance RS, we invert the voltage (RS = -V/I = -R). This means that if we pass a current through the S-shaped negative resistor, the input terminal becomes negative (instead positive as in the case of the ordinary "positive" resistor). That is why, circuits implementing this technique are named "voltage-inversion negative impedance converters" (VNIC). Note the power is also inverted (PS = -V.I = -P).
* REVERSING THE CURRENT DIRECTION. In the case of the N-shaped negative resistance RN, we invert the current (RN = V/-I = -R). This means that if we apply positive voltage across the N-shaped negative resistor, the current goes out of the negative resistor and enters the positive terminal of the voltage source (instead to leave the positive terminal of the voltage source and to enter the negative resistor as in the case of the ordinary "positive" resistor). That is why, circuits implementing this technique are named "current-inversion negative impedance converters" (INIC). Note the power is also inverted (PN = V.-I = -P).
But how do we invert an electrical quantity (e.g., the voltage? We can see the solution around us when we invert some (usually "bad") quantity by adding a two times bigger opposite ("good") quantity. So, we may convert the "bad" voltage drop across an initial "reference" positive resistor into a "good" voltage across a new negative resistor by adding a two times higher voltage (by connecting in series a doubling variable voltage source)
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#The_basic_idea_of_the_series_NR_compensation
An (op-amp) amplifier with a gain of 2 can serve as such a variable voltage source
https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance#Building_a_true_S-shaped_NR_.28voltage-inversion_NIC.29
and this is the famous circuit of the voltage-inversion negative impedance converter (VNIC). It is shown in the attached picture (Vin and Ri do not belong to the circuit; they represent the input source).
A few years ago I started a discussion in the Wikipedia page about NICs (under the names Circuit-fantasist and Circuit dreamer), where I enthusiastically presented my insights (then I had no notion about wikipedian's manners and customs)
https://en.wikipedia.org/w/index.php?title=Talk:Negative_impedance_converter&oldid=210801768#What_Is_the_Basic_Idea_behind_a_Negative_Impedance_Converter_(NIC)?
(July 1, 2006) is my first material about the fundamental ideas behind NICsBut the discussion did not happen and after several years my suggestions were removed (I hope this will not be repeated in RG:) After that, I created a few stories about NICs in Wikibooks:
https://en.wikibooks.org/wiki/Circuit_Idea/Linear_Mode_of_Voltage_Inversion_NIC
https://en.wikibooks.org/wiki/Circuit_Idea/Linear_Mode_of_Current_Inversion_NIC
https://en.wikibooks.org/wiki/Circuit_Idea/Bistable_Mode_of_Current_Inversion_NIC
You can see also my stories about NICs uploaded on circuit-fantasia.com:
http://www.circuit-fantasia.com/circuit_stories/understanding_circuits/nic/vnic/vnic.htm
http://www.circuit-fantasia.com/circuit_stories/inventing_circuits/ser_nr_comp/ser_neg_res_comp.htm
http://www.circuit-fantasia.com/my_work/conferences/cs_2006/paper.htm
So, what does the op-amp do in the circuit of the negative impedance converter?
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Yet what is NIC? Lutz, I will repeat here the simple truth about true negative resistors (NICs) - they are just sources... self-variable sources... functional converters: VNIC is a 1-port current-to-voltage functional converter (voltage source - see the attached picture); INIC is a 1-port voltage-to-current functional converter (current source). The function is set by a sample "positive impedance" element (resistor, capacitor, diode...) inside the NIC...
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I just can not believe it - three months after I asked this question there is no any (at least one!) reaction to it! And that about the negative impedance converter - the most mysterious, unexplainable, mystic electronic circuit...
Maybe I am wrong? Maybe this circuit is trivial and is explained in detail in many sources? Then be pleased to list them here:
1......
2......
3......
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Two days ago, I (Circuit dreamer) began discussing the sophisticated INIC circuit in Wikipedia arguing with my main opponent (Zen-in):
https://en.wikipedia.org/wiki/Talk:Negative_impedance_converter#Questions_on_this_circuit_description
https://en.wikipedia.org/wiki/User_talk:Circuit_dreamer#A_discussion_about_NIC_and_TIA
Perhaps these discussions will awaken your interest in the mystic circuit?
Cyril Mechkov: What does "negative impedance" mean in electricity and electronics? Has the capacitor a negative impedance? How do we create a "negative" capacitor?
We had a problem with "negative resistance" since it represented two different types of resistances - "true 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
and "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
Now we have a similar problem with "negative impedance" since it represents different things in electronics and electrotechnics...
IN ELECTRONICS, we believe that all natural passive components (resistors, capacitors and inductors) absorbing energy from the input source have "positive impedance" (or simply "impedance"). So, from this viewpoint, the impedances of capacitors and inductors have the same positive signs. Conversely, the artificial electronic circuits - NICs (negative "resistors", negative "capacitors" and negative "inductors"), behaving in an opposite way (adding energy to the input source in the same manner as the according passive components do it), have a true "negative impedance". So, this classification regards to the way of processing energy - "positive impedance" means consuming while "negative impedance" means producing energy; "positive impedance" means "ordinary impedance" while "negative impedance" means something opposite as "inverse impedance", "opposite impedance" or "anti-impedance".
IN ELECTROTECHNICS, they classify the impedance of the reactive elements capacitor and inductor according to their behavior in time when a DC input voltage is applied - "negative impedance" symbolizes an "increasing voltage opposition" while "positive impedance" symbolizes a "decreasing voltage opposition". From this viewpoint, the impedances of capacitors and inductors have opposite signs.
IN ELECTRONICS, BOTH CAPACITORS AND INDUCTORS HAVE POSITIVE IMPEDANCE WHILE IN ELECTROTECHNICS, CAPACITORS HAVE NEGATIVE IMPEDANCE BUT INDUCTORS HAVE POSITIVE IMPEDANCE.
This concept is extremely simple, clear and intuitive if we think in terms of voltages when we apply a constant input voltage to the elementary RC and RL circuit. Then, voltage drops appear across capacitors and inductors; they change in a different (opposite) way through time but both they are voltage drops. Conversely, voltages appear across negative capacitors and inductors; they also change in a different (opposite) way through time but now both they are (electromotive) voltages, not voltage drops.
After these speculations, it is interesting to remember what a negative impedance converter did. What does it convert? Does it make a capacitor behave as an inductor and v.v., an inductor as a capacitor? No, it doesn't. A gyrator can do this magic. A negative impedance converter can make capacitors and inductors behave as sources (negative impedance elements) instead as passive elements having positive impedance: