I dedicate this question to Abdelhalim Zekry as an appreciation for his competent comments posted in the right place at the right time...
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On Page 3 of the question below...
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/3
... I have suggested that we can think of the negative impedance converter (NIC) as of a balanced bridge. Then I have elaborated in details this idea on Page 4 of another question...
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/4
I have done it in a form of a 4-step scenario where I considered in parallel the bridge and op-amp versions (I have copied it below). Thus the electrical implementation of the 19th century (Wheatstone's bridge) and the electronic implementation of the 21st century (NIC) as though were connected with some kind of a "bridge" through time.
With this I have demonstrated the power of "pure ideas" when they are released from the bondage of the specific circuit implementations (tube, transistor, op-amp, etc...), technology constraints and all kinds of imperfections. I believe that pure ideas do not need modern technologies... or sophisticated math analysis and simulations... they are clear and simple... eternal and immortal... To understand how a circuit operate, we have to see on which pure idea this circuit is based... otherwise we have not understood the circuit... we only know the concrete circuit implementation...
So the pure idea behind of a NIC can be materialized in many possible ways... and the electronic implementation is only one of them (it could be realized even in a mechanical form many, many years ago (as a "lever implementation" by Archimedes, centuries BC:)
If this "bridge viewpoint" is true, we can say that the abstract circuit of a NIC is invented in the middle of 19th century by Sir Charles Wheatstone:)
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/4
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...My guess is that this circuit was invented even in the middle of 19th century, most probably by Sir Charles Wheatstone, in 1843:) I don't know if this was indeed the case... but if it was... he could called it "balanced bridge."
This bridge is balanced by varying the supply voltage in response to the input disturbance caused by the inclusion of an electrical source in one of the lower legs (assume the upper legs are equal)...
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/4
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... or real voltage source (voltage source + resistor in series)...
Unfortunately, I have not drawn such a circuit diagram... that would be most interesting for our dispute about the stability... but you can easily imagine it - a classical textbook Wheatstone bridge with a voltage source inserted between ground and one of the lower resistors...
To investigate the operation of this "19th century NIC", one of us should act as the modern op-amp - to vary the supply voltage watching at a zero indicator (galvanometer) connected as a "bridge" between the two middle points, until zero the indicator... as a response of another of us disturbed the bridge by changing the input voltage changes...
It would be interesting to explain what and why happens when inserting the voltage source in the one or the other lower leg... and when swapping the lower resistors...
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/4
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I will try to generalize a few viewpoints at this 3-component circuit.
We can present it at four descending levels of abstraction thinking of it as of a:
... balanced bridge circuit (electrical idea)...
... negative resistance circuit (unconventional op-amp idea)...
... mixed-feedback circuit (more conventional op-amp idea)...
... op-amp circuit (without seening any basic idea).
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/4
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...Actually, the voltages of the inverting and non-inverting input are subtracted... and the resulting voltage is applied to the differential input. So, as you guess, we can consider this configuration as an amplifier with negative feedback between the single-ended op-amp output and its differential input...
I would add to your explanations that, as a response to the input "disturbance", the op-amp changes both the voltages (of the inverting and non-inverting input)... and as the former changes more vigorously, the op-amp always reaches the equilibrium...
It is interesting that in the case of the VNIC, both equal voltages have inverse polarity regarding the input polarity. This is possible since the input source and the inverting input are separated by a resistor.
In the case of INIC, the voltages remains with the same polarity but the current changes its direction.
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/7
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Step 1. We assemble a bridge circuit by four resistors (R1-R4). It is convenient to think of it as of a combination of two voltage dividers - R1-R2 (the left leg) and R3-R4 (the right leg). Let R1 = R3 and R2 < R4.
In the 2nd century BC lever implementation........................................
- In the 19th century electrical implementation (the first picture below), we supply the bridge by a varying voltage source OA, and observe its output voltage by a zero indicator (galvanometer). Our job is to balance the bridge by varying the supply voltage.
- In the 21st century electronic implementation (the second picture below), an op-amp OA supplies the bridge by its output voltage, and "observes" the bridge output voltage by its differential input. Its job here is the same - to balance the bridge by varying the supply voltage.
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/7
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Step 2. We begin to fulfill your obligations...
- In the 2nd century BC lever implementation........................................
- In the 19th century, when we try to increase the supply voltage VOA, both output voltages of the voltage dividers begin increasing. But since we have chosen R2 < R4, VR4 increases more vigorously than VR2... this makes us decrease the supply voltage... and, as a (quite surprising) result, we do not change the supply voltage... it remains zero. VR2, VR4 and their difference dV also remain zero. Figuratively speaking, the whole circuit is "dead"... there are no voltages across and currents through resistors... but still it is balanced.
- In the 21st century, the op-amp does exactly the same... When the power supply is turned on, its output voltage VOA tries to change (e.g., increase)... and the voltages of its inputs begin increasing. But since R2 < R4, V- increases more vigorously than V+ (as they say, the negative feedback dominates over the positive one). This makes it decrease its output voltage... and again the result is thaty the output voltage VOA remains zero... V+, V- and their difference dV also remain zero. The whole op-amp circuit is "dead"... there are no voltages across and currents through resistors.
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/7
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Step 2. We begin to fulfill your obligations...
- In the 2nd century BC lever implementation........................................
- In the 19th century, when we try to increase the supply voltage VOA, both output voltages of the voltage dividers begin increasing. But since we have chosen R2 < R4, VR4 increases more vigorously than VR2... this makes us decrease the supply voltage... and, as a (quite surprising) result, we do not change the supply voltage... it remains zero. VR2, VR4 and their difference dV also remain zero. Figuratively speaking, the whole circuit is "dead"... there are no voltages across and currents through resistors... but still it is balanced.
- In the 21st century, the op-amp does exactly the same... When the power supply is turned on, its output voltage VOA tries to change (e.g., increase)... and the voltages of its inputs begin increasing. But since R2 < R4, V- increases more vigorously than V+ (as they say, the negative feedback dominates over the positive one). This makes it decrease its output voltage... and again the result is thaty the output voltage VOA remains zero... V+, V- and their difference dV also remain zero. The whole op-amp circuit is "dead"... there are no voltages across and currents through resistors.
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/7
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Step 3. It is time to break the "bliss" of these well balanced bridge circuits, e.g. by inserting a positive voltage source VIN in the lower part of the left leg.
- In the 2nd century BC lever implementation........................................
- In the 19th century, the output voltage VR2 of the left voltage divider will increase (since VIN adds to VOA by means of the resistive summer R1-R2). We react to this intervention by increasing VOA. Our will is to increase only VR4... but unfortunately, VR2 also changes... but luckily for us, more slowly. Thus finally, we manage to balance the bridge circuit.
- In the 21st century, the op-amp "sees" that V+ increases, and reacts to this intervention by increasing its output voltage VOA (with the purpose to increase V-). Unfortunately for it, V+ also changes... but luckily for it, more slowly. Thus finally, due to the dominating negative feedback, the op-amp manages to balance the bridge circuit.
My comment below is copied from the question:
https://www.researchgate.net/post/Can_a_negative_impedance_converter_NIC_act_as_a_current_mirror_If_so_is_it_a_perfect_circuit_What_kind_of_NIC_do_we_use-INIC_or_VNIC/7
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Step 4. With the same success, we can disturb the balanced bridge circuit by inserting (e.g., a negative) voltage source in the lower part of the right leg.
- In the 2nd century BC lever implementation........................................
- In the 19th century, the output voltage VR4 of the right voltage divider will decrease (since VIN subtracts from VOA by means of the resistive summer R1-R2). We react to this intervention (again?) by increasing VOA. Our will is, as above, to increase only VR4... but unfortunately, VR2 also increases... luckily for us, more slowly. Thus we manage to balance the bridge circuit.
- In the 21st century, the op-amp "sees" that V- decreases, and reacts to this intervention by increasing(?) its output voltage VOA (with the purpose to increase V-). Unfortunately for it, V+ also changes... luckily for it, more slowly. Thus, due to the dominating negative feedback, the op-amp manages to balance the bridge circuit.
The idea that a bridge circuit can act as a voltage-to-voltage converter with a singel-ended input and differential output occurred to me in 2009, when I managed to debunk the Chung's myth about the existence of "apparent negative resistance".
Then I was impressed by the property of this "bridge converter" to have various transfer ratio depending on the proportion between the leg's transfer ratios K1 and K2 - positive (K1 > K2), zero (K1 = K2) and negative (K1 < K2). This allowed to obtain positive feedback, no feedback or negative feedback in op-amp circuits..
https://en.wikibooks.org/wiki/Circuit_Idea/Deborah_Chung%27s_%22Apparent_Negative_Resistance%22#Presenting_the_carbon_fiber_network_as_a_bridge_circuit
https://www.researchgate.net/post/What_is_the_truth_about_the_Deborah_Chungs_apparent_negative_resistance_Was_it_a_reliable_scientific_experiment_or_only_a_scientific_sensation
Then I used it to explain the circuit of Wien bridge oscillator where the bridge plays the role of a negative feedback network (non-linear and frequency dependent)...
https://www.researchgate.net/post/What_is_the_basic_idea_of_Wien_bridge_oscillator_How_does_it_operate/2
Finally, I used it to reveal the basic idea behind the negative impedance converter (NIC).
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/3
https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Impedance_Converter#Presenting_the_op-amp_NIC_as_a_bridge
It would be better to talk about “half – bridge”. The half – bridge (R1C1 + R2C2 “Wien – divider”) in the positive feedback loop produces a maximum response at its characteristic frequency ω0 and gives us zero phase shift. The remaining two arms are used in a negative feedback loop and provide necessary gain of the amplifier. Thus Wien oscillator is formed from the “half – bridge” and amplifier – with vacuum tubes, transistors, operational amplifiers and other modern amplifier structures
Yes, this is another viewpoint at the Wien bridge oscillator... and I have considered it in the end of the header of the question about it.
But our purpose here is to see a bridge circuit; so, for our purposes here, it is better to think of all the passive components as of a balanced bridge. Its left arm (left half-bridge) is a non-linear voltage divider; the right arm (right half-bridge) is a frequency-dependent voltage divider (Wien network).
BTW, I was not long ago entered into the page about the Wien network... and now I found with pleasure how interesting it is. I see that there I developed an original point of view at this 4-element passive network (an RC circuit acting as a passive "virtual inductor")... that unfortunately has gone unnoticed...
https://www.researchgate.net/post/What_is_the_basic_idea_of_Wien_bridge_oscillator_How_does_it_operate/2
https://www.researchgate.net/post/What_is_the_basic_idea_behind_the_Wien_network_How_does_it_operate_in_the_frequency_and_time_domains/1
Dear Cyril,
Than you for your question and your visual explanations. They are very useful.
The circuit configuration of the negative impedance converter has similarities to the bridge circuit;
It has four branches with every two branches are connected in series to form a half bridge, as hinted by Josef ,and powered by a supply voltage, here the output voltage of he op amp, while the voltage at the common point of every half bridge is connected to the voltage detector. Which in case of the negative impedance converter the differential input of the op amp itself.
The normal bridge is balanced by voltage detector whose output is not connected to supply the bridge. Therefore the normal bridge is balanced by changing the impedance of one arm. It can be balanced with a voltage detector theoretically arriving zero. In the bridge configuration of the negative impedance converter the bridge is supplied by the an output voltage proportional to the input difference voltage of the op amp. Since the output has a specific value the input voltage will not be zero and since he gain of the op amp is high, the input differential voltage will be small for all practical values of the output voltage.
So, after this comparison one can conclude,
The circuit has basically a bridge configuration with basic differences from the conventional bridge thanks to the introduction of the op amp acting as a detector
at its input and as a bridge supply at its output.
In this way from the point of view an application circuit on op amp, the two sides of the bridge circuit act as a feed back network for the op amp, a negative feedback circuit and a positive feed back, or as a a two potential dividers one for the inverting input and the other for the non inverting input. The positive feed back and the bridge configuration enabled the negative impedance converter of the circuit.
In the sense:
The impedance seen looking at the positive input is equal to the impedance connected between the negative input and ground. This fact can be seen directly when one sees the bridge formed by the feed back resistors, the load resistor, and the input equivalent resistor.
To realize that the circuit works as a negative impedance converter one just connect an active voltage source with its positive pole connected to the positive input of the op amp. One sees directly that the current will be pushed from the positive input entering the source opposite to its nominal current flow.
According to the bridge balance condition, this current will be equal to the current passing in the load resistance while the voltage of the input source will be inherited by the load resistance.
In conclusion the analogy between the the negative impedance converter and the bridge facilitate the understanding of the circuit and brings easily its quantitative behavior.
Best wishes
A very interesting and profound answer, Abdelhalim! You always show a creative thinking... You made me think deeply about the bridge idea... and I will soon take a position on it...
Gentlemen, may I contribute some of my consisderations?
1.) Of course, each opamp-based circuit with positive and negative feedback (like the NIC under discussion) can be seen as a balanced bridge - as long as the circuit works under linear condition (differential opamp input voltage nearly disappearing).
2.) Therefore, also the classical WIEN oscillator can, of course, be seen as an NIC-based oscillator. In this case, there is one single frequency wo where the negative (and frequency-dependent) input impedance at the non-inverting opamp input terminal equals the frequency-dependent impedance connected between this terminal and ground (which is the parallel RC-combination). Hence, the circuit can be seen as a parallel combination of a positive and a negative impedance which cancel each other at one single frequency (resulting in an infinite impedance at w=wo). ***
3.) Such a view is no surprise because each 4-pole oscillator (finite-gain amplifier with frequency dependent positive feedback) can always be seen as a negative-resistance oscillator. In many cases, this equivalence helps to understand and analyze other oscillator structures (Colpitt, Hartley,...).
4.) As another example, the so-called "DEBOO"-intergator is nothing else than a tuned bridge circuit consisting of a classical NIC block with 3 resistors and a RC combination which is connected at the NIC input.
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*** The same basic working principle does apply to the GIC resonator, where a frequency-dependent negative resistor (resistor !! - without frequency-dependent phase shifts) creates a resonant effect with a positive ohmic resistor connected in parallel.
Hi Lutz! I am glad to see you here again. Apparently, the vacation was good for your creative activity and now you generate a bunch of ideas:)
Obviously, all of us here share the belief that the balanced bridge circuit is omnipresent and can be seen in many applications. But the profound Abdelhalim's thoughts above made me think more deeply on the nature of the bridge circuit itself... and I felt a frantic desire to reveal the philosophy of its essence... maybe in a separate question like:
"What is the idea of a balanced bridge circuit? Why it is named in this way? What is the bridge in the bridge circuit?"
https://www.researchgate.net/post/What_is_the_idea_of_a_balanced_bridge_circuit_Why_it_is_named_in_this_way_What_is_the_bridge_in_the_bridge_circuit
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