Understanding Circuits on the Whiteboard...Negative Impedance Converter (NIC)  
Negative impedance converter (NIC) is one of the most interesting, odd, strange and even "mystic" electronic circuits, which are still unexplained (I have not yet met some "humanfriendly" explanations of this legendary circuit on the web or in the books). Reading the formal and dull explanations of existing sources dedicated to this circuit, we can learn what NIC is (for example, "a circuit introducing a shift of 180° between the voltage and the current"); however, we can't understand it! In order to understand really this sophisticated circuit, we need something more. As human beings (not computers), we first need to know what the general idea behind negative resistance is (that is, what negative resistance is), then, how to obtain negative resistance and finally, how the opamp does that work (or what the opamp actually does in the circuit of NIC). From many years, I have been thinking about the phenomenon of negative resistance and its circuit implementation as NIC. Finally, I have managed to grasp the general idea behind them; now, I would like to share my penetration with you. In the story below, I have shown how can we reason, in order to reveal the secret of this sophisticated circuit. 

Reasoning 
Graphical representation 
At first glance, the NIC circuit diagram looks apparently complex and unintelligible. However, if we scrutinize it, we will begin discern wellknown circuit solutions. Let's begin braking circuit into smaller subparts and try to guest what they do. 

top < prev step  1  2  3  4  next step > end Real voltage source. First, look at the left bottom side of the picture. What are the two components VIN and Ri? They represent a real voltage source acting as an input generator. Voltage divider. Then, look at the top side of the picture. What are the two resistors with equal R? They constitute a voltage divider with K = 0.5. Detach temporarily it from the rest part of the circuit. Transimpedance amplifier. Finally, look at the right bottom side of the picture. What are the opamp and the resistor R connected between the opamp output and the inverting input? A tip: temporarily ignore the upper voltage divider and suppose that the noninverting input is grounded. Eureka! But this is the familiar opamp currenttovoltage converter (transimpedance amplifier). What does the opamp do in this circuit? Walking through the loop VIN  VRi  VR  VOA we can see that a voltage drop VR = I.R loses across the resistor R; however, the opamp adds the same voltage into the loop. As a result, the opamp compensates perfectly the voltage drop across the resistor R; both the "harmful" voltage drop VR and the resistance R disappear (the real voltage source "has the feeling" that it is shorted). Aha, the main task of the opamp here (and why not, in all the opamp inverting circuits?) is just to zero the resistance R! How simply it is! Actually, the opamp acts as an additional supplementary voltage source, which "helps exactly" the excitation voltage source VIN in its efforts to create the current IIN  note that the two voltage sources are connected in series, in one and the same direction ( +,  +) so that their voltages are added. Reinventing transimpedance amplifier How I revealed the secret of parallel negative feedback circuits Wikipedia: Transimpedance amplifier 
Braking down the circuit of NIC
What does the opamp do in a transimpedance amplifier? The opamp continuously compares its own output voltage VOA with the voltage drop VR across the resistor R by subtracting the two voltages. It "observes" the result of the comparison  the voltage VA = VR  VOA of point A (the socalled virtual ground) and keeps it almost zero by adjusting the output voltage VOA = VR = I.R. Currenttovoltage passive converter, Reinventing opamp inverting summer Opamp circuit builder (click the resistor on the right hand side) 
top < prev step  1  2  3  4  next step > end It's time to see what the voltage divider does in this odd circuit. Connect it and see what the opamp will do. What does the opamp do in NIC? The opamp continuously compares 1/2 of its own output voltage VOA with the voltage drop VR across the resistor R by subtracting the two voltages. It "observes" the result of the comparison  the voltage difference between the two inputs and keeps it almost zero by adjusting the output voltage VOA = 2VR = 2I.R. Aha! Now, the opamp is "misled"  it has to generate two times higher voltage VOA = 2VR = 2I.R, in order to keep zero voltage between its two inputs. Half the voltage (VR) compensates the voltage drop VR; the rest half (VR) is added to the excitation voltage source VIN. So, the voltage divider (with K = 0.5) connected to the noninverting input makes the opamp "overcompensate" twice the voltage drop VR. Let's make a conclusion. NIC is just an "overcompensating" transimpedance amplifier. A heuristic approach to teaching negative resistance phenomenon Wikipedia: My viewpoint at transimpedance amplifier, What is the basic idea behind a negative impedance converter (NIC)? 
Reassembling the circuit of NIC 
top < prev step  1  2  3  4  next step > end Once we revealed what the opamp does in the circuit of NIC, we can generalize the "overhelping" idea in a form of an equivalent electrical circuit.
NIC components An internal resistor. Obviously, the "ordinary" resistor R acts as a passive currenttovoltage converter, which output voltage drives the "helping" voltage source BH. What a paradox! In order to get a negative resistor, they have connected internally an ordinary resistor! Well, we can make the first general conclusion: NIC (a negative resistor with resistance R) contains internal resistor with resistance R. An internal doubling voltage source. Evidently, the opamp acts as an "overhelping" voltage source that doubles the voltage across the resistor R (voltage amplifier with K = 2). So, we can make the second general conclusion: NIC contains also an internal doubling voltage source (voltage amplifier with k = 2). NIC = "ordinary" resistor + inverting voltage amplifier Wikipedia: What is the basic idea behind a negative impedance converter? 
NIC presented by an equivalent electrical circuit 
top < prev step  1  2  3  4  next step > end So far, we have managed to reveal the function of each component in the opamp circuit of NIC. What is more, we have generalized it in a simple equivalent electrical circuit. But yet, can we finally answer in the possibly simplest way to the question "What is NIC?" Let's try. Actually, NIC is an opamp circuit implementation of an "overhelping" negative resistor. So, we have first to answer the question "What is negative resistor?" For this purpose, let's compare the two kinds of resistors. Let's a current I passes through a "positive" resistor R and through a negative resistor R. As a result, a voltage drop VR = R.I appears across the resistor R and the same voltage VH = VR = R.I appears across the negative resistor R. Only, the resistor R sucks a voltage VR = R.I from the circuit (it is a voltage drop) while the negative resistor R adds a voltage VR = R.I into the circuit. So, a resistor acts as a currenttovoltage drop converter while a negative resistor acts as a currenttovoltage converter. The element named "resistor" is really a resistor while the "negative resistor" is actually a voltage source, whose voltage is proportional to the current passing through it. Then, let's make the final conclusion. NIC is just an additional voltage source, which produces a voltage proportional to the current passing through the source; this voltage is added to the input voltage. Wikipedia: What is the basic idea behind a negative impedance converter? 
NIC presented as an "overhelping" negative resistor
NIC = "helping" current controlled voltage source 
circuitfantasia > circuit stories > understanding circuits > NIC Last updated November 21, 2006 