# Is static negative resistance practically available?

I learned that negative resistance (NR) could be simulated by involving active devices like op-amps and others. I'm interested in the static/absolute NR rather than the differential NR.
My question is whether it is really practically feasible to be used when making an AC circuit network with about a hundred RLC components and nodes grounded through NR. The purpose is to cancel some effect of R, but not all (otherwise I would go completely without R). Is it just a routine thing or out of the reach of current techs? And any possible reasons.

People are asking why I need such a thing. It’s not for a particular engineering purpose. It’s more of a construction to show some mathematics of a certain circuit with only RLC and NR. The original problem is just outside what EE usually concerns and distracting to show here. We're interested only in the linear equations of ideal circuits and want to build a real working example.

• Why do you feel the need to make about a hundred negative resistances? What problem do you think you are solving? - What is your actual/original problem that you are trying to solve? – Harry Svensson Dec 13 '18 at 1:25
• I guess you could, but the question remains: Why? – Hearth Dec 13 '18 at 1:42
• Most negative resistance circuits are non-linear, and operate over a small range of voltage and current. As others have suggested, a more specific description of your intended application would help determine if your idea is workable. – glen_geek Dec 13 '18 at 2:12
• Tunnel diodes (Esaki diodes) have a negative resistance region. As a kid, spent good money for one and was able to find the -R region by contriving a sort of curve-tracer using a couple of analog pointer-dial meters; I concluded the "gap in the curve" was the -R region, and then built a moderate frequency RF oscillator using that tunnel diode. – analogsystemsrf Dec 13 '18 at 3:14
• We must clearly distinguish between STATIC negative resistances (which are LINEAR) containing active devices (opamps,...) and DIFFERENTIAlL negative restances which are identical to the slope of a non-linear V-I characteristic (Esaki diodes). – LvW Dec 13 '18 at 10:15

## 2 Answers

It's easy to simulate a negative resistor with one side grounded. See also this Wiki entry. For example: simulate this circuit – Schematic created using CircuitLab

Here the circuit to the right of the capacitor has an impedance of -R1(R3/R2).

I've demonstrated in this case to cancel out the resistance of the inductor R4. Here you can see the results with R1 = 0 and R1 = 100 ohms:

R1 = 0 R1 = 100 ohms For reasons that should be obvious, it's a bad idea to completely cancel out the positive resistance in most cases. Some DC motor controls cancel out much of the armature resistance to improve speed regulation under varying loads.

You can also look at GICs (Generalized impedance converters), which are related.

This is an interesting parlour trick, however usually there are much better ways of doing filtering or whatever it is that has to be done.

• The only place where I've seen it used is to cancel out large capacitances associated with the physical construction of bio -electrodes, which often involve conductors with very thin insulating layers in between them (e.g., glass microelectrodes). – Scott Seidman Dec 13 '18 at 18:05

There are active circuits which have a negative input resistance - they are so-called "Negative Impedance Converters (NIC)". In contrast to some comments made in this thread, they are static linear circuits and operate over a broad range of voltages and frequencies.

Such an NIC block consists of an operational amplifier with negative feedback (two resistors) and one resistor between opamp output and non-inv. input which - at the same time - forms one node of the grounded negative resistor. There is another NIC-type with both opamp inputs interchanged.

NIC blocks are rather common for active filters and harmonic oscillators, where the undamping properties of these devices are exploited.

More than that - two such NIC blocks can be combined to a very versatile active circuit - the so-called "Generalized Impedance Converter (GIC)". GIC circuits play a rather important role in active filter realizations. It was shown that GIC-based filters have superior quality properties as far as the passive tolerance senstivity is concerned.

These GIC units can be used for linear applications as realizing (a) active inductances and (b) Frequency-dependent negative resistors (FDNR). Both circuits are very common in analog filtering.

EDIT (Example):

R1: Feedback resistor to the non-inv. opamp,

R2: Fedback resistor to the inv. opamp input,

R3: Resistor between inv. input and ground.

Input resistance (ref. to ground) at the non-inv. opamp inout: Rin= - R1R3/R2

• Thanks for the answer. What does 'static linear circuits' mean here? It's good to know they 'operate over a broad range of voltages and frequencies'. Is there any reference regarding this claim? – xiaohuamao Jan 9 at 23:06
• Well.....the classical part we call "resistor" can be used as a linear part (Ohms law) and its resistance is not only a differential one (like the small-signal dynamic input resistance of a pn junction). And the same properties apply to the negative input resistance of an NIC block. References (explanation, applications) can be found in each textbook dealing with operational amplifier applications. Or start a Google search for "NIC" and/or "GIC". – LvW Jan 10 at 10:49