Talk:Negative impedance converter

Helpful, Application Errors

you can easily explain this by drawing 2 voltage sources, each at Vs, but otherwise unconnected. from here the amplifier makes one of the Av*Vs and the other is just Vs. Av*Vs - Vs is applied across the resistor. this is the explaination for what it does, and you can easily show that the two sources could be merged into a single source. Using a single source makes the circuit "simpler" but adds more confusion as it seems there is an additional feedback path. only when the reader realizes that there is no feedback because there is no series resistance on the ideal voltage source does this become clear.

This also allows the application section to make sense. with an added series impedance, another feedback path is formed if there is only one source. this prevents the negative resistance from canceling out the series resistance, and can cause the circuit to latch in cases where an increase in output voltage would lead to a larger differential voltage.

likewise, the analysis's statment of the summing point constraint is not terribly valid. there are plenty of opamp circuits that fail this, furthermore, this circuit is very close to being one of such circuits. —Preceding unsigned comment added by 63.229.181.173 (talk) 04:04, 1 May 2008 (UTC)

Lengthy derivation

Is the lengthy input impedance derivation in the "Basic circuit and analysis" section really necessary? I'm inclined to just state the final result and link to the input impedance article or something. -Roger (talk) 17:52, 23 February 2009 (UTC)

Negative impedance is a novel result, but it's true that it seems like something trivial that follows from the circuit. Nevertheless, I think most references at least have a brief commentary on circuit operation. I think it would be fine to reduce the section to a paragraph, but I don't think it should be removed entirely. An alternative is to take the approach used on, say, Bernoulli principle where derivations are hidden by a collapsed table that can be expanded with a click. —TedPavlic (talk) 14:00, 24 February 2009 (UTC)

Moved content

Circuit dreamer's discussion has been moved to user space. Hellbus (talk) 17:47, 4 February 2012 (UTC)

Questions on this circuit description

I think a circuit analysis (math) is essential, especially with a speculative circuit like this. These NIC circuits all seem to ignore some basic properties of opamps and rules about circuit analysis. For example there is an element that is both a current source and a voltage source but there is nothing that says what the relationship is between the two. There is an independent I and V so I suspect the analysis is incorrect. The reference cited on the negative resistance page has a date 1953. Are there any more recent references or any evidence someone has actually built this circuit and demonstrated the claimed negative resistance effect?Zen-in (talk) 07:06, 14 December 2013 (UTC)

I believe there is an error in the transfer function for this circuit going back to the first editor of this page. He used the wrong method to derive the transfer function by starting with V_a = V_b instead of using the equation V_o = (V_a - V_b)α, where α = the open loop gain. That method is ok for some opamp circuits but is incorrect in this case. The correct transfer function I believe is:

$R_{\text{in}}\triangleq {\frac {V_{s}}{I_{s}}}=-R_{3}{\frac {R_{1}}{2R_{1}+R_{2}}}.$

I'm not convinced the circuit would really work as stated. An increase in V_s might just cause it to rail.Zen-in (talk) 08:42, 14 December 2013 (UTC)

There is nothing speculative in this circuit. It is based exactly on the "basic properties of opamps and rules about circuit analysis". To show it, here is another ("functional") analysis based on the properties of the classic non-inverting amplifier and the two versions of the Ohm's law (I = V/R and V = I.R). I (a still banned Wikipedian) give it to you, Wikipedians editing this talk page, as a gift (Spinningspark, sorry; I hope you will forgive me this little "trespass":)

Current-inversion NIC (INIC)

The op-amp keeps up the voltage drop V_R1 across R₁ equal to the input voltage V_S (the op-amp acts as a voltage-to-voltage converter or voltage follower) by passing a current I₂ = V_R1/R₁ = V_S/R₁ through the resistor R₂ (so R₁ acts as a voltage-to-current converter). The current I₂ creates a voltage drop V_R2 = I₂.R₂ across R₂ (so R₂ acts as a current-to-voltage converter). The op-amp keeps up the voltage drop across R₃ equal to the voltage drop across R₂ (the op-amp acts as another voltage-to-voltage converter or voltage follower) by passing a current I_S = V_R3/R₃ = V_R2/R₃ = (I₂.R₂)/R₃ = ((V_S/R₁).R₂)/R₃ through the input source. So, the input resistance is really -R₃.R₁/R₂.

If R₂ = R₃ (the usual case), the circuit injects the same current I_S = -I₂ that would be drawn by the resistor R₁ if it was connected directly to the input source. So, it behaves as a "negative resistor" R₁ having the same voltage as the positive R₁ but with an inverted current; thus the name of the circuit - "negative impedance converter with current inversion" (INIC). The circuit "inverts" every positive/negative element (resistor, capacitor or inductor) connected in the place of the resistor R₁ to the "opposite" negative/positive element with equivalent impedance; it is just a "current inverter" (actually, the very INIC consists of the two resistors R₂ and R₃, and the op-amp). According to this explanation, the direction of I_S in the figure should be the opposite (the current should enter the input source when it produces a positive voltage).

"The circuit would really work as stated" (would be stable) if the internal resistance Ri of the input source is low enough; in the case of an "ideal" voltage source (Ri = 0), it is unconditionally stable. More precisely, the inequality Ri/(Ri + R₃) < R₁/(R₁ + R₂) must be satisfied so that the negative feedback dominates over the positive one. Circuit dreamer (talk, contribs, email) 23:50, 14 December 2013 (UTC)

Your first statement I₂ = V_R1/R₁ = V_S/R₁ is incorrect. V_R1 = V_O - V_S. You cannot ignore V_O in deriving the transfer function. And just stating a few "Ohms Law" equalities and then pulling a transfer function out of the air is not algebra. Zen-in (talk) 00:09, 15 December 2013 (UTC)

I checked my derivation and found the mistake. The transfer function as stated in the page is correct. I copied the derivation to user space, where most of the other discussion is. Zen-in (talk) 02:32, 15 December 2013 (UTC)

Zen-in, you have really stressed me and I still can not realize that you have analyzed this simple circuit with a full screen of formulas while I have done it on one line! The difference between you and me is that you have "blindly" analyzed the circuit as a "black box" without seeing well-known sub-circuit building (functional) blocks. You have done it like a computer (a simulating program) while I have done it like a human being seeing familiar patterns inside the unknown circuit: voltage-to-current converter, current-to-voltage converter, voltage follower, non-inverting amplifier, non-inverting current source, current inverter... and even a balanced bridge. Yes, this circuit is exactly a bridge that is balanced by adjusting the supply voltage... and the result is V_R1 = V_S, V_R3 = V_R2. IMO the most useful way of presentation is as two cascaded devices - voltage-to-current converter and current inverter.

About your initial remarks, "there is an element that is both a current source and a voltage source but there is nothing that says what the relationship is between the two. There is an independent I and V so I suspect the analysis is incorrect"... The NIC circuit is a current source (a special kind of a voltage-to-current converter, voltage-controlled current source VCCS or a transconductance amplifier) that, in contrast to the ordinary current source, "pushes" its output current back to the input voltage source. This circuit does not use the op-amp output voltage V_O; it is a 2-terminal (1-port) device. So, it is not represented by a transfer function; it is represented by an IV curve (with a negative slope). Circuit dreamer (talk, contribs, email) 15:17, 15 December 2013 (UTC)