Cyril:

I agree totally and wholeheartedly with Christian. Another way of thinking about the FUNDAMENTALS (always a good idea, wouldn't you say?) is as follows:

1. A real, physical resistor - the only kind that matters in down-to-earth practice - is a device that converts electrical power into heat, as the flowing electrons are made to give up their energy to the material of which the physical resistor is formed. Thus, it is a DISSIPATIVE device.

On the other hand (and it's always a good idea to look at both, n'est ce pas?) we have:

2. A negative resistance, taken first as a linear element - is a source of power. Thus, it is an ACTIVATING device. Bounded regions of negative resistance can be arranged to occur in nonlinear electronic devices (such as tunnel diodes or tetrode tubes, and many other examples) and they also can be EMULATED in active circuits composed of linear elements but only when provided with a power source.

Accordingly, real resistors (nor to be confused by Der Lehrmeister with the simple mathematical resistances of circuit theory) can take on innumerable forms. The resistance does not need to be linear. Thus, a junction diode acts as a resistance whether forward- or reverse-biased. A rectifier diode will get detectably hot to the hand in either condition, at a certain power level.

In the other hand, you may have on our palm of your hand the cold side of a Peltier device. It is consuming power from the source, so shouldn't it be getting hot? In fact, one side IS; you have the cold side on your hand, and the heat appearing on the other side is the sum of the heat extracted from the power source and your hand. It HAS to be that way, if God's laws are to be observed, and He has made sure they always have been and always will be.

So it seems now we need to start a new thread on Theology......

Barrie

Dear Cyril, a positive resistance descript a load, a negative resistance descript a source and an electrical network with zero resistance is a perpetual motion machine. A perpetual motion machine has not technical relevance!   

Cyril:

I agree totally and wholeheartedly with Christian. Another way of thinking about the FUNDAMENTALS (always a good idea, wouldn't you say?) is as follows:

1. A real, physical resistor - the only kind that matters in down-to-earth practice - is a device that converts electrical power into heat, as the flowing electrons are made to give up their energy to the material of which the physical resistor is formed. Thus, it is a DISSIPATIVE device.

On the other hand (and it's always a good idea to look at both, n'est ce pas?) we have:

2. A negative resistance, taken first as a linear element - is a source of power. Thus, it is an ACTIVATING device. Bounded regions of negative resistance can be arranged to occur in nonlinear electronic devices (such as tunnel diodes or tetrode tubes, and many other examples) and they also can be EMULATED in active circuits composed of linear elements but only when provided with a power source.

Accordingly, real resistors (nor to be confused by Der Lehrmeister with the simple mathematical resistances of circuit theory) can take on innumerable forms. The resistance does not need to be linear. Thus, a junction diode acts as a resistance whether forward- or reverse-biased. A rectifier diode will get detectably hot to the hand in either condition, at a certain power level.

In the other hand, you may have on our palm of your hand the cold side of a Peltier device. It is consuming power from the source, so shouldn't it be getting hot? In fact, one side IS; you have the cold side on your hand, and the heat appearing on the other side is the sum of the heat extracted from the power source and your hand. It HAS to be that way, if God's laws are to be observed, and He has made sure they always have been and always will be.

So it seems now we need to start a new thread on Theology......

Barrie

Cyril, My immediate answer is NO because electrical circuits are nonlinear.

If we assume that the circuit is linear with lumped elements then we may look at the circuit seen from the negative resistance. It must be a two-terminal (an input port). We can measure the input impedance or the input admittance of this port so it may be equivalent to a voltage source in series with an impedance or a current source in parallel with an admittance. The negative resistance may neutralize the real part of the input impedance but this is not equivalent to neutralizing each of the resistors in the circuit. If the circuit is a passive RC circuit you may include

the negative resistor and calculate the poles of the circuit (the eigenvalues of the Jacobian of the linear differential equations). It might be that the poles may be placed on the imaginary axis by a specific value of the negative resistor.

The neutralisation talked so far, is in mathematically positive and negative cancels each other. However, in circuit behavioral aspect is, positive resistance means power absorbing phenomena. Negative resistance leads to unstable circuit (oscillation), and  in turn, sourcing the power. Thus in real sense, effect of resistance does not go away (the power loss is continued) but loss of power is compensated by other source.   

Vasile, I have added a circuit diagram (especially for you:)

Christian, I am afraid that the problem here is not the zero but sooner the infinite resistance...

Erik, I am thinking about the fact that here we compensate the positive "Re" with a negative "-Re"... but still the positive "C" remains... Maybe it will be enough to keep the circuit stable?

Barrie Gilbert, we talk here about circuits having true linear negative resistance (the negative impedance converter above); so I completely agree with your assertion that "a negative resistance, taken first as a linear element - is a source of power". Actually they are not only sources; they consist of two elements in series - a linear positive resistor (R1 in the figure) and a dynamic voltage source (the non-inverting amplifier composed of R2, R3 and the op-amp). I have thoroughly considered this idea in the funny Wikibooks story below:

https://en.wikibooks.org/wiki/Circuit_Idea/Revealing_the_Mystery_of_Negative_Impedance

You talk about elements having differential negative resistance. They really are non-linear elements having dynamic resistance; typical examples are, as you said, tunnel diodes. I have dedicated another funny Wikibooks story to this phenomenon: 

https://en.wikibooks.org/wiki/Circuit_Idea/Negative_Differential_Resistance

Also, I fully agree that "the resistance does not need to be linear. Thus, a junction diode acts as a resistance whether forward- or reverse-biased." And accordingly, we can make a "mirror copy" of such a non-linear resistor... and it will be a negative non-linear resistor. For example, the op-amp in the circuit of a diode log converter acts as such a negative diode:

https://en.wikibooks.org/wiki/Circuit_Idea/Voltage_Compensation#A_negative_diode

a  resistance/resistor at a given node towards another node can be compensated, and this is called bootstrapping.

a resistance is defined and exists only between two nodes! by injecting opposite currents at these two nodes the given resistance can be virtually compensated and disconnected, but only between these two nodes and whit the price of consumed extra power from the compensation circuitry

Dobromir, I would like only to refine your assertions...

When "bootstrapping" a resistor, we apply an opposite voltage from the other side of the resistor so there is no current flowing... and no extra power consumed; the result is infinite resistance between the two nodes. Thus we have neutralized this resistance by means of an opposite voltage (the Miller arrangement for voltages).

When neutralizing a positive resistance (e.g., the leakage Rc in the picture above), we inject an additional current Vc/Rc in the same direction with the initial currrent (V - Vc)/Rc. The result is again infinite resistance in the place of the voltmeter. Now we have neutralized this resistance by means of a "helping" current (the Miller arrangement for currents).

In these applications, "neutralizing" means "increasing up to infinite"...

"bootstrapping" means increasing the impedance. Generally it is done by positive  shunt-shunt feedback. it does not matter how it is realized in details by amplifiers, current sources, passive components, etc.

always extra power is consumed, because we do not talk about  "perpetual motion machine", nuclear reactions, cold fusion, etc

Dobromir Dobrev's method of injecting opposite currents at the two terminals between which the positive Resistance is connected ,I am afraid, leads to no current through the Resistance and is as good as Open circuiting or Switching off the Circuit.

By connecting in Series an Equal Negative Resistance amounts to short circuiting the Resistance.

In that case if it is a circuit having D. C Source with only Pure Inductance (having neutralized the resistance of the coil) finally short circuits the Voltage Source. If it is a Pure Capacitive Ckt.  the Capacitance gets charged fully Impulsively and acts as Open circuit for D.C.Supply  If it is LC series Ckt. with D.C. Source there will be no  current flow at all , since  L acts as O.C. initially. and C acts as O.C.finally.(Time Constant RC = RL =0 since R = 0 the Capacitor gets charged Fully Insantaneously - Impulse Charging)

In the case of A.C. Source the circuit will act as Pure Inductive ckt. or  capacitive ckt or LC series circuit or Series Resonance Circuit leading to undamped sustained oscillationss,depending on the Values of L and C if connected alone or in Series when all the Resistance values is Neutralized.

P.S.

.

If you refer to my publication “Very-high-Q inductor simulation for active tuned filters”, S. K. Biswas, International Journal of Electronics, vol.58, no.6, Jun. 1985, pp 1019 – 1023, you will find that I have used a negative resistor simulation in series to cancel the residual positive resistance in a simulated inductor such that very high Q is obtained in a practical analog circuit ! Thus, in a way, it is possible to neutralize all positive resistance in a circuit under certain conditions.

Dobromir, if I may, I will try again to refine the formulation of "bootstrapping".

"Bootstrapping" is a way to artificially increase the resistance by compensating the input voltage with an equivalent voltage; as a result, the current disappears. It is just an illusion... a clever trick... since the resistance is the same but we think of the combination "resistor + voltage source" as a new virtual resistor with infinite resistance... Generally it does not require a negative feedback; it only needs a second voltage source equal to the first one (e.g., a fixed gain amplifier with gain of 1). Since (almost) there is no current flowing through the resistor and the two sources, minimum power is consumed as well.

Sujit:

Your so-called "negative resistance" is actually a power source, one by which - however subtle and whatever the specific circuit topology - can, by careful design or manual adjustment, replenish the loss for any given resonator. This loss will include the added burden of a real load resistance where appropriate. To achieve effectively infinite Q-values it is necessary to provide exactly the power needed to make up the loss; a slightly lower power achieves a (often precariously uncertain) high value of Q.

There is no need to introduce the concept of a magical "negative resistance" - a classroom viewpoint that should be interpreted and applied cautiously.

The use of such controlled and carefully-balanced methods to effectively cancel the loss in a resonator - whether as part of a filter or an oscillator - is a very old art, as any study of the history of analog design will quickly reveal. Edwin Armstrong is credited with the invention of this method, which he called "regeneration", exactly one hundred years ago, shortly after Lee de Forest invented the triode tube, and thereby opened the door to achieving power gain and all of electronics.

http://www.rtm.ar88.net/Armstrong_Days_at_InfoAge.html

http://en.wikipedia.org/wiki/Regenerative_circuit

Circuit Q can be viewed simply as a measure of the power lost during each cycle of the resonant frequency. Assume a Q of 50 for an LC resonator (a "tank", having several lossy components). This means that 2% of the energy stored in the tank is being lost through dissipative processes during each cycle. If left to itself, this tank will "ring down" in a perfectly natural exponential way, resulting a relative amplitude of 0.133 after 100 cycles, in this example.

Thus, the art of LC oscillator design is to provide exactly the amount of power to the tank that is required to make up this loss - too little, and the oscillation decays (in fact, the oscillator probably won't start); too much, and the active devices will enter a region of operation when they are saturated, in which state they will add phase noise. I call this maxim MOMA - meaning one must ensure Minimum Overdrive while maintaining Maximum Amplitude - the condition where the tank's RF power is as large as possible, thus minimizing the adverse effects of circuit noise.

In oscillators and filters it is common to use local pairs of cross-coupled transistors whose effective negative resistance is controlled by the bias conditions. Any one of these widely-used topologies is known as a Negative Impedance Converter (NIC). When using BJTs, this is simply a matter of controlling the tail currents applied to the common emitter node; in the case of MOS one may control the value of the "negative impedance" in other ways.

Here's the important point about all this: whatever the specifics of the circuit topology, the function of these NICs is simply to make up some (in moderate Q enhancement) or all (in oscillators) of the power lost by each of the resonant cells (active RC or passive LC). That's all there is to "negative resistance".

Shouldn’t we move on to more important, interesting, urgent or practical matters?

Barrie

In case of oscillator or active filter the uses  passive components have positive resistance with active device  just do that  function to sustain its performance long time. But due to variation of  temperature coefficient of resistance of passive and active component, some time tough to maintain it.

Cyril, your explanation is just one case.

For my point of view, the term ''bootstrap feedback'' means positive shunt-shunt (parallel to input voltage) feedback. It increases the input impedance.

It should not be mess up with a negative shunt-shunt feedback, because in that case the input impedance is decreased. Example is the virtual ground impedance, at the inverting (summing) node of opamp stage when the opamp noninverting input is connected to ground and a feedback resistor R is connected from the summing node to the opamp output.  If the opamp gain is very large let say 100dB or  A=-100k, the summing node impedance towards ground is very low, but if the opamp gain is low, let say 0dB or A=-1, what is the summing node resistance, towards ground, in that case?

By the way, i do not understand your link https://en.wikibooks.org/wiki/Circuit_Idea/Voltage_Compensation#A_negative_diode

gain coefficient of -1, does not mean negative diode, capacitor, resistor or what ever 

Cyril,

With reference to your figure the negative resistor is equal to the product of R1 and R3 divided by R2 if you assume ideal opamp with infinite gain. The resistors Rv, Rc and R are in parallel so you may end-up with the capacitor C in parallel with the voltage source V and a conductor which may be positive, zero or negative.

With reference to the wien bridge oscillator based on a parallel RC circuit and a series RC circuit,  please note that if you remove the parallel capacitor you have a multivibrator.

Barrie,

I agree with your question:

"Shouldn’t we move on to more important, interesting, urgent or practical matters?"

Unfortunately basic circuit theory is disappearing from the electrical engineering courses.

Dobromir,

I just wanted to note that "bootstrapping" and "positive feedback" are not the same thing - it is possible to have bootstrapping without positive feedback...and positive feedback without bootstrapping... For example, drive the inputs of two identical non-inverting amplifiers (with equal gains) with the same input voltage; then connect a resistor between their outputs. As a result, each output will "see" an infinite resistance (a bootstrapped resistor). Is there any feedback in this arrangement?

Then, replace the one of amplifiers with an inverting amplifier (with the same gain). Now, the ubiquitous virtual ground will appear in the middle of the resistor... and each output will "see" two times lower resistance (a half resistor). Again, is there any negative feedback in this arrangement?

A positive feedback will appear in a bootstrapping arrangement if the input voltage source has some internal resistance... but if it is a perfect (ideal) voltage source, there will be no feedback.

Now about the "negative diode"... If you look at the circuit of the diode log converter, you will see that (to the right of the virtual ground) the input current flows through two elements in series - the diode and the op-amp output. As a result, a voltage drop VF appears across the diode and the same voltage (emf) -VF appears across the op-amp output. Thus the diode consumes voltage (power) while the output produces voltage (power)... so it acts as a negative diode... See more about this in the question below:

https://www.researchgate.net/post/Does_the_op-amp_in_all_the_inverting_circuits_with_negative_feedback_behave_as_a_negative_impedance_element_negative_resistor_capacitor_etc

Erik:

I’m all for the accurate presentation of circuit theory – from the most rudimentary level (of the sort we are often seeing in posts to these ResearchGate threads) to the most advanced and powerful analog circuit design practice (which I have not yet seen here).

The notion that we have passed the point in history where circuit theory has become practically irrelevant, and therefore less important in university curricula, is badly misplaced. Analog circuits will be needed as far into the future as we can possibly glimpse. Radios are forever: can you imagine a world without them?

However, the kind of products that need to be designed today are better understood, more clearly analyzed, more effectively improved and more quickly developed using accurate simulation studies. We frankly can LEARN basic circuit theory by posing daily “questions” to our simulator and then pondering its “answers”.

Often, things don’t behave the way we expected. Of course, it would not be wise to then cite such examples as “failures in the simulator”. We are most often the ones to fail; but we can do this in private and thus be free from appearing stupid in a group environment such as a classroom.

Furthermore, the modern analog designer does not need to understand much that filled the text-books of the past; for example, how the Fast Fourier Transform works its magic, as a “fully qualified electronics engineer” in our field once had to understand. There is no virtue in calculation: that is something better left to a computer. This is also a reflection on the speed with which a modern designer must present the production-ready solution to often very complex challenges.

There is no better way to learn than by doing, whether at an experimental bench laden with (sometimes inaccurate) test instrumentation, or by exploring new ideas using a reliable simulation environment, meaning: one having trustworthy modeling equations and accurate device characterization.

Alas, only a few of us are privileged to have had an important part in developing these very tools and the modeling of all manner of devices, as we have at Analog Devices. To provide just one example, a resistor in our models needs more than a dozen parameters to fully describe it. Indeed, a real resistor is a complicated dynamic element and one that is also prone to many environmental factors. In sharp contrast, the models for devices provided by foundries are often hopelessly incomplete, inaccurate and misleading.

It is very unfortunate that a lot of useless ideas are being bandied around in these ResearchGate windows. Some are downright nonsense and so much hot air. They cannot – in all honesty – be called valuable, especially as they frequently deviate far from the question originally posted.

Barrie

On the eve of the New Year, I want to congratulate all participants in this so interesting discussion with a series of "greeting cards" where to expose the evolution of  my "super-neutralization idea":)

I want to dedicate this "circuit comics" specially to Farzane, who inspired me to ask this question as a result of her question:

https://www.researchgate.net/post/whats_the_real_behavior_of_rc_circuits?

1. Non-disturbed RC circuit. First, imagine an "ideal" RC integrating circuit consisting of ideal elements ("pure" resistor R and capacitor C), and working at ideal load conditions (open circuit). So we assume the output voltage varies exponentially and eventually (ever, after thousands of years:) will reach the input voltage V...

2. Rc-disturbed RC circuit. Then imagine that, for some reasons, we replace the ideal (having no leakage) with a real (with leakage Rc) capacitor. The leakage acts as a pull-down "resistor" that diverts a current Vc/Rc and the output voltage will never reach the input voltage V (even after thousands of years:( Or, more professionally speaking, the two resistances form a voltage divider with a ratio of Rc/(Rc + R)... and the final voltage will be V*Rc/(Rc + R)...

3. Rc-neutralized RC circuit. But fortunately, a powerful idea dawns on us - as the "resistor" Rc needs the current Vc/Rc, why not to give (inject) this current from an external current source? Then the resistor Rc will "suck" this current from the external current source instead from the input source V through the resistor R... and the RC circuit will have the "feeling" that it is unloaded... just as in the beginning.

To produce the "replacing" current, we double (amplify with a gain of 2) the voltage Vc across the leakage Rc and apply it through an external resistor Rc back to the circuit output. As a result, the needed current Vc/Rc through the external resistor Rc reverses its direction and supplies the leakage Rc... as though the combination of the external Rc + non-inverting amplifier acts as a negative resistor -Rc. Thus we insensibly have "invented" the current-inversion negative impedance converter (INIC)...

4. RcIIRv-disturbed RC circuit. But we are curious and want to see this exponentially changing voltage... so we connect a voltmeter or oscilloscope to the circuit output, across the capacitor C (we still have not come to the powerful idea to connect it to the op-amp output of the INIC circuit above). The measuring device adds another resistance Rv in parallel to the capacitor leakage... and the total pull-down resistance (Rc||Rv) decreases even more...

5. RcIIRv-neutralized RC circuit. But we already know the remedy and accordingly decrease the magnitude of the negative resistance (make it equal to Rc||Rv). Now the negative resistor (INIC) supplies (neutralizes) both the resistances Rc and Rv... and again the RC circuit has the "pleasant feeling" that it is unloaded... just as in the beginning. In this way, we have provided a fully exponential shape of the output voltage...

6. RIIRcIIRv-disturbed RC circuit. But it is quite possible (and likely) that we do not want an exponential but sooner linear shape of the output voltage. What is to blame for the fact that we do not get linear but exponential shape of the output voltage? Of course, the low (finite) resistance of the resistor R...

7. RIIRcIIRv-neutralized RC circuit.  Then the boldest idea comes upon us - to neutralize the resistance R as well... to make it infinite. And the remedy is the same again - to decrease the magnitude of the neutralizing negative resistance further (to make it equal to R||Rc||Rv)...

8. R-neutralized RC circuit. Finally, let's remember who were the pioneers of this powerful idea - Howland (the Howland current source, pump) and Deboo (the Deboo integrator - the attached circuit below). As we can see, these circuits are designed to work at ideal load conditions (no leakages, no voltmeters, no oscilloscopes...) Here the INIC compensates (neutralizes, makes infinite...) the only resistor R.

So the question is, "Can we think of our circuit as of an improved Deboo integrator?" Or, "Can we think of it as of a combination of two negative resistance circuits - Deboo integrator and load canceller?"

Prof.Cyril,

I agree that the Circuit acts as Improved Howland Current Pump.

Refer AN-1515 A Comprehensive Study of the Howland Current Pump given by Texas Instruments.

http://www.ti.com/lit/an/snoa474a/snoa474a.pdf

But the same negative Current of the Current enters the Jn. node of R and C and gets divided between R and C. If the Current Source Current is equal and opposite to that in R, (ignoring the Voltage Source internal Resistance ) -R sets in and the R gets Neutralized, This Problem is overcomed as follows.

NON-INVERTING (DEBOO) INTEGRATOR. Here, we connect in parallel to the capacitor an additional "helping" current source. It produces a compensating current Vc/R, which is proportional to the voltage drop Vc across the capacitor. In this way, the source adds the "missing" current Vc/R to the insufficient input current Iin = Vin/R - Vc/R; thus, it "helps by current" the input source to create the right current Ic = Vin/R - Vc/R + Vc/R = Vin/R. Thus we obtain the famous Howland circuit, which acts as a perfect voltage-to-current converter (if we include the input voltage source, we name it Howland current source).

A negative resistor -R can serve as the "proportional helping current source" needed. It does this magic by "pushing" a current I = Vc/R through the capacitor instead by "sucking" the same current (if it was an ordinary "positive" resistor R). In order to create a negative resistor -R, we may convert a positive resistance R into a negative one -R ; thus we will create the famous negative impedance converter (NIC).

Refer "Talk:Circuit Idea/Deboo Integrator" vide Link: http://en.wikibooks.org/wiki/Talk:Circuit_Idea/Deboo_Integrator

Hence I think Your Idea is Correct.

P.S.

Prof. Pisupati,

Thanks for the comment and nice links. Happy New Year! Cyril.

Barrie:

Thank you for your comments. I agree with you. Leaning by doing is the main road to knowledge and understanding. You must learn from your own mistakes and errors.

Modelling and simulation is an art. Make it simple but not too simple.

Happy New Year

ERIK

Erik, but still "is it possible to neutralize all the positive resistances in a circuit by an equivalent negative resistance"?

Cyril.

Yes maybe - it depends on your assumptions, your models and your definition of the "neutralize" mechanism  !!!

Best regards ERIK

Erik,

Your previous answer was a far more explicit:

"With reference to your figure the negative resistor is equal to the product of R1 and R3 divided by R2 if you assume ideal opamp with infinite gain. The resistors Rv, Rc and R are in parallel so you may end-up with the capacitor C in parallel with the voltage source V and a conductor which may be positive, zero or negative."

Cyril,

only a concrete resistance/impedance between two nodes can be compensated. More over, to make such compensation, you should have a goal or a real problem to solve, e.g. to increase the input impedance, decrease loading etc.

It is impossible to compensate all positive resistances, because such compensation simply is a nonsense without practical meaning!

Why? because, if you have no positive resistance, your circuit will not do any job, and so you will have no circuit.

Dobromir,

I agree with you that "only a concrete resistance/impedance between two nodes can be compensated". If you take a look at my "New Year greeting" (for which I have not get at least one "thank you" from someone, excluding Prof. Pisupati)...

https://www.researchgate.net/post/Is_it_possible_to_neutralize_all_the_positive_resistances_in_a_circuit_by_an_equivalent_negative_resistance/3

... you will see a completely concrete positive resistance (Rc||Rv and then R||Rc||Rv)... and a "goal or a real problem to solve" (compensating the leakage or/and voltmeter resistances)...

Notice also that in this arrangement something "positive" still has remained - the impedance of the capacitor...

By the way, there is "some" sense to compensate all the positive resistances by a negative resistance. In this case, there will be only a "pure" negative resistance... and such a circuit will be completely unstable... bistable... But this is exactly what is called "latch", "flip-flop"... the basic building element of registers, static RAMs, computers... Is this a "nonsense without practical meaning"? 

Oh, PLEASE folks!!!!

Get real, which means THINK PRACTICAL - even if it means 

breaking out of the academic shell that seems to be covering

some of the contributors to this peculiar thread, like a warm

blanket.

A designer of real circuits invokes HUNDREDS of circuit tricks

to meet a certain set of performance objectives - ROUTINELY,

DAILY, INSTINCTIVELY - usually judging the best of several

possibilities - counting such things as the use of the smallest

number of devices (or otherwise optimizing a chip area, with 

cost in mind); the sparse use of extra power; the effect of an

alteration of a circuit topology on such matters as frequency

response and HF stability, on noise and other such aspects of

performance; and above all, the assurance of ROBUSTNESS

of a design over process, voltage and temperature - the vital

PVT initiative.

In short, there's nothing AT ALL UNUSUAL about using means

to convince the circuit to ignore positive resistances where they

matter. For example, a simple BJT current mirror has a finite --

and relatively low - incremental output resistance within a small

current and voltage range, a simple consequence to base-width

modulation. Now, suppose a certain application requires that

the output current is almost perfectly independent of the voltage

applied to its output node. Do we impulsively reach for a magical

negative resistance to cancel the mirror's output resistance? Or

do we get smart?

What do you think? (By the way - a simple cascode is not going

to get the net output resistance high enough).

Barrie

Dear Barrie Gilbert, I will think seriously on your problem... but would you appreciate (impartially) my Wikibooks stories about the basic idea behind the simple BJT current mirror (the first picture below)?

http://en.wikibooks.org/wiki/Circuit_Idea/How_to_Reverse_Current_Direction

http://en.wikibooks.org/wiki/Circuit_Idea/Group_67b#Lab_3:_Transistor_circuits_.28.22inventing.22_a_BJT_current_mirror.29

... and about the Wilson's idea (the second picture)...

https://en.wikibooks.org/wiki/Circuit_Idea/How_the_Wilson_current_mirror_keeps_the_current

... which may be one possible answer to your question?

As a long-time practicing engineer, I second Barrie G's statements.  Compensation is the science and art of controlling effects to achieve some goal.  While it may be a thought-provoking exercise to consider how to neutralize R using -R, the point of doing so is rather limited at best in all but the most exotic of situations.  Rather like some of the ethics paradoxes they pose in a philosophy class - fun but not terribly useful. Negative resistance is far more useful as a source of nonlinearity to the EE.  That is the area of focus I would suggest  for those interested in real applications.

Barrie, for increasing the current mirror output resistance

the first option  is to use cascode (as you say) or double cascode,

second option is to use regulated cascode.

third option is to use a combination of cascode and regulated cascode.

in cmos design I will propose you a combination of low-voltage wide swing cascode, coscoded with a regulated cascode. 

Dobromir, would you illustrate your cascode ideas with some pictures to try to understand them (a picture is worth a thousand words)?

Cyril, attached figure is for you.

Barrie, you can see my proposal. There is no need of NIC.

It looks very sophisticated... and all this just to obtain Iout  = Iin? In the output part I see in total four MOSFETs in series... what would be the compliance voltage of this current sink?

Vin=2Vt+2Vdsat~2V

min output swing Vout=1Vt+3Vdsat~1.5V

if only a regulated cascode is used (instead of wide swing) Vout can be lowered to 2Vdsat~0.4V

It is not so bad... but  still worse than the simple current mirror... especially in low-voltage applications...