Inventing Circuits on the Whiteboard...

How do We Create Dynamic Resistance?

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Basic electrical circuit

Graphical representation

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In our life, we usually experience a steady resistance when we implement our purposes. Similarly, in electricity we usually deal with ordinary (ohmic) resistors having a steady resistance, which does not depend on the voltage across them and also on the current passing through them. For example, let's consider a simple circuit consisting of three components: a voltage source V, a constant resistor Ri and a varying resistor RL. You might think of this circuit just as two resistors Ri and RL connected in series. Or, you might discern here a voltage divider formed by the resistors Ri and RL. Finally, you might imagine that we have connected two components to each other: a real voltage source V with internal resistance Ri and a load with a resistance RL.

However, no matter what this arrangement is, the resistor Ri represents an ordinary ohmic resistance. We may convince of that speculation by investigating the resistance Ri. For this purpose, first connect a voltmeter across the resistor Ri and an ammeter in series with it; then, vary the load resistance RL. As a result, you will "see" an ordinary ohmic resistance Ri = (V-VA)/IA just as it is written on the resistor body.

Starting point: An ordinary "static" (ohmic) resistance

In order to present graphically the circuit operation, we have to superimpose the load IV curve RL and the IV curve VRi of the real voltage source (V + Ri) on the same coordinate system. In this arrangement, the intersection point A (the so called working point) represents the current (local) magnitudes of the voltage VA and the current IA.

When you vary the resistance of the load RL, its (your) IV curve rotates round the zero of the coordinate system. As a result, the working point A slides over the IV curve of the real voltage source.

Here, the slope of VRi IV curve represents graphically the resistance Ri. We may name it "static" resistance as it does not depend on the location of the working point A. Note that it is equal to the so called differential resistance - Ri = (V-VA)/IA = Rd = dVA/dIA.

Wikipedia: Ohmic device, Resistor,

Another fresh viewpoint at negative resistance,

What Is the Basic Idea behind a Negative Impedance Converter (NIC)?

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Only, there are many situations in our life where we experience a varying (dynamic) resistance when we implement our purposes. In these cases, someone (something) changes dynamically his/her/its resistance so that we have the feeling that the resistance is decreased or increased.

Well, let's apply this idea in electronics - I will change the resistance Ri while you vary RL. As a result, the static resistor Ri becomes dynamic one!

For concreteness, imagine that when you increase the load resistance RL I decrease the resistance Ri and v.v. As a result, you will have the illusion that the resistance Ri has increased. You will "see" a new, in this case increased dynamic resistance Rd > Ri. The output parts of transistors, tubes and other current-stable components act in such a way.

Similarly, when you increase the load resistance RL I might also increase the resistance Ri and v.v. In this case, you will "see" decreased dynamic resistance Rd < Ri. All kinds of diodes and other voltage-stable components act in this way.

An idea 1: Getting a dynamic resistance by varying the ohmic one

As above, when you increase the resistance of the load RL, its (your) IV curve rotates clockwise. But now, as I decrease the resistance Ri at the same time, its (my) IV curve rotates clockwise as well. As a result, the working point A slides from left to right over a new more horizontal IV curve, which represents the new dynamic resistance Rd > Ri.

And v.v., when you decrease the resistance of the load RL, its (your) IV curve rotates contraclockwise. Now, I increase the resistance Ri at the same time; so, its (my) IV curve rotates also contraclockwise. The working point A slides now from right to left over the same IV curve.

Note that you will see only the new dynamic IV curve; however, you will continue thinking that it is the IV curve of the resistor Ri. What an illusion!

Keeping a constant current by a varying internal resistance

What is the idea behind a simple bipolar transistor current source?

Wikipedia: Negative resistance

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Finally, there are such interesting situations in our life where we have again the feeling that the resistance is decreased or increased although, in fact, the resistance stays unchanged. In these cases, someone (something) injects or sucks dynamically (and inconspicuously for us) an additional power thus creating the illusion that the initial static resistance is changed.

Following this powerful idea, I might dynamize the "static" resistance Ri by changing the excitation voltage V while you vary RL. Well, let's try it.

For example, imagine that when you increase the load resistance RL, I increase the voltage V and v.v. As a result, you will have again the illusion that the resistance Ri has increased but actually it stays unchanged. You will "see" again a new, in this case an increased dynamic resistance Rd > Ri. Some constant-current generating electronic circuits act in such a way.

How do We Make Increased, Infinite and Negative Resistance?

Similarly, when you increase the load resistance RL, I might decrease the voltage V and v.v. In this case, you will have the illusion that the resistance Ri has decreased. You will "see" a new, in this case a decreased dynamic resistance Rd < Ri. Some constant-voltage generating electronic circuits act in a similar way.

How do We Make Decreased, Zero and Negative Resistance?

An idea 2: Getting a dynamic resistance by varying the voltage

Let's now see again the graphical presentation. Here, when you increase the resistance of the load RL, its (your) IV curve rotates clockwise. But now, as I increase the voltage V at the same time, its (my) IV curve moves from left to right. As a result, the working point A slides from left to right over a new more horizontal IV curve, which represents the new dynamic resistance Rd > Ri.

And v.v., when you decrease the resistance of the load RL, its (your) IV curve rotates contraclockwise. In this case, I decrease the voltage V at the same time; so, its (my) IV curve moves from right to left. The working point A slides now from right to the left over the same IV curve.

Note again that you will see only the new dynamic IV curve; but you will think that it is the IV curve of the old but smaller resistor Ri. What do you think, it's a nice illusion, isn't it? But yet, do you understand what a great idea it is? Well, let's finally generalize it.

You think that the current I depends only on the resistance Ri. But actually, it depends on both the resistance Ri and the voltage V. It is a function of two variables and someone (here I) changes inconspicuously the second variable. Obviously, this trick is more synthetic than the previous above.

Keeping a constant current by a following excitation voltage

Bootstrapped transistor current source with shifting diode