Negative resistance - lcamtuf’s thing
lcamtuf’s thing
SubscribeSign in
Negative resistance<br>Jul 23, 2026
Share
Hello! The blog you’re trying to reach is currently unavailable. I am Skippy, your friendly blog assistant. How can I help you today?<br>> quit<br>I’m sorry. This function is currently available only to Skippy Premium and Premium+ subscribers. Would you like to talk about ✨ negative resistance instead?<br>> nope<br>I’m sorry. This function is currently available only to Skippy Premium and Premium+ subscribers.<br>Welcome. Welcome again. If you tinker with analog electronics, you might have heard that some circuits can exhibit negative resistance. This is usually followed by a current-to-voltage plot featuring some sort of a kinked curve and an assertion that this property might help the circuit designer in some way.<br>But what does it mean, exactly? The concept of negative resistance is interesting, counterintuitive, and explained on Wikipedia in a rather rambling way. If you’re up for it, I think we can do better than that.<br>The article assumes familiarity with voltage, current, and the behavior of operational amplifiers. If you need a refresher, start with this primer, then read up about transistors here and signal amplification here.<br>Defining resistance
As a quick recap, resistance (R) can be understood as the opposition to the flow of steady current through some portion of the circuit. The quantity describes the relationship between the applied electromotive force — that’s voltage — and the amount of charge moving per second (that’s current).<br>In contrast to some other phenomena in electronic circuits, resistance is not inherently dependent on time or signal frequency. If you know the voltage (V) applied to a purely-resistive component, the current (I) flowing at that exact moment is simply:<br>\(I = \frac{V}{R}\)
In resistors, the parameter remains constant across a wide range of operating conditions. This means that if we plot I in relation to V, we get a straight line that crosses through the center of the coordinate system. The slope of the line depends only on the component’s resistance:
Resistor I = V/R plots for R = 0.2, 1, and 5 Ω.<br>For example, in a 5 Ω resistor (blue line), the current is 200 mA if the voltage across the terminals is 1 V, rising to 1 A if the electromotive force increases to 5 V.<br>Some other components, such as diodes and transistors, oppose the flow of current in a manner that depends on the applied voltage. We can still model their behavior using the concept of resistance, but we don’t get a constant reading. In an earlier article, I provided a V-I curve for a small diode; if we take these measurements and calculate the effective R by rearranging the earlier equation (I = V / R ⇒ R = V / I), we obtain the log-scale V-to-R plot shown on the right:
Apparent resistance of a small diode (1N4148), log vertical scale.<br>For a chosen point of the V-I curve, we can also calculate so-called differential resistance; this parameter doesn’t tell us anything about the overall relationship between voltage and current; instead, it models the relative response to small deviations from the chosen baseline. For example, in the vicinity of 1.2 V on the plot above, the slope of the V-I curve is such that a change of Δv = +/- 10 mV causes the current to change by Δi = +/- 20 mA. If we divide Δv by Δi and squint our eyes hard enough, we can say that the “local” resistance is 500 mΩ. Again, that number has nothing to do with the bulk resistance of the diode at 1.2 V, but it’s a useful abstraction for modeling what happens to small signals that are piggybacking on top of a constant bias voltage.<br>In physical terms, resistance is associated with the consumption of energy. We’re making an effort to push charges through; some of the energy is absorbed by the medium and then taken out of the picture — turned into heat, light, motion, or captured in chemical bonds.<br>To model these dynamics, we need to tap into the official definition of voltage. It’s the amount of energy (E, in joules) we’re willing to expend to move the unit of electrical charge (Q, in coulombs, equal to about 6.2 quintillion electrons):<br>\(V = \frac{E}{Q}\)
We also need the definition of current; as noted earlier, it’s the amount of charge that’s moved per second through a point in the circuit:<br>\(I = \frac{Q}{t}\)
We can rearrange the second equation to solve for Q (Q = I · t), and then shuffle the first one to solve for E (E = V · Q). Combining these forms, we get E = V · I · t.<br>Finally, we tap into the physical definition of power (P, watts); it’s the rate at which energy is expended:<br>\(P = \frac{E}{t}\)
If we plug the earlier E = V · I · t formula into the fundamental power equation, we obtain:<br>\(P = \frac{V \cdot I \cdot \cancel{t} }{\cancel{t}} = V \cdot I\)
That’s to say, the amount of electrical power consumed by an electronic circuit depends on the supplied voltage, the resulting current, and nothing else. For resistive circuits, we...