In honor of my site re-design, I want to write a follow-up to the very first post I made: a physical interpretation of “voltage lags current” and highlight a very important and deceptively simple concept that trips up new engineers, driving different types of loads. What does it mean for the driver, what does it tell us about the load?
Drop A Load On ‘Em
Loads are often talked about in circuit books as an afterthought. For example, in a chapter describing op-amp circuits, or designing regulators, the load is hand-waved with some assumptions. They talk about designing a circuit, and then say “well let’s say the load were X, it would have Y effect”. It’s a little backwards from how the circuit is designed in industry, because the load is the whole reason the circuit exists. Driving the load is the purpose, and your specs and circuit topology and design and analysis all follow from that.
Circuits in and of themselves are just thought-experiments, abstract math puzzles, it’s the application that gives it any purpose. You may have a motor to turn, and an electrical circuit is the best way to make that motor turn. You may have an object to heat, depending on the circumstance it might be best to use electronics. You may have a battery to charge, it’s usually pretty convenient to use circuits. I say “may” and “might” because even in these scenarios which seem so obviously electrical, you can and we usually still do use steam. In my last apartment, the heat was with radiators, a centuries old thermal technology, while in my current apartment I have baseboards which are driven electrically.
That means in practice, the load is the starting point, 50/50 chance we decide to control or supply it electrically, and if we do then we design a circuit for it. Change the load and the whole circuit changes, from the voltage and current down to the thermal budget and the price. The properties of the load dictate and constrain most of the specs before a single component has been chosen. This is quite backwards from how circuits are designed in class, with a hypothetical perfect load that only exists as an end to our means.
Loads can be physical objects that can be modeled as a passive electrical component, such as a solenoid valve that behaves like an inductor, or can be the parasitic part of another electrical component, such as the base resistor of a BJT, or can literally be an electrical component like the sampling capacitor of an ADC.
In either case, the vast majority of loads “appear” to the driving circuit like a resistor, inductor, or capacitor. Let’s dive into what that means and how they differ.
Resistors: The Late Night Diner
Resistive loads are the simplest to understand as they just act in accordance with Ohm’s law, V=IR. The voltage across it and the current through it are proportional at every instant and in phase with each other. Heaters, toaster elements, incandescent bulbs, brakes on a VFD, and PTC temperature sensors are just a few examples of loads which you can drive with a voltage and they’ll draw a proportional current. A resistive load is like a late night diner off the interstate, where cars pull into at a steady rate day and night, just a constant stream of long-distance commuters who want eggs and coffee and then leave.
Driving one is straightforward and your options are flexible, since it doesn’t care whether you use voltage or current and you’re not really thinking of transient effects. The downside though is that you have this constant power draw which generates heat at every step, degrading your driver and the load (the staff at the diner get exhausted after a long shift). The total power sets how much heat you have to get rid of, but the voltage and current split determines what the driver actually looks like, so designing something that drives a small current at high voltage will look quite different than a high current at low voltage.
And even if resistors are simple, resistive loads can be tricky in their own ways. Their resistance may change, sometimes rapidly, so you may have to design for varying power draw. The power rating is specified at some ambient temperature with a derating curve, so a resistor rated 5 W at 25 °C is not a 5 W resistor at 100 °C inside an enclosure. Even a literal resistor isn’t purely resistive either, since wirewound power resistors are secretly inductors above a certain frequency, everything has a little parasitic capacitance (I went into that here); at 10 MHz your 10Ω resistor is not 10Ω anymore.
NB: Terminology
Quick note on terminology here, in electronics language, a smaller resistor is a bigger load, because it pulls more current. Sources supply voltage, and loads pull current, so larger current pulled by the load means it’s a bigger load. As a result, a 5Ω resistor is a large load while a 50kΩ resistor is a small load, because the 5Ω pulls more current thus has a bigger effect on the source/driver.
If you take a random circuit and put an infinitely large resistor on the output, that’s the same as an open circuit. It’s like having no load at all. It has no effect on the circuit, and in fact it already probably has multiple small parasitic loads all over, like leakages through a substrate or cable dielectrics. As you’ll see coming up, the opposite is true for capacitors. Big capacitors are big loads.
Capacitors: The Food Truck
Because a capacitor is fundamentally defined by its electric field, which cannot change instantaneously without violating basic physics, a capacitor resists changes in voltage. Voltage changes lag current changes by 90°, I = C·dV/dt, and the energy it holds is ½CV². A discharged capacitor sits at 0 V, so the instant you connect it it pulls as much current as possible, limited by nothing but the rest of the resistance in the loop. As the capacitor charges up, the current the falls off and depending on the circumstance it can become an open circuit. Piezo actuators, buzzers, ultrasound transducers, long shielded cables, touch panels, supercaps, and the gate of a power MOSFET are all examples of capacitive loads.
It’s kind of like a food truck. You open the window and the entire lunch rush is already standing there, a big crowd of people, all of them hungry and all of them wanting to order at once. There’s no ramp-up, you serve everybody on their lunch break at once, with the only limit being how fast the kitchen can move, and then after the rush you close up and move on. Short-circuit, charge, open-circuit. That is the quintessential problem a capacitive load presents to its driver.
Driving one is often a problem of peak in-rush current. Applying 12V to a 1000 µF cap with 10 mΩ of series resistance comes out to 1200 A, and even if it’s brief it’s still how you weld contacts and trip breakers, so you either limit dV/dt or you limit current with a precharge resistor, an NTC, a hot swap controller or a soft start. If this is a capacitive load you are switching on and off, your driver also has to be able to drain that charge back out in approximately the same time.
Charging a cap from a fixed voltage through any resistance wastes exactly ½CV² as heat no matter what the resistance is, so half the energy is gone every time and lower resistance only wastes it faster and hotter. Class II ceramics also lose most of their capacitance under DC bias, 50 to 80% at rated voltage being normal, so your 10 µF is a 3 µF and the nominal value only applies at 0 V.
Another issue with driven capacitive loads is stability, which affects linear circuits in steady-state. Op-amps, for example, are explicitly specified by their load capacitance. The load capacitance is usually the largest capacitance in the entire loop, and so it is the limiting factor in both linear and non-linear dynamics such as small-signal bandwidth and large-signal slew rate.
Circling back to the terminology, a larger capacitor means that the super high in-rush current lasts longer and takes longer to charge up and stop being a problem, so “large capacitive load” does mean a literally large capacitor.
Inductors: The Party Divas
Because an inductor is fundamentally defined by its magnetic field, which cannot change instantaneously without violating basic physics, an inductor pushes back against change in current. Changes in current lag changes in voltage by 90°, V = L·di/dt, and the energy stored is ½LI². It takes some force to get them going, but once they’re The problem is that it will do whatever it takes to keep its current flowing, and whatever it takes sometimes includes destroying your transistor. Examples of inductive loads are relays, motors, solenoids, valves, transformers, speakers.
An inductor is like the worst guests at a dinner party. Imagine you throw a dinner party, but most of them show up “fashionably late”. They hang around, and when it gets late you tell them the party’s over and they have to leave. But instead of actually eating dinner, turns out they’ve just been getting drunk all night (on an empty stomach!). They turn into total divas, and have the nerve to take everything home for leftovers. All the leftovers are gone, but some of them still don’t have any food, so they go through your pantry and steal your snacks and raid your fridge! Son of a bitch!
Inductive loads are those which make a slow and difficult entrance, but they especially make a dramatic exit. This can cause a variety of headaches. Open a switch in series with an inductor and di/dt goes to negative infinity, so the voltage spikes to whatever it takes to keep current moving, either by arcing across your switch or punching through the MOSFET. A relay coil sitting at 12 V and 100 mA will cheerfully make several hundred volts on the way out. You have to give that current somewhere to go, maybe a freewheeling diode, or an active clamp.
Which clamp you pick matters too, since a plain diode is cheap and clamps at one diode drop but lets current decay slowly at L/R, so the relay releases lazily, which is fine for a solenoid and bad for a fuel injector, while a zener or TVS clamps higher so the current collapses faster at the cost of your switch seeing supply plus clamp voltage. Every motor driver has those diodes for this reason, and under PWM the freewheel path has to be there every cycle, not just at shutdown.
There’s also the atrocious problem of oscillations and resonance that happens. Resonance occurs when you have an LC tank of some kind, where the energy goes back and forth between the magnetic field of the inductor and electric field of the capacitor. With capacitive loads, you’re *usually* fine. Reason being that while parasitic inductance exists, in the vast majority of situations it’s negligibly small and can be ignored. Parasitic capacitance on the other hand is usually significant enough even when you’ve designed around it, so once you introduce a sizeable inductor, you now have a real LC resonator.
Share The Load
I’ve presented the three types of loads as if they exist in isolation, but reality is more complicated. Motors and transformers can be made of literally kilometers of wire, so that even if they have low resistance the total series resistance is quite high. The gate of a MOSFET is capacitive, but in the right configuration and depending on the frequency it can actually look like an inductor. You might be designing a voltage regulator for a digital circuit which is somewhat like a resistor but switches a lot and creates all these spikes that can’t be accurately modeled as any purely passive load. Speakers are largely inductive but have some other funky dynamics that make their impedance look like this graph, which you can then shape into being mostly resistive by adding a Zobel network.
The three types of loads are just a vocabulary for working out which effect dominates at the timescale you care about so you can model that one and ignore the rest. It’s one of many trade-offs made during the design process. Look at the physical object at the end of your signal-chain, decide which of the three it mostly is, and design the driver around that.
| Resistive | Capacitive | Inductive | |
| Resists | Voltage/Current | Change in voltage | Change in current |
| V-I phase | V and I in phase | V lags I | I lags V |
| Energy converted to | Heat, lost forever | Electric field, stored | Magnetic field, stored |
| When it presents itself | Continuously | At turn-on | At turn-off |