# Computing stuff tied to the physical world

## TK – Equivalent Series Resistance

In Hardware on May 3, 2012 at 00:01

Welcome to the Thursday Toolkit series, about tools for building Physical Computing projects.

Equivalent Series Resistance, or ESR, is the resistance of a capacitor. Huh? Let me explain…

A perfect capacitor has a specific capacitance, no resistance, and no inductance. Think of a capacitor as a set of parallel plates, close to each other, but isolated. When you apply a voltage, electrons flow in on one side and electrons flow out on the other side until the voltage (potential difference) across the plates “pushes back” enough to prevent more electrons from flowing. Then the flow stops.

It’s a bit of a twisted analogy, but that’s basically what happens. A capacitor acts like a teeny weeny battery.

But no real capacitor is perfect, of course. One of the properties of a capacitor is that it has an inner resistance, which can be modeled as a resistor in series with a perfect capacitor. Hence the term “ESR”.

Resistance messes up things. For any current that flows, it eats up some of that energy, creating a voltage potential and more importantly: generating waste heat inside the capacitor.

ESR is something you don’t want in hefty power supplies, where big electrolytic capacitors are used to smooth out the ripple voltage coming from rectified AC, as provided by a transformer for example. With large power supplies, these currents going in and out of the capacitor lead to self-heating. This warms up the electrolyte in the caps, which in turn can dramatically reduce their lifetimes. Caps tend to age over time, and will occasionally break down. So to fix old electronic devices: check the big caps first!

Measuring ESR isn’t trivial. You have to charge and discharge the cap, and watch the effects of the inner resistance. And you have to cover a fairly large capacitance range.

This ESR70 instrument from Peak Instruments does just that, and also measures the capacitance value:

It’s protected against large voltages, in case the capacitor under test happens to still have a charge in it (a cap is a tiny battery, remember?). The clips are gold-plated to lower the contact resistance – and removable, nice touch!

In this example, I used a 47 µF 25V electrolytic capacitor, and it ended up being slightly less than 47 µF and having an ESR of 0.6 Ω as you can see.

It this cap were used in a 1A power supply to filter the ripple from a transformer, then its ESR could generate up to 0.6 W of heat – which would most likely destroy this little capacitor in no time.

Fortunately, big caps have a much lower ESR. It measured 0 (i.e. < 0.01 Ω) with a 6800 µF unit, for example.

As with last week’s unit, this is not an indispensable instrument. But very convenient for what it does.

1. One small addition: ESR is also very useful to detect bad caps. High ESR might indicate those bad caps.

2. Certainly a useful device. My multimeter can test transistors and give the hfe, and also read small capacitor values, but it doesn’t do ESR, something which is rather useful when working with regulators and confronted with a box of random caps!

How would you go about calculating the ESR? Is this something that can be solved with a bit of DIY?

3. For an ideal capacitor, I = C * dV/dt, or C = I/(dV/dt). So a cap-meter can source or sink a given current I, measure the rate of change of voltage (dV/dt) and calculate C. It should be the same C for any given I. But for a capacitor with non-zero ESR, you will find a different C depending on the I you choose, due to the changing voltage drop across the internal effective resistance.

4. Since the ESR symbol on the capacitor equivalent circuit looks so neat, it lulls us into thinking it is somehow a real component. It is an approximation to the capacitor behaviour under A.C. conditions – it disappears at D.C.

That at least gives a clue to one method for estimation – drive the capacitor at ~ frequency of interest (e.g. double the mains frequency for a power supply filter capacitor) and observe the phase angle between V and I.

The reactance of the capacitor is known from Z=1/{2.pi.f.C} (worth an independent check since larger capacitors have quite broad and offset tolerance bands).

The equation to solve is written up here.

• Thanks Martyn, I knew I shouldn’t visit that page before my first coffee… Now my head hurts.

Can I go back to simple 1’s and 0’s where everything is simple? ;-)