For another example of just how negligible the leakage of a capacitor is, I measured a 4700 uF electrolytic.

The measured leakage resistance was 300 kΩ (100 μA with 30 volts applied), and the measured series resistance at 50 Hz is about 45 mΩ.

Yet, when I measure the parallel AC resistance at 50 Hz, the measured value is 11.4 Ω.

The 45 mΩ series component transforms into about 98 Ω of parallel loss, which is negligible compared to the measured total parallel loss resistance of 11.4Ω. And, the parallel loss component due to the leakage resistance of 300 kΩ is completely negligible.

Clearly, there is something besides leakage resistance, or the transformed series resistance, causing a parallel component of loss. It's the AC losses at 50 Hz in the dielectric.

The conclusion is that if the capacitor is carrying ripple current, and is of good quality, the DC leakage resistance is a negligible component of the parallel loss resistance, so we don't care what the DC loss is when there is ripple current.

This is not to say that leakage resistance is not sometimes significant, but in ordinary power supply filtering use, which is where we usually care about ESR, the leakage resistance is not significant, and doesn't contribute materially to the measured parallel loss component.

The parallel loss component is a significant part of the measured ESR at low audio frequencies, and (in a quality capacitor) is primarily due to the (AC) dielectric loss.

 

What's an X+jR calculation? Do you mean R+jX?

Yes, sorry I was 500 miles away from base and in a hurry, of course it should be the latter.

Quote:
Originally Posted by studiot
I did not propose a current source, real or perfect. I proposed a voltage source.

What is your point for saying this?

Because it is true.

In fact a voltage source is better because you can have a voltage without a current and you can impress this upon a capacitor.

But you are still missing the point.

If you take a voltage source and charge any real capacitor up and then remove the voltage source you will find that in time the charge will leak away.

It is impossible to account for this by modelling your real capacitor as an ideal resistor in series with an ideal capacitor. If this were a true and accurate representation the charge would not leak away.

At this point, there is no frequency dependency to consider of either the ideal capacitor or the ideal resistor. Simple application of Ohm's law of resistance will suffice and force you to the conclusion that there must be an ideal resistance path in parallel with the capacitor, whatever the ideal series resistance or even whether it exists at all. In fact the ideal series resistance plays no part in the explanation and could be omitted from the model.

So why do we require a series resistance, you may well ask.


Well if you then apply an alternating voltage to the real world capacitor you will find that both the resistive and reactive components are functions of frequency themselves. So you are forced to supply two resistive elements to your model, one that is independent of frequency (the leakage) and one that is frequency dependent. You cannot avoid this.

I would agree that the objective of manufacture is to maximise the former and minimise the latter.

 

To go right back to the start of the thread, the question: Why is ESR frequency dependant.

In practice, electrolytic caps (and many wound film types) can be inherently inductive (far beyond the inherent inductive property of the leads etc).

It's largely down to the physical assembly of the component.
In some, the component leads are attached across one end of the strips of foil that form the capacitor plates & the rest of the foil (with insulator layers, if separate) are then wrapped around - imagine using the leads on the ends of an axial cap as the spindle to wind the foil/dieletric.

Another design offsets the two foil strips slightly before winding them into a cylinder form. After winding, the whole of each end of the cylinder has one or the other foil strip edge exposed over it's entire area, this can be tinned or metallised and the capacitor lead attached.

The first design is simpler to produce, but as the connections are literally at the end of a coil, the component has a high effective inductance and the ESR at high frequencies will be very poor. (Not counting the resistance of the foil over it's length).

The second type, with the entire length of the plate connected directly to the terminal, will have low inductance and low ESR.

These are just two examples, there are no doubt other styles of construction with different characteristics.

Note, I'm trying to give a broad idea of the physical build of some caps, not the actual materials or chemistries.

Take some different types of scrap ones apart yourself, but be very careful of the electrolyte, it may be caustic and it often smells extremely unpleasant!

 

Yes self inductance does play a part in the impedance, but since this is a physical characteristic of the 'metalwork' within a capacitor it is fixed and does not alter or age with time.

Further, pure inductance alters the reactive component of impedance not the resistive.

One reason service techs monitor ESR is because it increases with age and can reach an unacceptable level.

 

To go right back to the start of the thread, the question: Why is ESR frequency dependant.

In practice, electrolytic caps (and many wound film types) can be inherently inductive (far beyond the inherent inductive property of the leads etc).

It's largely down to the physical assembly of the component.
In some, the component leads are attached across one end of the strips of foil that form the capacitor plates & the rest of the foil (with insulator layers, if separate) are then wrapped around - imagine using the leads on the ends of an axial cap as the spindle to wind the foil/dieletric.

Another design offsets the two foil strips slightly before winding them into a cylinder form. After winding, the whole of each end of the cylinder has one or the other foil strip edge exposed over it's entire area, this can be tinned or metallised and the capacitor lead attached.

The first design is simpler to produce, but as the connections are literally at the end of a coil, the component has a high effective inductance and the ESR at high frequencies will be very poor. (Not counting the resistance of the foil over it's length).

The second type, with the entire length of the plate connected directly to the terminal, will have low inductance and low ESR.

These are just two examples, there are no doubt other styles of construction with different characteristics.

Note, I'm trying to give a broad idea of the physical build of some caps, not the actual materials or chemistries.

Take some different types of scrap ones apart yourself, but be very careful of the electrolyte, it may be caustic and it often smells extremely unpleasant!

Is there a scale to which you can compare the ESR of given capacitors of the same construction type?
I have had people ask me for lower esr caps both polar and non polar electrolytic while building amps and speaker crossover circuits. I know there is a huge ESR difference from say tantalum to ceramic to electrolytic. But how to compare within the same type? How come the industry doesn't rate them except for "low esr" and just normal? That's sort of vague. How low is low? Do we know?
Given that you replaced one cap with another of the same type and several in the same spot in the circuit.

 

Your confusing DC Resistance with the AC equivalent of Resistance unique to capacitors as the conductors in a capacitor start life as wires, become geometrically much wider for a very short period, then become a completely different element, which is unique Capacitors and their Equivalent Series Resistance. DC Current is always blocked by Capacitors so if you were to think of ESR exactly like resistance it actually has two values, Zero and Infinity, while at the same time, one resistance per plate.

A dialectics' resistance is the reciprocal of dielectric constant. The dielectric constant is how well a dielectric works at allowing a changing current pass through it's polarized structure. If it is a non-polar dielectric then it has neither ESR or Resistance because it has no effect whatsoever. Pure water is frequently a dielectric. Imagine a plat fully charged with electrons, the water molecules adjacent to the plate have a really strong force pulling them into a specific orientation. This makes the second row of water molecules feel a polar force as well although not as strong. So the Resistance of the dielectric is its intrinsic opposition of magnetic fields' inducing the movement of the dielectric into a an orderly structure of polar rows. This could be due to the magnetic field induced by the electrons on the plates, it could be that its polarity is reduced at higher temperatures as entropy increases.

To know electricity you have to be able to explain it without a calculator. So try going through the Encyclopedia of electronic components and for each component write out how you would explain it to your grandma!

 

My understanding of ESR says that
(1) Focault effect means that as higher frequency as smaller part of wires and electrodes may do their work, therefore it `looks` like resistance had been increased.
And (2) the dielectric Megaohms are connected paralelly, whilst ESR is connected in series with capacitance. Therefore recalculating the parallel representation to the serial You get from Meagohms those miloOhms what was the goal.