ESR

ESR is short for equivalent series resistance, which translates to "equivalent series resistance".

Theoretically, an ideal capacitor by itself will not produce any energy loss, but in reality, since the material of the capacitor has resistance and the insulating medium of the capacitor has losses, the capacitor becomes not "ideal" for various reasons. This loss is external and it behaves like a resistor in series with a capacitor, which is why it is called "equivalent series resistance".

If you think this is still too abstract, I'll give you an intuitive explanation.

Each capacitor will have an ESR, and there is always electrical resistance between the electrodes of a capacitor, such as the resistance of the metal pin, the resistance of the electrode plate, the connection resistance between them, etc.

Aluminum electrolytic capacitors also have resistance in wet electrolyte solutions and resistance in alumina (hydrated alumina) which contains a lot of "water".

The figure below shows the ESR forming factors of an electrolytic capacitor.

Usually, to facilitate the analysis of the ESR of a capacitor, it is expressed in a simplified way, as shown in the figure below:

Factors that lead to a change in ESR

Firstly, the resistance of the lead and the metal plate of the capacitor electrode is negligible because both are very small.

Two common causes of high ESR:

1) Poor electrical connection;

2) Drying of the electrolytic solution.

For 1) both new and old electrolytic capacitors may appear;

For 2) old electrolytic capacitors are mostly used.

Problems with poor electrical connections are mainly due to the fact that the pins connected to the inside of the capacitor are not made of aluminum, and aluminum is traditionally not solderable.

For the aluminum material of the electrode plate and the copper pin, the electrical connection mainly uses the so-called "welding" and mechanical crimping. But in both cases, the ESR will be higher.

As water evaporates from the electrolyte, ESR also increases.

What is the relationship between ESR and electrolytic capacitor leakage?

Leakage is the parallel resistance between the electrode plates of a capacitor. And ESR is just series resistance, so they are completely different, meaning ESR has nothing to do with leakage.

Conversely, when the ESR is large enough, the leakage current can also be reduced.

ESR influence

The appearance of ESR causes the behavior of the capacitor to deviate from the original definition.

For example, we assume that the voltage across a capacitor cannot suddenly change. When current is suddenly applied to the capacitor, the voltage across the capacitor will rise from 0 due to self-charging. But at ESR, the resistor itself produces a voltage drop, which causes a sudden change in voltage across the capacitor. Undoubtedly, this will reduce the filtering effect of the capacitor, which is why many quality power supplies use low ESR capacitors.

Similarly, in oscillatory circuits and other cases, ESR also causes changes in the circuit's operation, causing serious consequences such as failure or even damage to the circuit.

Therefore, in most cases, low ESR capacitors perform better than high ESR capacitors.

Relationship between ESR and frequency

The figure below shows a DC coupling capacitor used in the audio output circuit (the red circle in the figure is the capacitor).

The figure below shows the curve of output power vs. output frequency using two 100µF capacitors (ESRs are 0 and 6 ohms respectively).

There is not much difference between them at the low end (60Hz), but there is a big difference at the high end (1kHz). The main factor behind this difference is the relationship between ESR and capacitive reactance of the capacitor.

Take one more step.

Assuming that the corner frequency is ω and the capacitance of the capacitor is C, the impedance Z of the capacitor (Fig. 1) in the ideal state can be expressed by formula (1).

Drawing of an ideal capacitor

Z=1/jωC (1)

It can be seen from formula (1) that the value of the impedance |Z| shown in the figure below and decreases inversely with frequency. Since there is no loss in an ideal capacitor, the equivalent series resistance (ESR) is zero.

Draw the frequency response of an ideal capacitor

In practice, the frequency response |Z| represents a V-shaped (some capacitors may become U-shaped) curve as shown in the figure below, and the ESR also shows the frequency response corresponding to the amount of loss.

Image of actual capacitor

Fig. Frequency response |Z|/ESR of a real capacitor (example)

The reason why |Z| and ESR become crooked is as follows:

Low frequency range: |Z| in the low frequency range is the same as that of an ideal capacitor, and decreases inversely with frequency. The ESR value also shows characteristics corresponding to dielectric losses due to dielectric polarization delay.

Near the resonance point: when the frequency increases, |Z| will depend on the ESR generated by parasitic inductance or electrode resistivity, etc., and deviate from an ideal capacitor (red dotted line), shows the minimum value. Frequency when |Z| is the minimum value, is called natural frequency, and at this time |Z|=ESR. If it is greater than the natural frequency, then the characteristics of the component change from a capacitor to an inductance, and |Z|, in turn, increases. The range below the natural frequency is called the capacitive region and vice versa is called the inductive region.

In addition to dielectric losses, ESR is also affected by the loss of the electrode itself upon impact.

High frequency range: Characteristic |Z| in the high frequency range above the resonance point is determined by the parasitic inductance (L). |Z| in the high frequency range is approximated by formula (2) and tends to increase in proportion to the frequency.

ESR progressively shows the influence of electrode skin effect and proximity effect.

It is important that the higher the frequency, the less the influence of ESR or ESL spurious components can be ignored. With the increasing use of capacitors in the high frequency range, ESR and ESL, as well as the value of capacitance, have become important parameters that reflect the performance of capacitors.

Relationship between ESR and power

When a capacitor needs to carry a large current, problems arise even at low operating frequencies. For example, in some high-current switching power supplies.

For example, a 20,000uF capacitor running on a 60Hz, 5A power supply, assuming its ESR is 0.5Ω, according to Ohm's law P=I×I×R, the capacitor will consume 12 .5 watts of energy inside, the resulting heat will accelerate the drying of the electrolyte and cause the capacitor to fail.

And ESR will also reduce the filtering effect. For example, if there is a 0.5 ohm resistor in a 5V TTL supply circuit, a ripple voltage of up to 2V will be generated, which is equivalent to a ripple voltage of 40%.

If the capacitor works in a high frequency high current circuit, the situation will be more serious.

ESR also has "positive energy"

ESR is not useless, it can be used for good. For example, in a voltage regulation circuit, a capacitor with a certain ESR will immediately oscillate and trigger the feedback loop upon transient load changes. capacitor capacitance is strictly limited. This situation is seen in some 3-terminal regulators or similar circuits that use mos lamps as control lamps. At this time, too low an ESR will reduce the overall performance.

ESR is the equivalent "series" resistance. This means that when two capacitors are connected in series, this value increases, and when two capacitors are connected in parallel, it decreases.

Actually, there are more cases where lower ESR is required, and the price of high capacity low ESR capacitors is relatively high, so many switching power supplies use a parallel connection strategy using several aluminum electrolytes with relatively high ESR. in parallel to form a low ESR capacitor. It is economically beneficial to sacrifice a certain amount of PCB space in exchange for a lower device cost.

Another concept similar to ESR is ESL, equivalent series inductance. Early twisted capacitors often had high ESLs, and the larger the capacitor, the higher the ESL. ESL often becomes part of ESR and ESL also causes some circuit faults such as series resonance. But compared with capacitance, the proportion of ESL is too small, and the chance of problems is very small. Combined with the progress of capacitor manufacturing technology, ESL is gradually being ignored, and ESR is used as the main reference factor in addition to capacitance.

By the way, capacitors, like inductors, also have a quality factor Q. This coefficient is inversely proportional to ESR and is related to frequency, so it is rarely used.

Why doesn't the manufacturer want to label the ESR?

In the example of electrolytic capacitors, the electrolyte resistance makes up the bulk of the equivalent series resistance (ESR) of aluminum electrolytic capacitors. Most manufacturers of aluminum electrolytic capacitors do not provide ESR data for the main reason: Compared with capacitors with other dielectrics, the ESR of aluminum electrolytic capacitors is toooh great. For example, the ESR of a typical 1uF/16V aluminum electrolytic capacitor is typically around 20 ohms; The ESR of a 100uF aluminum electrolytic capacitor is also 1.5 to 2 ohms.

Just imagine, writing such data in the data sheet will definitely affect the user's confidence in the use of aluminum electrolytic capacitors. Therefore, to some extent, the use of aluminum electrolytic capacitors is a helpless choice. The use of aluminum electrolytic capacitors will affect.

For the general application of aluminum electrolytic capacitors, most aluminum electrolytic capacitor manufacturers do not provide ESR data, but for low ESR aluminum electrolytic capacitors for switching power supplies or relatively large pin aluminum electrolytic capacitors, this data is provided. .

Other

Circuit failures caused by ESR are often difficult to detect, and the effects of ESR are easily overlooked during the design process. An easy way is that if you can't choose specific capacitor parameters during simulation, you can try to artificially connect a small resistor in series with the capacitor to simulate the effect of ESR. Typically, the ESR of tantalum capacitors is usually below 100 milliohms, while aluminum electrolytic capacitors are higher than this value, and the ESR of some types of capacitors can be as high as several ohms.

The relationship between ESR value and ripple voltage can be expressed as V=R(ESR)×I. V in this formula represents the ripple voltage, R represents the ESR of the capacitor, and I represents the current. It can be seen that as the current increases, the voltage ripples increase exponentially, even when the ESR remains constant.