Two equivalent circuits of capacitors

nathanzhang

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Recently, when I was learning about decoupling, I saw two equivalent circuits of capacitors. Although both models are based on their structure, materials and production processes, there are still some differences between the two models. I will summarize them below for your reference.

The first one:

The source is a book called "ANALOG CIRCUITS WORLD CLASS DESIGNS", written by Robert A. Pease. In its Chapter 5 "Review of Passive Components and a Case Study in
PC Board Layout", there is a section dedicated to the device of capacitor. Based on the structure, material and production process of the capacitor, the author simplifies the equivalent model of the actual capacitor into the following figure:

Rs : is the parasitic resistance caused by the capacitor pin;

Rd : is the parasitic resistance caused by the dielectric;

C : is the total capacitance value;

So the input impedance of the capacitor in the actual circuit isZi（s）The impedance of C and Rd in parallel plus the series resistor Rs is:

(Cs=JbXj)

Slightly change the above formula and usejwTo replace S: (We will ignore the actual S transformation used here and directly use the simplest substitution idea to consider the calculation here)

Here the real part is called the equivalent series resistance ESR of the capacitor , that is,

From the ESR calculation formula, we can know that the equivalent series resistance of the capacitor includes the parasitic resistance generated by the capacitor pins, the parasitic resistance generated by the dielectric, and the capacitive reactance generated by the total capacitor; in addition, from the formula

wIt can be known that ESR is related to frequency: as the frequency increases, ESR decreases . (However, in reality, after ESR decreases to a certain extent with the frequency, when the frequency increases again, ESR will increase again).

The actual total capacitance is the imaginary part of the above formula, that is,

In this model, the effect of ESL on impedance is not actually considered.

Second type:

From ANALOG's technical paper "Decoupling Techniques". Based on the structure, material and production process of the capacitor, it equates the capacitor to the following circuit:

Among them:

R _P: insulation resistance (or leakage resistance);

Rs: ESR;

L:ESL;

RDA _: equivalent resistance caused by dielectric absorption phenomenon of electrolyte ;

C _DA: equivalent capacitance caused by dielectric absorption phenomenon of electrolyte ;

Although the DA effect of capacitors is generally not important in decoupling applications (but for example, for sample-and-hold amplifiers, the parasitic effects of the DA phenomenon may cause errors in circuit operation), the second type of capacitors provides a more detailed understanding of the impact of the capacitor's process, material, and structure on its use. Under different use conditions, we should pay attention to the specific parasitic parameters of capacitors, not just ESR and ESL.

The capacitor is one of the most commonly used components, and is usually not taken too seriously. However, in fact, only by having a deep understanding of the basic components can we be more adept at work.

Fred_1977

I deal with capacitors every day and understand their basic characteristics, but I have never understood them in such detail.

nathanzhang

Fred_1977 posted on 2022-2-20 17:28 I deal with capacitors every day and understand their basic characteristics, but I have never understood them in such detail.

Who says it isn’t true? Maybe it’s because we see it every day, so we mistakenly think we know a lot about it, but in fact, we only understand a tiny bit of it.