101SHS100CS1LE datasheet(6/34 Pages) EXXELIA

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CERAMIC CAPACITORS

122

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Taping : dimensions

Page revised 06/20

SERIAL AND PARALLEL RESONANCE FREQUEN-

CIES (SRF & PRF) OF CAPACITORS ON PCB

I. INTRODUCTION AND DEFINITIONS

The equivalent model for a capacitor is usually deﬁned by the ﬁgure 1 where:

C is the capacitance of the Capacitor

RS is the equivalent serial resistance (ESR)

L is the equivalent serial inductance (ESL)

Cp is the parasitic parallel capacitance

Rp is the Insulation Resistance

s21

s11

s22

s12

DUT

Device Under Test

Figure 1: Equivalent Model

Figure 2: S parameters

The complex impedance Z is deﬁned by:

Z=ESR + j X and z=Z/Z0 (1) where z is the reduced impedance, X the reactance,

Z0 the characteristic impedance (usually 50 ohm)

TheimpedancecanbedeterminedbytheSparameters(ﬁgure2)measurement

for example with a serial conﬁguration (Figure 3)

Port 1

Port 2

Z + 2

S11 =

(2)

Z + 2

S21 =

(3)

Figure 3: DUT Serial measurements

The variation of S11 (ﬁgure 4) and S21 (ﬁgure 5) show the different resonance

frequencies SRF (serial resonance frequency) and PRF (parallel resonance

frequency)

• The SRF is deﬁned when the capacitor is a pure very small resistance:

p√LC

SRF =

(4a)

Therefore as X=0 the impedance deﬁned in (1) is:

Z = ESR (5)

At this frequency the ESR is usually low.

For example for a 251SHF150 (size 0805 and capacitance 15pf):

SRF=2.64 GHz and the ESR at this frequency is 0.200 ohm (ﬁgure 5)

• The PRF is associated with the parasitic capacitance CP deﬁned in ﬁgure 1.

Assuming that Cp<<C, then:

p√LCP

PRF;

(4b)

At this frequency the impedance is a pure very high resistance.

For example for a 251SHF150:

PRF=3.66 GHz and the ESR at this frequency is very high (ﬁgure 6)

The PRF could be determined by the S21 measurements (ﬁgure 5)

The lumped model shown in Fig. 1 explains only the existence of one serial self-

resonant frequency and one parallel self-resonant frequency, consequently,

the lumped model is unable to explain why real measurements exhibits a

double inﬁnity of self-resonant frequencies (see ﬁgures 4, 5 & 6).

It is currently admitted [Ref. 1] that the lumped model shown in Fig. 1 is

convenient only for frequencies that are lower than roughly the half of the ﬁrst

SRF. For frequencies close or above the ﬁrst SRF, it is mandatory to consider the

distributed model or transmission line model [Ref. 1].

This distributed model can be established more easily with the equivalent

circuit of a Single Layer Capacitor (SLC) shown in Fig. 7:

I >> h

Figure 7: Transmission line model of a Single Layer Capacitor

After examination of Fig. 7, one can see that a Single Layer Capacitor can be

modeled by a transmission line with an open termination that is currently

called an “open stub “.

According to classical courses relatives to transmission lines theory, it is well

known that the variation with frequency of the input impedance of an open

stub is given by:

Ze = –jZc.cot g

( )=–jZc.cotg( ƒ) (5)

Validity domain

lumped model

+jX

–jX

Figure 8: Plot of the theoretical expression (5) of the impedance of a Single

Layer Capacitor modeled by an open stub

General Information

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