Traditional lumped parameter circuit theory faces challenges in impedance analysis of chip inductors 2

admittance function  diode

Y(j )=({1}over{R_{O}}+{r}over{r^{2}+ ^{2}L^{2}_{O}})+j( C_{O}-{ L_{O}}over{r^{2}+ ^{2}L^{2}_{o}})

Then the impedance function

Z(j )={1}over{Y(j )}=R( )+j ( )

The impedance can be approximately derived  diode

Z( )=sqrt{R^{2}( )+ ^{2}( )}

={ L_{O}}oversqrt{({ L_{O}}over{R_{O}}+{r}over{ L_{O}})^{2}+(1-{ ^{2}}over{SRF^{2}})^{2}}  diode

inductance

L( )={ ( )}over{ }={L_{O}(1-{ ^{2}}over{SRF^{2}})}over{({{ L_{O}}over{R_{O}}+{r}over{ L_{O}})^{2}+(1-{ ^{2}}over{SRF^{2}})^{2}}

Quality factors

Q( )={ ( )}over{R( )}={(1-{ ^{2}}over{SRF^{2}})}over{({ L_{O}}over{R_{O}}+{r}over{ L_{o}})}

among which

SRF={1}over{2 sqrt{L_{O}C_{O}}}

=2 F

The following conclusions can be drawn from these function expressions:  diode

(1) When the operating frequency is below the self-resonant frequency (SRF), the impedance characteristics of chip inductors closely resemble those of an ideal inductor, exhibiting excellent linearity and a relatively high quality factor (Q). Therefore, this is typically used to determine the rated operating frequency range of the inductor;