Document 363-1

Measuring Self Resonant Frequency
Introduction
When comparing published electrical values, engineers
require a common basis for comparison. Ideally, a 100 nH
inductor with a self resonant frequency (SRF) of 1 GHz
from one manufacturer is equivalent to inductors with thesame published values from every other manufacturer.
Realistically, however, the test instrument and fixture affect the SRF measurement. Since all manufacturers do
not use the same instruments and fixtures, not all published SRF specifications are equivalent, which makes
inductor comparisons difficult. The following discussion isintended to provide insight into practical SRF determinations and comparisons.

Self Resonance of Inductors
Ideal inductors would have zero resistance and zero capacitance. But, real inductors have “parasitic” resistanceand capacitance. The first self resonant frequency of aninductor is the lowest frequency at which an inductor resonates with its self-capacitance. The first resonance can bemodeled by a parallel combination of inductance and capacitance, shown in Figure 1. Resistor “R1” limits impedance near the resonant frequency.
CR1A measurement of any of these conditions can be used todetermine the SRF of an inductor.

How Capacitance Affects SRF
Historically, inductor capacitance is called “inter-windingcapacitance” based on the assumption that it is the resultof charge separation between insulated coil windings.
However, if the inductor is measured over a conducting
ground plane, capacitance between the coil and the groundplane is also part of the measurement. The distance of thecoil from the measurement ground plane and the effective
dielectric constant of the measurement substrate affects
the capacitance to ground. This partially explains how thetest fixture affects the SRF measurement. The followingequation shows how the SRF is related to inductance andcapacitance in an LC circuit.

SRF =1in Hz2앟 (LC)

where :
L is the inductance in Henries
C is the capacitance in Farads
From this equation, it is clear that increasing inductance orcapacitance lowers the measured SRF. Reducing inductance or capacitance raises the SRF.

Fixture Effects on SRF Measurements
R2RVAR

LFigure 1. Inductor ModelAt the SRF of an inductor, all of the following conditions aremet:• The input impedance is at its peak.
• The phase angle of the input impedance is zero, cross••••ing from positive (inductive) to negative (capacitive).
Since the phase angle is zero, the Q is zero.
The effective inductance is zero, since the negative capacitive reactance (Xc = 1 / jωC) just cancels the positive inductive reactance (XL = jωL).
The 2-port insertion loss (e.g. S21 dB) is a maximum,
which corresponds to the minimum in the plot of frequency vs. S21 dB.
The 2-port phase (e.g. S21) angle is zero, crossing fromnegative at lower frequencies to positive at higher frequencies.

A fixture is required to connect an inductor to the terminals
of a test instrument. After calibration and fixture compensation are performed, it is assumed that all fixture effects havebeen de-embedded (removed) from the measurement.
Fixture compensation uses open and short standards, but
it cannot predict the interaction of a specific inductor withthe test fixture. Therefore, some residual capacitance between the measured inductor and the fixture may exist
after calibration and fixture compensation. The result isthat SRF measurements of the same inductor can changewith each different combination of instrument and fixture.
Coilcraft states the specific instrument and fixture used tomeasure the SRF of its inductors.
To illustrate the effect of residual fixture capacitance on
SRF, Figure 2 plots the effective series inductance of a
100 nH chip inductor using AWR Microwave Office / Visual
System Simulator 2002. The modified SPICE model simulation shows the effect of an additional 0.01 pF of capacitance to ground at the input terminal. The term “effectiveinductance” is used, because the low-frequency inductance is the same (100 nH) for both models, but the induc-Specifications subject to change without notice.

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Document 363-2

Effective inductance
3000

Inductance (nH)2000

150 MHz100 nH

1694 MHz
0 nH

1000

0
L_SRL (nH)original SPICE model–1000

150 MHz100 nH–2000

1606 MHz
0 nH

L_SRL (nH)
Modified SPICE model

–3000
0500

1000

1500

2000

Frequency (MHz)Figure 2. Effective Inductance With Residual Capacitance Effects
tance near the SRF is affected by capacitance between
the inductor and the fixture.
The effect of residual fixture capacitance is more pronounced
on lower value inductors. The effect of residual fixture capacitance on larger power inductors is often negligible.
Several important conclusions can be made from Figure 2:• A slight difference in fixture design and calibration can•••have a large effect on the measured SRF.
In the region of the measured SRF, a small difference in
fixture design and calibration can mean the difference
between reading a large positive inductance or a large
negative capacitance.
If the parasitic capacitance (and inductance) of the circuit board to which an inductor is attached is different
from the test fixture, the SRF measurement of the boardmounted inductor will be different.
Since SRF measurements are fixture/substrate-dependent, a “typical” SRF cannot be defined when the fixture
effect is significant.

How Small Differences in Capacitance Affect Q
Figure 3 illustrates the effect of residual fixture capacitance on Q values. The values represent the Q for theoriginal inductor model plotted in Figure 2 compared to theQ of the same inductor with an additional 0.01 pF of capacitance to ground at the input terminal. At lower frequencies, the residual fixture capacitance has little effect on theQ value. At higher frequencies, the effect on Q becomessignificant. In this example, the small residual capacitanceto ground causes the peak Q value to shift by 132 MHz
and to decrease in magnitude by 23% of the original value.

How Coilcraft Measures Inductor SRF
When compiling data for publication, Coilcraft normallyuses the same instrument and fixture to measure the SRFof all our chip inductors and power inductors: an Agilent/
HP Vector Network Analyzer and a Coilcraft SMD-D (2port) test fixture. The SRF is determined to be the frequency at which the insertion (S21) phase changes fromnegative through zero to positive.
Because SRF measurements are so sensitive to fixture
effects, we specify the SRF for our low inductance RF chip
inductors as a “minimum” value, approximately 15% to
20% below the actual average measurement of a representative sample. Since fixture effects become negligiblefor higher inductance values, SRF for our power inductors
is specified as “typical.”Comparing Coilcraft Inductor SRF to OtherInductors
When comparing the SRF of Coilcraft chip inductors toother inductors, the same instrument, fixture, calibration,and fixture compensation standards should be used. If
not, any differences in SRF specifications may be masked
by instrument and fixture effects, possibly causing incorrect conclusions.

Specifications subject to change without notice.

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Document 363-3

Q of inductor
9080654 MHz75150 MHz3970

Q Factor

605040522 MHz58301694 MHz0150 MHz
3820|Eqn| Q original

1606 MHz010|Eqn| Q modified

00500

1000

1500

2000

Frequency (MHz)Figure 3. Effect of Capacitance on Measured Q

Simulating Substrate-Dependent SRF
Remeasuring the SRF of inductors for each new application circuit board is clearly not convenient or timely for circuit designers. There is an easier way to determine the SRFof an inductor in a specific application: circuit simulation.
To the best extent possible, fixture effects are removed
from our measurements before we create our SPICE models and S-parameters. As a result, the SRF of the deembedded measurement is higher than the measuredvalue.
And yet, the de-embedded SRF is not the true SRF. Thetrue SRF of any inductor always depends on the specificcharacteristics of the circuit board to which it is mounted.
In other words, the SRF is substrate-dependent.
By simulating the Coilcraft model over a specific circuitboard substrate, you can determine the SRF of an inductor for your application. The circuit board substrate dielec-tric constant and thickness, and the size and layout of theconductor traces in the vicinity of the inductor determine
the SRF of the inductor.
Eagleware’s RF and microwave design software offers highaccuracy libraries of many of our chip inductor series.
The models are substrate-scalable, based on measurements of our inductors over various thicknesses of FR4and alumina.
By applying the circuit board characteristics and tolerances
to the simulation, circuit designers can see the effects they
have on the SRF and all other electrical characteristics,
such as inductance, Q, input impedance, phase, insertion
loss and return loss. This knowledge gives the designer apractical basis to apply when comparing inductors, andultimately can answer the question of whether an inductor
is appropriate for the application.

Specifications subject to change without notice.

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Revised 09/16/03