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Figure 1. Inductor Model

At the SRF of an inductor, all of the following conditions are met:

- The input impedance is at its peak.
- The phase angle of the input impedance is zero, crossing 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 from negative at lower frequencies to positive at higher frequencies.

L is the inductance in Henries

C is the capacitance in Farads

From this equation, it is clear that increasing inductance or capacitance lowers the measured SRF. Reducing inductance or capacitance raises the SRF.

Fixture compensation uses open and short standards, but it cannot predict the interaction of a specific inductor with the test fixture. Therefore, some residual capacitance between the measured inductor and the fixture may exist after calibration and fixture compensation. The result is that SRF measurements of the same inductor can change with each different combination of instrument and fixture. Coilcraft states the specific instrument and fixture used to measure 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 “effective inductance” is used, because the low-frequency inductance is the same (100 nH) for both models, but the inductance near the SRF is affected by capacitance between the inductor and the fixture.

Figure 2. Effective Inductance With Residual Capacitance Effects

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.

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 negligible for higher inductance values, SRF for our power inductors is specified as “typical.

Figure 3. Effect of Capacitance on Measured Q

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 de-embedded measurement is higher than the measured value.

And yet, the de-embedded SRF is not the true SRF. The true SRF of any inductor always depends on the specific characteristics 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 circuit board substrate, you can determine the SRF of an inductor for your application. The circuit board substrate dielectric constant and thickness, and the size and layout of the conductor traces in the vicinity of the inductor determine the SRF of the inductor.

Eagleware’s RF and microwave design software offers high accuracy libraries of many of our chip inductor series. The models are substrate-scalable, based on measurements of our inductors over various thicknesses of FR4 and 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 a practical basis to apply when comparing inductors, and ultimately can answer the question of whether an inductor is appropriate for the application.

- Assistance with Safety Agency Approvals
- Basics of Inductor Selection (from Electronic Design magazine)
- Calibration, Compensation, and Correlation
- Current and Temperature Ratings
- Getting Started: An Introduction to Inductor Specifications
- Hipot Testing of Magnetic Components
- How Current and Power Relates to Losses and Temperature Rise
- Operating Voltage for Inductors
- Selecting Current Sensors and Transformers
- Simulation Model Considerations: Part I
- Simulation Model Considerations: Part II
- S-parameters for High-frequency Circuit Simulations
- Testing Inductors at Application Frequencies
- Working Voltage Ratings Applied to Inductors

- PCB Washing and Coilcraft Parts
- Selecting Flux for Soldering Coilcraft Components
- Soldering Surface Mount Components

- Broadband Chokes for Bias Tee Applications
- Inductors as RF Chokes
- Key Parameters for Selecting RF Inductors

- Beyond the Data Sheet: The Need for Smarter Power Inductor Specification Tools
- Choosing Inductors for Energy Efficient Power Applications
- Current Sense Transformers for Switched-mode Power Supplies
- Determining Inductor Power Losses
- Ferrite Vs Pressed Powder-core Inductors
- Forward or Flyback? Which is Better?
- Notes on Thermal Aging in Inductor Cores
- Selecting Coupled Inductors for SEPIC Applications
- Selecting Inductors to Drive LEDs
- Selecting the Best Inductor for Your DC-DC Converter
- Structured Design of Switching Power Transformers
- Transformers for SiC FETs

- Coilcraft LC Filter Reference Design
- Common Mode Filter Design Guide
- Common Mode Filter Inductor Analysis
- Data Line Filtering
- Fundamentals of Electromagnetic Compliance
- Passive LC Filter Design and Analysis
- Selecting Common Mode Filter Chokes for High Speed Data Interfaces

- Applying Statistical Techniques to the Design of Custom Magnetics
- Choosing Power Inductors for LiDAR Systems
- Coilcraft Conical Inductors
- Designing a 9th Order Elliptical Filter for MoCA® Applications
- Measuring Sensitivity of Transponder Coils
- Power-handling Capabilities of Inductors
- Signal Transformer Application
- Transponder Coils in an RFID System
- Using Baluns and RF Components for Impedance Matching
- Using Standard Transformers in Multiple Applications