# Passive Components

Introduction

Resistors, capacitors, and inductors are fundamental components used for filtering and energy storage in electronic circuits. Resistors impede current flow, while capacitors and inductors store energy in electric and magnetic fields, respectively. Resistors are classified as real components, while capacitors and inductors are reactive components.

Background

Several important terms and characteristics are relevant to circuit modeling and frequency analysis:

ESL (Equivalent Series Inductance): Inductance used in circuit modeling.

ESR (Equivalent Series Resistance): Resistance used in circuit modeling.

Cpar (Parasitic Capacitance): Capacitance used in circuit modeling.

SRF (Self Resonance Frequency): Frequency used for circuit frequency analysis.

Q (Quality Factor): measure of the efficiency of a reactive component, such as a capacitor or inductor. A higher Q signifies minimal energy losses and is more efficient

Resistor: Characteristics:

Ideal Circuit Model: Represented by a single resistor (R) with a flat impedance vs. frequency graph.

Real Circuit Model: Consists of an inductor (L) in series with a parallel combination of a capacitor (C) and a resistor (R), denoted as ESL + (C||R).

Impedance vs. Frequency Curve: Exhibits three regions: Flat, Dip, and Up.

Flat: Resistive region with a constant impedance from DC to 1/(2πRC).

Dip: Capacitive region where impedance decreases at a rate of 20 dB/decade from 1/(2πRC) to 1/sqrt(2πCESL).

Up: Inductive region where impedance increases at a rate of 20 dB/decade from 1/sqrt(2πCESL) and beyond.

Capacitor: Characteristics:

First Principles: Voltage across a capacitor cannot change instantaneously.

Ideal Circuit Model: Represented by a single capacitor (C) with an impedance vs. frequency curve that decreases at a rate of 20 dB/decade from DC and upward.

Real Circuit Model: Comprises a series combination of a resistor (R), an inductor (L), and a capacitor (C), denoted as ESR + ESL + C.

Impedance vs. Frequency Curve: Displays three regions: Dip, Trough, and Up.

Dip: Capacitive region where impedance decreases at a rate of 20 dB/decade from DC to SRF.

Trough: Resistive trough with the lowest impedance at the LC SLF point, which is equal to the ESR.

Up: Inductive region where impedance increases at a rate of 20 dB/decade from SRF and beyond.

Inductor: Characteristics:

First principles: Current through an inductor cannot change instantaneously.

Ideal Circuit Model: Represented by a single inductor (L) with an impedance vs. frequency curve that increases at a rate of 20 dB/decade from DC and upward.

Real Circuit Model: Composed of a capacitor (C) in parallel with a series combination of a resistor (R) and a capacitor (C), denoted as (ESR + ESL) || Cpar.

Impedance vs. Frequency Curve: Exhibits three regions: Up, Peak, and Dip.

Up: Inductive region where impedance increases at a rate of 20 dB/decade from DC to SRF.

Peak: Peak impedance occurs at the SRF point.

Dip: Capacitive region where impedance decreases at a rate of 20 dB/decade from SRF and beyond.

Applications

Resistor:

Pull-Up and Pull-Down Resistor: Used for GPIO input to set an initial voltage state. Tolerance can be relatively large (typically 5%).

Current Sensing: High-precision, high-power-wattage resistors are used for current sensing, with precision typically at 1%.

Temperature Sensing: NTC (Negative Temperature Coefficient) resistors decrease resistance with rising temperature. They are used for temperature sensing or as soft-start circuits, where resistance is inversely proportional to current flow.

Over Current Protection: PTC (Positive Temperature Coefficient) resistors increase resistance with rising temperature, providing protection against overcurrent. Commonly found in battery packs.

Capacitors:

Applications: Power supply storage and filtering.

Bulk Capacitor: Aluminum electrolytic capacitors have high capacitance but also high ESR and ESL due to lossy dielectrics and long leads. They are suitable for energy storage in power supplies but inefficient for responding to AC current loads. Tantalum capacitors, smaller and with lower ESR and ESL, are ideal for AC current filtering and widely used as power supply filters.

Decoupling Capacitors: Ceramic capacitors (such as X5R or X7R) with mid-range capacitance and small package sizes (0402, 0603, etc.) have low ESR and ESL. They exhibit a bathtub-shaped impedance vs. frequency curve, making them efficient in responding to a wide range of AC current loads. Decoupling capacitors are commonly placed next to fast switching digital ICs.

RF Capacitors: C0G/NP0 dielectric capacitors provide temperature stability and are used for RF circuits requiring precise matching networks across temperatures for maximum power transfer.

Inductors:

Applications: Switch mode power supply output filtering, power line chokes, oscillation circuits, and impedance matching in RF paths.

Wirewound: High SRF (Self Resonance Frequency) expands the useful frequency range of the inductor. High Q, low DC resistance, and the ability to support larger currents are desirable characteristics.

Ceramic: Smaller in size and cost compared to wirewound inductors. Lower Q is a trade-off, but they are still suitable for many applications.

Q&A

Q: What can be used to shunt ESD energy?

A: To shunt ESD energy from the antenna, an RF shunt inductor placed near the antenna is effective. Since ESD currents typically occur in the tens of MHz range, the RF shunt inductor provides a low impedance path for the ESD energy to be directed to the ground.

Q: How can ESD energy from a connector be shunted?

A: To shunt ESD energy coming from a connector, a 0.1 uF ceramic shut capacitor placed near the connector can be used. ESD or transient voltages generally have a spectrum in the tens of MHz range, and small ceramic capacitors offer low impedance at this frequency, providing an efficient path for ESD energy to be directed to the ground.

Summary & Conclusion

Resistors impede current flow, capacitors resist changes in voltage, and inductors resist changes in current.

Non-ideal models of R, C, and L consider parasitic capacitance, ESR, and ESL caused by packaging and dielectric materials.

RLC components are crucial for filtering, measurements, protection, and impedance matching networks.

Understanding their non-ideal effects helps engineers choose the right components for their designs.

## Further Reading

"Capacitor Guide", http://www.capacitorguide.com/

"Basic Factors about inductors", https://article.murata.com/en-us/article/basic-facts-about-inductors-lesson-2