# Passive Components

## Introduction

Resistor, capacitor, and inductors are the fundamental building blocks of filtering and energy storage. Resistor's main function is to impede current flow while capacitor and inductor provides energy storage in electric field and magnetic field respectively. We generally categorize resistor as a real component while capacitor and inductor as reactive components.

## Background

ESL: Equivalent Series Inductance for circuit modeling

ESR: Equivalent Series Resistance for circuit modeling

Cpar: Parasitic Capacitance for circuit modeling

SRF; Self Resonance Frequency for circuit frequency analysis

Q: Quality factor

Very High Q means the reactive components C or L contains little or minimal loss components

**Resistor**

Characteristics

Ideal Circuit Model

R

Flat impedance vs frequency graph

Real Circuit Model

L in series with parallel C & R: ESL+ (C||R)

parasitic capacitance due to package lead

parasitic inductance due to package lead

Impedance vs frequencies curve

Three regions: Flat - Dip - Up

**Flat:**Resistive region: Flat impedance DC to 1/(2π *R*C))**Dip:**Capacitive region: impedance starts to fall 20dB/decade from 1/(2PI*R*C) to 1/sqrt(2π *C*ESL)**Up:**Inductive regions: impedance starts to rise at 20 dB/decade from 1/sqrt(2π *C*ESL) and up

**Capacitor**

Characteristics

Voltage cannot change instantly across capacitor

IC=C*delta_V/delta_T

Ideal Circuit Model

C

Impedance vs frequency starts to fall 20dB/decade for DC and up

Real Circuit Model

Series RLC circuit: ESR+ESL+C

parasitic resistance due to package lead and dielectric loss.

parasitic inductance due to package lead

SRF = 1/(2π*sqrt(C*ESL)) [Hz]

Impedance vs frequencies curve

Three regions: Dip - trough - Up

**Dip:**Capacitive region: impedance starts to fall 20dB/decade from DC to SRF**Trough:**Resistive trough: the lowest impedance is at the LC SLF point, which is equal to the ESR**Up:**Inductive regions: impedance starts to rise at 20 dB/decade from SRF and up

**Inductor**

Characteristics

current cannot change instantly across capacitor

VL=L*delta_I/delta_T

Ideal Circuit Model

L

Impedance vs frequency starts to rise 20dB/decade from DC and up

Real Circuit Model

C in parallel with series RC circuit: (ESR+ESL)||Cpar

parasitic resistance due to package lead resistance and mostly due to dielectric loss.

parasitic inductance due to package lead

SRF = 1/sqrt(2π *C*ESL)

Impedance vs frequencies curve

Three regions: up - peak - dip

**up:**Inductive region: impedance starts to rise 20dB/decade from DC to SRF**peak:**Peak Impedance: highest impedance at SRF point**dip:**Capacitive regions: impedance starts to fall at 20 dB/decade SRF and up.

## Detailed Analysis

**Resistor**

Pull up and Pull down resistor

Resistor is used for GPIO Input as a pull up and pull down resistor to set a initial state voltage. If used this way, the tolerance of can be large (typ. 5%)

Current Sensing

If a resistor is used or current sensing, a high precision and high power wattage resistor is sued. Precision is generally at 1%.

Temperature Sensing

Negative Temperature Coefficient (NTC) resistor

Resistance of NTC resistor decrease with rise of temperature. NTC resistor is generally used of of temperature sensing resistor (thermistor) or used as a soft-start circuit where resistance is inverse to current flow, so at the beginning of the operation the current is small but as resistor's internal temperature rises, more current is going through.

Over Current Protection

Positive Temperature Coefficient (PTC) resistor

Resistance of PTC resistor increases with rise of temperature. This is generally a protection circuit for over current protection. As current increases due to a fault, the resistor will increases its internal resistance rapidly to reduce load current. This is generally found in battery packs.

**Capacitors**

Application

power supply storage and filtering

Bullk Capacitor

Aluminum Electrolytic capacitor has very high capacitance but also high ESR and ESL due to lossy dielectric and long leads.

It is ideal to used as energy storage located at output of power supply but it's not efficient to response to ac current load.

Tantalum capacitor is very reliable, low leakage current, and ages well. it's much smaller than Aluminum Electrolytic capacitor which results in much lower ESR and ESL and is ideal for ac current filtering.

It's commonly used as the power supply filter.

Decoupling Capacitors

Ceramic, X5R (temperature upper limit 85) or X7R (temperature upper limit 125) , capacitors has a mid range capacitance and small package in 0402, 0603, etc. that has low ESR and low ESL. This allows the capacitor to have a low and wider impedance vs. frequency curve that resemples a bathtub shape. This bathub shape is efficient to respond to a wide range of ac current load and is ideal to place it next to fast switching digital ICs.

RF Capacitors

A C0G/NP0 dielectric capacitor is temperature stable is used for RF circuits that require precise matching network across temperature for maximum power transfer.

**Inductors**

Application

Switch mode power supply output filter.

power line Chokes (filter)

Oscillation circuit

Impedance matching for RF path.

**Wirewound**

High SRF.

High SRF expends useful frequency range of inductor

High Q

Low DC resistance

Support larger current

**Ceramic**

smaller size and cost than wire wound

Lower Q

## Q&A

What can be used to shunt ESD energy?

An RF shunt inductor placed near the Antenna can be used to shunt ESD energy that comes from the Antenna.

ESD current specturn around 10s of MHz, which is much lower than Radio Frequency used in cellular or wifi. An RF shunt inductor at 10s of MHz frequency provides a low impedance path for ESD energy to go to ground.

An 0.1 uF ceramic shut capactor placed near the connector can be used to shut ESD energy that comes from the connector.

ESD or transient voltage has spectrum of 10s of MHz, a small ceramic capacitors has low impedance at around this frequency which provides low impedance for ESD energy to ground.

## Summary & Conclusion

**Resistor**resists current regardless frequency and temperature**Capacitor**resists change in voltage**Inductor**resists change in current**Non-ideal model of R, C, and L**includes parasitic capacitance, ESR, and ESR due to packaging and dielectric materials.

RLC are essential components in electronic design in the area of filtering, measurements, protection, impedance matching network ,etc. Understanding the non-ideal effect helps engineer choose the right components for the design.

## 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