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