PCB Design

Passives: resistors, capacitors, inductors

Packages, tolerances, dielectrics, ESR, saturation, and the DC-bias trap in ceramic capacitors.

Day 4 · 45 min

After this lesson

You can read a passive's package code, tolerance and rating.
You can pick capacitor dielectrics for decoupling, timing and filtering.
You can explain ESR, ESL and inductor saturation current.

Three passive parts, and what their labels leave out

Resistors: value, tolerance, power, package

A chip resistor is defined by four numbers: value, tolerance, power rating and package. Thick-film parts are ±1% (E96 series) or ±5% (E24) with a tempco of about ±100 ppm/°C, so a 10 kΩ resistor drifts 60 Ω over a 60 °C swing. Thin-film parts reach ±0.1% and ±25 ppm/°C for precision dividers and current sensing. Through-hole metal-film parts are the classic 1/4 W resistor, and wirewound or metal-strip parts handle watts and milliohm current shunts. Chip packages are named in hundredths of an inch:

Package	Size	Typical power	Where it fits
0402	1.0 × 0.5 mm	62.5 mW (1/16 W)	dense boards, decoupling
0603	1.6 × 0.8 mm	100 mW	prototypes, hand soldering
0805	2.0 × 1.25 mm	125 mW (1/8 W)	easy rework, bulk capacitors
1206	3.2 × 1.6 mm	250 mW (1/4 W)	higher power, 10 µF X7R

Pull-ups and pull-downs are the humble workhorse: 10 kΩ on reset, enable and strap pins, 4.7 kΩ on I²C at 3.3 V, and 100 kΩ where quiescent current matters. Too weak a pull is slow and noise-sensitive; too strong wastes current, because 3.3 V across 1 kΩ is 3.3 mA.

Capacitors: what the label hides

Ceramic (MLCC) capacitors dominate boards, and the dielectric code tells you how they behave. Class I C0G (NP0) stays within ±30 ppm/°C and does not change with voltage, but tops out near 100 nF in an 0805; use it for timing, filters and RF. Class II X7R is ±15% from −55 to +125 °C and packs far more capacitance, but it ages about 2.5% per decade-hour, can be microphonic, and loses capacitance under DC bias. Y5V swings +22/−82% and has no place where the value matters. The letters decode as lowest temperature, highest temperature and allowed change.

DC-bias derating is the trap. A small-case, high-value X7R may keep 60% of its capacitance at half its rated voltage and only 35% at the rating, so a 10 µF, 10 V part on a 3.3 V rail delivers about 7.5 µF, and the same capacitor rated 6.3 V delivers about 6 µF. Choose a voltage rating of 2 to 3 times the working voltage and read the manufacturer's bias curve.

Other families fill other roles. Aluminium electrolytics give hundreds of microfarads cheaply but are polarised (reverse voltage vents them), have ESR from 0.05 Ω to a few ohms, and wear out: life roughly doubles for every 10 °C below the 105 °C rating, so 2000 h becomes about 64,000 h at 55 °C. Tantalum is compact and stable with low ESR, but MnO₂ types can fail short and ignite, so run them at half their rated voltage and never reverse them. Polymer types add very low ESR, and film capacitors are stable and non-polarised, used for timing, audio, snubbers and mains safety.

The role decides the part: 100 nF X7R next to every IC supply pin plus 4.7 to 10 µF bulk per rail for decoupling, C0G or film for timing and filters, and X7R, polymer or electrolytic for bulk storage and coupling.

Top: a multilayer ceramic capacitor cut open with the series ESR and ESL model of a real part, and a wire-wound inductor. Bottom: how an inductor's inductance collapses past its saturation current.

ESR, ESL and self-resonance

A real capacitor is a series chain of capacitance, ESR and ESL. ESR turns ripple current into heat (P = I² · ESR) and sets the ripple of a switching supply; some older LDOs, the AMS1117 among them, even need a minimum ESR in the output capacitor to stay stable. ESL, about 0.5 to 1 nH for an 0402 plus a nanohenry or so from pads and vias, makes the part resonate at f = 1 / (2π√(LC)): 100 nF with 1 nH resonates near 16 MHz, 10 µF with 2 nH near 1.1 MHz, and above that frequency the capacitor behaves like an inductor. This is why decoupling capacitors sit millimetres from the pin with the shortest possible path to the plane.

Inductors and ferrite beads

An inductor stores energy in a magnetic field, E = ½ · L · I². Three numbers matter. Saturation current (Isat) is where the core can hold no more flux and the inductance has fallen by 20 to 30%; above it the current ramps almost without limit, which can destroy the switch of a buck converter. RMS current is the continuous current that heats the part by about 40 °C. DCR is the winding resistance: a 10 µH inductor with 50 mΩ wastes 0.45 W at 3 A. Choose L from the ripple target, ΔI = (Vin − Vout) · D / (L · f), usually 20 to 40% of the load current, and keep the peak current Iload + ΔI/2 below Isat with margin. Shielded parts radiate less.

A ferrite bead acts like a small inductor at low frequency and a resistor at high frequency, for example 600 Ω at 100 MHz, so it absorbs noise as heat instead of reflecting it. Put one in series with an analog supply or a cable shield, and remember that its impedance drops as DC bias current rises.

Interactive: charge a capacitor, then derate it

RC charging and the DC-bias trap

Step a voltage onto a resistor and capacitor and watch the plates fill. Turn on X7R derating to see the real capacitance shrink as the voltage rises.

Resistance R100 kΩCapacitance C (zero-bias value)10 µF

Time constant τ = R · C: 1 s
5τ (99.3% settled): 5 s
Time to 63.2% of the step: 1 s
Capacitor voltage now: 0.00 V
Capacitance now: 10 µF (100%)
Current now: 50 µA

Step voltage Vs5 V

The time axis always spans 5τ, so changing R or C stretches the labels while the curve keeps its shape; the electrons slow down as the current decays. Playback is slowed so one 5τ window lasts about five seconds.

In practice

Practice

Specify the decoupling for a small MCU

A 3.3 V microcontroller in an LQFP-48 has three VDD pins and a VDDA analog supply pin, fed from an LDO. List the capacitors you would place, with value, dielectric, package, voltage rating and position. Then compute the real capacitance of your bulk capacitor at 3.3 V, assuming a 10 µF X7R keeps about 75% of its capacitance at one third of its rating and 86% at one fifth.

Answer: show the worked solution

text

VDD pins   3 x 100 nF X7R 0402, 16 V   one per pin, within 2 mm, ground via at the pad
VDDA       1 x 1 µF X7R 0603, 16 V     plus 1 x 10 nF to 100 nF 0402, behind a ferrite bead
Bulk       1 x 10 µF X7R 0805, 16 V    near the MCU, on the 3.3 V rail
LDO        per datasheet (AMS1117-3.3: 22 µF solid tantalum out for stability; 10 µF in is good practice)

Bulk capacitance at 3.3 V:
  16 V rating: 3.3 / 16 = 0.21 of rating, about 86% -> 8.6 µF
  10 V rating: 3.3 / 10 = 0.33 of rating, about 75% -> 7.5 µF
  6.3 V rating: 3.3 / 6.3 = 0.52 of rating, about 59% -> 5.9 µF

The 100 nF parts supply the fast edges, so they go closest to the pins, on the same side as the MCU, with the ground via at the pad instead of a long trace. The 10 µF part covers slower load steps and the interaction with the regulator. Choosing the 16 V rating over the 6.3 V rating recovers about 2.7 µF of real capacitance for a few cents.

Real-world scenario

The blink timer runs 30% faster on fresh cells

A battery-powered asset tag paces its transmissions with an RC relaxation oscillator: a Schmitt-trigger inverter, a resistor and a 100 nF capacitor, nominally a 10 ms timebase. The bill of materials said '100 nF, 6.3 V', and purchasing picked the cheapest match, a Y5V 0402. The designer could only reach 100 Hz on the bench by raising R from the calculated 100 kΩ up to about 220 kΩ, then froze the design. In the field the tags run roughly 30% faster with fresh cells and slow down as the batteries sag, and the spread between tags is wider than the resistor tolerance can explain.

Symptoms

Frequency differs by more than 30% between a fresh 4.2 V cell and a nearly flat 3.0 V cell, even though the Schmitt thresholds scale with the supply.
An LCR meter at 1 kHz with no DC bias reads the capacitor at 98 nF, in spec, yet in circuit it behaves like roughly 45 nF.
R had to be raised from the calculated 100 kΩ to about 220 kΩ to hit 100 Hz, which is the clue that C is not 100 nF in circuit: the period is proportional to R × C, so a capacitor of about 45 nF needs about 2.2 times the resistance.
Cooling a board in a freezer shifts the frequency again.

Interview questions

screenHow do you choose decoupling capacitors for a microcontroller?

I put one 100 nF X7R capacitor in an 0402 or 0603 on every supply pin, as close to the pin as the footprint allows, with the ground via right at the capacitor pad. Then I add a bulk capacitor of 4.7 to 10 µF per rail, nearer the regulator, to cover slower load steps. I pick a voltage rating of 2 to 3 times the rail because X7R loses capacitance under bias, so a 10 µF, 6.3 V part on 3.3 V may only be 6 µF. For an analog supply such as VDDA I add 1 µF behind a ferrite bead or a small resistor to keep digital noise out.

screenWhat is the difference between C0G, X7R and Y5V ceramic capacitors?

They are dielectric classes. C0G, also called NP0, is Class I: ±30 ppm/°C, no change with DC bias and almost no aging, but limited to roughly 100 nF in an 0805. X7R is Class II: ±15% from −55 to +125 °C and far more capacitance per volume, but it loses 40% or more under DC bias and shows some aging and microphonic effects. Y5V swings +22/−82% over temperature and loses even more under bias, so I avoid it for anything that matters. In practice I use C0G for timing and RF, X7R for decoupling and bulk, and Y5V almost never.

screenA 10 µF, 6.3 V X5R capacitor sits on a 5 V rail. What is wrong with that?

Two things. First, 5 V is 79% of the rating, which leaves no margin for ripple, spikes or aging, and ceramics can crack or degrade when run near their limit. Second, DC-bias derating: at 5 V a 10 µF, 6.3 V part in an 0603 can deliver less than half of its marked capacitance, so the rail has far less bulk capacitance than the schematic claims. I would move to a 16 V or 25 V part, maybe a larger case, and read the manufacturer's bias curve for the real capacitance at 5 V.

screenWhat does ESR do, and when does it matter?

ESR is the equivalent series resistance of a capacitor, the small resistance in series with its ideal capacitance. It turns ripple current into heat, P = I² · ESR, so it sets the ripple rating of an electrolytic, and together with the capacitance it sets the output ripple of a switching regulator. For some older LDOs, the AMS1117 among them, it matters in the other direction, because the control loop expects some ESR in the output capacitor and a very low-ESR ceramic can make it oscillate. As a rule, ceramics are tens of milliohms, polymers a few tens of milliohms, and aluminium electrolytics a few hundred milliohms to ohms.

deepWhat happens when an inductor saturates, and how do you pick one for a buck converter?

Above its saturation current the core can hold no more flux, so the inductance collapses, usually defined as a 20 to 30% drop, and the current ramps almost unchecked until something else limits it. In a buck converter that sends a current spike through the switch, which can trip the current limit or destroy the FET. I choose L from the ripple target, ΔI = (Vin − Vout) · D / (L · f), usually 20 to 40% of the load current. Then I pick a part whose saturation current is above the converter's current limit with margin and whose RMS rating covers the load, and I check that DCR keeps the I² · R loss and heating acceptable.

deepWhy do designers put several capacitor values in parallel, and what is self-resonance?

Every real capacitor is a series RLC: the capacitance, its ESR, and an equivalent series inductance of about 0.5 to 1 nH for an 0402 plus a nanohenry or so from the pads and vias. At the self-resonant frequency, f = 1 / (2π√(LC)), the reactances cancel and the impedance is just the ESR, and above it the part behaves like an inductor. 100 nF with 1 nH resonates near 16 MHz and 10 µF with 2 nH near 1.1 MHz, so each value covers a different band. Mixed values can create anti-resonance peaks between them, so I use a few well-chosen values placed close to the pins instead of a pile of different ones.

References and further reading

Where the ideas in this lesson come from, and what to read next. Books are the standard texts; papers are the original sources; standards are what employers work to.

Book
Paul Horowitz and Winfield Hill (2015). The Art of Electronics. Cambridge University Press, 3rd edition.
Read: Chapter 1 and the components appendix: capacitor types, inductors, how to read ratings.
Bookfree online
Hank Zumbahlen (editor), Analog Devices (2008). Linear Circuit Design Handbook. Newnes.
Read: The passive-components chapter, including DC-bias effects in ceramics.
Book
Clyde F. Coombs Jr. and Happy T. Holden (editors) (2016). Printed Circuits Handbook. McGraw-Hill, 7th edition.
Read: The surface-mount components chapter for package sizes.

← Previous Next: Active components: regulators, op-amps, MCUs →

Key terms

Tolerance and tempco: Tolerance is the allowed error from the marked value (±1% for E96, ±5% for E24). Tempco is drift per degree: ±100 ppm/°C on a thick-film resistor moves a 10 kΩ part by 60 Ω over a 60 °C swing.
Package code (0402, 0603, 0805, 1206): Imperial size in hundredths of an inch: 0402 is 1.0 × 0.5 mm, 0603 is 1.6 × 0.8 mm, 0805 is 2.0 × 1.25 mm, 1206 is 3.2 × 1.6 mm. Rated power grows with size, from 1/16 W (0402) to 1/4 W (1206).
C0G, X7R and Y5V: Ceramic dielectric codes. C0G (NP0) holds ±30 ppm/°C with no bias effect. X7R is ±15% from −55 to +125 °C but loses capacitance under DC bias. Y5V swings +22/−82% and is unsuitable for timing, filtering or decoupling.
DC-bias derating: Class II ceramic capacitance falls as DC voltage rises. A small-case, high-value X7R part can lose 40% at half its rated voltage and over 60% at the rated voltage, so the label is only its value at 0 V.
ESR: Equivalent series resistance: the small real resistance in series with a capacitor, from milliohms (ceramic, polymer) to ohms (small electrolytic). It turns ripple current into heat and can decide LDO stability.
ESL and self-resonance: Equivalent series inductance, about 0.5 to 1 nH for an 0402 plus the mounting. A capacitor resonates at f = 1 / (2π√(LC)), roughly 16 MHz for 100 nF with 1 nH, and behaves like an inductor above that frequency.
Decoupling capacitor: A local capacitor that supplies an IC's fast current transients so the rail does not sag: 100 nF X7R at every supply pin, within a few millimetres, plus a 4.7 to 10 µF bulk capacitor per rail.
Saturation current (Isat): The current at which an inductor's core saturates and its inductance falls, usually quoted at a 20 to 30% drop. Past it the current ramps almost without limit, which can destroy a buck converter's switch.
DCR: DC resistance of an inductor's winding. It sets the copper loss I² · DCR and, with the heating (RMS) current rating, how much continuous current the part can carry.
Ferrite bead: A lossy, inductor-like part that looks resistive at high frequency (typically 600 Ω at 100 MHz), so it absorbs noise as heat instead of reflecting it. Its impedance drops with DC bias current.