Prerequisites · read first

Impedance basics

Z=R+jXReactanceSRFwiki/embedded-impedance-basics

TL;DR

Impedance $Z$ is, in one line, 'resistance whose value changes with frequency.' In DC, where current flows one way, you only watch resistance $R$ ; but in AC, where the signal wiggles fast, an extra 'frequency-dependent opposition' appears — and the two together are $Z = R + j X$ . The one fact that matters most: capacitors and inductors do the opposite of each other. As frequency rises a capacitor passes more ( $X_{C}$ falls) while an inductor blocks more ( $X_{L}$ rises). That single symmetry explains filters, decoupling, and resonance.

First — DC and AC

New to electronics? Start here. DC means current flows steadily in one direction (a battery); AC means its direction and size wiggle tens to millions of times a second (a wall outlet, an audio signal). How fast it wiggles is the frequency $f$ (in Hz).
A resistor opposes current the same in DC or AC and turns that energy into heat. But capacitors and inductors oppose differently depending on how fast things wiggle (frequency) — so one number (resistance) isn't enough, and we need impedance.

	DC	AC
Current direction	fixed, one way	keeps reversing
Example	battery · USB	outlet · signals
What opposes current	resistance R only	R + reactance = impedance Z

DC vs AC — what you watch

Impedance = resistance + reactance

Impedance $Z$ adds two things. One is the familiar resistance $R$ — constant regardless of frequency, burning the blocked energy as heat. The other is reactance $X$ — it changes with frequency and, instead of burning energy, briefly stores and returns it.
So we write $Z = R + j X$ . The unit is the same ohm ( $Ω$ ) as resistance, and how much it actually blocks is the magnitude $∣ Z ∣$ . Don't fear the $j$ — it just flags that voltage and current are $90°$ out of step in timing; that's all you need for now.

Z = R + j X

$R$: resistance — freq-independent, heats
$X$: reactance — varies w/ freq, stores↔returns
$j$: 90° timing offset

impedance = fixed R + varying reactance

The key — capacitor and inductor are opposites

A capacitor's impedance falls as frequency rises, so it passes high frequencies: $X_{C} = \frac{1}{2 π f C}$ . Intuitively, if things wiggle too fast it reverses before it fills up, so current flows freely. At DC ( $f = 0$ ) it's infinite — a full block.
The inductor is the mirror: $X_{L} = 2 π f L$ . The higher the frequency, the more it blocks. At DC it's $0$ — just a wire. Plot both and they cross like an X; where they meet is resonance.

Capacitor Xc=1/2πfCInductor XL=2πfL

As frequency rises, the cap passes (↓), the inductor blocks (↑)

RC filter — sorting by frequency

Just one resistor $R$ and one capacitor $C$ make a filter that 'passes some frequencies, blocks others.' The boundary is the cutoff $f_{c} = \frac{1}{2 π R C}$ . Pass below $f_{c}$ and it's a low-pass filter (LPF); pass above and it's high-pass (HPF).
As the graph shows, output bends down around $f_{c}$ . Exactly at $f_{c}$ the output is $0.707 \times$ the input ( $- 3 dB$ ) — the meaning of the $f_{c}$ formula you saw on the capacitor page.

Low-pass — frequencies above fc get cut

Real parts betray you — resonance (SRF)

Those formulas describe 'ideal' parts. A real capacitor hides a little inductance (ESL) in its leads and body, so past a certain frequency it suddenly starts acting like an inductor. That boundary is the self-resonant frequency (SRF) — the point where the two curves met in the previous graph.
So a decoupling capacitor loses effect above its SRF. On real boards you'll see a big and a small value side by side ( $10 μ F$ + $0.1 μ F$ ) because each works best over a different band and they cover each other's gaps.

low freqcapacitive

⚡SRFXc = XL

high freqinductive

Roles flip across the SRF

So where is this used

Decoupling: place a small capacitor right next to an IC's power pin so high-frequency noise sees a low-impedance shortcut (→ ground GND). Noise takes the low-impedance path and never reaches the chip.
Ferrite bead: the opposite — it raises impedance at high frequency (acting like a resistor) to block noise and burn it as heat. Both come straight from this page's one idea: impedance changes with frequency.

🎚using impedance

decoupling caplow-Z to HF → shunt to GND

ferrite beadhigh-Z to HF → burns as heat

Exploiting frequency-dependent impedance

Pitfalls & gotchas

Lumping 'impedance = resistance' means filters and decoupling never click — the one key is that the value changes with frequency. And when picking parts from a datasheet, read the impedance-vs-frequency curve ( $∣ Z ∣$ vs $f$ ), not a single number. Leave $j$ (phase) as just a 'timing offset' for now; deeper complex math can wait until you truly need it.