Propagation Delay, εeff & Timing

Effective dielectric constant, propagation delay per length, trace length matching from a skew budget, rise time to bandwidth and knee frequency, critical length and wavelength on the board.

Method, formulas and references

Relations used

(1)t_pd = √ε_eff / c

A signal travels at c/√ε_eff. In stripline ε_eff equals the laminate εr. In microstrip part of the field is in air, so ε_eff is lower. The microstrip option uses the Hammerstad–Jensen expressions with thickness correction. For coated or coupled lines, take ε_eff from the impedance calculator's field solver.

(2)f_3dB ≈ 0.35 / t_r, f_knee ≈ 0.5 / t_r

The critical length is a rule of thumb: once a trace's delay exceeds about one sixth of the rise time, reflections become visible and the line should be terminated and impedance-controlled.

References

E. Hammerstad, Ø. Jensen, “Accurate Models for Microstrip Computer-Aided Design,” IEEE MTT-S, 1980.
H. Johnson, M. Graham, High-Speed Digital Design, Prentice Hall, 1993.
E. Bogatin, Signal and Power Integrity – Simplified, 3rd ed., 2018.

Related guides

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Signal integrity

Impedance Calculator – Single-ended and differential microstrip, coated and embedded microstrip, stripline, coplanar lines and broadside differential pairs, solved with a 2D field solver.
Propagation Delay, εeff & Timing – Propagation delay, length matching from skew, rise time to bandwidth, critical length and wavelength.
Signal Termination Calculator – Source-series, single-ended load and differential load termination from trace impedance, with E-series values, reflection and resistor stress.
Trace Loss (Insertion Loss) Calculator – Insertion loss in dB/in and over the full length: conductor loss with copper roughness and dielectric loss from the field solver, with laminate Dk/Df across frequency.
Crosstalk Calculator – Near- and far-end crosstalk between parallel traces from the field solver, with a sweep over the spacing (3W rule check).
Differential Via – Via-pair differential impedance through the plane clearance from a 2D field solution, antipad sizing for a target, stub resonance and delay.
Via Stitching & Via Fence Spacing – Stitching and fence via pitch from the wavelength (λ/10, λ/20), via-grid cell resonance, leakage between vias and plane-pair cavity resonances.
Interface Design Rules – Impedance, skew, loss budget and length limits of PCIe, USB, Ethernet, HDMI, DDR and other interfaces, applied to a layer of your own stackup with the field solver.
Phase Noise to Jitter & Jitter Budget – RMS phase jitter from an oscillator phase noise curve by exact segment integration, jitter-limited ADC SNR and ENOB, and total jitter at a BER from random and deterministic terms.
S-Parameter Viewer (.s2p, .s4p) – Open .s1p to .s16p Touchstone files in the browser: insertion and return loss, phase, group delay, mixed-mode SDD21/SCD21 for 4-ports, TDR impedance and interface loss budgets.

Communication interfaces

SPI Timing Calculator – Opposite-edge SPI read timing: clock and MISO path delay, peripheral tCO, setup margin and the timing-limited clock ceiling.
I²C Pull-up Calculator – Pull-up resistor range for Standard, Fast and Fast-mode Plus I²C from bus capacitance, rise time and device sink current.
CAN / CAN FD Bit Timing Calculator – CAN and CAN FD bit timing, sample point, prescaler and segment search with Bosch M_CAN limits, plus standard and split termination.
RS-485 / Modbus RTU Calculator – Two-wire RS-485 end termination, conservative external bias sizing, rise-time-based stub length and Modbus RTU frame and polling timing.

RF

VSWR, Return Loss & Mismatch Loss Calculator – Convert between VSWR, |Γ|, return loss, mismatch loss and reflected power, find Γ of a complex load, and bound the mismatch uncertainty and cascaded VSWR of two ports.
Coaxial Line Impedance Calculator – Characteristic impedance of a coaxial line from D, d and εr, or the diameter for a target Z0, with offset centre conductor, delay, C and L per metre, TE11 cutoff and loss.
L-Network Impedance Matching & Smith Chart – Two-element L-section matching of a complex load: every low-pass and high-pass solution with L and C values, node Q, swept return loss, bandwidth, nearest E-series parts and a Smith chart.
Quarter-Wave Transformer & Stub Calculator – Single and multisection binomial or Chebyshev λ/4 transformers with exact response and bandwidth, open and short stubs, and single-stub matching, with physical lengths and trace widths.

Stackup

Stackup Advisor – Find rigid, flex and rigid-flex region stackups by thickness and layer count, then rank candidates by impedance and solve trace widths.
Layer Stack Manager – 178 rigid fab stackups plus six flex and rigid-flex design starters, with linked regions, editable materials and per-layer impedance.
KiCad Stackup Impedance Calculator – Reads the stackup of a .kicad_pcb file or project folder in the browser, gives 50 Ω and 90/100 Ω differential widths and loss per layer, and checks the impedance, skew and loss of every routed pair.
KiCad Project – The active KiCad project of this browser: stackup, layer roles, net classes, pairs, impedance by layer and routing check, read once and shared with the calculators.
PCB Laminate Materials (Dk / Df) – Datasheet Dk and Df of FR-4, low-loss, RF and flex laminates (Isola, Panasonic, Rogers, Shengyi…) at any frequency, plus solder masks and copper foil roughness.

Thermal

Junction Temperature – Junction temperature from power and the thermal-resistance chain (θJA or θJC + θCS + θSA), and the maximum power for a Tj limit.
Thermal Via Array – Thermal resistance of a via array under a hot pad, with plugged or filled vias, and the temperature drop through the board.
Copper Area for Heat Spreading – How much copper a hot part needs: copper-pour thermal resistance by convection and radiation, junction temperature and the smallest pour for a Tj limit.

Power & conductors

Trace Width, Current & Temperature Rise – IPC-2221: width for a current, current for a width, or temperature rise of a trace, with resistance, voltage drop and loss.
Via Calculator – Via current capacity, resistance, thermal resistance, capacitance, inductance and rise-time impact.
Skin Effect & AC Resistance – Skin depth in copper and the AC resistance of a trace across frequency.
Fusing Current – Current that melts a trace in a given time (Onderdonk), for fault and surge analysis.
Wire Gauge & Voltage Drop – AWG diameter, area and resistance, cable voltage drop and loss, the smallest gauge for a drop limit, and Preece fusing current.
Conductor Spacing (IPC-2221) – Minimum electrical clearance between conductors from IPC-2221 Table 6-1: internal, external, coated, high altitude, assemblies.
Creepage & Clearance (IEC 60664-1) – Minimum clearance and creepage per IEC 60664-1: impulse voltage from mains and overvoltage category, pollution degree, CTI material group, reinforced insulation, altitude.

Power integrity

PDN Impedance Calculator – Target impedance, plane-pair capacitance, decoupling-capacitor resonance and the number of capacitors needed, with a log-log |Z|(f) plot.
EMI Filter Designer – Differential-mode LC, π and ferrite-bead filters: loaded attenuation, parasitics, resonance, RC damping, DC loss and preferred component values.

Power supply

Power Tree Planner – Budget source and regulator currents across cascaded rails and loads, estimate losses, check ratings and record power-up dependencies.
Buck Converter Calculator – Buck power-stage sizing with conduction-mode checks, real inductor and capacitor ratings, IC timing limits and current waveforms across the input range.
Boost Converter Calculator – Boost power-stage sizing with conduction-mode checks, real inductor and capacitor ratings, IC timing limits and current waveforms across the input range.
LDO Regulator Power Dissipation – Linear regulator dissipation, junction temperature, efficiency and dropout headroom, with the maximum load for a Tj limit.
Feedback Resistor Divider – Standard-value R1/R2 for adjustable regulators: the best E12/E24/E96 pairs, output error, FB bias current and worst case with tolerance.

Components

Planar Spiral Inductor – Inductance of square, hexagonal, octagonal and circular PCB spirals (modified Wheeler and current-sheet models), with DC resistance and Q.
Through-Hole Padstack Calculator – Plated through-hole sizing per IPC-7251 / IPC-2221 / IPC-2222: hole, outer and inner pads, antipad, thermal relief and annular ring for levels A/B/C.
Two-Terminal SMD Land Pattern Calculator – Size the two copper pads, pitch, courtyard and solder-mask openings for a chip resistor or MLCC from the exact part dimensions and process tolerances.
BGA Land Pattern – IPC-7351 land diameter for collapsing and non-collapsing BGA balls, with tolerance and courtyard, and escape-routing capacity between lands.
Resistor Color Code Calculator – Value, tolerance and temperature coefficient of 4-, 5- and 6-band resistors from their colours (IEC 60062), and the bands for any value.
SMD Resistor Code Calculator – Decode 3-digit, 4-digit and EIA-96 SMD resistor markings and R/m decimal notation, and find the code for any value.
Capacitor Code Calculator – Decode capacitor markings such as 104K and 2A473J: value, tolerance letter, voltage code, and dielectric codes such as X7R and C0G.

Electronics

Ohm's Law & Power – Enter any two of voltage, current, resistance and power to get the other two.
Reactance & LC Resonance – XL and XC at a frequency, LC resonance, the L or C for a target frequency, and series/parallel LC impedance with Q.
RC Low-Pass & High-Pass Filter Calculator – Passive RC low-pass and high-pass filters with source/load resistance, standard component selection, tolerance bounds and interactive gain and phase plots.
Active Filter Designer – Sallen-Key and MFB low-pass and high-pass filters to 8th order (Butterworth, Bessel, Chebyshev): component values, standard-value response, and op amp GBW and slew-rate requirements.
Op-Amp Gain Calculator – Inverting, non-inverting, difference and summing stages: noise gain, bandwidth, output swing, DC offset, noise and resistor tolerance, with standard-value pairs for a target gain.
Crystal Load Capacitors & PPM Budget – Crystal load capacitors with the nearest E12/E24 values and the pulling they cause, a ppm frequency budget checked against USB, Ethernet, PCIe and SATA clock tolerances, and ppm ↔ frequency error and drift.
555 Timer Calculator – Astable frequency and duty cycle, resistor values for a target frequency, and monostable pulse width, from the TI NE555 equations.
Logic-Level Compatibility Checker – Check worst-case VOH/VOL against VIH/VIL, static noise margins and receiver input-voltage limits.
Comparator Hysteresis Calculator – Inverting and non-inverting switching thresholds: design reference and feedback resistors, choose standard values and check resistor, offset and reference uncertainty.
ADC Input Settling Checker – SAR ADC source and RC filter settling during acquisition, filter-node recovery, and an optional DC accuracy budget for offset, gain, reference, INL and quantisation.
NTC Thermistor Calculator – Beta and Steinhart–Hart models with coefficient fitting, a thermistor divider into an ADC with °C/LSB, series-resistor choice, self-heating, tolerance error and a CSV or C lookup table.
Current-Sense Shunt Selector – Select a shunt from current range and voltage-drop budget, with power, tolerance, TCR and amplifier-offset checks.
Resistor Tools – Voltage divider with best E12/E24/E96 pairs, LED series resistor with power rating, and series/parallel R, C and L.
Attenuator Pads – Matched Pi, T and bridged-T pads with the nearest standard values, their actual loss and return loss, and resistor power.

Utilities

Gerber Viewer & Compare – Inspect one Gerber layout or compare two PCB revisions, choose layers independently and highlight added, removed and common geometry. Files stay on your device.
Unit Converter – Length, copper weight, temperature, power (dBm/W/V) and frequency/wavelength.
Reference Charts – Drill sizes (number, letter, fractional, metric), ISO metric and Unified threads with tap and clearance drills, and the AWG wire table.