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Module 3.3 - Power & Ground Planes

Plane pair design, current density management, copper weight selection, and resonance control

Checkpoint 1: Plane Pairs Closely Coupled (< 4mil Dielectric) Critical

A closely-spaced power/ground plane pair acts as a distributed capacitor across the entire board area. This plane capacitance provides high-frequency decoupling (above 500MHz) that discrete capacitors cannot achieve due to their mounting inductance. The closer the planes, the higher the capacitance per unit area and the lower the spreading inductance.

Plane Capacitance Formula

C_plane = (epsilon_0 * epsilon_r * A) / d

Where:
  epsilon_0 = 8.854e-12 F/m (permittivity of free space)
  epsilon_r = relative permittivity of dielectric (FR4: 4.2-4.5)
  A = overlapping plane area (m^2)
  d = dielectric thickness between planes (m)

Example: 100mm x 100mm board, FR4 (er=4.3), 3mil (76um) spacing:
C_plane = (8.854e-12 * 4.3 * 0.01) / 76e-6 = 5.01 nF

Capacitance density:
  2 mil spacing: 2.37 nF/cm2 (23.7 pF/mm2)
  3 mil spacing: 1.58 nF/cm2 (15.8 pF/mm2)
  4 mil spacing: 1.19 nF/cm2 (11.9 pF/mm2)
  8 mil spacing: 0.59 nF/cm2 (5.9 pF/mm2)

Spreading Inductance vs. Dielectric Thickness

Inductance per square of plane pair:
L_square = mu_0 * d = 4*pi*1e-7 * d

  2 mil (50um): L = 63 pH/square
  3 mil (76um): L = 95 pH/square
  4 mil (100um): L = 126 pH/square
  8 mil (200um): L = 251 pH/square

Thinner dielectric = Lower spreading inductance = Better HF performance

Stackup Design for Optimal PI

  1. Place primary power/ground plane pair on adjacent inner layers with thinnest possible dielectric (2-4 mil prepreg).
  2. For multi-power-rail designs, dedicate the tightest plane pair to the lowest-impedance supply (typically VCCINT/FPGA core).
  3. Maintain symmetry in stackup to prevent board warpage during lamination.
  4. Use high-Dk dielectric materials (Dk > 4) between plane pairs for maximum capacitance.
  5. Verify with your fabricator that the specified thin dielectric is achievable and repeatable.

Example Stackup (12-layer FPGA board)

Layer  Type      Material         Thickness   Purpose
--------------------------------------------------------------
L1     Signal    Copper 1oz       1.2 mil     Top components/routing
       Prepreg   FR4 2116         4.0 mil
L2     Power     Copper 1oz       1.2 mil     VCCINT (0.85V)
       Core      FR4              2.0 mil     ** TIGHT COUPLING **
L3     Ground    Copper 1oz       1.2 mil     GND (primary reference)
       Prepreg   FR4 1080         3.0 mil
L4     Signal    Copper 0.5oz     0.6 mil     High-speed routing
       Core      FR4              8.0 mil
L5     Signal    Copper 0.5oz     0.6 mil     General routing
       Prepreg   FR4 2116         4.0 mil
L6     Power     Copper 1oz       1.2 mil     3.3V
       Core      FR4              3.0 mil     ** COUPLED **
L7     Ground    Copper 1oz       1.2 mil     GND (secondary)
       Prepreg   FR4 2116         4.0 mil
L8     Signal    Copper 0.5oz     0.6 mil     General routing
       Core      FR4              8.0 mil
L9     Signal    Copper 0.5oz     0.6 mil     High-speed routing
       Prepreg   FR4 1080         3.0 mil
L10    Ground    Copper 1oz       1.2 mil     GND (tertiary)
       Core      FR4              2.0 mil     ** TIGHT COUPLING **
L11    Power     Copper 1oz       1.2 mil     1.8V
       Prepreg   FR4 2116         4.0 mil
L12    Signal    Copper 1oz       1.2 mil     Bottom components/routing
--------------------------------------------------------------
Total thickness: ~62 mil (1.57 mm)
            
L2-L3 plane pair with 2mil core:
- VCCINT/GND pair spacing: 2 mils (50um)
- Board area: 150mm x 100mm = 150 cm2
- Plane capacitance: 2.37 nF/cm2 * 150 cm2 = 355 nF distributed
- Spreading inductance: 63 pH/square -- excellent for GHz operation
- Equivalent to ~350x 1nF discrete caps distributed perfectly across the board!
Power and ground planes separated by 20mil core:
- Spacing: 20 mils (508um)
- Plane capacitance: 0.3 nF/cm2 * 150 cm2 = 45 nF (7.9x less)
- Spreading inductance: 638 pH/square (10x worse)
- Capacitor effectiveness limited above 200MHz due to high spreading inductance
- Requires 3-5x more discrete capacitors to compensate (cost and area penalty)
  • Fabricator minimum dielectric: Not all fabs can hold 2mil reliably. Verify capability. 3mil is safe for most Class 2 fabricators.
  • Thin dielectric with heavy copper: 2oz copper with 2mil dielectric may not laminate well. Use 1oz or 0.5oz on thin cores.
  • Ignoring registration tolerance: Thin dielectrics amplify the effect of layer-to-layer misregistration on impedance control.
  • Not specifying core vs prepreg: Cores have tighter thickness tolerance than prepregs. Use core material for critical plane pairs.

Checkpoint 2: No Unnecessary Plane Splits Critical

Every split (gap, cutout, or void) in a power or ground plane creates an impedance discontinuity, increases current path length, reduces plane capacitance, and can create a slot antenna that radiates EMI. Plane splits should only exist where electrically necessary (different voltage domains) and never as an artifact of careless routing.

Impact of Plane Splits

A slot (split) in a plane with width W and length L creates:

Additional inductance: L_slot = (mu_0 * L * W) / (2 * pi * d) [approximate]
Radiation potential: f_resonant = c / (2 * L * sqrt(epsilon_r))

Example: 50mm long slot, 0.5mm wide, in GND plane with 4mil dielectric:
L_slot = (4*pi*1e-7 * 0.05 * 0.0005) / (2*pi * 0.1e-3) = ~50 nH

Slot resonance: f = 3e8 / (2 * 0.05 * sqrt(4.3)) = 1.45 GHz
At this frequency, the slot becomes an efficient radiator (EMI issue)

How to Check for Plane Splits

  1. In PCB layout tool, view each power/ground plane layer individually.
  2. Look for any gaps, channels, or narrow necks in the copper pour.
  3. Check for routing channels that cut through planes (common in auto-routed boards).
  4. Verify no thermal relief spokes create effective splits between plane regions.
  5. Check via fields (BGA areas) -- dense via patterns can create Swiss cheese effect that fragments the plane.
  6. Use DRC/connectivity check to verify all plane regions are electrically connected.

Acceptable vs. Unacceptable Splits

Necessary split with proper handling:
Analog ground (AGND) separated from digital ground (DGND) per IC manufacturer requirement.
- Split is straight, narrow (10mil gap), and short (15mm)
- Single-point connection at the ADC star ground pin
- No high-speed signals cross the split boundary
- Stitching capacitors (10nF) every 5mm along the split for HF continuity
- Return current paths verified for all signals near the split
Unnecessary split from careless routing:
Auto-router placed a trace on the ground plane layer to complete a connection.
- Creates a 40mm split in the ground plane
- 12 high-speed signals cross over the split without any return path
- These signals now radiate as a loop antenna (6dB increase in radiated emissions)
- Crosstalk between the 12 signals increases by 15-20dB due to shared return discontinuity
Allegro/OrCAD: Display > Plane Analysis > Show Plane Coverage. Look for islands or narrow connections.

Altium Designer: Design > Board Shape > Show Board Outline vs copper fill. Use Design Rule Check for minimum plane copper width.

Sigrity PowerSI: Use "Current Density" analysis to see where current is forced through narrow paths (indicating effective splits).

Checkpoint 3: Split Planes with Stitching Capacitors Major

When plane splits are necessary (different voltage domains, analog/digital separation), stitching capacitors provide a low-impedance AC path across the split at high frequencies. This maintains signal return path continuity and reduces EMI radiation from the slot.

Stitching Capacitor Selection

Stitching cap value selection:
- Minimum frequency of concern: f_min
- Maximum impedance at f_min: Z_max (typically < 1 ohm)
- Capacitance needed: C >= 1 / (2*pi*f_min*Z_max)

Example: f_min = 10 MHz, Z_max = 0.5 ohm
C >= 1/(2*pi*10e6*0.5) = 31.8 nF --> use 100nF

Spacing between stitching caps:
d_max = lambda/20 at highest frequency of concern
At 1 GHz in FR4: lambda = 146mm, d_max = 7.3mm
At 3 GHz in FR4: lambda = 49mm, d_max = 2.4mm

Practical rule: Place one stitching cap every 5-10mm along the split.

Placement Rules

  1. Place stitching caps across the split at regular intervals (every 5-10mm for GHz designs).
  2. Always place a stitching cap at each point where a signal trace crosses the split.
  3. Place caps as close to the split as possible (within 1mm of the gap edge).
  4. Use 100nF X7R 0402 as standard stitching cap value (good from 1MHz to 100MHz).
  5. For GHz applications, add parallel 1nF C0G caps for extended high-frequency coverage.
  6. Connect capacitor ground pads to respective planes with short, low-inductance paths (via-in-pad preferred).
Proper stitching across analog/digital ground split:
Split length: 30mm, highest signal frequency crossing: 500 MHz
- 6x 100nF 0402 X7R spaced 5mm apart along the split
- 6x 1nF 0201 C0G co-located with each 100nF cap
- Additional cap pair at each of the 3 signal crossing points
- Impedance across split: < 50 mOhm from 5MHz to 500MHz
- Signal return path disruption: < 2dB (negligible)
Missing stitching caps on power plane split:
Two power domains (1.8V and 3.3V) share a plane layer with a split.
No stitching caps placed. 8 high-speed SPI signals cross the split.
- Return current forced around 40mm split end
- Loop area: 8 signals * 40mm * 0.2mm trace height = 64 mm2 per signal
- Radiated emissions fail by 15dB at 400 MHz
- Crosstalk: -25dB (specification: -40dB) -- communication errors

Checkpoint 4: Current Density Uniform Major

Non-uniform current density in power planes creates localized heating (hot spots), increased voltage drop, and potential reliability issues. Current tends to crowd at narrow necks, sharp corners, and near via clusters. Simulation is the only reliable way to verify current density distribution.

Current Density Limits

Maximum recommended current densities (IPC guidelines):

Internal plane (1oz copper, 35um):
  Continuous: 15 A/mm width (for 10C rise)
  Conservative: 10 A/mm width

External plane (1oz copper, 35um):
  Continuous: 25 A/mm width (for 10C rise, with airflow)
  Conservative: 15 A/mm width

Current density: J = I / (W * t)
Where W = width, t = copper thickness

1oz copper = 35um = 0.035mm
For 20A through 50mm wide plane: J = 20/(50*0.035) = 11.4 A/mm2
This is well within limits for uniform distribution.

How to Identify Hot Spots

  1. Run DC IR-drop simulation (Sigrity PowerDC or SIwave DCIR) with maximum load currents.
  2. Examine current density map -- look for red/yellow regions indicating high density.
  3. Identify bottlenecks: narrow plane sections, connector areas, via clusters.
  4. Check current density at all plane necks (areas where width is constrained by cutouts or other nets).
  5. Verify temperature rise at hot spots is within board material limits (FR4: +50C max over ambient).
  6. Widen narrow sections or add copper relief to reduce current crowding.
Uniform current distribution verified by simulation:
VCCINT plane carrying 20A:
- Plane width at narrowest point: 40mm
- Current density at narrow point: 20A / (40mm * 0.035mm) = 14.3 A/mm2
- No point exceeds 20 A/mm2
- Temperature rise at hottest spot: 8C above ambient
- IR drop from VRM to farthest IC: 12mV (within 1.5% of 0.85V rail)
Current crowding at plane neck:
20A plane has a 5mm wide neck where a cutout for a connector exists.
Current density at neck: 20A / (5mm * 0.035mm) = 114 A/mm2 (8x over limit!)
Temperature rise: 45C above ambient (approaching Tg of FR4!)
Long-term reliability: Copper migration, delamination, and eventual failure.
Sigrity PowerDC: Setup > DC Analysis > Set current sources/sinks > Solve. View "Current Density Map" in results. Use threshold coloring to highlight violations.

Ansys SIwave DCIR: HFSS > DC IR Drop > Define sources/sinks > Solve. "J Map" shows current density with thermal overlay.

HyperLynx PI: DC Drop Analysis > Set loads > Run. Current density view shows crowding with adjustable threshold.

Checkpoint 5: Plane Resonance Above Operating Frequency Major

Power/ground plane pairs behave as resonant cavities at frequencies where the board dimensions are multiples of the half-wavelength. At these resonant frequencies, the plane impedance shows sharp peaks that can amplify power supply noise and cause EMI radiation at board edges.

Plane Resonance Frequency Calculation

Rectangular board resonance frequencies:

f_mn = (c / (2*sqrt(epsilon_r))) * sqrt((m/L)^2 + (n/W)^2)

Where:
  c = 3e8 m/s (speed of light)
  epsilon_r = dielectric constant (FR4 ~ 4.3)
  L = board length (m)
  W = board width (m)
  m, n = mode integers (0, 1, 2, 3...)

Fundamental modes for 100mm x 80mm board (FR4, er=4.3):
  f_10 = (3e8/(2*sqrt(4.3))) * (1/0.1) = 723 MHz
  f_01 = (3e8/(2*sqrt(4.3))) * (1/0.08) = 903 MHz
  f_11 = (3e8/(2*sqrt(4.3))) * sqrt((1/0.1)^2+(1/0.08)^2) = 1.16 GHz
  f_20 = 1.45 GHz, f_02 = 1.81 GHz, ...

Resonance Mitigation Strategies

Board resonance well above operating frequency:
Board: 60mm x 40mm, FR4, 3mil plane pair
f_10 = (3e8/(2*2.07)) * (1/0.06) = 1.21 GHz
System clock: 100 MHz (f_knee = 350MHz at 1ns rise time)
First resonance (1.21 GHz) is 3.5x above f_knee -- safe margin.
Added precaution: 10x 1nF 0201 caps along board edges damp residual resonance.
Plane resonance coincides with clock harmonic:
Board: 200mm x 150mm, FR4
f_10 = (3e8/(2*2.07)) * (1/0.2) = 362 MHz
System has 100 MHz clock with significant 3rd harmonic content at 300 MHz and 5th at 500 MHz.
The f_01 = 483 MHz is close to the 5th harmonic!
Result: Plane resonance amplifies clock noise at 483 MHz by 20dB.
Board edges radiate at this frequency -- fails FCC Class B by 8dB.
  • Ignoring resonance for small boards: A 30mm x 30mm board has f_10 = 2.4GHz. Safe for most designs, but not for 10G+ SerDes.
  • Not considering plane shape: Irregular planes have different resonant modes than simple rectangles. Simulation required for complex shapes.
  • 20H rule as sole mitigation: The 20H rule only reduces edge radiation by 3-6dB. It is not sufficient for resonance control alone.

Checkpoint 6: Adequate Copper Weight for Current Critical

Copper planes must carry the required current without excessive temperature rise. IPC-2152 provides the standard methodology for determining required copper area (width x thickness) based on current, acceptable temperature rise, and whether the conductor is internal or external.

IPC-2152 Current Capacity Calculation

IPC-2152 formula (simplified, for internal layers):

I = k * dT^0.44 * A^0.725

Where:
  I = current capacity (A)
  k = 0.024 (internal layers), 0.048 (external layers)
  dT = temperature rise above ambient (C)
  A = cross-sectional area (mil^2) = Width(mil) * Thickness(mil)

Copper thickness per weight:
  0.5 oz = 0.7 mil (17.5 um)
  1 oz = 1.4 mil (35 um)
  2 oz = 2.8 mil (70 um)
  3 oz = 4.2 mil (105 um)

Example: Internal plane, 1oz copper, 20mm (787mil) wide, 20C rise:
A = 787 * 1.4 = 1102 mil^2
I = 0.024 * 20^0.44 * 1102^0.725 = 0.024 * 3.89 * 197.6 = 18.4A

For 20A requirement: Need wider plane or heavier copper.

Copper Weight Selection Guide

Current (A) 0.5oz Internal 1oz Internal 2oz Internal 2oz External
5A 8mm wide 4mm wide 2mm wide 1mm wide
10A 20mm wide 10mm wide 5mm wide 2.5mm wide
20A 50mm wide 25mm wide 12mm wide 5mm wide
40A Full plane 60mm wide 28mm wide 12mm wide

Values assume 20C temperature rise above ambient, FR4 substrate. Conservative; verify with IPC-2152 charts or simulation.

Proper copper specification for high-current design:
Requirement: 30A on VCORE plane, internal layer
- Selected: 2oz copper (2.8 mil thickness)
- Minimum plane width at any point: 20mm (verified by simulation)
- Cross-section: 20mm * 70um = 1.4 mm2
- Current density: 30A / 1.4mm2 = 21.4 A/mm2
- Simulated temperature rise: 15C (within 20C budget)
- IR drop across plane: 8mV (0.9% of 0.85V rail) -- acceptable
Insufficient copper for power delivery:
Requirement: 30A on VCORE, but designer used 0.5oz copper
- Plane has 15mm neck near mounting hole
- Cross-section at neck: 15mm * 17.5um = 0.26 mm2
- Current density at neck: 30A / 0.26mm2 = 115 A/mm2!
- Temperature rise: 80C+ (board delamination risk)
- IR drop at neck: 50mV (5.9% of 0.85V) -- exceeds voltage tolerance