¿Qué es el Efecto Piel?
El efecto piel es un fenómeno electromagnético fundamental donde la corriente alterna (AC) tiende a fluir principalmente cerca de la superficie externa de un conductor, en lugar de uniformemente a través de su sección transversal. A altas frecuencias, esta concentración de corriente en la "piel" del conductor reduce efectivamente el área conductora utilizable, aumentando dramáticamente la resistencia AC en comparación con la resistencia DC.
Perspectiva Clave
En DC (0 Hz), la corriente se distribuye uniformemente a través de la sección transversal de un conductor. A medida que aumenta la frecuencia, la corriente se concentra hacia la superficie debido a la inducción electromagnética. Esto no es un defecto del material o un problema de fabricación: es una ley fundamental de la física que afecta a todos los conductores.
For modern high-speed digital interfaces like PCIe Gen4/5 (8-32 GT/s, with harmonics to 25+ GHz) or 100G Ethernet (56 Gbaud PAM4), skin effect is the dominant source of conductor loss and must be carefully managed through trace geometry, copper quality, and material selection.
Por qué el Efecto Piel es Importante para el Diseño de PCB
- Pérdida de inserción aumentada: A 10 GHz, una traza PCB puede tener una resistencia 10-20× mayor que en DC, atenuando directamente la amplitud de la señal
- Comportamiento dependiente de la frecuencia: La pérdida aumenta con √frecuencia, haciendo que los componentes de alta frecuencia de señales rápidas sufran más atenuación que las frecuencias bajas
- Cierre del diagrama de ojo: La pérdida excesiva reduce la altura y el ancho del ojo, aumentando la tasa de error de bits (BER) y potencialmente requiriendo retransmisión o ecualización
- Agotamiento del presupuesto del enlace: Los protocolos de alta velocidad tienen presupuestos estrictos de pérdida de inserción (por ejemplo, PCIe Gen5 permite ~28 dB en Nyquist). El efecto piel puede consumir la mitad o más de este presupuesto
Comprender el efecto piel le permite tomar decisiones informadas sobre el ancho de traza, el peso del cobre, el acabado de la superficie y la selección de materiales para minimizar las pérdidas y cumplir con sus requisitos de integridad de señal.
Física y Principios Electromagnéticos
Para diseñar correctamente para el efecto piel, es útil comprender la física subyacente. El efecto piel surge de la inducción electromagnética y la ley de Faraday.
El Mecanismo
- 1Alternating current creates a time-varying magnetic field: When AC flows through a conductor, it generates a magnetic field that oscillates at the same frequency as the current (Ampère's Law: ∇×H = J).
- 2The magnetic field induces eddy currents: This time-varying magnetic field penetrates the conductor and induces circulating eddy currents within it (Faraday's Law: ∇×E = -∂B/∂t).
- 3Eddy currents oppose the main current: By Lenz's Law, the induced eddy currents create their own magnetic field that opposes the change in the original field. The eddy currents flow in a direction that opposes the main current in the center of the conductor.
- 4Current crowds to the surface: The opposition is strongest at the center and weakest at the surface. This causes current density to be highest at the conductor surface and decay exponentially toward the center.
Descripción Matemática
The current density J as a function of depth x from the surface follows an exponential decay:
// Densidad de corriente vs profundidad
J(x) = J₀ · e^(-x/δ)
Donde:
J₀ = densidad de corriente superficial
x = profundidad desde la superficie
δ = profundidad pelicular (donde J cae al 37% de J₀)
Significado Práctico
Aproximadamente el 63% de la corriente total fluye dentro de una profundidad pelicular desde la superficie. El 86% fluye dentro de dos profundidades peliculares, y el 95% dentro de tres. Más allá de 3-4 profundidades peliculares, la corriente es despreciable.
Esto significa que una vez que el espesor de cobre excede aproximadamente 3-4× la profundidad pelicular, hacerlo más grueso proporciona casi ningún beneficio para la resistencia de CA a esa frecuencia. Por eso el cobre ultra-grueso (4 oz, 6 oz) no ayuda para señales de alta velocidad - solo ayuda para la capacidad de corriente DC.
Fórmula y Cálculos de Profundidad Pelicular
La profundidad pelicular (δ) es la distancia desde la superficie del conductor a la cual la densidad de corriente ha disminuido a 1/e (aproximadamente 37%) de su valor en la superficie. Cuantifica qué tan profundamente penetra la corriente de CA.
Fórmula General
// Skin depth general formula
δ = √(ρ / (π · f · μ))
Where:
δ = skin depth (meters)
ρ = resistivity of conductor (Ω·m)
f = frequency (Hz)
μ = permeability (H/m) = μᵣ · μ₀
μ₀ = 4π × 10⁻⁷ H/m (permeability of free space)
Fórmula Simplificada para Cobre
Para cobre a 20°C con ρ = 1.68×10⁻⁸ Ω·m y μᵣ = 1 (no magnético), la fórmula se simplifica a:
Unidades Métricas
δ(mm) = 66 / √f(MHz)
or
δ(μm) = 66000 / √f(MHz)
Unidades Imperiales
δ(mil) = 2600 / √f(MHz)
or
δ(mil) = 82.2 / √f(GHz)
Ejemplos de Cálculos
Example 1: 1 GHz (PCIe Gen3, 10G Ethernet)
f = 1 GHz = 1000 MHz
δ = 66 / √1000 = 66 / 31.62 = 2.09 μm (0.082 mil)
This is only 6% of 1 oz copper thickness (35 μm)
Example 2: 10 GHz (PCIe Gen5, 25G SerDes)
f = 10 GHz = 10000 MHz
δ = 66 / √10000 = 66 / 100 = 0.66 μm (0.026 mil)
This is only 2% of 1 oz copper - most copper is unused!
Example 3: 28 GHz (56G PAM4, 5G mmWave)
f = 28 GHz = 28000 MHz
δ = 66 / √28000 = 66 / 167.3 = 0.39 μm (0.015 mil)
Comparable to copper grain size - extreme regime!
Efectos de Temperatura
La resistividad del cobre aumenta con la temperatura (~0.4%/°C), lo que aumenta ligeramente la profundidad pelicular. Sin embargo, este efecto es pequeño comparado con la variación de frecuencia. Para la mayoría del trabajo de PCB a temperaturas de operación típicas (0-85°C), usar los valores a 20°C es suficiente. Para ambientes extremos (>100°C), use:
Skin Effect at Different Frequencies
This comprehensive table shows how skin depth varies with frequency and its practical impact on PCB trace design. Reference: 1 oz copper = 35 μm (1.4 mil) finished thickness.
| Frequency | Skin Depth | vs 1oz Cu | Impact | Typical Uses |
|---|---|---|---|---|
| 100 kHz | 0.21 mm (8.3 mil) | 600% de Cu 1 oz | Despreciable - Resistencia DC domina | Audio, Conmutación de potencia |
| 1 MHz | 66 μm (2.6 mil) | 189% de Cu 1 oz | Despreciable para trazas PCB | Electrónica de potencia, EMI |
| 10 MHz | 21 μm (0.83 mil) | 60% de Cu 1 oz | Comienza a importar - ~1.5× DC R | Buses paralelos de alta velocidad |
| 100 MHz | 6.6 μm (0.26 mil) | 19% de Cu 1 oz | Significativo - ~3× DC R | Fast Ethernet, USB 2.0 |
| 1 GHz | 2.1 μm (0.08 mil) | 6% de Cu 1 oz | Domina la pérdida - ~10× DC R | PCIe Gen3, 10G Ethernet |
| 10 GHz | 0.66 μm (0.026 mil) | 2% de Cu 1 oz | Crítico + efectos de rugosidad | PCIe Gen4/5, 25G+ SerDes |
| 28 GHz | 0.39 μm (0.015 mil) | 1.1% de Cu 1 oz | Extremo - Cobre VLP requerido | 56G PAM4, 5G mmWave |
Key Takeaway: The √f Relationship
Notice that skin depth is inversely proportional to the square root of frequency. This means:
- • Doubling frequency reduces skin depth by ~29% (factor of √2 = 1.41)
- • 10× frequency reduces skin depth by ~68% (factor of √10 = 3.16)
- • Going from 1 GHz to 10 GHz reduces skin depth from 2.1 μm to 0.66 μm
Since AC resistance is inversely proportional to the conductive area (which shrinks with skin depth), resistance increases as √f. This is why conductor loss increases roughly linearly with frequency on a dB scale.
Impact on PCB Trace Resistance
As skin depth decreases with frequency, the effective resistance of a PCB trace increases dramatically. This is the primary mechanism of conductor loss in high-speed transmission lines.
AC Resistance vs DC Resistance
For a rectangular trace (typical PCB microstrip or stripline), the DC resistance is:
// DC resistance
R_DC = ρ · L / (W · T)
Where:
ρ = resistivity (1.68×10⁻⁸ Ω·m for copper)
L = trace length (m)
W = trace width (m)
T = trace thickness (m)
At high frequencies where skin effect dominates, the effective thickness becomes limited by skin depth:
// AC resistance (simplified, rectangular trace)
R_AC ≈ ρ · L / (W · δ) for T >> δ
Resistance ratio:
R_AC / R_DC ≈ T / δ (when T > 3δ)
Practical Example: 50Ω Microstrip at 10 GHz
Scenario:
- • Trace: 5 mil wide, 1 oz copper (1.4 mil thick), 2 inch long
- • Substrate: FR-4, εᵣ = 4.3, h = 8 mil
- • Frequency: 10 GHz, skin depth = 0.66 μm = 0.026 mil
DC resistance:
R_DC = 1.68×10⁻⁸ × 0.0508 / (0.000127 × 0.0000356) = 0.19 Ω
AC resistance at 10 GHz:
δ = 0.66 μm, T/δ = 35 μm / 0.66 μm = 53
R_AC ≈ 53 × R_DC = 10 Ω
Result: At 10 GHz, this trace has ~53× higher resistance than at DC! For a 2-inch trace, that's 10Ω of resistance. For a 50Ω transmission line carrying a 1V signal, the voltage drop is significant.
Insertion Loss Calculation
Conductor loss in dB per unit length is commonly expressed as:
// Conductor loss (dB/inch)
Loss = 0.433 × R_AC / Z₀
Where:
R_AC = AC resistance per unit length (Ω/inch)
Z₀ = characteristic impedance (typically 50Ω or 100Ω diff)
0.433 = conversion factor (ln(10)/20)
For our example above (10Ω for 2 inches = 5 Ω/inch):
Loss = 0.433 × 5 / 50 = 0.043 dB/inch
For 10 inches: 0.43 dB total conductor loss at 10 GHz
Why This Matters
High-speed protocols have strict loss budgets. For example:
- • PCIe Gen5 (32 GT/s): Max ~28 dB insertion loss at 16 GHz (Nyquist)
- • USB4 (40 Gbps): Max ~20 dB at 20 GHz
- • 100G Ethernet (56 Gbaud PAM4): Max ~30 dB at 28 GHz
Con trazas largas, conectores, vías y otras discontinuidades, cada 0.1 dB importa. Minimizar la pérdida del conductor a través del diseño adecuado es esencial.
Frequently Asked Questions
¿Qué es el efecto piel y por qué ocurre?
El efecto piel es la tendencia de la corriente alterna (CA) a fluir principalmente cerca de la superficie de un conductor, en lugar de uniformemente a través de su sección transversal. Ocurre debido a la inducción electromagnética: la corriente cambiante crea un campo magnético que induce corrientes de Foucault dentro del conductor. Estas corrientes de Foucault se oponen a la corriente principal en el centro y la refuerzan en la superficie, empujando la corriente hacia los bordes. Cuanto mayor es la frecuencia, más fuerte es este efecto. Esto reduce efectivamente el área conductora utilizable, aumentando la resistencia CA en comparación con la resistencia CC.
How do I calculate skin depth for copper?
Skin depth (δ) for copper is calculated using: δ = √(ρ / πfμ), where ρ is resistivity (1.68×10⁻⁸ Ω·m for copper), f is frequency in Hz, and μ is permeability (μ₀ = 4π×10⁻⁷ H/m for copper). A simplified formula for copper at 20°C is: δ(mm) ≈ 66 / √f(MHz). For example, at 1 GHz: δ = 66/√1000 ≈ 2.1 μm. At 10 GHz: δ ≈ 0.66 μm. This is the depth where current density drops to 37% (1/e) of the surface value.
When does skin effect become significant for PCB design?
Skin effect becomes noticeable above 10 MHz and significant above 100 MHz. For 1 oz copper (35 μm thick), skin depth equals the copper thickness at ~9 MHz. Above this frequency, increasing copper thickness doesn't reduce AC resistance. At 1 GHz, skin depth is only 2.1 μm - just 6% of 1 oz copper thickness - so the AC resistance is roughly 10× the DC resistance. For high-speed digital (>1 Gbps), skin effect is the dominant source of conductor loss and must be carefully managed through trace width optimization and copper surface quality.
Why does copper surface roughness matter at high frequencies?
When skin depth approaches the scale of copper surface roughness (Rz), current must travel a longer path following the rough surface profile rather than a smooth path. Standard electrodeposited (ED) copper has Rz of 8-12 μm with a tooth profile for adhesion. At 10 GHz where skin depth is 0.66 μm, this roughness increases the effective path length by 20-40%, directly increasing loss. The Hammerstad-Bekkadal model quantifies this: loss increases by factor of [1 + (2/π)arctan(1.4(Rz/δ)²)]. Very Low Profile (VLP) copper with Rz <2 μm can reduce loss by 20-30% at 10+ GHz compared to standard copper.
What's the difference between conductor loss and dielectric loss?
Conductor loss (skin effect resistance) is caused by finite conductivity of copper and increases with √frequency due to skin effect. Dielectric loss is caused by energy absorption in the insulating material (PCB substrate) and increases linearly with frequency. At low frequencies (<1 GHz), conductor loss dominates. At very high frequencies (>10 GHz), both contribute significantly. The crossover depends on material: standard FR-4 has high dielectric loss, so conductor loss dominates to ~5 GHz. Low-loss materials like Megtron 6 have lower dielectric loss, so conductor loss dominates to higher frequencies. Total loss is the sum of both.
Does thicker copper help at high frequencies?
Thicker copper helps significantly for DC and low-frequency AC current capacity and voltage drop. However, for high-frequency signals (>100 MHz), once copper thickness exceeds about 3× skin depth, further thickness provides minimal benefit for AC resistance. At 1 GHz, 3δ = 6.3 μm - much less than even 0.5 oz copper (17.5 μm). The benefit of thicker copper at high frequency comes primarily from increased trace width (more perimeter for current), not thickness. Use 0.5-1 oz copper for high-speed signals. Use 2 oz+ only for power/ground planes where DC current capacity matters.
How do I specify low-roughness copper for my PCB?
Include copper roughness requirements in your PCB fabrication notes and stackup specification. For signals >10 Gbps, specify 'Low Profile (LP) or VLP copper on signal layers, Rz <3 μm maximum'. For >25 Gbps, specify 'VLP copper, Rz <2 μm'. Request RTF (reverse-treated foil) instead of standard ED foil. Not all fabricators offer VLP copper, and it increases cost by 10-30%. Verify fab capability before finalizing design. Premium materials like Megtron 6/7 often come with smoother copper as standard. Always request a cross-section analysis to verify roughness in manufactured boards.
What are the Hammerstad and Huray roughness models?
These are mathematical models to predict how copper roughness increases high-frequency loss. The Hammerstad-Bekkadal model (1986) is simpler and uses the roughness parameter Rz (peak-to-valley height): Loss multiplier = 1 + (2/π) × arctan[1.4 × (Rz/δ)²]. The Huray model (2010) is more accurate and models roughness as spherical nodules on the surface. It requires more detailed roughness characterization but better predicts loss at very high frequencies. Most PCB design tools use Hammerstad for simplicity. For designs >25 GHz, consider Huray model with roughness data from your fabricator.