What is the formula for PCB controlled impedance?

What is PCB Trace Impedance?

Trace impedance, also known as characteristic impedance, refers to the inherent opposition to the propagation of an electrical signal through a PCB trace. It is determined by the physical properties of the trace, such as its width, thickness, and the dielectric constant of the surrounding PCB material.

In an ideal transmission line, the characteristic impedance remains constant along the entire length of the trace. When a signal encounters a change in impedance, a portion of the signal is reflected back toward the source, causing signal integrity issues.

Factors Affecting PCB Trace Impedance

Several factors influence the characteristic impedance of a PCB trace:

  1. Trace width: Wider traces have lower impedance than narrower traces.
  2. Trace thickness: Thicker traces have lower impedance than thinner traces.
  3. Dielectric constant (Dk) of the PCB material: Materials with higher Dk, such as FR-4, result in lower impedance than materials with lower Dk, like Rogers laminates.
  4. Height of the trace above the reference plane: Traces closer to the reference plane (ground or power) have lower impedance than traces farther away.
  5. Presence of adjacent traces: Nearby traces can affect the impedance of a trace through electromagnetic coupling.

PCB Controlled Impedance Formula

To calculate the characteristic impedance of a PCB trace, designers use formulas that take into account the trace geometry and the properties of the dielectric material. The most commonly used formulas are for microstrip and stripline traces.

Microstrip Impedance Formula

A microstrip is a trace on the outer layer of a PCB, with a reference plane on the layer beneath it. The characteristic impedance of a microstrip trace can be calculated using the following formula:

Z0 = 87 / sqrt(εr + 1.41) * ln(5.98 * h / (0.8 * w + t))

Where:
– Z0 is the characteristic impedance in ohms (Ω)
– εr is the dielectric constant of the PCB material
– h is the height of the trace above the reference plane in mils (thousandths of an inch)
– w is the width of the trace in mils
– t is the thickness of the trace in mils

Stripline Impedance Formula

A stripline is a trace embedded within the PCB, with reference planes above and below it. The characteristic impedance of a stripline trace can be calculated using the following formula:

Z0 = 60 / sqrt(εr) * ln(4 * h / (0.67 * (0.8 * w + t)))

Where the variables have the same meaning as in the microstrip formula.

Differential Pair Impedance Formula

Differential signaling uses two traces to carry a signal, with the voltage difference between the traces representing the actual signal. The characteristic impedance of a differential pair can be calculated using the following formula:

Zdiff = 2 * Z0 * (1 - 0.48 * exp(-0.96 * s / h))

Where:
– Zdiff is the differential impedance in ohms (Ω)
– Z0 is the characteristic impedance of a single trace (calculated using the microstrip or stripline formula)
– s is the edge-to-edge spacing between the traces in mils
– h is the height of the traces above the reference plane in mils

PCB Impedance Control Design Guidelines

To ensure proper impedance control in PCB design, follow these guidelines:

  1. Choose an appropriate dielectric material based on the required impedance and frequency range.
  2. Use a PCB stackup that provides consistent dielectric thickness and symmetry.
  3. Determine the target impedance for each signal type (e.g., 50Ω for USB, 100Ω for Ethernet).
  4. Use an impedance calculator or the formulas provided to determine the trace width and spacing required to achieve the target impedance.
  5. Route traces using a uniform geometry and avoid abrupt changes in width or direction.
  6. Maintain a consistent spacing between traces and reference planes.
  7. Use ground planes and power planes to provide a low-impedance return path for signals.
  8. Terminate transmission lines with matching impedances to prevent reflections.
  9. Simulate and test the PCB design to verify impedance control and signal integrity.

PCB Impedance Calculator Tools

While the formulas provided can be used to manually calculate trace impedances, many PCB design software packages include built-in impedance calculators that simplify the process. Some popular impedance calculator tools include:

  1. Saturn PCB Toolkit
  2. Polar Instruments Si8000m
  3. Keysight ADS
  4. Mentor Graphics HyperLynx
  5. Cadence Allegro PCB Designer

These tools allow designers to input the PCB stackup, material properties, and target impedance, and they automatically calculate the required trace geometries.

FAQ

1. What is the importance of impedance control in PCB design?

Impedance control is crucial in PCB design to ensure signal integrity and minimize issues such as reflections, crosstalk, and EMI. By matching the impedance of traces to the components they connect, designers can achieve clean, undistorted signals and reliable high-speed communication.

2. What is the difference between microstrip and stripline traces?

Microstrip traces are located on the outer layers of a PCB, with a single reference plane beneath them. Stripline traces are embedded within the PCB, with reference planes above and below them. Striplines have better shielding and lower crosstalk than microstrips, but they are more challenging to route and manufacture.

3. How does the dielectric constant affect PCB trace impedance?

The dielectric constant (Dk) of the PCB material directly affects the characteristic impedance of traces. Materials with higher Dk, such as FR-4, result in lower impedance than materials with lower Dk, like Rogers laminates. Designers must consider the Dk when selecting PCB materials and calculating trace geometries.

4. What is the target impedance for common high-speed interfaces?

Some common target impedances for high-speed interfaces include:

  • USB: 90Ω differential
  • Ethernet: 100Ω differential
  • PCIe: 85Ω differential
  • HDMI: 100Ω differential
  • SATA: 100Ω differential

5. How can PCB designers verify impedance control?

PCB designers can verify impedance control through simulation and testing. Signal integrity simulations can predict the behavior of traces and identify potential issues. Physical testing, such as time-domain reflectometry (TDR) and impedance measurements, can validate the actual impedance of manufactured PCBs and ensure they meet the design requirements.

Conclusion

Controlling the characteristic impedance of PCB traces is essential for maintaining signal integrity in high-speed designs. By understanding the factors that influence trace impedance and using the appropriate formulas or impedance calculator tools, PCB designers can determine the optimal trace geometries for their target impedance.

Following best practices for impedance control, such as consistent routing, proper termination, and the use of reference planes, designers can minimize signal distortions and ensure reliable communication between components.

As high-speed interfaces continue to push the limits of PCB technology, mastering the concepts and techniques of impedance control will remain a critical skill for PCB designers.