The Differential Microstrip Impedance conversion calculator computes the single-ended impedance (Z0) and differential impedance (Zd) for a pair of microstrip transmission lines based on their geometry and dielectric constant. It helps engineers design controlled impedance traces on printed circuit boards used in high-speed and RF signal applications.
Formulas
Z0 = (87 / √(εr + 1.41)) * ln((5.98 * h) / (0.8 * w + t))
Zd = (174 / √(εr + 1.41)) * ln((5.98 * h) / (0.8 * w + t)) * (1 – 0.48 * exp(-0.96 * (d/h)))
Formula Explanation
- w: trace width in mils
- t: trace thickness in mils
- h: dielectric height between trace and ground plane in mils
- d: spacing between differential pair traces in mils
- εr: dielectric constant of the PCB material (FR4 ≈ 4.4)
- Z0: single-ended impedance of a single trace
- Zd: differential impedance between two coupled traces
Uses of this calculator
- Designing differential transmission lines for high-speed signals like USB, HDMI, or Ethernet.
- Calculating precise impedance to ensure proper signal integrity and matching.
- Adjusting spacing or geometry to meet differential impedance requirements (e.g., 90 Ω).
- Analyzing how dielectric material and trace thickness affect impedance.
What is the differential impedance for 5 mil trace width, 4 mil spacing, and FR4 dielectric?
Input: w = 5 mils, d = 4 mils, t = 1.4 mils, h = 3.5 mils, εr = 4.4
Output:
- Z0 = (87 / √(4.4 + 1.41)) * ln((5.98 * 3.5) / (0.8 * 5 + 1.4)) = (87 / 2.43) * ln(20.93 / 5.4) = 35.8 * 1.34 = 48.0 Ω
- Zd = (174 / √(4.4 + 1.41)) * ln((5.98 * 3.5) / (0.8 * 5 + 1.4)) * (1 – 0.48 * exp(-0.96 * (4/3.5))) = (71.6 * 1.34) * (1 – 0.48 * exp(-1.1)) = 95.9 * (1 – 0.48 * 0.33) = 95.9 * 0.84 = 80.6 Ω
- Differential Impedance (Zd) = 80.6 Ω