The formula to calculate the differential impedance is:
\[ Zd = \frac{2 \cdot Z0}{\sqrt{1 + \left( \frac{2 \cdot Z0}{Zc} \right)}} \]
Where:
Differential Impedance is a key parameter in the design of high-speed digital and analog circuits. It refers to the electrical resistance encountered by a signal when it travels along a pair of conductors in a differential transmission line, such as a twisted pair cable or a printed circuit board (PCB) trace pair. The differential impedance is the impedance that one line would have when driven in relation to the other line, which is ideally grounded. It is crucial for maintaining signal integrity, reducing electromagnetic interference, and achieving optimal performance in high-speed data transmission systems.
Example 1:
Using the formula:
\[ Zd = \frac{2 \cdot 50}{\sqrt{1 + \left( \frac{2 \cdot 50}{100} \right)}} = \frac{100}{\sqrt{1 + 1}} = \frac{100}{\sqrt{2}} = \frac{100}{1.414} \approx 70.71 \text{ Ohms} \]
Example 2:
Using the formula:
\[ Zd = \frac{2 \cdot 75}{\sqrt{1 + \left( \frac{2 \cdot 75}{150} \right)}} = \frac{150}{\sqrt{1 + 1}} = \frac{150}{\sqrt{2}} = \frac{150}{1.414} \approx 106.07 \text{ Ohms} \]