Enter the characteristic impedance of the microstrip and the height and width of the microstrip trace into the calculator to determine the differential impedance, and this calculator can also evaluate any of the variables given the others are known.

## Microstrip Differential Impedance Formula

The following formula is used to calculate the differential impedance of a microstrip:

Z_diff = (Z0 / 2) * sqrt((1 + (2 * h / w)) / (1 - (2 * h / w)))

Variables:

• Z_diff is the differential impedance of the microstrip
• Z0 is the characteristic impedance of the microstrip
• h is the height of the dielectric substrate
• w is the width of the microstrip trace

To calculate the differential impedance of a microstrip, divide the characteristic impedance of the microstrip by 2. Multiply the result by the square root of the ratio of (1 + (2 * h / w)) to (1 – (2 * h / w)).

## What is a Microstrip Differential Impedance?

Microstrip Differential Impedance is a key parameter in the design of high-speed digital and high-frequency analog circuits. It refers to the impedance that a pair of differential (opposite phase) signals will see in a microstrip transmission line configuration. A microstrip line is a type of electrical transmission line used to convey microwave-frequency signals and consists of a conducting strip separated from a ground plane by a dielectric layer known as the substrate. The differential impedance is determined by the physical dimensions of the microstrip lines, the distance between them, and the properties of the substrate material. It is crucial to match this impedance to the source and load impedances to prevent signal reflections, which can degrade the signal integrity. Therefore, accurate control and prediction of the microstrip differential impedance are essential for the successful design of high-performance electronic systems.

## How to Calculate Microstrip Differential Impedance?

The following steps outline how to calculate the Microstrip Differential Impedance.

1. First, determine the width of the microstrip trace (W) in millimeters.
2. Next, determine the height of the dielectric substrate (H) in millimeters.
3. Next, determine the relative permittivity of the dielectric substrate (εr).
4. Next, calculate the effective dielectric constant (εeff) using the formula εeff = (εr + 1) / 2.
5. Next, calculate the characteristic impedance (Z0) using the formula Z0 = 87 / √(εeff) * ln(5.98 * H / W + 1.74 * W / H).
6. Finally, calculate the differential impedance (Zdiff) using the formula Zdiff = Z0 / √(1 – (W / (2 * H))^2).

Example Problem:

Use the following variables as an example problem to test your knowledge.

Width of the microstrip trace (W) = 2 mm

Height of the dielectric substrate (H) = 1 mm

Relative permittivity of the dielectric substrate (εr) = 4.2