Understanding Fractional Bandwidth: A Comprehensive Guide

Fractional bandwidth is a key concept in engineering and signal processing, defining the relative bandwidth of a signal or system. It essentially measures how wide a range of frequencies a signal or system occupies compared to its center frequency.

Expressed as a ratio or percentage, fractional bandwidth finds widespread use in fields like telecommunications, RF engineering, and electronics.

Let’s delve into the details, including the fractional bandwidth formula and a practical UWB example.

What is Fractional Bandwidth?

The fractional bandwidth represents the ratio of a transmission’s bandwidth to its center frequency (fc). It’s typically measured at the -10 dB points on the frequency spectrum.

Mathematically, it’s defined as:

FBW = (Δf/fc) x 100 %

Where:

• Δf = (fH - fL)
• fc = (fH + fL)/2

And:

• fc = Center frequency
• fH = High frequency limit
• fL = Low frequency limit
• Δf = Bandwidth of the signal or system
• FBW = Fractional bandwidth (expressed as percentage)

In this formula, Δf signifies the width of the frequency range where the signal’s power or energy is significant. Think of it as the difference between the highest and lowest frequencies that contain the majority of the signal’s energy.

The ‘fc’ represents the signal’s center frequency, usually the frequency around which the signal is centered.

Fractional bandwidth helps characterize signals and systems based on how spread out or concentrated their frequency content is. For instance, a signal with a wide fractional bandwidth (e.g., 50% or higher) occupies a broad range of frequencies around its center frequency. Conversely, a signal with a narrow fractional bandwidth (e.g., less than 10%) is concentrated around its center frequency, with most of its energy contained within a small frequency range.

Engineers frequently use fractional bandwidth to specify and design filters, antennas, communication systems, and other devices. This ensures they operate within a defined frequency range, considering factors such as signal purity, interference rejection, and available bandwidth.

Absolute Bandwidth (B) and Center Frequency (fc)

Before moving forward, let’s clarify two related terms:

• Absolute Bandwidth (B or Δf): The total range of frequencies occupied by a signal or system. It’s the difference between the highest and lowest frequencies with significant power or energy: B or Δf = fH - fL

• Center Frequency (fc): The frequency at which the signal is centered or concentrated. It’s the midpoint of the absolute bandwidth: fc = (fH + fL) / 2

UWB Technology and Fractional Bandwidth

Ultra-Wideband (UWB) technology leverages frequencies from 3.1 GHz to 10.6 GHz. The FCC has defined 11 channels within this band for global use.

UWB operates in an unlicensed band, making it suitable for telecom applications without needing a license, as long as the system adheres to EIRP (Effective Isotropic Radiated Power) and regulated frequency spectrum guidelines.

UWB PSD Curve

The PSD (Power Spectral Density) versus frequency curve of a UWB system illustrates the low frequency (fL), high frequency (fH), and center frequency (fC) of a UWB channel. Both the center frequency and fractional bandwidth (Bfrac) can be calculated using fL and fH. The absolute bandwidth (‘B’) can also be derived from fC and fractional bandwidth (Bfrac).

Fractional Bandwidth Calculator

Let’s look at a UWB example:

INPUTs:

• Low Frequency (fL) = 1 GHz
• High Frequency (fh) = 3 GHz

OUTPUTs:

• Center Frequency (fc) = 2 GHz
• Fractional BW = 1 (Unit less)
• Absolute BW = 2 GHz

UWB Formulas

The following formulas are used for calculating center frequency, absolute bandwidth, and fractional bandwidth in UWB and similar wireless technologies:

![UWB Absolute Bandwidth vs UWB Fractional Bandwidth] (../../assets/UWB-Absolute-Bandwidth-vs-Fractional-Bandwidth.jpg)

UWB Absolute Bandwidth vs UWB Fractional Bandwidth

Conclusion

In summary, fractional bandwidth, absolute bandwidth, and center frequency are fundamental parameters for engineers to design, analyze, and optimize various systems and components. Accurate calculation of these parameters ensures efficient use of the frequency spectrum across a broad spectrum of engineering applications.