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Bits, Bytes, and Hertz
Last updated: 3/23/2005

Q.  Is there an equation for coverting Hz (Hertz) into Mbps (mega bits per sec)?

A. Communications speeds when transferring data are usually, but not always, measured in bits per second.  A bit is a binary or logical 1 or 0.  Data transfer speeds when transferring data, etc. in a computer, such as between memory and a hard disk drive, are often, but not always, measured in bytes per second.  A byte of data is a chunk of bits used to represent a character, but not always.  There are usually eight bits in a byte, but not always.  So, roughly speaking in general and common terms, one byte equals eight bits.  Bytes are abbreviated with a capital B and bits are abbreviated with lower-case b, but not always.  Microsoft Windows often shows communications speeds in bytes per second.  Thus the confusion, which I hoped this unscrambled a little.

However, to complicate matters even more...  The Hertz is often used as a unit in the measurement of data transfers.  A Hertz is one cycle per second.  A cycle is a single occurrence of a periodically repeating phenomenon.  For example, one revolution of a bicycle wheel is a cycle.  Plot the vertical height (amplitude) of a spot on the tire versus distance or time on a graph and you will have a sinusoidal waveform.  Your house electrical power is a sinusoidal wave.

A communications waveform may have a repeated shape. For example, the Ethernet can be measured in cycles per second (Hz).  Roughly speaking, and for measurement purposes, it can be considered a repeated "square wave," the same thing sent over and over again.

The 100BASE-TX Ethernet has a specified data rate of 100 Mbps and it operates at 33 MHz.  It can be shown that a square wave can be represented by a bunch of sinusoidal waves (an infinite series of discrete sinusoidal waves) with a base frequency equal to the square wave frequency and even and odd harmonics, which are multiples of the base frequency. They comprise the frequency spectrum.  At minimum, one of these sinusoidal waves, the third harmonic (3 X 33 MHz = 100 MHz, must be transmitted for a reliable Ethernet transmissions.  For it can also be shown that the odd harmonics determine the sharpness of the leading and trailing edges of a square wave (which are critical to the Ethernet) and the even harmonics make up the flat parts of the wave.  When analyzing the characteristics of network cables it often more relevant to state the rated speed in MHz (the frequency domain) instead of Mbps (the time domain).  So, you will often see me use MHz and Mbps interchangeably when discussing the Ethernet.  They are in fact interchangeable and one can go back and fourth mathematically between the frequency and time domains with the Fourier transform (or Fast Fourier transform).  That's what a spectrum analyzer does.

Cool link to the Fourier Series Square Wave Tool , which graphically and dynamically demos some of this stuff in a more easily understood way!

How does one transmit information at 100 Mbps with a 33 MHz square wave?  One doesn't.  The 100Base-TX uses compression.

For others out there, please correct me or elaborate if I did not get this 100% correct.  I am 26 years rusty on some of the finer points.

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