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<title>Frequency modulation encoding</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Frequency modulation encoding</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about a system used on early magnetic disk drives. For the radio broadcasting techology, see <a href="Frequency_modulation" title="Frequency modulation">Frequency modulation</a>.</div>

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<p><b>Frequency modulation encoding</b>, or simply <b>FM</b>, is a method of storing data that saw widespread use in early <a href="Floppy_disk" title="Floppy disk">floppy disk drives</a> and <a href="Hard_disk_drive" title="Hard disk drive">hard disk drives</a>. The data is modified using <a href="Differential_Manchester_encoding" title="Differential Manchester encoding">differential Manchester encoding</a> when written to allow <a href="Clock_recovery" title="Clock recovery">clock recovery</a> to address timing effects known as "jitter" seen on disk media. It was introduced on <a href="IBM" title="IBM">IBM</a> mainframe drives and was almost universal among early <a href="Minicomputer" title="Minicomputer">minicomputer</a> and <a href="Microcomputer" title="Microcomputer">microcomputer</a> floppies. In the case of floppies, FM encoding allowed about 80 kB of data to be stored on a <style data-mw-deduplicate="TemplateStyles:r1154941027">

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</style><span class="frac">5<span class="sr-only">+</span><span class="num">1</span>⁄<span class="den">4</span></span>-inch disk.

</p><p>IBM began introducing the more efficient <a href="Modified_frequency_modulation" title="Modified frequency modulation">modified frequency modulation</a>, or MFM, starting in 1970. They referred to this format as "double density", with the original FM retroactively becoming "single density". MFM was more difficult to implement and it was not until the early 1980s that low-cost all-in-one MFM floppy drive controllers like the <a href="Western_Digital_FD1771" title="Western Digital FD1771">WD1770</a> emerged. This led to the rapid demise of FM encoding in favor of MFM by the mid-1980s.

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<div class="mw-heading mw-heading2"><h2 id="Underlying_storage_mechanism">Underlying storage mechanism</h2></div>

<p><a href="Main_memory" class="mw-redirect" title="Main memory">Main memory</a> systems in modern <a href="Computer" title="Computer">computers</a> store binary information using two different electrical signals, typically voltages. In <a href="DRAM" class="mw-redirect" title="DRAM">DRAM</a> for instance, the presence of a <a href="Voltage" title="Voltage">voltage</a> over a certain threshold represents a binary one, while any voltage below that value represents a zero. The letter "A" in <a href="ASCII" title="ASCII">ASCII</a> is represented as 01000001 in binary, which might be stored in a typical late-1970s DRAM like the Mostek MK4116 as a series of 0 and 5 V voltages in the individual <a href="Capacitor" title="Capacitor">capacitors</a> making up the memory.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>In contrast, <a href="Magnetic_recording" class="mw-redirect" title="Magnetic recording">magnetic recording</a> systems like <a href="Floppy_disk" title="Floppy disk">floppy disks</a> record this data as a change in <a href="Magnetic_polarity" class="mw-redirect" title="Magnetic polarity">magnetic polarity</a>. This is due to the way the data is read and written, using <a href="Electromagnetic_induction" title="Electromagnetic induction">magnetic induction</a>. During reading, the disk is rotating so its surface moves rapidly past the <a href="Read/write_head" class="mw-redirect" title="Read/write head">read/write head</a>, a small <a href="Electromagnet" title="Electromagnet">electromagnet</a>. When the polarity of the magnetic charge on the disk changes, a brief pulse of electricity is induced in the head which is read as a one, any section where the polarity does not change produces a zero.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19951_2-0" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19951-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> To encode the same letter A, assuming the previous data ended with a zero, a disk would use 01111110. The first zero-to-one transition causes a 1 to be output, the stream of ones following causes no output, and finally the last one-to-zero creates the final 1.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-0" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>In addition to the data being stored in patterns that require on-the-fly conversion to and from their internal format, the disk faces additional problems associated with being an analog system – noise, mechanical effects and other issues. In particular, disks suffer from an effect known as <a href="Jitter" title="Jitter">jitter</a> due to small changes in timing as the media speeds up and slows down during rotation. One form of unavoidable jitter is due to the <a href="Hysteresis" title="Hysteresis">hysteresis</a> of the magnetic media, which can lead to an effect known as bit shift that causes the strings of magnetic transition to be stretched out in time. These effects make it difficult to know which bit a particular transition belongs to.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-1" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>To address this problem, disks use some form of <a href="Clock_recovery" title="Clock recovery">clock recovery</a> using additional signals written to the disk. When the data is read, the clock signal is separated out and data bits can then be clearly seen in the signal and be cleanly lined up into the appropriate slots in memory.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-2" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Encoding">Encoding</h2></div>

<p>FM encoding uses a simple system to encode the original data in such a way that every bit of data will contain at least one transition, ensuring there are enough transitions during a given period for a successful clock recovery. To do this, it operates with a basic data period twice that of the maximum frequency of the recording media. These are known as "clock windows", with up to one clock transition and one data transition per window. Since each bit of data requires two minimum times, FM encoding stores about half the amount that is theoretically possible on that media.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-3" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>FM uses an implementation of the <a href="Differential_Manchester_encoding" title="Differential Manchester encoding">differential Manchester encoding</a>. A zero in the original data is encoded by a single magnetic flux transition during the period, and ones are encoded as two transitions. For instance, if a byte of data from the original system contains the bits <b>01000001</b>, the <a href="Floppy_disk_controller" class="mw-redirect" title="Floppy disk controller">floppy disk controller</a> will translate this into the series 1<b>0</b>1<b>1</b>1<b>0</b>1<b>0</b>1<b>0</b>1<b>0</b>1<b>0</b>1<b>1</b>, inserting additional signals in front of every bit to represent the clock. When this signal is then sent to the read/write head, the polarity will be flipped every time there is a pulse. In this example, if the head was originally in the low state at the end of writing the last data, the leading 1 will flip it to the high state, and the following zero will leave it there. The result is a single transition in that window. The next bit will first flip the state back to low, and then flip it back to high, for two transitions in the window.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-4" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Encoding these transitions requires the system to accept digital data from the host computer and then re-code it into the underlying FM format. On reading, the system has to separate out the clock signal again and leave only the data bits. Because the FM system is so simple, it could be implemented in single-chip forms using late 1970's <a href="Semiconductor_fabrication" class="mw-redirect" title="Semiconductor fabrication">semiconductor fabrication</a> techniques. This greatly lowered the cost of implementation of a complete drive controller, which consisted largely of a clock, a drive controller chip, a chip to communicate with the host computer, and some buffer memory. Especially popular was the <a href="Western_Digital_FD1771" title="Western Digital FD1771">Western Digital FD1771</a> and its variations.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading3"><h3 id="Data_encoding_vs_format">Data encoding vs format</h3></div>

<p>The material above refers to bytes being written to disk, but this is a simplification. In most disks, the only unit of data is the <a href="Disk_sector" title="Disk sector">sector</a>, and the individual bytes within it have no meaning to the controller. When data is written, the controller is handed a full sector's worth of data and told to write it as a single atomic operation as a series of bits. The controller cannot align the bits with the bytes based solely on the FM information. Thus it is not only the bits within the data that have to be aligned on reading, but the starting point of the sector's data as a whole.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-5" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>This is not accomplished with the encoding scheme, but the <a href="Disk_format" class="mw-redirect" title="Disk format">disk format</a> instead. When the controller writes a sector of data, it adds a header section containing information about the data that follows, as well as the address of the sector so it can be found in the future. During the write process, the controller also writes out a series of special "sync bytes" before the header and the data. In the IBM format, this consists of a series of thirteen zeros followed by three <a href="Hexadecimal" title="Hexadecimal">hexadecimal</a> <code>A1</code>'s in front of the header and data areas. These are not FM encoded, so the controller can easily identify them on-the-fly. The controller locks onto these signals to find the start of data, which immediately follows the last sync byte. After that, it reads out each eight bits into subsequent bytes in the buffer.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-6" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="Replacement_with_MFM">Replacement with MFM</h2></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Modified_frequency_modulation" title="Modified frequency modulation">modified frequency modulation</a></div>

<p>As each bit of data requires two transition periods in the FM system, it makes use of only half the potential storage capacity of the disk. This led to a series of more advanced encodings that make better use of the available space. The most widely used replacement was <a href="Modified_frequency_modulation" title="Modified frequency modulation">modified frequency modulation</a>, or MFM. This system recorded only a single bit in every window, which produced the underlying clock signal. The value of the bit, 1 or 0, was encoded by the location of the pulse within the window. 1's were encoded with pulses in the center of the window; 0's with the pulse at the end.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-7" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Because the accuracy of the transition transition timing is more demanding, MFM requires a more complex solution to recovering the clock signal. Generally this takes the form of a <a href="Phase_locked_loop" class="mw-redirect" title="Phase locked loop">phase locked loop</a> or similar system that will produce a steady output clock signal from a noisy input. This was beyond the capabilities of low-cost ICs from the late 1970s, which is why FM remained popular during the early <a href="Home_computer" title="Home computer">home computer</a> era in the early 1980s. MFM IC's were available, and were used on more expensive platforms like the <a href="IBM_PC" class="mw-redirect" title="IBM PC">IBM PC</a>, but using them required the clock recovery to be performed by external hardware, the "data separator". IC manufacturing was advancing rapidly during this period, and by the mid-1980s all-in-one MFM controllers appeared and the market rapidly moved to the double-density format.<sup id="cite_ref-FOOTNOTELutzMelloniWakeman19952_3-8" class="reference"><a href="#cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

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<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3></div>

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</style><cite id="CITEREFSt._Michael2019" class="citation web cs1">St. Michael, Stephen (1 August 2019). <a rel="nofollow" class="external text" href="https://www.allaboutcircuits.com/technical-articles/introduction-to-dram-dynamic-random-access-memory/">"Introduction to DRAM"</a>. <i>All About Circuits</i>.</cite></span>

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<li id="cite_note-FOOTNOTELutzMelloniWakeman19951-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELutzMelloniWakeman19951_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLutzMelloniWakeman1995">Lutz, Melloni & Wakeman 1995</a>, p. 1.</span>

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<li id="cite_note-FOOTNOTELutzMelloniWakeman19952-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-FOOTNOTELutzMelloniWakeman19952_3-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFLutzMelloniWakeman1995">Lutz, Melloni & Wakeman 1995</a>, p. 2.</span>

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<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFMichalopoulos1976" class="citation journal cs1">Michalopoulos, Demetrios A (October 1976). "New Products: Single-chip floppy disk formatter/controller". <i>Computer</i>. <b>9</b> (10). IEEE: 64. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FC-M.1976.218414">10.1109/C-M.1976.218414</a>.</cite></span>

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<div class="mw-heading mw-heading3"><h3 id="Bibliography">Bibliography</h3></div>

<ul><li><cite id="CITEREFLutzMelloniWakeman1995" class="citation techreport cs1">Lutz, Bob; Melloni, Paolo; Wakeman, Larry (1995). <a rel="nofollow" class="external text" href="http://info-coach.fr/atari/hardware/_fd-hard/AN-505.pdf"><i>TL/F/9419 Floppy Disk Data Separator Design Guide for the DP8473</i></a> <span class="cs1-format">(PDF)</span> (Technical report). National Semiconductor.</cite></li>

<li><cite id="CITEREFSchouhamer_Immink1990" class="citation journal cs1"><a href="Kees_Schouhamer_Immink" title="Kees Schouhamer Immink">Schouhamer Immink, Kees</a> (December 1990). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/2984369">"Runlength-Limited Sequences"</a>. <i>Proceedings of the IEEE</i>. <b>78</b> (11): <span class="nowrap">1745–</span>1759. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F5.63306">10.1109/5.63306</a>.</cite></li></ul>

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</style><div id="Line_coding_(digital_baseband_transmission)443" style="font-size:114%;margin:0 4em"><a href="Line_coding" class="mw-redirect" title="Line coding">Line coding</a> (digital baseband transmission)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Unipolar_encoding" title="Unipolar encoding">Unipolar encoding</a></li>

<li><a href="Bipolar_encoding" title="Bipolar encoding">Bipolar encoding</a></li>

<li><a href="On%E2%80%93off_keying" title="On–off keying">On–off keying</a></li>

<li><a href="Mark_and_space" title="Mark and space">Mark and space</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="4" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Basic <a href="Line_code" title="Line code">line codes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Return-to-zero" title="Return-to-zero">Return to zero (RZ)</a></li>

<li><a href="Non-return-to-zero#Non-return-to-zero_level" title="Non-return-to-zero">Non-return-to-zero, level (NRZ/NRZ-L)</a></li>

<li><a href="Non-return-to-zero#Non-return-to-zero_inverted" title="Non-return-to-zero">Non-return-to-zero, inverted (NRZ-I)</a></li>

<li><a href="Non-return-to-zero#Non-return-to-zero_space" title="Non-return-to-zero">Non-return-to-zero, space (NRZ-S)</a></li>

<li><a href="Manchester_code" title="Manchester code">Manchester</a></li>

<li><a href="Differential_Manchester_encoding" title="Differential Manchester encoding">Differential Manchester/biphase (Bi-φ)</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extended line codes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Conditioned_diphase" class="mw-redirect" title="Conditioned diphase">Conditioned diphase</a></li>

<li><a href="Bipolar_encoding#Alternate_mark_inversion" title="Bipolar encoding">Alternate mark inversion</a></li>

<li><a href="Modified_AMI_code" title="Modified AMI code">Modified AMI code</a></li>

<li><a href="Coded_mark_inversion" title="Coded mark inversion">Coded mark inversion</a></li>

<li><a href="MLT-3_encoding" title="MLT-3 encoding">MLT-3 encoding</a></li>

<li><a href="Hybrid_ternary_code" title="Hybrid ternary code">Hybrid ternary code</a></li>

<li><a href="6b/8b_encoding" title="6b/8b encoding">6b/8b encoding</a></li>

<li><a href="8b/10b_encoding" title="8b/10b encoding">8b/10b encoding</a></li>

<li><a href="64b/66b_encoding" title="64b/66b encoding">64b/66b encoding</a></li>

<li><a href="Eight-to-fourteen_modulation" title="Eight-to-fourteen modulation">Eight-to-fourteen modulation</a></li>

<li><a href="Delay_encoding" class="mw-redirect" title="Delay encoding">Delay/Miller encoding</a></li>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Optical line codes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Carrier-suppressed_return-to-zero" class="mw-redirect" title="Carrier-suppressed return-to-zero">Carrier-suppressed return-to-zero</a></li>

<li><a href="Alternate-phase_return-to-zero" class="mw-redirect" title="Alternate-phase return-to-zero">Alternate-phase return-to-zero</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>

<ul><li><i>See also:</i> <a href="Baseband" title="Baseband">Baseband</a></li>

<li><a href="Digital_signal" title="Digital signal">Digital signal</a></li>

<li><a href="Digital_transmission" class="mw-redirect" title="Digital transmission">Digital transmission</a></li>

<li><a href="Ethernet_physical_layer" title="Ethernet physical layer">Ethernet physical layer</a></li>

<li><a href="Modulation" class="mw-redirect" title="Modulation">Pulse modulation methods</a></li>

<li><a href="Pulse-amplitude_modulation" title="Pulse-amplitude modulation">Pulse-amplitude modulation</a> (PAM)</li>

<li><a href="Pulse-code_modulation" title="Pulse-code modulation">Pulse-code modulation</a> (PCM)</li>

<li><a href="Serial_communication" title="Serial communication">Serial communication</a></li>

<li>Category:Line codes</li></ul>

</div></td></tr></tbody></table></div></div></div><div><div class="zim-footer">

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