[Bandwidth]     [Duty-Cycle]     [References]


blue_line.GIF (897 bytes)



Bandwidth ... often a controversial topic. When operating a transmitter, knowing (or at least being aware of) your bandwidth is just as important as knowing your operating frequency. Part of the controversy stems from the definition of "bandwidth". Often, the term is qualified with “necessary”, “occupied”, “actual”, “effective”, "specified", etc., or is not qualified at all. Either way, a proper definition should refer to power levels (ref. 11):


The fractional power containment bandwidth is the definition of bandwidth that has been most used to define channel bandwidth for digital modulation.... It is the most appropriate measure of necessary bandwidth because it is a measure of the integrated power spectrum density, and can be related to system performance.


The CCIR and the ARRL (ref. 12) use this definition:


Bandwidth -- The width of a frequency band outside of which the mean power is attenuated at least 26 dB below the mean power of the total emission, including allowances for transmitter drift or Doppler shift. Bandwidth describes the range of frequencies that a radio transmission occupies. [26 dB beyond each bandwidth limit, i.e., factor 0.5% total]  


The IARU gives an example of "transmitted signal bandwidth" (ref. 10):

The -6 dB bandwidth of a properly shaped CW signal is approximately 4 times the sending speed in WPM (Words Per Minute). Example: CW at 25 WPM takes 100 Hz (at -6 dB).

Note that the latter example is equivalent to a Feld-Hell machine, directly keying a CW transmitter.

If – and only if – we operate in Feld-Hell mode with a text font that complies with the “Hell 2-pixel rule”, do we have a minimum duration of a pixel (black or white!) that is equal to 2 x 1000 / (2.5 cps x 7 columns x 14 lines) = 8.16 msec. Hence, the shortest pixel cycle (1 black + 1 white pixel) is 2 x 8.16 = 16.32 msec. This equivalent to a pixel rate (“Punktfrequenz”; ref. 20) of 1000 / 16.32 = 61.25 Hz. As the Hell-pixels are binary, the equivalent “telegraphy speed” is 1000 / 8.16 = 122.5 baud.

Extensive experiments and measurements conducted by Siemens-Halske, Cable & Wireless, and the Reichspostzentralamt (central office of the German national postal authority) around 1935 (ref. 4) resulted in the recommendation for filtering the modulation (i.e., at the transmitter, not at the receiver!) with a low-pass corner frequency of 1.2 times the pixel rate. This effectively suppresses the third and higher harmonics of the pixel rate, and significantly reduces the second harmonic. I have not looked into this, but it could be a similar effect as applying raised-cosine modulation. In any case, this filtering yields perfectly acceptable printed text at the receiving Hellschreiber. This can actually be verified by using a very narrow IF or AF filter at the receiver. Of course, filtering at the receiver does not affect the bandwidth of the transmitted signal, and may worsen print quality.

The above companies recommended against widening the transmitter filter beyond 1.6 times the pixel rate, i.e., 1.6 x 61.25 ≈ 100 Hz (-3 dB) at 2.5 cps, or 200 Hz at 5 cps (ref. 18). Actually implemented low-pass filters of the era also blocked frequencies above 200 Hz (ref. 21). As usual, the referenced literature does not indicate steepness of the applied filters, beyond the corner frequency. The factor 1.6 is also supported by Shannon's theorem (and the Hartley-Shannon law) regarding the maximum data rate for "near error-free" communication across a bandwidth limited channel. This factor is used in the table below (though normally applied to the Baud-rate).

These experiments and analyses led to the official acceptance of Hellschreiber-telegraphy at the International Radiocommunications Conference held in Cairo in 1938 for use of frequencies reserved for A1-modulated telegraphy.

Shannon bandwidth for Hellschreibers with two and four times the speed of Feld-Hell

(source: p. 65 in ref. 5; same results shown in ref. 22)

The next table captures the definition of the FCC (ref. 9) and the ITU for "necessary bandwidth". The formulas date back at least to the Joint Telegraph and Radiotelegraph Conference in Madrid (1932), as confirmed at the 1938 International Radiocommunications Conference. For Feld-Hell, the "necessary bandwidth", in combination with a non-fading transmission path, is 3 x 122.5 ≈ 367 Hz. Ref. 3. The factor 3 is used in order to be able to preserve a reasonably shaped square wave (ref. 8), and this requires at least the third harmonic of the pixel rate (ref. 7).

Necessary bandwidth of amplitude modulated signal with quantized or digital information

(note: the formula for tone modulated carriers applies to AM (double sideband) modulation)


In the above table, the formula for tone modulated carrier applies to AM modulation: double sideband, unsuppressed carrier. Hence, the formula includes 2 x fmodulation, to account for the sidebands. However, the spectrum of an on-off keyed single-tone modulated carrier with SSB modulation (single sideband, suppressed carrier) is basically indistinguishable from the spectrum of an on-off keyed carrier (CW). The real Feld-Hell machines can operate in two on-off keyed modes: 1) of a CW transceiver, and 2) of the internally generated 900 Hz signal, in combination with an SSB or AM transceiver.


Note that "necessary bandwidth" is absolutely not the same as "occupied bandwidth"! The latter depends on the shape of the pulse envelope, resulting from the (CW) transmitter's keying characteristics or applied by DSP/software processing ("raised-cosine comes close to the ideal shape). Improper pulse shaping may cause the actual bandwidth to be several 10s of kilohertz under good propagation conditions! Obviously overdriving/over-modulating the transmitter will also result in (much) higher actual signal bandwidth (many kHz!). Unfortunately this is not at all uncommon for operators with PC-Hellschreibers (or digi-modes in general) that use a PC-soundcard...


Note that the Nyquist minimum bandwidth for Feld-Hell is 2 x 122.5 = 245 Hz. This is the theoretical minimum bandwidth that can be used to represent a signal and still allow loss-less reconstruction after transmission over an ideal, noiseless transmission channel. Shaping a rectangular pulse with (root) raised-cosine (or Gaussian) filters allow this minimum bandwidth to be approximated. The frequency response of raised-cosine filters is flat in the band-pass, follows a gradual s-curve at the leading and trailing edges of the band-pass, and is zero outside the band-pass. Discrete implementations of such filters are common place in portable phones and modems. But today's digi-mode software is also fully capable of providing such approximations. Software-implemented Feld-Hell (e.g., IZ8BLY, DM780, FLdgi and MULTIPSK) typically applies raised-cosine pulse shaping - except of course for FM-modes.


Raised-cosine pulses


Spectrum of a raised-cosine pulse


Contact bounce at the character drum of a mechanical Hellschreiber (e.g., due to dirty of worn slip-contacts or a dirty drum) will result in near-rectangular pulse shapes and spikes. If the Hellschreiber's keyed-tone output  is used in combination with an SSB or AM transmitter, then the bandpass of the transmitter's microphone input and the PTT rise & fall times may limit the excessive bandwidth of the output signal. Likewise, If the character drum is used to direct-key a CW transmitter, then the keing rise- and fall-times will filter out spikes.


Contact-bounce at the start of a pulse


Based on all of the above formulas, Feld-Hell has a necessary bandwidth of 245-367 Hz. This is well below 500 Hz, hence qualifies as a "narrow bandwidth" mode. This may be compared to the bandwidth of an other popular narrow digital amateur radio mode: PSK31. It has a specified bandwidth of 62.5 Hz at -30 dB (in practice about 80 Hz). PC-software Hellschreiber using a soundcard and an SSB transceiver, should produce a transmitted signal with a bandwidth per the various formulas stated above.


Can we "do" Hellschreiber with less bandwidth? Well... yes. That is the beauty and strength of this system! The original Hell font, combined with the pattern-recognition capability of the human brain, allows us to read Hell text well into the noise level, and with as much as 60% distortion due to pixel shortening or lengthening ("smearing"), see ref. 4. We do not need loss-less reconstruction of the transmitted signals. An otherwise clean signal, may be readable down to, or below, a bandwidth equal to the reciprocal of the baud rate, i.e., ≤ 122.5 Hz.


blue_line.GIF (897 bytes)


I cannot stress this enough: the stated necessary Feld-Hell bandwidths ONLY apply when using fonts that result in a minimum pixel (black or white!) duration of 8.16 msec. Of course, today's PC software implementations of the Hellschreiber can use any font set, and the Hell-system as such has no limitations in this respect. However, not abiding by the 2-pixel rule raises the baud rate and thereby unnecessarily increases the occupied bandwidth of the transmitted signal - as much as 4-5 times!


Also, shorter "PC" pulses are not compatible with mechanical Feld-Hellschreibers. The filtering in the pulse-detector and the speed of the electromagnet in the Feld-Hell's printer act as low-pass filters that are dimensioned for the Hell font. Hence, short "PC" pixel pulses result in printed text that is hard to read. Please only use the original Hell font with PC-Feld-Hellschreibers. Do not use "cute" or "fancy" PC-fonts! It is OK to use the so-called "double width" or "DX" Hell-fonts - this does not violate the 2-pixel rule. The original ("capitals only") Hell-font is optimized for minimum bandwidth, and maximum readability in the presence of noise/interference in the received signal.


Obviously overdriving/over-modulating the transmitter will also result in excessive bandwidth of as much a 5 kHz. Unfortunately this is not at all uncommon for operators with PC-Hellschreibers (or digi-modes in general, for that matter) who use a PC-soundcard, and try to squeeze out a bit more output power by increasing the modulation level. Add to this propagation conditions (note the factor K in the FCC/ITU bandwidth formulas above), and you may be occupying more than 10 kHz of bandwidth!

"Hardness" and shape of the transmitter's keying characteristics (shape and steepness of the keyed pulse-envelope), non-linearities in the modulator and amplifier, distortions due to over-modulation, etc., all unnecessarily and significantly increase the bandwidth. Clearly, keying a carrier with perfectly rectangular pulses (zero rise & fall times along the entire path between the transmitter's keying input and RF output) results in infinite RF sidebands that interfere with adjacent communication channels. I am not going enter into a discussion here on if & how bandwidth depends on data rate (it doesn't), keying characteristics, etc. This will lead to lengthy popular- and quasi-scientific discussions, as interesting as they may be, see this discussion chain at eHam. Ref. 13-15 provide the necessary insight.

If you'd like to more closely analyze the spectrum of the audio signals you receive, consider "Spectrum Lab" freeware from DL4YHF. You can also use this to look at the spectrum of the audio signal that the digi-mode software sends to your transmitter. I have put the spectrum plot of a various other Hell-modes on the "Modern "software" modes (FM, MT, etc.)" page.


 - (double) click on any of the spectrum plots below to get the full-size picture -

Feld-Hell (IZ8BLY software)                                                Feld-Hell (DM780 software)
(with raised-cosine pulse shaping)                                    (with raised-cosine pulse shaping)


Audio "waterfall" spectrum of a Feld-Hell signal (with raised-cosine pulse shaping)


RTTY 45.45 Bd   (DM780 software)                                                PSK31 (DM780 software)


blue_line.GIF (897 bytes)



Feld-Hell is typically reported as having a duty cycle of 22%. This is  based on the word "HELL" having a duty-cycle of 22.5%. Note that:


it is only the duty-cycle of this specific word.


it is the average duty cycle of that word.


it is only the duty-cycle of the original Hell-font. Some Hellschreiber software has the option to use a "DX" version of the Hell-font: it is double-wide, and all columns are sent twice. This does not change the average duty cycle. PC-fonts have a different duty-cycle (they should not be used anyway, as discussed above).


Hell-modes other than Feld-Hell (Hell-80, FM-Hell, PSK-Hell) have a duty cycle of 100% - independent of the font that is used. FSK-Hell has an average duty-cycle of about 80%.


But yes: the Feld-Hell font does have a low average duty-cycle, which makes it easy on the transmitter. My binary file of the Feld-Hell font shows that the character "8" has the highest duty-cycle: 39% (it consists of 38 out of the 7x14=98 possible pixel-bits). The "period" (a.k.a. "full stop") has the lowest duty-cycle: 6% (6 pixels total out of 98).


blue_line.GIF (897 bytes)




Ref. 1: "The shape of bits to come", James Miller (G3RUH), version 29 October 2005

bullet Ref. 3: "The care and feeding of digital, pulse-shaping filters", K. Gentile, RF Design, April 2002
bullet Ref. 3:" CW Envelope as a Function of Rise Time", by Greg, W8WWV, version 26 February 2003

Ref. 4: "Bandbreitenfragen bei Anwendung der Siemens-Hell-Fernschreibtechnik“ [signal bandwidth issues with A2 and A3 modulation], Rudolf Zimmermann, 7 pp., Technische Mitteilungen des Fernmeldewerks, Siemens & Halske A.G., Wernerwerk, Abteilung für Telegrafengerät, Berlin-Siemensstadt, May 1940, SH 7998, 1. 8. 40. T T1.


Ref. 5: "Bedeutung der Shannon-Theorie für die Fernschreibtechnik" [Importance of the Shannon theory for telecommunications], Fritz Schiweck, Section 1.18 (pp. 63-70) in "Fernschreibtechnik", Band 9 of “Lehrbücher der Feinwerktechnik“, 4th ed., 1962, C. F. Winter, 894 pp.


Ref. 6: "Fernschreibleistung, Schrittgeschwindigkeit, Bandbreite, Vergleich mit Morsetelegraphie" [telegraphy speed, data rate, bandwidth, comparison with Morse telegraphy], Fritz Schiweck, section 9.5.3 (pp. 374-375) in "Fernschreibtechnik", Band 9 of “Lehrbücher der Feinwerktechnik“, 4th ed., 1962, C. F. Winter, 894 pp.


Ref. 7: "Punktfrequenz und Bandbreite" [pixel frequency and bandwidth], Gerhard Brunn, Funktechnische Monatshefte (FTM), Heft 2, February 1942, pp. 26-27


Ref. 8: "Hellschreiber - what it is and how it works", Stan Cook /GB5XB), Radio Communication, 4/1981


Ref. 9: "Bandwidths", FCC Rules Title 47, Part 90, Section §2.202, 2008


Ref. 10: "Ethics and Operating Procedures for the Radio Amateur", IARU, July 2008


Ref. 11: "Necessary bandwidth and spectral properties of digital communication", D.J. Cohen, U.S. Department of Commerce, NTIA Report 84-168, February 1985, 69 pp.


Ref. 12: "Ham radio glossary", ARRL


Ref. 13: "Keyclicks" [explanation of CW  bandwidth, occupied bandwidth, cause of clicks, CW bandwidth analysis], Tom Rauch (W8JI)


Ref. 14: "CW Bandwidth Analysis: Effect of Keying Waveform on CW Bandwidth", Jim Proctor, (KE3HO)


Ref. 15: "Spectral Analysis of a CW keying pulse", Kevin Schmidt (W9CF)


Ref. 16: "Hellschreiber, Part I - History and description; Part II - getting on the air; Part III - Signal analysis and digital philosophy; Part IV - Frequency domain", Murray Greenman (ZL1BPU), Break-In Amateur Radio Magazine (NZART), Vol. 71, October 1998, pp. 7-8, Vol. 71, November 1998, pp. 4-6, Vol. 71, December 1998, pp. 6-8, Vol. 72, Jan/Feb 1999, p. 6.


Ref. 17: "Der Hell-Schreiber”, pp. 15-19 in “Einführung in die Nachrichtenübertragungstechnik”, Volker Aschoff, Springer-Verlag, 1968, 147 pp


Ref. 18: "Elektrisches Nachrichtenwesen - Telegraphie", p. 535 in "ETZ: Elektrotechnische Zeitschrift  Ausgabe A", Jg. 59, Heft 20, 19 May 1938


Ref. 19: "Hellschreiber - what it is and how it works", S. Cook GB5XB, Radio Communication, 4/1981


Ref. 20: pp. 170-172 in "Hochfrequenz-Nachrichtentrechnik für Elektrizitätswerke", 2nd ed., Gerhard Dreßler, Heinrich-Karl Podszeck, Springer Verlag, 1952, 183 pp. 


Ref. 21: "Verstärker für Bildfunk und Hellschreiber", Fritz Vilbig, Jonathan Zenneck, pp. 615-616 in "Fortschritte der Hochfrequenztechnik", Band 2, 1945    


Ref. 22: p. 74 in "Siemens-Hell-Geräte", pp. 61-77 in "Telegrafentechnik", Band 6, Teil 6 of "Der Dienst bei der Deutschen Bundespost - Leitfaden für die Ausbildung", Fritz Schiweck (ed.), R. v. Decker's Verlag, G. Schenck, 1960, 970 pp.      

blue_line.GIF (897 bytes)

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