David L. Hershberger, W9GR 10373 Pine Flat Way, Nevada City, CA 95959; [email protected] Controlled Envelope Single Sideband Introducing Controlled Envelope SSB; greatly increase your SSB “talk power” by accurately limiting envelope peaks in the SSB modulator. Generate SSB without the big overshoot peaks that make ALC necessary with conventional SSB modulators. Watch your wattmeter read higher than before. Abstract Achieving simultaneous accurate control 1.5 of both amplitude and bandwidth is a difficult problem. When amplitude-limited 1.0 audio is filtered to limit its bandwidth, the filter may overshoot substantially. It loses 0.5 its amplitude limiting ability. If the resulting overshoots are clipped, the amplitude 0 is controlled but the signal’s bandwidth increases because of the clipping distortion. –0.5 The signal loses its bandwidth limiting. Systems exist for correcting audio low-pass Overshooting Squarewave filter overshoot. But single sideband (SSB) –1.0 is a more difficult problem, because of the inevitable Hilbert transform regardless –1.5 of the method of SSB generation. ALC 0.0 0.002 0.004 0.006 0.008 0.01 systems reduce the amplitude of an SSB signal in response to overshooting envelope QX1411-Hershberger01 Time (seconds) peaks. Fast ALC may result in clipping and splatter. Slow ALC will significantly reduce Figure 1 — 100 Hz square wave filtered by 3 kHz elliptic low-pass filter. transmitted power. This paper presents a method for generating SSB without system overshoots. The result is higher transmitted Benjamin Franklin expressed it well: “As necessary to prevent crosstalk between power without audible distortion. we enjoy great advantages from the inven- the left plus right and left minus right tions of others, we should be glad of an subchannels. As the stereo generator’s opportunity to serve others by any invention filters would overshoot, the modulation Objective of ours; and this we should do freely and would have to be reduced to keep infrequent One of the reasons for the existence of the generously.” peaks from exceeding 100% modulation. Amateur Radio Service is the development A number of manufacturers responded of new techniques for radio communication. with systems that controlled overshoot I hope that this paper will present a useful Background accurately, allowing a loudness increase method for improving the effectiveness In the 1970s, FM stereo broadcasters’ of 2 to 4 dB without any audible increase of SSB transmitters for both amateur and on-air loudness was affected by overshoot in distortion. The overshoots themselves commercial applications. This technique is in the sharp cutoff 15 kHz low-pass filters contained relatively low energy. Eliminating being placed into the public domain and in (or 19 kHz notch filters) used in stereo them resulted in a substantial loudness particular, the “ham domain.” generators of the time. These filters were QEX – November/December 2014 3 increase without any perceptible increase in such as square waves. Figure 1 shows what overshoot control must be nonlinear. distortion. Such overshoot control systems happens when a 100 Hz square wave signal, My system for overshoot control of low- are still in widespread use today. accurately limited to a value of 1.0, is filtered pass filters (expired US patent #4,134,074) In this paper a classic method for real by a sharp cutoff 3 kHz elliptic low-pass started from the notion that overshoot could signal low-pass filter overshoot control is filter. It overshoots substantially. be reduced, but not eliminated, by clipping presented. Then the technique is extended There are several classes of non- and refiltering. Clipping controlled the to the complex baseband signals used to overshooting or low-overshoot low-pass overshoots, but created harmonic distortion generate SSB. filters. These include Gaussian, Bessel, beyond the cutoff frequency of the filter. transitional, and parabolic filters. These are A filter after the clipper would remove all linear filters. All of them have a roll-off the harmonic distortion — but it would Overshoot Control for Low-pass Filters characteristic that is far too slow to be useful overshoot. The overshoot of the second filter The problem with low-pass filters is that for FM broadcasting or SSB generation, was not as high as the first filter, however. they overshoot on amplitude-limited signals however. Therefore, an effective system for Theoretically, the clip, filter, clip, filter process could be repeated ad nauseum until the overshoot was insignificant. Figure 2 shows what happens with seven stages of 1.5 filter, clip, filter, clip, and so on. One cycle of a square wave is shown after the first, second, third stage, and so on. Even 1.0 after the seventh pass, the overshoot is still over 4%. This method does not converge very quickly. Such a system would be impractical in analog circuitry. So, I came up 0.5 with a method to make the system converge in “one fell swoop.” What was needed was something that did “more than clipping.” 0 A clipper can be visualized as a circuit that creates a series of peaks, which are then subtracted from the input signal. That is, it creates “clippings” that are the “tops” (and –0.5 bottoms) of the input waveform. These are subtracted from the input to create a clipped Clip, Filter, Repeat waveform. The gain of the “clippings” in a –1.0 simple clipper is unity. Figure 3 shows what happens when the overshoots are simply clipped off. The –1.5 overshoot “clippings” (lower amplitude trace) may be separated by subtracting the 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 output from the clipper from its input. When Time (seconds) QX1411-Hershberger02 the square wave with clipped overshoots is filtered, the second waveform in Figure 2 Figure 2 — Effects of repeated clipping and filtering. above is the result. The overshoot is reduced but not eliminated. Something that would do “more than clipping” could apply a gain factor to the “clippings” — such as a gain of 2. The 1.0 original overshooting signal shown in Figure 1 with such processing is shown in Figure 4. Note that the overshoots that would have 0.5 exceeded 1.0 are turned around and made to go the other way. The signal of Figure 4 contains out of band distortion and should 0 be low-pass filtered with linear phase. When the “more than a clipper” processes the signal, and the result is linear phase low- –0.5 pass filtered, the result is a large reduction Clipped Overshoot And Clippings in overshoot. Almost all of the overshoot is removed in this single more-than-clip and –1.0 filtering process. The result is shown in 0 0.002 0.004 0.006 0.008 0.01 Figure 5. The block diagram for this system is shown in Figure 6. Time (seconds) QX1411-Hershberger03 Audio is assumed to come from a peak limiter device, which ensures that nothing Figure 3 — Overshoots clipped off and separated. over 100% is being applied to the system. 4 QEX – November/December 2014 This signal is low-pass filtered, and the low- control. In DSP, single sideband is usually as implemented in analog hardware required pass filter will overshoot. The output of the generated by creating two orthogonal very close matching and phasing of the two low-pass filter is clipped. The output of the baseband audio signals, such as the well- signal paths. This was difficult to do in analog clipper is subtracted from the clipper’s input, known phasing method. The phasing method to obtain the “clippings.” The clippings are then amplified by a factor of about 2. They are then subtracted from the low-pass filter’s 1.0 output to create the waveform of Figure 4. That waveform is then low-pass filtered again with a linear phase low-pass filter. The 0.5 result is simultaneous control of both peak amplitude and bandwidth. There are two possible enhancements to 0 this system. First, the simple gain factor of 2 generally results in insufficient overshoot correction at lower amplitudes, and too –0.5 much correction at full amplitude. So rather than applying a simple gain factor of 2 in the “gain” element shown in Figure 6, the Overshoot Corrected Drive To Second Filter –1.0 clippings are divided by the greater of 1.0 or the absolute value of the clipper input. 0 0.002 0.004 0.006 0.008 0.01 Then a slightly lower gain factor of 1.9 is Time (seconds) applied. The signal shown in Figure 4 has QX1411-Hershberger04 been processed this way. As an expression, the correction is: Figure 4 — 100 Hz filtered square wave processed with “more than clipping.” 1.9clippings() t corr() t = [Eq 1] max 1, lpf() t Where: 1.0 corr is the additive correction signal clippings is the input of the clipper minus its output 0.5 max is the function that returns the greater of its two inputs lpf is the output of the first low-pass filter 0 The vertical bars operator is absolute value Second, there is a way to reduce the signal –0.5 processing complexity. Rather than passing the entire signal through the second low-pass filter, just the “clippings” may be passed through the filter if the rest of the signal is Overshoot Corrected Squarewave At 100% –1.0 delayed to match the delay of the second 0 0.002 0.004 0.006 0.008 0.01 low-pass filter. This modification is shown Time (seconds) later in Figure 13. QX1411-Hershberger05 When we generate SSB, the system as described above will not work for overshoot Figure 5 — Square wave filtered with overshoot compensation.