by Victor Kampf
When it comes to guitar sound the issues of signal range formation by means of amplification and limitation take the lead. It is tradtionally assumed that only tube-caused limitation is able to furnish the guitar signal with THAT specific quality, that is so worshipped by guitarists and guitar music fans. The objective of this article is to unveil the basic differences between the triode-based limitation any any other.
First of all, let us consider how triod limitation works. To demonstrate it we will need a popular 2АХ7 valve powered by 20V double-amplitude sine voltage.
The upper half-wave is limited by Uk level ( Uk – cathode potential in relation to «ground»). As Uk voltage rises, the current occurs between the grid and the cathode. In such a way the triode can be regarded as a vacuum diode placed between the grid and the cathode from input side (Fig.1).
Fig.1. Triode-caused positive half-wave limitation on the grid (UK=1,8V)
This phenomenon is not my discovery, since it’s been known for ages. Under cathode value fo 1…3 kOhm, which is customary for 12АХ7, the level of upper half-wave signal limitation equals about 2V.
Anode signal is the inverted and КU times amplified input stage signal (Fig.2)..
Fig.2. Standardized stage of 12АХ7.
Stage voltage amplification:
m – triode voltage gain;
S – steepness of the working point;
RA – resistor in anode circuit;
rA – anode dynamic resistance;
RH – load resistance.
KU is mainly determined by the internal resistance of the transistor rA, which usually equals 50 … 60 kOm. In the absence of the load, the stage amplification of 12AH7 is about 65. Let us look at the output signal in relation to half-waves. All that a transistor can do in order to provide the maximum signal of the upper half-wave is to close completely. In this case the maximum of positive half wave at the output is determined by the ratio between RA andRH, which form regular voltage divider. In the absence of the load the upper half-wave reaches +340 V. If the load is applied (for example, 200kOm) the upper half-wave will reach only +280 V. As a result, we have the signal, shown in Figure 3. (the slopes of the signal tops is conditioned by the charge of the passing capacitor СН and depends on its capacity)
The lower half-wave in this figure is nothing but the limited input positive half wave, amplified KU times. Since the “Input diode” of the transistor limits the positive wave at the input by level of 2V, anode gets the lower half-wave signal with a characteristic “diode” rounding (in this case, KU = 55, and the signal gets “rounded” at 220-2V * 55 = 110V, Fig.3).
Thus, the transistor’s output actually limits only the upper half-wave.
Why don’t the limiters sound like a tube?
Well, a transistor limits only the positive half-wave both on the grid and the anode. Due to the fact that the stage within the circuit with common cathode is inverted, we obtain the limitation on both half-waves on the stage output. However, the limitation of both half-waves occurs at different points of amplification stage (one half-wave – on the grid, the second – at the anode).
It is this feature makes the transistor limitation pleasant sounding and musical, as any attempt to limit the signal path in one point on both half-wave always results in “transistorness” and “dirt” in sound.
Therefore, no limiters, whether they are with diodes in negative feedback or limiting, can be close enough to tube sound: symmetrically or asymmetrically they limit the signal on both half-waves. Skeptics might argue: two series-connected stages on vacuum triodes also provide current limitation on both half-waves, eventually forming a sort of meander processing a single sinusoidal signal. But the signal limitation first via one half-wave, and then the other is not the same in comparison with the simultaneous limitation of both half-waves. The authentic guitar signal is not sinusoidal; there are many of them. This is why the spectrum of intermodulation distortions shaped by triode cascade is so sweet-sounding – the basic emerging new tones are consonant with the main tone. In the case of simultaneous bilateral limitation obtained in the op-amp devices or the ones with discrete transistors the intermodulation distortion spectrum contains a large number of non-musical combinational components, discordant with the main tone, which is perceived as “dirt” in sound. So, it is ridiculous to attempt giving “tube-like nobility” to the sound of limiting stages using op amps with diodes in negative feedback through the use of different number of diodes for the upper and lower half-waves. This will probably provide a few even harmonics during single tones processing, but when there comes the second tone in the signal, the sound gets instantly contaminated.
To prove the above-said let us illustrate the signals ranges at the output of the transistor in two cases:
Standard triode stage and standard cascade with an additional vacuum diode placed between the grid and the ground (for bilateral limitation on the grid).
The stages input are fed with dual-tone signal of 200Hz (10V) and 300Hz (10V)
The top: 100Hz, 500Hz, 800Gts, 1kHz, 1.3kGts, 1,5 kHz, 2kHz, 2.5 kHz .. and so on.
The bottom: 400Hz, 700Gts, 1,3 kHz, 1,7 kHz, 2,3 kHz, 2,7 kHz .. and so on.
First, the high level of difference frequency 100Hz is quite obvious (that’s it – the power and density of the transistor). Its level is 10 dB higher than that of the stage with two-way limitation on the grid (bottom spectrogram).
Second, the structure of the dominant tones on the top spectrogram is much more structured: except for the 800Hz and 1.3 kHz, all dominating tones are the sum of the initial tones multiplied by an integer.
Our ears “love” consonant tones, so it is not surprising that the spectrum on the bottom figure seems to them much less musical and “dirtier” because its structure is far worse.
It also should be noted that during the limitation of a single sinusoid the differences in the spectra of discussed above stages are minimal.
Even worse is the situation with limiters based on op-amps.
Below you will see the spectrogram received at the output of the inverting op amp stage with the feed limitation and the stage with a common cathode. Two tones – 100Hz and 200Hz – were fed to the input (the amplitude of the input signal in case with op-amp was decreased proportionally to ensure identical stage limitation threshold).
Quite evident is the dominance of the total tonal harmonics of 100 Hz +200 Hz: 600Hz. 1.2kHz, 1.8kHz, etc. on the bottom figure (limiter with common cathode), and virtually complete absence of such in the spectrum of the op-amp-based limiter on the top of the figure. However, despite the high ordering of the spectral components on the top figure, they are not consonant in relation to the overall tone and are perceived by us as noise or “dirt” mixed in the input tones.
Given the initial tones produced by a guitar, all the above phenomena are observed in the most informative for an ear segment covering 400 Hz … 3 kHz. As a result, in the case of vacuum tube limiters, we enjoy the beauty of the spectrum in this segment. In case of bilateral limiters, the developers tend to give at least some range of euphony completely cutting out the most informative “mids” and boosting low frequencies. There is no other way, though. You can clearly see how the level of the difference tone is lower in the case of bilateral limitation. What else can they do with the spectrum, which is initially non-consonant with the resulting tone?
Unfortunately, except for the triode one, the bilateral limitation is provided by almost all limiting stages, whether they are op-amp or discrete transistors-based. Understanding of this fact is the key to obtaining a “correct” tube sound from transistor-based devices.
Limitation of stage with common source and resistive load
Of all transistor types, FETs, with volt-ampere characteristics very similar to the ones of pentodes and having high resistance from the part of the gate, are the closest to tube devices.
Us – source potential.
Fig.4. Stage with common source limited at output and input.
The problem of FET in the circuit with common source and resistive load is that by limiting the signal output from the top like a vacuum triode, “it manages” to limit the bottom half-wave as well at the output. Besides, it does so prior to the moment it is limited at the input (Fig. 4). By the time of input limitation we have already fully open device, and the entire input current is added to the current through the FET channel. This current easily penetrates the output signal, forming on the bottom half-wave the so-called “reverse bite”. The effect can be somewhat weakened by means of sequential adding large denomination (0.4…1MOhm) to the resistor’s gate. But this method of reducing the “bite” does not eliminate the limitation at the output from the bottom. Thus, FETs themselves cannot sound like limited triode. This applies equally to all the stages with common source including m-stages. It should be said that vacuum pentodes have not been used in guitar preamps for the same reason: having a huge amplification, they behave like a stage with a common source, limiting the signal at the stage output via both half-waves, which, in general, predetermined their destiny in guitar preamps building.
Now we know what the picture of signal limitation by means of a triode stage looks like, and also know why the FET-based stage with common source does not provide the proper limitation. The main problem is that the relative level of input limitation of FET-based stage is much higher. Let us try to solve this problem.
First, remembering the relationship between triodes input feed and limitation (200 … 400V / 1 … 3V), FET should receive the highest possible voltage. Besides we need to use devices with low voltage cutoff.
Second, to reduce the input limitation level we should use a silicon diode or Schottky diode, connecting them parallel to FET’s own junction.
Third, we should provide such stage amplification that the input limited positive half wave multiplied by the stage’s Ku does not result in bottom output limitation. The easiest way to do this is by introducing additional resistance in the source.
The figure below shows the FET-based stage meeting all these conditions
Fig.5. Stage with common source and «triode» limitation
A few words about the dynamics
There is another interesting feature of the transistors, which is very valued among guitarists. This is the so-called “tube dynamics”. From the point of view of a guitarist, the dynamics is very noticeable dependence of the signal from the output of the distorting device on the physical impact on the strings. Naturally, it gives additional possibilities for emotional coloring of performance.
Let’s look into the “dynamics” from the position of an engineer.
From the viewpoint of an engineer the tube dynamics is the dependency on the level of the input signal in relation to the three parameters:
1) signal level
2) density of the spectrum
3) duty factor of limitation
The level of the limited signal at the output tube stage is dependent on the level of the input signal due to 2 reasons: on the one hand the lower half-wave of the output signal increases as vacuum diode at the input has a very soft dynamic resistance dependence on the applied voltage. But, in addition, we can see the increase in “upper” section of the output signal, which is caused by displacement of operating point downwards under the influence of large input amplitude. The increase in the capacity of the cathode leads to the shift of the operating point downwards, as well as the additional increase of the upper half-wave. This happens because of the fact that the grid current merges with the anode current and flows through the cathode resistor increasing its potential.
(Note: The effect of this component is often blocked by a capacitor in the cathode circuit of the transistor, hence, it’s obvious that beside the fact that cascades with the cathode shunt and without it have a different output dynamic resistance they also have different dynamics – stages without shunts have a slightly more pronounced dynamics.)
For distortions with little amount of gain the pronounced dependence of the output level in combination with the spectrum density along with amplified input signal provides those playing sensations that are so valued by guitarists. After all, they genuinely feel the way they control the limitation process.
Of course, the op amp with diodes in the negative feedback circuit also can give some “dynamics”, but in this case you should use silicon diodes having a rather abrupt change of dynamic resistance within the range of 0.4… 0.6 V; this kind of dynamics is manifested in a very narrow range, and to use it is not easy, to put it mildly. The option of op amp limiters in relation to feed in general is completely devoid of any kind of amplitude dynamics: in this instant the whole dynamics manifests itself only in the distortion spectrum squeeze depending on the level of the input signal.
And finally, the duty factor. Duty factor is essentially the ratio between the “width” of the upper and lower half-waves at the limiter’s output. In case of weak signals the duty factor is close to the duty factor of a meander, but with signal increase the spectrum receives more even low-frequency harmonics that ears can hear pretty well. The tube limiters, because of their multistage structure, have better pronounced dependence of the duty factor on the level of the input signal, and when it comes to the high-gain limiters this component sometimes comes to the fore. OP-amp-based circuits are almost devoid of such dependence, and even the tricks in the form of unequal number of diodes in the op-amp feedback circuit fail to produce the limiter’s sound close tube-originated since changes in the duty factor are insignificant.
The proposed pseudo-triode FET-based stage having the current distribution similar to the stage of authentic vacuum triode behaves similarly in terms of dynamics too – we have the same smooth and uniform increase of the output signal on the bottom (this smoothness is due to CVC of germanium junction, which is close to the VAC of a vacuum diode), the working point going as the input signal increases, which gives us exactly the same stage behavior as that of a conventional triode’s. Therefore, in terms of dynamics, when you play using the device based on pseudo-triode you experience the same sensation as when playing with a tube-based preamp.
It is difficult to create something that is absolutely perfect. Therefore, the proposed stage is not the full replacement of the transistor. Let me remind you, that while developing the stage the emphasis was precisely on the limitation. The behavior of the stage in the “linear” region remained almost without any attention. But even here there is a very interesting observation – mutual compensation of nonlinearities of the additional diode and the passing performance of field-effect transistor (which has quadratic dependence vs the dependence 3 / 2 for tubes), which in case of thorough calculations will ultimately lead to a partial linearization of “linear region” and provides the distortion spectrum very close to the triode’s even without stage limitation mode engagement.
We love the tube-based sound and the sound of triode overdrive. A tube is a well-known and well-trodden path toward the truth, but it is not the only way. We have never thought, that the above-described researches were conducted by the author of the article exclusively. We are aware of some works, which dealt with FET-based triode limitation emulation. For examples the following patents: US Patent No.05647004 and US Patent No.05619578. The authors of the patents also found it necessary to limit the positive half wave at the input and limiting amplification stage by introducing additional resistance in the sources. But at the same time, it should be noted that the level of input limitation implemented in these patents:
1) was significantly influenced by temperature, which leads to significant variations in output signal amplitude (and in case the output signal limitation on the bottom – to significant deterioration of the spectrum). In our case, the level of input limitation is the sum of “constant” FET gate-source voltage and voltage drop across the germanium junction, which makes the limitation level a lot less sensitive to temperature changes.
2) in mentioned patents in case of input overload in this stage there is no current, similar to the grid-cathode current, which eliminates the offset of the operating point, depending on the level of the signal at the stage input. Accordingly, in this case, we do not have the required “tube”-like dynamics.
The proposed stage is different in the fact that limitation formation in the proposed stage caused by adding gate-source voltage and forward voltage of Schottky diode is more consistent with the processes occurring in the real vacuum triode than simple limitation of the positive half-wave by “grounded” diode.
The proposed cascade formed the basis of the LA series currently manufactured by AMT. But times goes on and the components choice expands, so we continue to actively study the “phenomenon” of tube sound and go on developing better ways of sound emulation. We hope that in the near future AMT will be happy to offer its fans more innovative developments.
© AMT Electronics
© Victor Kampf