Hopefully you have at least scanned the previous three pages about the operation of Leo Fender's 5F6-A tonestack and the significance of Jim Marshall's modifications to it. The achievements of these legendary circuit designers provide the framework for our own creations.
The tonestack is perhaps the most complex system in an amplifier, both technically and philosophically. Its components are purposely designed to have reactive impedances that vary significantly with frequency over the entire audio band. There is also considerable interaction between the controls, offering us more challenges. As a result, we need to pull out all the stops to make the design process simpler.
In situations like this, Spice simulation appears to be a convenient solution. We can specify all the parts values and get the frequency response with 64-bit digital precision. What we really want, however, is the reverse. We want to accurately describe the desired frequency response and thereby obtain the appropriate parts values. The procedure I describe here, which is based on Hendrik Bode's methods, represents a nostalgic, mid-twentieth century approach that would have been very familiar to Leo and Jim.
First, we need to observe our design environment. Leo Fender's tonestack is driven by a cathode follower. This means our driving stage has a relatively low output impedance of less than 1k.1 The tone stack also drives a phase inverter with a relatively high input impedance.2 Both of these conditions are ideal. They give us maximum flexibility to achieve our design goals, because the tone stack can be designed independently, without integrating the characteristics of the driving and driven stages. If we choose to drive this stack directly from a preamp stage, as in the Fender Vibro-Champ AA764, or use it to drive a 100k volume control, then all bets are off. In that case we need to go back and repeat the Bode analysis described in the previous two pages and include some extra variables. Leo Fender purposely placed his tonestack between a cathode follower and a long tailed pair, and Jim Marshall saw no reason to alter this concept. Neither do I - it offers maximum design flexibility by making the tonestack response independent of the driving and driven circuits.
I prefer to start with the midrange. This sets the overall attenuation for all frequencies when the bass and treble controls are minimum. First I choose a value for RM. For a lot of midrange scoop and finer midrange control it can be dropped to 10k, but 25k usually works fine. The value of R1 is then a function of RM and the desired midrange attenuation:
Here A is a positive number representing the amount of attenuation in dB with the midrange control at maximum. As reference points, for the Fender Bassman 5F6-A we have A = 10, whereas for the Marshall JMP50 the value is A = 7.3.
As the bass and treble control positions are increased, these frequencies bleed back into the mix and suffer less attenuation. At the center of the bass and treble passbands with the controls at maximum these signals suffer almost no attenuation.
At the boundaries between bass and midrange and between midrange and treble, the frequency response changes at a maximum rate of 6dB per octave. The positioning of these transition regions is very important to the tonal characteristics of the amplifier. It is here that the response changes as the player moves up and down the scale. It could be Lydian, Dorian, or perhaps even Mixolydian - it doesn't matter. As the guitar player moves up or down the scale, the response steadily changes at about 6dB per octave. As circuit designers, we're essentially deciding where on the neck these transitions take place. Once the signal is well into the passbands, the response is more constant, and under the full control of the bass and treble knobs.
Once I set the values of RM and R1, I define the upper end of the bass passband. This is a function of both R1 and C3, but since we've already set the resistor value we have only one variable to left adjust: the capacitor. The -3dB bass upper break frequency defines the top end of the bass band and the start of the transition from bass-knob control to midrange-knob control. As reference points, Leo's 5F6-A uses a frequency of 142Hz. Marshall increases this to 219Hz. For even more perspective, the guitar's low E string is at 82Hz; the open D string is at 147Hz; and the high E string is at 330Hz. You're the designer - decide!
The value of C3 corresponding to our desired break frequency f1 is
Setting the frequency higher places more lower-midrange frequencies under the direct control of the bass knob. This means more bass frequencies tend to move together as a group. Setting the upper break frequency lower puts more bass into the transition region between bass and midrange, where the response decreases as the frequency moves higher.
Next I prefer to finish off the base passband design by calculating the value of C2. The tonestack obviously has infinite attenuation at DC because the signal has to pass through at least one capacitor to get to the next stage. So there must be a lower end to the bass passband. It turns out, however, that the lower end is way below the range of guitar audio as long as we keep the bass control RB sufficiently large. I recommend we leave it at 1M, consistent with both Fender and Marshall designs.
The important characteristic determined by C2 is the amount of bass attenuation with the bass control set to minimum. In keeping with the spirit of Leo's design, bass attenuation should equal midrange attenuation if the bass control is at minimum and the midrange control is at maximum. (Feel free to violate this rule, however, if you have a particular grudge against bass.) The value of C2 as a function of the break frequency f2 for these control settings is
For Leo the break frequency was 49Hz, which was certainly influenced by the fact that the 5F6-A was intended to be a bass guitar amp. Jim Marshall increased the break frequency to 62Hz. Below the break frequency that we choose, the response drops off at a rate of 6dB per octave.
I save treble for last. For treble frequencies we have a lot of flexibility, because the lower break frequency is a function of the product of RT and C1. This kind of leeway represents are rare opportunity to consider the cost of the components. For purely economic reasons we want the capacitor to be fairly small, but not so small that it is nearly the same as parasitic capacitance due to parts placement. Otherwise the response will be dictated by how we route the wiring. For me, Leo Fender's choice of 250pF represents a lower limit. If we choose to increase the lower treble break frequency beyond Fender's design, then it would be wise to consider keeping Leo's 250pF capacitor value the same and reducing the value of RT. In the opposite direction, towards a lower treble passband, increasing C1 is the most convenient.
The capacitor value based on our choice of treble control and break frequency is
There you have it - tone shaping a la carte! A lot of math went into deriving these formulas, but using them is quite easy. The hardest part is understanding what the break frequencies represent.
As we tweak Leo's tonestack design, even to the point of completely changing all the parts values, it's important to maintain some humility and perspective. We're not creating an entirely new circuit, nor are we inserting it into a new signal environment. Moreover, Jim Marshall demonstrated decades ago that the passbands for bass, midrange, and treble can be altered in a systematic way. The methodology I have described here merely quantifies what has been achieved by two legendary circuit designers. There are certainly other ways to analyze this tonestack and other methods to compute the desired parts values. What I have outlined here is simply what works for me.
1Richard Kuehnel, Circuit Analysis of a Legendary Tube Amplifier: The Fender Bassman 5F6-A, 3rd Ed., (Seattle: Pentode Press, 2009).
2 ibid., p. 93-96.
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