Vacuum Tube Amplifier Modeling with Dynamic Convolution Jason Traub Department of Electrical and Computer Engineering, University of Florida Though nearly obsolete within electronics, vacuum tubes remain in high demand for musical amplification [1]; and particularly for electric guitar. This research discusses reasons for the observed preference and assesses its validity. Furthermore, amplifier electronic circuits are studied and comparisons are made between vacuum tubes and bipolar junction and metal oxide field effect transistors; the latter two have replaced vacuum tubes in nearly every application, and are responsible for the advancement of the digital computer. Undoubtedly, there exists extreme cost effectiveness in obtaining a computer processing technique to mimic the sound that is applied by a vacuum tube amplifier. Thus, many modeling techniques have been developed and used in commercially successful products. This research discusses several of these methods and ultimately attempts to mimic a vacuum tube amplifier using the dynamic convolution method, proposed by Kemp [2]. Introduction: Light Bulbs, Valves, and Transistors acuum tubes, or “valves”, as the British call them, were the first electronic component to be able to V function as an amplifier. To give a historical perspective: Thomas Edison invented and patented the light bulb in 1879 [3]; J.J. Thompson’s experiments led to the discovery of the electron in 1897 [4]; and the work of John Fleming and Lee de Forest ultimately led to the vacuum tube triode in 1906 [5]. This three terminal device allows us to amplify the current and/or voltage of an input signal. A vacuum tube triode consists of two electrodes, the plate (anode) and cathode, separated by a short distance in an Figure 1. 12AX7 Current vs. Plate Voltage characteristic at several evacuated tube. Figure 1(a) shows a body diagram of a grid voltages (Eg) [9] vacuum tube triode. A third electrode (grid) is placed as a the cathode, electrons will be emitted across the vacuum, i.e. wire mesh in between the plate and cathode. Figure 1(b) a current will flow. As we make the grid voltage more and shows the schematic representation. more negative, the more the current between the plate and cathode is impeded. Figure 2 depicts the operation of a 12AX7 vacuum tube triode (taken directly from its’ datasheet). We can clearly see, as we make the grid voltage more negative (lines moving to the right), the current gets corralled. From Tubes to BJTs and MOSFETs This relatively crude device was relied upon in electronics th throughout the first half of the 20 century. Everything from (a) Body diagram [6] (b) circuit symbol [7] radio, television, radar, sound reproduction and process Figure 2. Vacuum Tube Diagrams control, used vacuum tubes. Today, however, vacuum tubes As alluded to earlier, vacuum tubes act as an electronic are nearly extinct. By the early 1960s, solid-state transistors valve which controls the flow of current between the plate were steadily replacing vacuum tubes [10]. The same and cathode by the voltage applied to the grid. The device functionality that the vacuum tube pioneered, solid state conducts current through thermionic emission [8]. The transistors did in an immensely more size, power, and cost cathode is heated, directly or indirectly, by a filament efficient manner [11]. connected to a high voltage. A potential difference of The solid-state transistors most commonly used are hundreds of volts is applied between the plate and cathode Bipolar Junction (BJT) and Metal Oxide Field Effect terminals. When the plate is more positive with respect to (MOSFET) transistors. The physical operation of these University of Florida | Journal of Undergraduate Research | Volume 17, Issue 2 | Spring 2016 1 JASON TRAUB devices rely on charge transport between doped We will discuss the validation of this preference in the semiconductors [12]. A BJT is a current controlled device, following section. After an appreciation for the complex and while the MOSFET is a voltage controlled device. The “imperfect” signal processing that vacuum tube circuits construction of these devices consists of no gaps, or inherently apply, we will discuss methods of modeling this vacuums, and involves point to point contact of solid-state effect in the digital domain. The dynamic convolution doped semiconductors. method has been chosen for detailed study and A rudimentary cross section of a MOSFET and a BJT is experimentation. The final section documents the results and shown in Figure 3. The fundamental physics of MOSFET methodology of this experiment and explains the operation works like this: in the substrate, there exists a p- tribulations experienced. Finally, this research offers a doped region (hole dominant) between two n-doped regions course of action for our future successful implementation of (electron dominant). An oxide insulator is placed above the dynamic convolution. p-doped region and an electrode (gate) is placed on top. The two n-doped regions are the drain and source electrodes. Perception and Psychoacoustics: Why Do When a positive voltage is applied at the gate, electrons in Vacuum Tubes Remain Relevant? the p-doped region are attracted to it. Thus, a channel for current flow develops. The direction of the conventional It is known that a large amount of musicians and current in each device is given by the direction of the arrow. audiophiles prefer the sound of vacuum tube amplifiers over their solid-state counterparts [1]. Perhaps the sound of a vacuum tube amplifier has become iconic due to their extensive use on music from the 1960s. While this argument is somewhat relevant, it does not reveal the objective and subjective merits that tubes actually warrant. Much of the desired sound of electric guitar stems from how the signal distorts. In most practical engineering situations, we do not want to distort the signal at all. However, when musicality is our primary concern, this does not necessarily apply, since the listening experience is (a) MOSFET (b) BJT ultimately subjective. People continue to use tubes, because people simply like the sound better! Let’s explore the, fairly Figure 3. Transistor cross sections convincing, objective reasoning behind this. According to research done by Russel O. Hamm [14], A BJT works on similar fundamental. Here we have, there is an audible quality difference between tubes and again, a p-doped region (base) between two n-doped regions solid-state components that is perceivable and objectively (collector and emitter). In this case, instead of a voltage measureable. Vacuum tubes distort more gently than solid- induced channel, we directly inject carriers into the doped state transistors, particularly in the high frequency range. region, which allows for current flow. It is of note that, no Non-linearity causes distortion, and distortion generates current flows through the gate of a MOSFET, due to the harmonics. Hamm’s research explains the difference in insulator oxide. terms of the harmonics generated when driven into It is essential to note that, the principle of operation of all saturation. Tubes exhibit strong 2nd and 3rd harmonic three devices (tubes, BJT, and MOSFET) remain the same: content, with the 4th and 5th harmonic’s power increasing as the current between two nodes is controlled by the the signal is driven more and more into saturation. The current/voltage applied to the third. author claims that even harmonics add body to the sound, To conclude this introduction, the development of the whereas, the 3rd harmonic contributes to softening the sound. vacuum tube and its associated electronic functions have He adds that, the 5th harmonic adds a “metallic sound that been monumental in the advancement of technology and gets annoying in character as its amplitude increases” [14]. human achievement. The advent of the solid-state transistor The author further notes that, higher order harmonics add has progressed this technology, by implementing the same attack and bite to the sound. Thus, the perceived tonal electronic function, yet, much smaller, more power efficient, advantage of vacuum tubes can be explained by the fact that and more reliable. It is the fact that we can fit billions of solid-state components have strong, objectionable high transistors on a single computer chip [13] that is responsible frequency components when only slightly driven into for the highly advanced functions computers perform today. saturation. Tubes, on the other hand, deliver pleasing, and In spite of the many advantages of transistors, the major sought after, harmonic tones that rise in harmonic character question of this research remains: Why do vacuum tubes as the input signal increases. remain relevant? Why do they remain in high demand for According to the IEEE spectrum article, “The Cool Sound guitar and other audio amplification purposes? of Tubes” [1], other characteristics of vacuum tube amplifiers also have a substantial effect on their sound. For University of Florida | Journal of Undergraduate Research | Volume 17, Issue 2 | Spring 2016 2 VACUUM TUBE AMPLIFIER MODELING WITH DYNAMIC CONVOLUTION example, it is noted that the high voltage output transformer, Dynamic Convolution used specifically in vacuum tube amplifiers, has a tremendous effect. This effect is explained by the 2nd and 3rd Convolution can be implemented to model a system, with order harmonics generated with surprisingly low inter- perfect accuracy, in theory, if the system is linear, and time- modulation distortion [1]. The author further notes that the invariant. However, the distortion we seek to emulate is, in unique circuit components used can also affect the sound. it of itself, non-linear, therefore violating the conditions of Finally, it is claimed that a natural compression of the audio the convolution theorem. However, dynamic convolution signal takes place when played through a tube amplifier, an has been proposed and implemented, by Kemp [2], to get effect known as “infinite sustain” [1].