Real-Time Simulation of a Guitar Power Amplifier Ivan Cohen, Thomas Hélie

Real-time simulation of a guitar power amplifier Ivan Cohen, Thomas Hélie To cite this version: Ivan Cohen, Thomas Hélie. Real-time simulation of a guitar power amplifier. 13th Int. Conference on Digital Audio Effects (DAFx-10), Sep 2010, Graz, Austria. hal-00631752 HAL Id: hal-00631752 https://hal.archives-ouvertes.fr/hal-00631752 Submitted on 13 Oct 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Proc. of the 13th Int. Conference on Digital Audio Effects (DAFx-10), Graz, Austria , September 6-10, 2010 REAL-TIME SIMULATION OF A GUITAR POWER AMPLIFIER Ivan Cohen Thomas Helie Orosys / Two Notes, Ircam - CNRS - STMS UMR 9912, Ircam - CNRS - STMS UMR 9912, Analysis/Synthesis Team Montpellier, France Paris, France [email protected] [email protected] ABSTRACT Vp Vout Rg2 Rg1 Vg2 Vb1 T This paper deals with the real time simulation of a class A single Vin Vg1 ended guitar power amplifier. Power tubes and triode models are RL compared, based on Norman Koren’s work. Beam tetrodes and 6L6GC pentodes characteristics are discussed, and displayed as Norman Vk Vb2 Koren’s model parameters. A simple output transformer model is Rk Ck considered, with its parameters calculated from datasheets speci- fications. Then, the circuit is modeled by a nonlinear differential algebraic system, with extended state-space representations. Stan- dard numerical schemes yield efficient and stable simulations of Figure 1: The electronic circuit the stage, and are implemented as VST plug-ins. Vb1 Vb2 Rg1 Rg2 Rk RL Ck 300 V 400 V 5.6 k 1 k 220 8 100 F 1. INTRODUCTION Ω Ω Ω Ω µ Many analog audio circuit simulations (guitar amplifiers, synthe- Table 1: Typical values of the components used in the power am- sizers, studio devices etc.) have been released for musicians, who plifier want to replace their equipment with cheaper and more flexible digital equivalents. However, the realism of these digital simulations can still be improved. This is mainly due to nonlinearities The passive components are considered ideal. Using the Mill- that are responsible for the “sound signature of analog audio de- man’s theorem, Kirchoff laws and our component models, the elec- vices” the modeling of which is often complex and still keeps a lot tronic circuit can be modeled by a set of differential algebraic of people busy. equations. This paper deals with realistic simulation of guitar tube amplifiers, for real-time applications. Several papers have been pub- 3. POWER TUBES MODELS lished about this subject, often focused on triode amplifiers cir- cuits, and sometimes power amplifiers (see [1, 2, 3, 4, 5]). In this 3.1. Introduction article, we consider a single-ended tube power amplifier, using pentodes and an output transformer. First, we consider Norman Vg1 Vg2 Vp Koren’s model for several standard power tubes found in guitar power amplifiers. The control grid current and the parasitic capacitances are studied, and compared with the work done in [5] about triodes. Then, a simple linear model for the output transformer is introduced, with its parameters calculated from datasheets specifi- Ig1 Ig2 Ip cations. The circuit is simulated in real time using extended state space representations. Finally, the results are shown and discussed. Vk 2. THE CLASS A POWER AMPLIFIER Figure 2: The power tube’s model The class A power amplifier (figure 1) increases the power of the As seen in [7, 5], the triode has a capacitive behaviour between signal from a preamplifier to a speaker, with a matched output the grid and the plate, increased by the Miller effect. The adding impedance. This is a very simple power amplifier, chosen for its of the screen grid decreases the value of the capacitance (from 2 sound characteristics, and for the simplicity of its modelisation. It pF to 0.02 pF), and increases the power gain of the vacuum tube is defined as “single ended” because it uses a single tube to produce (µ is the voltage gain). This yields to a topology called the tetrode, an output, in contrast to push-pull amplifiers, another topology us- which has a unwanted side-effect, known as the Dynatron effect. ing more tubes and phase inverters for more power, operating in It gives the tetrode valve a distinctive negative resistance charac- classes AB or B (see [6] for more information about power ampli- teristic, sometimes called “tetrode kink”. This problem has been fiers classes). The voltages Vb1 and Vb2 are constant bias voltages. solved with the addition of a third grid (the pentode patented by Typical values for its components can be seen in table 1. Philips/Mullard [8]), and with another topology called the beam DAFX-1 Proc. of the 13th Int. Conference on Digital Audio Effects (DAFx-10), Graz, Austria , September 6-10, 2010 tetrode. These two kinds of vacuum tubes are very often described 3.3. Grid current and parasitic capacitances as pentodes. The I 1 current is often neglected in triode models [3, 9]. But it The pentode is a vacuum tube widely used in guitar and hifi g is responsible for the grid rectification effect that designers try to power amplifiers, a triode with the control grid (G1), the cathode limit using specific polarizations and the resistance R 1. In [5], (K), the plate (P), and two extra pins : the screen grid (G2) and g the grid current model was a simple approximation of a diode’s the suppressor grid (G3). Beam tetrodes and pentodes plate cur- characteristic. A smooth transition is added between the resistive rent curves in datasheets show they have a significantly different behaviour and the interval of voltages where the current is null, behaviour. In short, beam tetrodes have much sharped knees com- with a second order polynomial. This model gives results close to pared to pentodes, a lower ratio of screen to plate current, a lower SPICE’s diode models. The parameter R 1 controls the resistive third harmonic distortion [6]. Their model is very important for g k behaviour of the grid current, V is the voltage threshold between the realism of the complete stage’s simulation. γ the null and resistive behaviour. The parameter Kn is the length of the smooth transition. 3.2. Norman Koren’s model 0 if Vg1k <Vγ Kn Vg1k−V γ − Ig1 = if Vg1k >Vγ + Kn (4) The Norman Koren’s model [1] is said “phenomenological”. It Rg1k 2 models the behavior of physical phenomena using parameters not aVg1k + bVg1k + c otherwise derived from fundamental physics, to match published curves from datasheets. The expression of the Ip and Ig2 currents for pentode- with like vacuum tubes are the following : 1 a = 4KnRg1k K Vγ Vg2k 1 Vg1k b = − E1 = log 1 + exp Kp + (1) 2KnRg1k Kp µ Vg2k 2 Ex c = a(Vγ Kn) b(Vγ Kn) (5) E1 Vpk − − − − Ip = (1 + sgn(E1)) arctan (2) Kg1 Kvb Vg2k Vγ Rg1 Kn Ig2 = exp Ex log + Vg1k (3) µ 13 V 6000 Ω 3 V The table 2 displays typical tubes parameters, from [1] and Table 3: Typical values for the parameters of grid current’s model SPICE models. µ is the voltage amplification factor, Kg1 a parameter inversely proportional to overall plate current, Ex an ex- In [5], we consider the dynamic behaviour of the triode model ponent, Kvb a knee parameters in volts, Kg2 the inverse screen with its parasitic capacitances, in particular the capacitance be- grid current sensitivity, and Kp a parameter that affects the plate tween the grid and the cathode, because of the Miller effect. Pen- currents for large plate voltages and large negative grid voltages. todes and tetrodes have lower parasitic capacitances than triodes. The differences between the pentodes and the beam tetrodes in The parameter µ is lower than 20, instead of 100 for 12AX7 tri- general are displayed in this table, particularly with the parameters odes. So, considering the Miller effect for pentode-like tubes, the µ and Kvb. capacitances have no effect inside the bandwidth of audible fre- quencies, and including parasitic capacitances in tube models is not judged relevant. This result has been confirmed by SPICE sim- Pentode µ K 1 K 2 K K E g g p vb x ulations and informal listening tests. EL34 11 650 4200 60 24 1.35 EL84 16 570 4200 50 24 1.35 4. OUTPUT TRANSFORMER MODELS Beam Tetrode µ Kg1 Kg2 Kp Kvb Ex 6L6GC 8.7 1460 4500 48 12 1.35 Vacuum tube power amplifiers typically have a tube output impedance KT88 8.8 730 4200 32 16 1.35 around 1 kΩ, whereas loudspeakers have an impedance between 4 and 16 Ω. The high-impedance plate speaker load is transformed Table 2: The parameters of Norman Koren’s model for a few pen- into a low-impedance load using an output transformer. The ideal todes and beam tetrodes output transformer is defined by the number of turns in its primary winding Np and in its secondary winding Ns. The ratio between the input and output impedance of the transformer is a function of 2. 400 400 (Np/Ns) Vg1k =0 V We consider the Plitron PAT-3050-SE-02 output transformer, a 300 300 Vg2k =400 V typical output transformer for single ended power amplifiers.

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