Nashville SE 20 - Some basic Math on theSuperTriode ConceptBasic calculations require one component to start with.I chose the output transformer as the most crucial component. For the project the single ended versionof a Lundahl LL1693 seemed to be a good matchregarding quality, pricing, technical data and size (fig. 1).The SE version of the 4.5kg transformer has a core air gap of 450µm. Recommended idle current is230mA with all primary windings in series. Primaryinductance is 16H. With a secondary connection B(4Ohm, see Lundahl datasheet) the reflected primaryimpedance is 1kOhm.Inherent Output Power LimitThe recommended transformer idle current of 230mA allows a theoretical current swing from 0mA to 460mA peak to peak (p-p). According to I2 * R = P a simplified power calculation neglecting transformer losses reveals a maximum output power of(0.23A / sqrt2)2 * 1000Ohm = 26.45W ≈ 26.5W(equation 1)which is the inherent output power limit, not too much but fairly above the requested minimum of 20W. Hence I stayed with the LL1693 for further calculations. By the way, the push-pull version of the LL1693 is capable to handle around 300W output power.Output Voltage Swing (fig. 2)Considering a „worst case“ estimation of 30W output powerand 1kOhm primary impedance the power output voltageswing p-p at the primary coils according to U2 / R = P issqrt 2 * (sqrt(30W * 1000Ohm)) * 2 ≈ 490V p-p (equation 2)With an estimated minimum residual voltage of 100Vacross the triode the power supply voltage would haveto be around100V + 490V / 2 = 345V ≈ 350V (equation 3)Thus the maximum voltage peak expected to be at theplate is100V + 490V = 590V(equation 4)Adding a comfortable safety margin (speakers unintentionally disconnected) the circuit components should withstand900V to 1000V peak voltage, nothing special for a tube butpretty much for a transistor.Power DissipationFrom the above equation 3 and a given idle current of 0.23A the total power dissipation is 350V * 0.23A = 80.5W. Assuming an idle current of 30mA for the triode and an idle current of 200mA for the transistor plus a plate / collector voltage of 350 V power dissipation at the plate will be 10.5 W and power dissipation of the transistor will be around 70W. 350V and 200mA idle current must be within the DC safe operating area of the transistor with a comfortable safety margin. This will rule out BJTs because of their inherent secondary breakdown. That leaves power MosFets. Power MosFets meeting the specifications above are available for instance the IXFH14N100 or IXFN32N120P. However, these MosFets are designed for industrial high power switching applications. They are quite non-linear at low drain currents and have quite large gate capacitances. Below some data on the IXFN32N120P are discussed (fig. 3). Fig. 3: Maximum ratings and transconductance of the IXFN32N120P.At low currents transconductance gm is a linear function of Idrain. Estimated transconductance gm at 230mA is around 0.6S. Umax of the IXFN32N120P is 1200V, Pd is 1000W, gate capacitance Ciss is 21nF. With a load resistance of 1kOhm the effective (or Miller) capacitance isCM = Ciss * ( 1 + gain) = Ciss * (1+ (gm * 1000)) = 0.021µF + (1+(0.6*1000)) = 12.62µF (equation 5)12µF (!) dynamic input capacitance is difficult to drive without compromising high frequency response even without the essential gate stopper resistor. Thus the IXFN32N120P or similar devices with even lower gate capacitances are hardly suitable for a SE power amplifier according to the SuperTriode concept.Core MagnetizationThe SuperTriode configuration (fig. 4) suffers from an additional flaw: Even at large signals the plate current remains almost constant. Thus in a single ended design the current through the tube just magnetizes the output transformer‘s iron core but does not contribute to the output power. If 200mA idle current are assumed for the transistor, the inherent power limit calculation from above equation 1 drops to 20W and will be less if transformer losses are taken into consideration.ConclusionWith regard to the required minimum specifications ofthe transistor it may be concluded that the SuperTriodeconcept as illustrated in figure 4 is not suitable for SEpower amplifiers if an output power above a few wattsis requested despite its beauty and simplicity.On the other hand the concept is far too fascinating to besimply discarded…..