High transconductance vacuum tubes are strange animals, with electrical and   mechanical challenges fully surpassed only at the end of the western thermionic technology parabola.

            But....what’s their physical structure?

In Fig. 1 you can see the internal section of a triode with planar electrodes [1].

     For this geometry, complex calculi show [2]:








m                                    Gain Coefficient;

n                      Grid wires/cm;

a                      Cathode to Grid distance (cm);

b                      Grid to Plate distance (cm);

R                     Grid Wire Radius;

Eg                   Grid Voltage;

Ep                    Plate Voltage;

Jp                     Plate current density.


      In a triode the transconductance, gm is given by:


Since (where DS is the emitting surface area)  from eq. 2 you obtain:


The equations (1) and (3) are fundamental in the design of triodes (and particularly for the high gm class).

The Fig. 2 displays the transconductance gm and the m factor versus the grid to cathode distance a. The graph refers to the Russian triode 6C45-PE but the trend is common for similar triodes (such  6H30, 3A167M, WE437A, ....). You can observe that gm increases when a decreases. Also the m factor  slope is affected by a (since a+b is constant) but can be changed by the geometrical factors in eq. (1) as n and/or R.

Fig. (2) shows a strong dependance of gm with respect to plate current (indirectly shown in the graph with Ep=cost and Eg=(-2..0)V) more marked  in the low region of  a values.

Here you have a classical cost/benefit problem since the reduction of the distance a causing an increase  of gm (the benefit), submit this parameter to the caprices of plate current strongly (the cost).

The reduced dimensions (mechanically faced with non-standard building as frame grid structure) are the main source of the electrical limits in this tube typology:

a)     Microphonicity;

b)     Self -Oscillating Tendencies;

c)     High Parasitics;

d)     Mismatching.

The audio designer must manage this drawbacks properly for succesful results.




The Fig. 3 shows the basic schematics you can use as:

a)     Transformer Coupled Line Amplifier;

b)     Single Tube Power Amplifier;

c)     HeadPhone Amplifier.



For this applications the best results are obtained with triodes having  high the parameter

s = gm  m.         (4)



An high value in the s parameter reduces the input voltage swing and optmizes the transformer turn ratio for a low output impedance with good current capabilities and high damping factors.

High s  tubes are useful also in the design of Two-Stage Single Ended Amplifiers designed thinking to tubes as 211, 845, 300B, SV-572-XX....and deserve nice surprises in the design of Low Power OTL amplifiers.

The essential requirement for an OTL amplifier is a low open-loop output impedance. The utilization of  low rp tubes appers as an irrunciable requirement but you can obtain excellent results also with high s tubes. In fact the excellent performances in term of Zout for the 6C33 triode (s=0.128)  can be obtained and surpassed with other tubes as 6C45-PE (s=2.34) and E55L (in pseudotriode mode, s=1.5), Fig. 6.


Amplifiers designed around high gm, high s tubes present obvious advtages in term of noise, gain and bandwidth. In a triode in fact the Equivalent Noise Resistance, req is given by:

while for a common cathode amplifier you have:



Ao                               Gain


GBW                         Unity Gain Frequency.






            High gm, high s tubes present a wide spectrum of opportunity but also drawbacks derivated by their intrinsic nature. The variability in the electrical parameters, but also microphonicity and self oscillating phenomena must be evaluated with care by calculi, simulations and prototyping .



[1] W.G. Dow,  Fundamentals of Engineering Electronics,   John Wiley & Sons 7th Rep. 1948.

[2] Kusunose, Quziro, Calculation of Characteristics and the Design of Triodes,

                                                                                               Proc. I.R.E. , 17,   1706, Oct. 1929.  


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