Pentode Vacuum Tube Modeling

The pentode is a vacuum tube which has five electrodes, plate or anode, cathode and three grids G1, G2 and G3. The G3 grid is the suppressor grid and it's almost always connected with the cathode inside of the tube. The G1 grid is the control grid and the G2 grid is screen electrode (S). To be operated as an amplifier, the plate to cathode voltage and the screen to cathode voltage must be positive, and the grid to cathode voltage is usually negative and this is actually the controlled voltage for the plate current. Similar to the triode modeling, the pentode model is based on the equations shown on Picture 1.

Picture 1: Pentode Model Equations


The plate (anode) current Ia is determined with the first equation. Here, the G parameter is the tube perveance at zero bias, the Mu and the Mu12 parameter are the control grid and screen grid amplification factor respectively, Vg1 and Vg2 are the control and screen grid voltages and Va is the plate (anode) voltage. The second equation is for the screen grid current Ig2. The rest of the parameters are the constants determined by the particular tube. From the pentode model we can derive the tetrode model taking into account the device behavior when the virtual cathode (G3) dissapears. The tetrode model can be based on the equation shown on the Picture 2.

Picture 2: Tetrode Model Equation


The pentode and the beam tetrode control grid currents are both determined with the same equation as the control grid current for the triode tube. The models that we discuss should reflect the real tube characteristics, however, it should be emphasized that the tube manufacturing process allows a wide dispersion of the device characteristics and typical is a spread of 30%. Furthermore, the vacuum tubes are subject to aging, which results in a slow drift of some of their characteristics, like the cathode emissivity and the residual internal pressure.

Picture 3: The Pentode Vacuum Tube Model Circuit


The pentode vacuum tube model circuit is shown on the Picture 3. In basic, this model is similar to the triode model, except that we have one more elctrode and few more current and voltage sources. The pentode model consists two voltage controlled current sources Gp and Gk, and four voltage controlled voltage sources E1, E2, E3 and Esp. The rest of the model circuit elements are same as for the triode tube model. Using this model circuit and the equations for the pentode tube with proper aproximations we can derive the pentode SPICE model.

The EL34 subcircuit model for LT Spice

According to the model circuit for pentode tube shown on the Picture 3, we created a subcircuit model for the EL34 or 6CA7 vacuum tube pentode. The parameters values used in this model are from the EL34 pentode manufactured by JJ Electronic. The plate dissipation of this pentode is 25W. The amplification factors Mug1,g2 are equal to 11. The parasitic capacitances of the pentode are Cgk = 15.5 pF, Cgp = 1.3 pF and Cpk = 10 pF. The connections for the subcircuit are Cathode and Grid 3 at node 1, Grid 1 at node 2, Grid 3 or Screen grid at node 3 and Plate at node 4. This subcircuit can be used with already existing triode symbol in LT Spice, since the connection assignments are corresponding to the symbol, except that Grid 3 node should be removed from as the pin attribute and change the Plate pin attribute at Spice order 4, and of course, add the subcircuit file name as the symbol attribute. If you want to use this subcircuit with the LT Spice pentode symbol you will need just to enter this subcircuit file (.sub) as symbol attribute into the symbol file (.asy) for the pentode tube.

The EL34.sub file:

* Copyright © Mihail Electronics & Music ltd. 2010 All rights reserved.
* EL34 or 6CA7 A.F. Output Pentode (JJ Electronic)
* Plate dissipation 25W;
* Amplification factor Mug1 = Mug2 = 11;
* Cgk = 15.5 pF; Cgp = 1.3 pF; Cpk = 10 pF;
* Connections: Cathode, Grid 3
* | Grid 1
* | | Screen - Grid 2
* | | | Plate - Anode
* | | | |
.SUBCKT EL34 1 2 3 4
ESP n2 0 VALUE = {V(4,1) + 11*V(3,1) + 11*V(2,1)}
E1 n3 n2 VALUE = {5.39E-7*PWRS(V(n2),1.5) + PWR(V(n2),1.5)/2}
E2 n3 n4 VALUE = {5.39E-7*PWR(11*V(3,1),1.5)*V(4,1)/50}
E3 n5 n4 VALUE = {(1-V(n4,n2)/ABS(V(n4,n2) + .001))/2}
Gp 4 3 VALUE = {0.95*(V(n3,n4)*(1-V(n5,n4)) + V(n3,n2)*V(n5,n4))}
Gk 3 1 VALUE = {V(n3,n2)}
R1 n5 0 1K
Rgk 2 n1 2.7K
D1 n1 1 DM
Cgk 2 1 15.5PF
Cgp 2 4 1.3PF
Cpk 4 1 10PF
.MODEL DM D
.ENDS