Time ago I generated the tetrode curves for this great directly heated tetrode using my analog curve tracer. I originally used this tetrode in triode-mode. Although it’s a good candidate for a SET amplifier with its 21W in triode-mode, I always wanted to find out how it will perform with Schade-type anode to grid feedback. Building an accurate beam-type tetrode model was key. Luckily now, Derk Reefman has developed an accurate model for these type of valves.

I also worked with Ronald Dekker and insisted him to build in the “Schade” feedback capability in the uTracer using software rather than hardware:

The result was brilliant. Now you can quickly generate the anode-to-grid feedback curves using the uTracer by downloading the latest GUI (version 3p11p5) amongst other great features.

Here is a taster of how this looks for a 6P21S using feedback factor or 0.02:

 

 The tetrode curves

Now, back to the 6P21S tetrode curves, this is the way I wired the valve before submitting it to the mercy of the uTracer. The center tap of the filament is connected to the beam plates and is also used as an equidistant connection for the cathode. The filament supply is ideally a Rod Coleman regulator for best performance.

After several plots to generate an accurate tetrode model, here is a view of the 200V

The curves do approximate well to the datasheet average plots.

 

 

 

 

 

 

 

 

 

 

 

 

 

The great advantage of the uTracer is that we can generate multiple type of plots that aren’t available on the datasheets. I also generated the screen current plot as a separate graph:

Fitting the tetrode model using Derk’s tool

When initially attempted to generate the model using Derk’s tool, I found that the tool failed to converge for this tetrode. Here is Derk’s explanation and solution to this problem:

“See included some analysis on what went wrong, and how this now has been corrected in V1.99, which is also attached. I have to say, you are an excellent tester! Much appreciate your feedback, it leads to a better tool 🙂

In the fit of the 6P21S, I used the command “Icmax=100” in the .ini file to restrict the fit to data with a maximum cathode current of 100mA. You are free to use any other value for that, I used it because I saw quite some saturation effects for higher cathode currents. The 1624 seems not to suffer from such saturation effects.

Pls try V1.99 yourself, and in a week or so I will ask Ronald to post this new version on his website.

Let me know how it goes! Derk”

The 6P21S issues in ExtractModel were the result of convergence to a false minimum. This resulted in mu values of the order of 10^6, which clearly is unphysical. This problem I resolved by changing the order of the fitting parameter. This now leads to a good fit of the triode-strapped 6P21S:

The slight deviation at high Ia for Vg=-8 is due to saturation.

 

With this correction, the fits for the pentode went smooth, even though there are a few warnings:

 

Total number of datapoints in the fit equals: 1075.

This is 90.41% of the total number  1189 of datapoints.

************************

Dynamic range equals 1247.; Imin(Va,max) = 150., Imax(Va,max) =   .12 mA.

Best results obtained with dynamic range less than 10.0.

************************

Saturation effects detected for Vg2 = 247. and Vg =    .0.

 

Saturation effects detected.

Fit will continue – but results may be untrustworthy.

Hit return to continue.

 

The results are depicted below:

(Above the effect of saturation is visible, as the tube clearly cannot deliver a cathode current of 170mA)

blockquote

Now, thanks to the updated version of ExtractModel (v1.99) I could generate a very good model for this challenging DHT. Here are the results:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Finally  here are the triode-mode curves for the tetrode model:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The results are really good considering the nature of the curves shapes. We can see that the model doesn’t fit that well for screen voltages of 300V. Bear in mind that the maximum recommended screen voltage is 250V, not 300V! Also the triode-mode connection screen current is not accurate.  Derk explained me these findings:

“Ale

Good to hear, the results look as good as they can get at this point. Within the limitations of the model, also the 1624 currents converge pretty well. The slight misfit you see around the knee of the curves is because of the fact that the model uses a 3/2 exponential behaviour to describe the virtual cathode (see the theory description). This 3/2 behaviour is the ideal case, and I have seen many instances already where this behaviour deviates from the actual observation. I am experimenting with improving the model such that this behaviour is better described, and will keep you posted!

The triode-strapped fits seem to have a weird behaviour of the screen currents. However, we have to realize that these currents only represent about 5% of the total current. Extract Model tries to minimize the sum of errors^2, and to the tool a 1mA deviation in the anode current weighs equally heavy as a 1mA deviation in the screen current. However, 1mA deviation on a 100mA anode current looks very different than a 1mA deviation on a 5mA screen current! I can easily change this in ExtractModel, but have decided not to do that as in the end anode currents are more important than screen currents from a design point of view. […]”

Well, as you can see we managed to get a pretty good result. I also did the same for the 1624 valve, but unfortunately I run out of time to publish these results as well. I hope to do that soon.

The models (at last)

The tetrode model:

****************************************************

.SUBCKT 6P21S-tetrode-VS100V 1 2 3 4 ; A G2 G1 C;

*      Extract V1.990

* Model created: 30-Aug-2014

*

* Traced and model created by Ale Moglia (valves@bartola.co.uk) / www.bartola.co.uk/valves using ExtractModel and uTracer

*

* NOTE: LOG(x) is base e LOG or natural logarithm.

* For some Spice versions, e.g. MicroCap, this has to be changed to LN(x).

X1 1 2 3 4 BTetrodeDE  MU=  9.12 EX=1.298 kG1= 452.1 KP=  41.8 kVB = 2414.5 kG2= 4796.3

+Sc=.66E-01 ap=  .017 w=     0. nu=  2.47 lam=   307.8

+ Ookg1mOokG2=.200E-02 Aokg1=.17E-05 alkg1palskg2=.200E-02 be=  .068 als=  5.34 RGI=2000

+ CCG1=0.0P  CCG2 = 0.0p CPG1 = 0.0p  CG1G2 = 0.0p CCP=0.0P  ;

.ENDS

****************************************************

.SUBCKT BTetrodeDE 1 2 3 4; A G2 G1 C

RE1  7 0  1MEG    ; DUMMY SO NODE 7 HAS 2 CONNECTIONS

E1 7 0 VALUE=

+{V(2,4)/KP*LOG(1+EXP(KP*(1/MU+V(3,4)/SQRT(KVB+V(2,4)*V(2,4)))))}

E2   8 0 VALUE = {Ookg1mOokG2 + Aokg1*V(1,4) – alkg1palskg2*Exp(-be*V(1,4)*SQRT(be*V(1,4)))}

E3   9 0 VALUE = {Sc/kG2*V(1,4)*(1+tanh(-ap*(V(1,4)-V(2,4)/lam+w+nu*V(3,4))))}

G1   1 4 VALUE = {0.5*(PWR(V(7),EX)+PWRS(V(7),EX))*(V(8)-V(9))}

G2   2 4 VALUE = {0.5*(PWR(V(7),EX)+PWRS(V(7),EX))/KG2 *(1+als*Exp(-be*V(1,4) * SQRT(be*V(1,4))))}

RCP  1 4  1G      ; FOR CONVERGENCEA  – C

C1   3 4  {CCG1}   ; CATHODE-GRID 1C  – G1

C4   2 4  {CCG2}   ; CATHODE-GRID 2C  – G2

C5   2 3  {CG1G2}   ; GRID 1 -GRID 2G1  – G2

C2   1 3  {CPG1}  ; GRID 1-PLATEG1 – A

C3   1 4  {CCP}   ; CATHODE-PLATEA  – C

R1   3 5  {RGI}   ; FOR GRID CURRENTG1 – 5

D3   5 4  DX      ; FOR GRID CURRENT5  – C

.MODEL DX D(IS=1N RS=1 CJO=10PF TT=1N)

.ENDS BTetrodeDE

 

And the triode model:

****************************************************

.SUBCKT 6P21S-triode 1 2 3; A G C;

*      Extract V1.990

* Model created: 30-Aug-2014

*

* Traced and model created by Ale Moglia (valves@bartola.co.uk) / www.bartola.co.uk/valves using ExtractModel and uTracer

*

* NOTE: LOG(x) is base e LOG or natural logarithm.

* For some Spice versions, e.g. MicroCap, this has to be changed to LN(x).

X1 1 2 3 TriodeK MU=  9.12 EX=1.298 KG1= 452.1 KP=  41.8 KVB= 2415. RGI=2000

+ CCG=0.0P  CGP=0.0P CCP=0.0P  ;

.ENDS

****************************************************

.SUBCKT TriodeK 1 2 3; A G C

E1 7 0 VALUE=

+{V(1,3)/KP*LOG(1+EXP(KP*(1/MU+V(2,3)/SQRT(KVB+V(1,3)*V(1,3)))))}

RE1 7 0 1G

G1 1 3 VALUE={0.5*(PWR(V(7),EX)+PWRS(V(7),EX))/KG1}

RCP 1 3 1G    ; TO AVOID FLOATING NODES IN MU-FOLLOWER

C1 2 3 {CCG}  ; CATHODE-GRID

C2 2 1 {CGP}  ; GRID-PLATE

C3 1 3 {CCP}  ; CATHODE-PLATE

D3 5 3 DX     ; FOR GRID CURRENT

R1 2 5 {RGI}  ; FOR GRID CURRENT

.MODEL DX D(IS=1N RS=1 CJO=10PF TT=1N)

.ENDS TriodeK

Downloading the models

You can download the models here:

1. 6P21S Tetrode SPICE model using ExtractModel: 6P21S-tetrode-VS100V
2. 6P21S triode SPICE model using ExtractModel: 6P21S-triode

Hope this helps

Ale