Calculating ra and gain

[lowell]

Hi I would just like to confirm I have the right math here. For a typical fender gain stage I have found to be able to use the following equation to calculate ra, which is in turn needed to calculate the gain of the stage.

(Va/Vk)*Rk=ra
and
(100*100k)/(100k+ra)=gain

So is it true I need to have a number for Va before I can calculate a gain stage?

[martin manning]

Not sure what you're trying to do here...

Your second equation is (I think) the voltage gain A of a triode stage with a fully-bypassed cathode resistor, where A = mu*Ra/(Ra + ra). The 100 is the mu of the triode (this is a 12AX7, I assume), 100K is the plate resistor value Ra, and ra is the anode resistance, which would be ~63K Ohms. The mu and ra come from the tube data sheet, or from the exact operating point you've chosen if you want to be precise.

Is there more to the question?

MPM

[lowell]

Ok, yes more to the question. I've come to understand the ra (anode resistance) to be dependent on the circuit values and not a fixed value being that a tube is somewhat congruent to a variable resistor. In the RCA tube manual there is no value listed for 12ax7 ra. I came upon finding the ra of the tube by calculating:

(Va/Vk)*Rk

Does that make sense?

[martin manning]

ra is not a fixed value, but it is a characteristic of the tube itself. It changes with the operating point, so in that way it is dependent on the values of the components that set the operating point, namely the plate and cathode resistors. You should be able to find a nominal ra (for a typical operating point) on a tube data sheet, but I see you have to read the fine print in the RC-30 12AX7 listing, which says go look under 6AV6 for the curves and characteristics. It says there that ra is 62.5K Ohms for Va = 250V. Search on the web for a more complete 12AX7 spec.

ra = (Va/Vk)*Rk is an approximation, I think. If you assume Va is really Va-k the voltage from anode to cathode, and rearrange it to get Va-k/ra = Vk/Rk, you can see that all it is saying is that the current I = V/R through the cathode resistor Rk is equal to the current through the tube (ra). It's close as written, since Vk is a volt or two, and Va is 200 volts or so. You could use this to calculate ra from voltages measured on a real device in circuit.

I suggest that you go here:

http://www.freewebs.com/valvewizard1/gainstage.html

and read through this excellent explanation of the operation of a triode stage. You won't be sorry!

MPM

[lowell]

Hi Martin,
I guess I don't understand how the current through the tube is the same through the resistor. Is that the case in all series circuits or just this case? That's good to know. Thanks for pointing to the small print on that I did not see it. That valve wizard article is what has inspired my attempting to understand a basic common cathode gain stage.

[martin manning]

A series circuit is the simplest case of Kirchhoff's current law, which states that the net current at a circuit node must be zero. The node here is the cathode, so what goes in through the cathode resistor must go out through the plate (grid current is normally zero, so we can just ignore it). Take one more step like that and you can see that that same current flows through the plate resistor Ra. These three resistances are in series from B+ to ground.

I found this to be a nice tutorial on the basic tools:

http://www.pentodepress.com/circuit-...esson-001.html

MPM

[lowell]

ok i'll check that out. So that would also mean current through the plate resistor = current through the tube. Ok thanks.

[tubeswell]

ok i'll check that out. So that would also mean current through the plate resistor = current through the tube. Ok thanks.

With a triode - yes.

With a tetrode/pentode - no (because some of the current is being drawn by the screen as well, so the current at the cathode is sum of the plate current and the screen current).

(Bearing in mind that grid current, which happens in some cases under load, is assumed not to be an issue here)

[Suusi M]

So far your all dealing with the dc load line and the bias line.

Do not forget that the next step is the AC load line. The anode load also includes the decoupling cap and the input resistor to the next stage in parallel with Ra.

Which is normally simple, provided the grid of the next stage does NOT go positive with respect to its cathode, whence the grid - cathode becomes a diode and a good conductor with a radically different load line.

[Merlinb]

Ok, yes more to the question. I've come to understand the ra (anode resistance) to be dependent on the circuit values and not a fixed value being that a tube is somewhat congruent to a variable resistor. In the RCA tube manual there is no value listed for 12ax7 ra. I came upon finding the ra of the tube by calculating:

(Va/Vk)*Rk

Does that make sense?

Perhaps the RCA datasheet has it listed as rp instead of ra. (It will be there somewhere).

That formula you give will not work because ra is a dynamic resistance (AC), the anode voltage will tell you nothing about this.

[Suusi M]

Rat Tube tester info


Background:
There are 3 fundamental Vacuum Tube (Valve) constants. These are transconductance (gm), plate resistance (rp) and mu. For tetrode and/or pentode devices, mu is not significant, since the plate resistance is usually much higher than the load resistance. There is a simple relationship between these: mu = gm * rp. In a triode, the mu is substantially geometric factor, so it does not change much as the tube ages. Rather, the gm decreases with time and the rp increases. Therefore, a measure of the goodness of a tube is generally related to its measured gm. This is done in a "transconductance" tube tester, but, as the specific voltage and current used in a particular application is not possible or practical to set up, this limits the usefulness of the traditional tube tester. The purpose of the described device is to circumvent these limitations, and allow evaluation of tubes under operating conditions really used in your specific application.

DEFINITIONS:

Transconductance:

This is defined as the incremental change in plate current for an incremental change in grid voltage, with all other parameters (plate voltage, for example) held constant. The way this is done is to place a small AC voltage (lets say 100 mV) on the grid and measure the output AC current on the plate. In practice, this is done by measuring the voltage across a small resistor, (lets say 100 ohms) connected from plate to a constant DC voltage source. The current can be controlled by placing a constant current source in the cathode circuit of the tube under test, and bypass the cathode for AC purposes. For the example given (100 mV AC on the grid, and a 100 ohm plate "current sensing" resistor), a transconductance of 1 mS (1000 micro mhos) would be indicated as a 10 mV signal across the 100 ohm resistor.

Mu:

This is defined as the incremental change in plate voltage for an incremental change in grid voltage, with all other parameters (plate current, for example) held constant. The way this is done is to place a small AC voltage (lets say 100 mV) on the grid and measure the resulting AC voltage on the plate, with the plate connected to a high impedance load (current source). For the example given, (100 mV AC on the grid), a mu of 20 would be indicated as a 2 volt signal at the plate. Note: The "resistance" of the constant current load must be substantially higher than the plate resistance of the tube under test for the results to be accurate. Plate resistance: This is defined as the incremental change in plate voltage for an incremental change in plate current with all other parameters held constant. This is not directly measured in the proposed project (at least initially) but is calculated by the formula rp = mu/gm.

[martin manning]

Perhaps the RCA datasheet has it listed as rp instead of ra. (It will be there somewhere).

It's there, just under another type listing. I guess they didn't want to repeat it.

That formula you give will not work because ra is a dynamic resistance (AC), the anode voltage will tell you nothing about this.

No, it's not even close, is it. I should have thought it through a little more!

MPM

[lowell]

So far your all dealing with the dc load line and the bias line.

Do not forget that the next step is the AC load line. The anode load also includes the decoupling cap and the input resistor to the next stage in parallel with Ra.

Which is normally simple, provided the grid of the next stage does NOT go positive with respect to its cathode, whence the grid - cathode becomes a diode and a good conductor with a radically different load line.

Do you mean the coupling cap? Or the decoupling cap (filter cap)? Just to be clear. I assume you mean coupling cap.

[lowell]

If not lets try this a different way. Don't mean to be stubborn here but I still do not understand how to calulate a gain stage before actually wiring it. If you guys were designing a simple triode stage and wanted to calculate gain before wiring the actual circuit for testing what equation/s and calculations would you make if you had 300v supply voltage, 12ax7, 100kplate resistor, and 1.5k cathode resistor values? The ra value is what is confusing me here.

[martin manning]

If not lets try this a different way. Don't mean to be stubborn here but I still do not understand how to calulate a gain stage before actually wiring it. If you guys were designing a simple triode stage and wanted to calculate gain before wiring the actual circuit for testing what equation/s and calculations would you make if you had 300v supply voltage, 12ax7, 100kplate resistor, and 1.5k cathode resistor values? The ra value is what is confusing me here.

Go to www.aikenamps.com and look under tech info, advanced, designing common cathode triode amplifiers. There is an example there. I would use the Excel sheet I built. PM me if you want a copy.

MPM