A

#### Allan Adler

- Jan 1, 1970

- 0

I'm doing exercises from Kloeffler's book Electron Tubes on my own.

I'd be glad to know of a better book. Meanwhile, here is one problem

I've looked at, which I'll rewrite in my own words.

Page 78, #20. You have a 6AV6 triode. Its grid is connected to ground by

an unknown resistor and is at ground potential. The cathode is connected

to ground by a parallel RC circuit with a 5K resistor and a 1 microf capacitor.

The plate is connected to 300 V by a 145K resistor and connected to ground

by a series RC circuit wherein the 1 microf capacitor is closer to the plate

and the resistor is 100K. No other connection between 300 V and ground is

actually drawn in their circuit. They include a spec sheet for the 6AV6

for use with the problem.

They don't actually say that the grid is at ground potential. They just

say there is no voltage drop across the unknown resistor.

I don't want to get into the specific things the question calls for,

since I'm more interested in the comprehensive analysis of the circuit,

but I'll mention them: static load line, cathode grid-bias line, coordinates

of Q point, grid bias voltage, potentials across the capacitors and what

they will become if the cathode should suddenly burn out.

Regarding the analysis of the circuit: I began by drawing it as follows:

145K

(3)-----^v^v^------(2)-----------------

| | |

| --- Plate

| --- 1mmf (TUBE)

----- | Cathode

--- (4) |

----- 300V | |

--- < |

| > 100K |

| < |

| > |

| | ---^v^v^--- |

| | | 5K | |

------------------(0)-- --(1)

| 1mmf |

----) |----

where I've put some numbers in parentheses to indicate reference points

and where the 1 microf capacitor below (2) is supposed to be electrolytic

like the other one. Reference point (0) is ground. The current from (1)

through the tube is i_b. The current in the same direction through the

5K resistor is i1, the current through the capacitor in parallel with it

is i2, so i_b=i1+i2. The current through the series RC circuit joining

(2) to (0) is i4 and the current from (3) to (2) along the 145 K resistor

is i3, so i_b+i3=i4. I'll let V(a,b) denote the voltage drop from reference

point (a) to reference point (b). The value of V(2,1) is the voltage denoted

e_b in the spec sheets for the tube.

Since the problem tells us no current flows between grid and ground, I simply

left the grid out of the circuit and treated the tube as a black box with

an input (cathode) and one output (plate).

Since the spec sheets focus on i_b, e_b and the grid voltage, it seems

desirable to express everything in the circuit in terms of them. I eventually

did so, but it was necessary to solve a 1st order differential equation for i1

and a 1st order differential equation for i4. This expressed them as

indefinite integrals and I would need to know two boundary conditions in order

to know the constants of integration. Presumably the spec sheet ought to

help with that but I'm a little confused as to how to proceed with it.

Assuming I didn't make any mistakes in the above procedures, I then get

an integro-differential equation for i_b and e_b when I say that V(3,0)

is 300 volts along the various routes from (3) to (0).

Another resource, and I don't know if I am supposed to use it, is Child's

equation, which relates i_b, e_b and the grid voltage e_c within certain

operating limits, namely i_b is proportional to the 3/2 power of (e_b+mu.e_c),

where mu is the amplification factor. If I differentiate Child's equation

and use the fact that e_c is at ground potential, I get a relation between

the derivative of i_b and the derivative of e_b, which should help to simplify

the integro-differential equation, but I haven't used it yet to simplify it,

partly because the integro-differential equation looks ugly and I don't

want to deal with it if I don't really have to, and partly because I believe

that the reader for whom this book was intended was not supposed to think

about the problem this way.

So, what I would like to know is how people on this newsgroup would analyze

a circuit like this one.

Ignorantly,

Allan Adler

[email protected]

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* Disclaimer: I am a guest and *not* a member of the MIT Artificial *

* Intelligence Lab. My actions and comments do not reflect *

* in any way on MIT. Moreover, I am nowhere near the Boston *

* metropolitan area. *

* *

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