2 Балл. Вопрос: Что усвоено? task №2

Devices with quasi-static control. Triode.

Calculate the range of static angles of flight of charge carriers in the cathode-grid gap of a triode operating in one of the modes A, B or C (choose yourself). The phases of departure from the cathode are set from 0 to 360⁰. (The number of phases of your choice. Consider the voltage on the electrodes unchanged during the flight).

Operating frequency 600 MHz, cathode-grid distance 1,4 mm, constant voltage at the anode 350 V, mesh permeability 0,13. Calculate the interaction coefficient for these angles. Using the results obtained, explain why triodes are ineffective at high frequencies.

Given:

f = 600 MHz

d_cg = 1,4 mm = 1,4 10^-3 m

U_a = 350 V

D = 0,13

Solving:

1. Calculation of the range of static angles of electron flight in the cathode grid gap operating in a mode:

Consider a triode operating in mode A. The main advantage of this mode is the minimal distortion of the shape of the cathode and anode current relative to the shape of the control voltage.

First of all, we will find the voltage of the beginning of the anode-grid characteristic, that is, the locking voltage [9]:

U_glock = D U_a (17)

Then, by formula (17), we calculate:

U_glock = D U_a = -0,13 350 = 45,5 V

The locking voltage is equal to U_glock = -45,5 V, which means that we consider voltages greater than this value (up to 0).

The angle of electron flight in the cathode-grid gap is calculated by the formula [10]:

= = (18)

where v₀ - is the electron flight velocity [11]:

v₀ = (19)

Define the value U₀ according to the following formula [9]:

U₀ = U_g + D U_a (20)

where U_g – grid voltage (in our case higher than 45,5 V); U_a – anode voltage; D – mesh permeability.

Hence, the angle of passage of electrons in the cathode-grid gap, using formulas (18), (19) and (20), will be equal to:

= (21)

Then, for two values of the grid voltage: U_g = 0 and U_g = - 43 V calculate the values of the angles of the span:

= = 1,32 rad

= = 5,63 rad

2. Calculation of interaction coefficients for the obtained angles:

According to the formula for the interaction coefficient [12], we obtain:

M = (22)

Hence, for three values of the angles of flight according to the formula (22) we get:

M₁ = = = 0,93

M₂ = = = 0,11

That is, we conclude that with an increase in the value of the span angle, the interaction coefficient decreases significantly. So, in this case, with an increase in the angle of flight from 1,32 rad to 5,63 rad, that is 5,63/1,32 4 times, the interaction coefficient decreases in 0,93/0,11 8 times.

3. Explanation of why triodes are ineffective at high frequencies:

Analyzing the obtained values of the electron flight angle and the interaction coefficient, we conclude that triodes are ineffective at high frequencies for the following reasons:

Since we are considering vacuum tubes (namely, a triode), it should be said that the electron has a certain time of flight between the electrodes. At high frequencies, the microwave field has time to change its direction before the electron reaches from one electrode to another. This is clearly noticeable if we consider the formula for the interaction coefficient, which depends on the angle of electron flight. According to the formula (21) – with increasing frequency, the angle of flight increases, but at the same time the interaction coefficient (22) decreases. Here is a graph of the dependence of the interaction coefficient on the electron flight angle:

Picture 5 – Graph of the dependence of the interaction coefficient on the electron flight angle [13]

And, if we talk about the physical meaning of the coefficient M, that it takes into account the decrease in the depth of velocity modulation at a finite flight time compared to the ideal case of zero or infinitesimal flight time [13].

An interesting situation, that is, the electrons will oscillate inside the vacuum tube without reaching the external circuit. How to solve this problem? One of the solutions is to reduce the distance between the electrodes. But, again, to what values should this distance be reduced if we are talking about GHz? And is it possible to implement this interelectrode distance constructively? That is why tetrodes are ineffective in the microwave range [14].

Answer:

1. Static angles of flight of charge carriers in the cathode grid gap:

= 1,32 rad – at U_g = 0

= 5,63 rad – at U_g = - 43 V

That is, the range of static angles of electron flight in the cathode grid gap is equal to: [1,32 rad; 5,63 rad].

2. Interaction coefficients for the obtained angles:

M₁ = 0,93 – at U_g = 0

M₂ = 0,11 – at U_g = - 43 V