2 Балл task №5

5. Determine the amplitude of the «self-consistent» voltage at the grid gap of the resonator with a high intrinsic Q, if the amplitude of the first harmonic of the convection current at the input to the resonator is 8 [mA], the angle of flight 90⁰, the accelerating voltage is 7 kV, the beam current is 100 mA.

Given:

I_c1 = 8 mA

U₀ = 7 kV

I₀ = 100 mA

Solving:

The coefficient of interaction of the electron flow with the gap field [22]:

М (18)

where – angle of passage of an electron in a flat gap; I_i – amplitude of the induced current; I_c – amplitude of the convection current.

Thus, by the formula (16) we calculate M:

М = = 0,9

Conductivity formula [23]:

G_e = = (19)

Hence, we express the amplitude of the «self-consistent» voltage:

U_m = (20)

Also, we write the following expression for conductivity [24]:

G_e = G₀ (21)

Then, the conductivity according to the formula (21) is equal to:

G_e = = 1,243 10^-6 Ω^-1

«Self-consistent» voltage by the formula (20):

Thus, we conclude that the resulting «self-consistent» voltage (5,8 kV) is less than the accelerating voltage (7kV).

Answer:

U_m = 5792,44 V

1 балл

Task №6

6. Determine the noise factor of the amplifier in dB if its effective noise temperature is 115 k.

6.1 Calculate the effective noise temperature of two such devices connected in cascade if the gain of each device is 11,75 dB.

6.2 Analyze the result.

Given:

T₀ = 300 K

T_eff = 115 K

К_gain = 11,75 dB

Solving:

1. Calculation of the noise coefficient of the amplifying device:

The noise coefficient is calculated by the formula [25]:

К_n = 10∙lgN_F (22)

Where N_F – noise factor, calculated as [25]:

N_F = 1 + (23)

Then, the noise factor is:

N_F = 1 + = 1 + = 1,383

Hence, the noise coefficient of the amplifying device is equal to:

К_n = 10∙lgN_F = 10∙lg1,383 = 1,408 dB

2. Calculation of the effective noise temperature of two such devices connected in a cascade:

According to the Friis formula, the noise factor of two devices connected in a cascade is equal to [26]:

N_Fsum = (24)

Considering that in our case for each of the devices N_F1 = N_F2 = N_F, then:

N_Fsumm =

Calculate the gain of the device [27]:

G = = = 14,962

Then, according to the formula (24):

N_Fsumm = = = 1,409

The effective noise temperature of the cascade through the formula (23) is equal to:

T_eff.summ = T₀∙(N_Fsumm – 1) = 300∙(1,409 – 1) = 122,7 К

Thus, the effective noise temperature of two cascaded devices is greater than the effective noise temperature of one device by (122,7 – 115) = 7,7 K.