MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA

SAINT PETERSBURG STATE ELECTROTECHNICAL UNIVERSITY

«LETI» N.A. V.I. ULYANOVA (LENINA)

DEPARTAMENT ME

6+1а=7 балл

REPORT

on individual homework №1

in the discipline «Microwave electronics»

Topic: THEORETICAL FOUNDATIONS OF MICROWAVE ELECTRONICS

Student №8 gr. 3206 __________

Teacher __________ Ivanov V. A.

Saint Petersburg

2026

Content

Task 1 3

Task 2 7

Task 3 12

Task 4 17

Task 5 19

Task 6 20

Task 7 22

Task 1

1. Present your arguments (logical and numerical) on the assessment of the nature and features of the effects of microwave radiation on humans. To do this, use the results of the following calculations.

   1. Calculate the quantum energy of microwave radiation with a frequency of: f_0GSM + N_group + N_student [GHz] and f_05G +N_group + N_student [GHz].

   2. Compare this energy with the energy of thermal vibrations of molecules at Т = 42⁰C

   3. Compare the quantum energy of microwave radiation with a frequency of: 2.45 GHz with the binding energy of clusters in water. To what temperature should water be heated to destroy its cluster structure?

   4. Compare the energy of a 2.45 GHz microwave radiation with the energy of a chemical bond in a DNA molecule.

Given:

GSM:

f_0GSM = 1725 МHz => f_GSM = 1,725 + 6 + 8 = 15,725 GHz

5G:

f_05G = 27,5 GHz => f_5G = 27,5 + 6 + 8 = 41,5 GHz

T = 42 + 273 = 315 K

Solving:

1. Calculation of the quantum energy of microwave radiation:

Calculation formula:

Where h = 6,626 ∙ 10-³⁴ J∙s – Planck’s constant; f-radiation frequency.

According to the formula, for the GSM standard:

For the 5G standard:

The radiation energy of the 5G standard is more than twice that of the GSM standard.

2. Calculation of the energy of thermal vibrations of molecules at Т=42 , comparison with the quantum energy of microwave radiation:

The energy of thermal vibrations is calculated by the formula:

where k=1.38∙10^-23 J/K – Boltzmann constant, T – temperature.

According to the formula, the energy of thermal vibrations of molecules:

Comparison with energy of microwave radiation, for GSM standard:

For 5G standard:

3. Comparison of the quantum energy with the binding energy of cluster in water. Calculation of the water heating temperature necessary for the destruction of its cluster structure:

Water cluster binding energy:

Comparison with energy of microwave radiation, for GSM standard:

For 5G standard:

Temperature for the destruction of its cluster structure:

4. Comparison of the quantum energy of a 2.45 gHz microwave radiation with the energy of a chemical bond in a dna molecule

Let's take the binding energy of one A-T or G-C pair as the binding energy of a DNA molecule.:

W_DNA = W_A-T

W_A-T - Energy per base pair, taking into account hydrogen bonds and stacking.

Thus:

Based on the calculated values ​​of radiation and binding energy, we can draw the following conclusion: Microwave radiation always affects humans, raising their body temperature and depleting their energy. At work, this exposure leads to more rapid exhaustion. Radiation energy is much less than the binding energy of water clusters—this is good, since humans are 80% water, and this additional negative impact is absent. Microwave radiation energy is much less than the binding energy of a DNA molecule—therefore, there is no reason to fear the structural effects of radiation on the body.

Answer:

1. Quantum energy of microwave radiation:

W_GSM =  J

W_5G =  J

2. The energy of thermal vibrations of molecules:

W_T =  J

This energy is 626 times more energy at the GSM frequency and 237 times more energy at the 5G frequency.

3. Water heating temperature necessary for the destruction of its cluster structure:

T = 2786 K

Binding energy of clusters in water:

W_H20 = 0,24 eV = 3,845 10^-20 J

The binding energy of clusters in water is 6651 times more energy at GSM frequency and 1682 times more energy at 5G frequency.

4. The binding energy of a DNA molecule.

W_DNA =

Quantum energy of microwave radiation for 2,45 GHz:

W₂₄₅ =  J

This energy is 51805 times less than the binding energy of a DNA molecule.

1.75 Балл Task 2

2. What is the power density of microwave radiation considered acceptable in everyday life and at work according to the standards of the Russian Federation? According to international standards?

1. Evaluate how your body temperature will increase at home and at work at a power density level equal to (50 + N_student) % of the maximum allowable. What role does heat loss play in this process?

2. Estimate how many quanta of microwave radiation will be required for such heating.

Given:

data from the Sanitary rules and norms 2.2.4/2.1.8.055-96 , and the values of the permissible power density of microwave radiation according to international standards:

Table 1 – The values of the permissible power density of microwave radiation

Standard\Where	In everyday life	In production
Standards of the Russian Federation	10   W/cm2	200 W/cm2
International standard	1 mW/cm2	10 mW/cm2

Power density

P = (50 + 8)*10^-3*P_max = 0.58P_max

Body mass:

m = 58 kg

Height:

h = 176 cm = 1,76 m

Exposure time, everyday life:

t1 = 86 400 s

In production:

t2 = 28 800 s

Solving: