Calculation of chains with periodic non-sinusoidal input effects.

Task 1
Determine the capacitance of the capacitor, if its resistance at the third harmonic is 500 Ohms.

Decision:
capacitor resistance XС = 1 / 3ɷС = 500 Ohm
C = 1 / XC ∙ 3ɷ = 1/500 ∙ 3 ∙ 314 = 2, 12 μF

Task 2
Determine the resistance of the coil, at the signal with the fifth harmonic, if the first harmonic
XL = 5 ohms.
XL5 = 5 ∙ ɷ ∙ L = 25 Ohm

Task 3
Determine the distortion factor and harmonic coefficient, if a signal is input to the device:


Solution: calculate the effective value of the source voltage

U1 = 0
CI = U1 / U = 0
Harmonic factor KG = Ug / U
harmonics actual value

KG = Ug / U = 104, 4 / 106.3 = 0.928

Task 4
Determine the values: U1, I2


Given:


The calculation is carried out by the method of superposition (superposition).
1. Calculation of the constant component of U = 20 B
The scheme takes the form


2. First harmonic calculation



Decision

4 branches, two knots
You can solve any method: equivalent transformations, two nodes

Solve the method of equivalent transformations.
Find the equivalent resistance:


The effective value of the input voltage:


Complex stress


Determine the current source:


Determine the voltage between the nodes "av"


Effective voltage value:


Determine the currents in the branches:


Rated current:


Rated current:


Rated current:


3. Calculation of the second harmonic


Complex stress



Decision
4 branches, two knots
You can solve any method: equivalent transformations, two nodes

Recalculation of reactance values


The effective value of the input voltage:


Determine the current source:

Determine the voltage between the nodes "av"


Effective voltage value:


Determine the currents in the branches:


Rated current:


Rated current:


Rated current:


4. Final calculations. We determine the total effective values: