how to calculate transfer impedance of RLC circuit
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The Impedance of a Series RLC Circuit
As the three vector voltages are out-of-phase with each other, XL, XC and R must also be “out-of-phase” with each other with the relationship between R, XL and XC being the vector sum of these three components thereby giving us the circuits overall impedance, Z. These circuit impedance’s can be drawn and represented by an Impedance Triangle as shown below.
The impedance Z of a series RLC circuit depends upon the angular frequency, ω as do XL and XC If the capacitive reactance is greater than the inductive reactance, XC > XLthen the overall circuit reactance is capacitive giving a leading phase angle.
Likewise, if the inductive reactance is greater than the capacitive reactance, XL > XC then the overall circuit reactance is inductive giving the series circuit a lagging phase angle. If the two reactance’s are the same and XL = XC then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance which we will look at in more detail in another tutorial.
Then the magnitude of the current depends upon the frequency applied to the series RLC circuit. When impedance, Z is at its maximum, the current is a minimum and likewise, when Z is at its minimum, the current is at maximum. So the above equation for impedance can be re-written as:
The phase angle, θ between the source voltage, VS and the current, i is the same as for the angle between Z and R in the impedance triangle. This phase angle may be positive or negative in value depending on whether the source voltage leads or lags the circuit current and can be calculated mathematically from the ohmic values of the impedance triangle as:
cos fi= R/Z
As the three vector voltages are out-of-phase with each other, XL, XC and R must also be “out-of-phase” with each other with the relationship between R, XL and XC being the vector sum of these three components thereby giving us the circuits overall impedance, Z. These circuit impedance’s can be drawn and represented by an Impedance Triangle as shown below.
The impedance Z of a series RLC circuit depends upon the angular frequency, ω as do XL and XC If the capacitive reactance is greater than the inductive reactance, XC > XLthen the overall circuit reactance is capacitive giving a leading phase angle.
Likewise, if the inductive reactance is greater than the capacitive reactance, XL > XC then the overall circuit reactance is inductive giving the series circuit a lagging phase angle. If the two reactance’s are the same and XL = XC then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance which we will look at in more detail in another tutorial.
Then the magnitude of the current depends upon the frequency applied to the series RLC circuit. When impedance, Z is at its maximum, the current is a minimum and likewise, when Z is at its minimum, the current is at maximum. So the above equation for impedance can be re-written as:
The phase angle, θ between the source voltage, VS and the current, i is the same as for the angle between Z and R in the impedance triangle. This phase angle may be positive or negative in value depending on whether the source voltage leads or lags the circuit current and can be calculated mathematically from the ohmic values of the impedance triangle as:
cos fi= R/Z
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