RL differentiator calculation
Calculator and formulas for calculating a RL differentiator
This function can be used to calculate the properties of a a resistor and a coil differentiating circuit. The function calculates the coil, the resistance or the period or the frequency.
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Formulas for RL differentiator
The differentiator works as a pulse shaper. The RL element generates a pulse-like alternating voltage at the output of the circuit from a square-wave voltage at the input of the circuit.
T = Period
t1 = Pulse
The time constant τ (Tau) of an RL element is calculated using the following formula:
\(\displaystyle Τ= \frac{L}{R}\) ⇒ \(\displaystyle R=\frac{L}{Τ} \) ⇒ \(\displaystyle L= Τ · R \)
τ (Tau) is the symbol for a time constant and should not be confused with the period time T in the graphic above.
If the length of the rectangular pulse (t1) corresponds to 5 times the time constant τ of the RL element, a pulse train like the one in the figure below is created.
\(\displaystyle t1= 5 · \frac{L}{R}\) ⇒ \(\displaystyle R=\frac{5 ·L}{t1} \) ⇒ \(\displaystyle L=\frac{t1 · R}{5} \)
If the pulse duration of the input voltage is much greater than 5 τ , short pulses equal to the input voltage are generated. The following figure shows a pulse train that occurs when the pulse length (t1) corresponds to 10 τ .
\(\displaystyle t1= 10 · \frac{L}{R}\) ⇒ \(\displaystyle R=\frac{10 ·L}{t1} \) ⇒ \(\displaystyle L=\frac{t1 · R}{10} \)
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