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RC Circuit Frequency Response:
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The RC circuit frequency response describes how the circuit's output signal amplitude and phase change with frequency. For a simple RC low-pass filter, the transfer function shows how higher frequencies are attenuated while lower frequencies pass through.
The calculator uses the RC circuit transfer function:
Where:
Explanation: The magnitude of the frequency response is calculated as \( |H(j\omega)| = \frac{1}{\sqrt{1 + (\omega R C)^2}} \), which represents the ratio of output to input signal amplitude at a given frequency.
Details: Understanding the frequency response is crucial for filter design, signal processing, and analyzing how circuits behave at different frequencies. It helps determine cutoff frequencies and filter characteristics.
Tips: Enter angular frequency in rad/s, resistance in ohms, and capacitance in farads. All values must be positive numbers. The calculator computes the magnitude of the frequency response.
Q1: What is the cutoff frequency of an RC circuit?
A: The cutoff frequency (\( f_c \)) is \( \frac{1}{2\pi R C} \) Hz, where the output power is half (-3dB) of the input power.
Q2: How does the phase shift vary with frequency?
A: The phase shift is \( \phi = -\arctan(\omega R C) \), ranging from 0° at DC to -90° at very high frequencies.
Q3: What is the difference between angular frequency and regular frequency?
A: Angular frequency (\( \omega \)) is measured in rad/s, while regular frequency (\( f \)) is in Hz. They are related by \( \omega = 2\pi f \).
Q4: Can this calculator handle complex numbers?
A: This calculator computes the magnitude of the frequency response. For complete complex analysis including phase, additional calculations would be needed.
Q5: What are typical applications of RC circuits?
A: RC circuits are used as low-pass filters, high-pass filters, integrators, differentiators, and in timing circuits across various electronic applications.