Introduction To Electronic Filters – Peter Dalmaris (1)

You will calculate the missing resistor or capacitor value, and sketch the resulting phasor. This exercise will help you connect theory and design, and strengthen your understanding of phasor-based circuit behaviour. I’ll give you the steps you will need to follow to solve this problem. At the end of the instructions, you’ll find the known problem parameters and the unknown you will need to calculate. Step 1: Understand the problem You are given: – The type of filter: RC Low-Pass Filter – One component value: either R or C – A target behaviour at a specified frequency, described by: – A desired magnitude (gain) – And/or a desired phase shift Step 2: Recall the transfer function The transfer function of the RC low-pass filter is: where: – 𝜔 = 2𝜋𝑓 (angular frequency) – 𝑓 is the given frequency The magnitude of the transfer function is: The phase of the transfer function is: Step 3: Set up your equations Depending on what you are asked to match (magnitude, phase, or both), set up the appropriate formula: Introduction to Electronic Filters ● 138 • For magnitude: Solve for 𝑅 or 𝐶 using: • For phase: Solve for 𝑅 or 𝐶 using: Step 4: Solve for the unknown component • Rearrange your formula algebraically to isolate R or C.

• Carefully substitute the given values and calculate. Step 5: Sketch the phasor • Draw a real-imaginary axis. • Draw an arrow (phasor) starting at the origin: Length (the calculated magnitude) and Angle (the calculated phase shift relative to real axis) Step 6: (optional) verification • You may check your answer by simulating the circuit in CircuitLab or another simulator. • Measure the output magnitude and phase at the specified frequency.

• Confirm if your design meets the target. ### Practice Problem 1 Given: • 𝐶 = 1 𝜇F • Desired behaviour at 𝑓 = 159 Hz: o Magnitude ≈ 0.707 o Phase ≈ -45° Task: Calculate the required resistor value 𝑅.

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