Circuit Theory/Lossy Tuned Circuits/Band-stop filter

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Example 1[edit | edit source]

Problem: Compute the magnitude and phase of the frequency response of the circuit below, where R=1Ω, L=0.025H and C=0.4F. Find both of the frequency boundaries of the stop-band.

We use our method of considering the circuit as a voltage divider to find the frequency response:

 
 

Let us first consider the general shape of the graph before we plot it.

  • At ω=0, the imaginary part of the denominator disappears and the response is unity (1∠0°). At ω=∞, the quadratic dominates and the numerator and denominator cancel and the response is unity (1∠0°). Therefore, the magnitude of the response tends to 1 at ω=0 and ω=∞, and the phase tends to 0.
  • At ω=10, the magnitude falls to zero. However, if we approach this frequency from below, we find that at ω=10, the response amplitude is 0∠–90°, but from above, at ω=10+, the response amplitude is 0∠90°, indicating a very rapid phase flip.

We see that the graph shows exactly this: