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Solved Problems-10

For the Notch-filter (Twin-T) network, determine:
Description: Description: 1189.png
  1. y-parameters,
  2. the voltage ratio transfer function V2/V1 when no-load impedance is present, and
  3. the value of the frequency at which the output voltage is zero.
  1. The given network is the parallel combination of the two networks:
Description: Description: 2632.png
(a) Network               (b) Network
For network (a),
Description: Description: 5971.png
∴ Description: Description: 5977.png
∴ Description: Description: 5983.png Description: Description: 5989.png
Description: Description: 5995.png 
For network (b),
Description: Description: 6001.png
∴ Description: Description: 6010.png
∴ Description: Description: 6016.png Description: Description: 6022.png
Description: Description: 6030.png 
Thus, the overall y-parameters are,
y11 = Description: Description: 6036.png
and y12 = Description: Description: 6042.png
  1. Now, Description: Description: 6048.png
When no-load impedance is present, I2 = 0,
∴ Description: Description: 6054.png
  1. For V2 = 0 ⇒ 1 + R2C2s2 = 0
Putting s = , 1 – ω2R2C2 = 0
∴ ω = Description: Description: 6063.png
Thus, the notch frequency is given by, fN = Description: Description: 6069.png

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