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The characteristic equation for the output voltage of an All-pass filter is given by:

 

99. The characteristic equation for the output voltage of an All-pass filter is given by:

  1. Vo = Vin [ 1 - 2 / (jωRC + 1) ] [Option ID = 1225]
  2. Vo = Vin [ 1 - 2 / (jωRC) ] [Option ID = 1226]
  3. Vo = Vin [ -1 + 2 / (jωRC + 1) ] [Option ID = 1227]
  4. Vo = Vin [ 2 / (jωRC + 1) ] [Option ID = 1228]
Correct Answer: 1

Solution

Based on the question, the correct characteristic equation is Option 1:

Vo = Vin [ 1 - 2 / (jωRC + 1) ]

Comparison: How others look

To identify filters quickly, look at the numerator (the top part of the fraction):

1. Low-Pass Filter (Blocks Highs)
Notice: It has only a "1" on top. It is the simplest one.
Vo = Vin [ 1 / (jωRC + 1) ]
2. High-Pass Filter (Blocks Lows)
Notice: It has the frequency symbol (jωRC) on top.
Vo = Vin [ jωRC / (jωRC + 1) ]
3. All-Pass Filter (Phase Shifter)
Notice: It uses a "1 minus 2/..." structure to keep the output volume exactly the same as the input.
Vo = Vin [ 1 - 2 / (jωRC + 1) ]
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