Unity gain in lowpass STC circuit

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SUMMARY

The discussion centers on determining the unity gain frequency in a low pass Single Time Constant (STC) circuit. The solution manual indicates that the 3dB frequency is 106 Hz, and the gain decreases at a rate of -20dB/decade. Consequently, the gain reaches 0dB after 2 decades, resulting in a unity gain frequency of 108 Hz. The confusion arises from interpreting the log scale graph, particularly regarding how the gain transitions from the DC gain of 40dB to the 3dB frequency.

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  • Understanding of low pass filter characteristics
  • Familiarity with Single Time Constant (STC) circuits
  • Knowledge of gain and decibel (dB) calculations
  • Ability to interpret log scale graphs
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gambit1414
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One of the question asks to find the frequency at which the gain becomes 0dB for a low pass Single Time Constant circuit. In the solution manual after finding the 3dB frequency = 10^6, it states that since the gain falls off at a rate of -20dB/dec (see attatchment for graph) starting at w0(Omega-knot) , which is 10^6, the gain will reach 0dB in 2 decades (a factor of 100), therefore unity gain frequency = (10^6)(10^2)= 10^8. Now i don't understand how the gain will reach 0dB in 2 decades, because if you look at the graph of a low pass stc circuit it starts off at 0dB then falls by -20dB/dec. Am i reading the log scale graphs incorrectly? Please clarify. Thank You.
 

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Sorry, the dc gain (K) is also given which is 100 V/V = 40dB, so it seems like the gain should be 40dB until w=w0 (omega = omega-knot), then the gain starts to attenuate at -20dB/dec. I'm not really good at reading the log graphs so does this mean depending on what your dc gain value is, it will start there and then start decreasing at -20dB/dec after 3dB frequency? Thanks Again.
 

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