General Terms and Gain/Atteunation Numerical

General Terms

fig: General terms

Pass Band: Range of signal frequency that are allowed to pass through a filter with little or no change to the signal level.

Pass band cut off frequency is the pass band edge where there is 3db reduction in its reduction amplitude.

Stop Band: band of frequencies between specified limits through which circuit doesn’t allow the signal to pass. 

Roll off: Slope of the filter response in the transition region between pass band and stop band. It is the rate at which the signal increases or decreases. 

Skit Response: It is the portion of magnitude of the curve at the high frequency. It is the response where reduction in signal amplitude (attenuation) gradually changes. 

General Numerical

At frequency f=20 khz and f-30lhz a filter is design to attenuate the input signal by 78db and 90db respectively. Fint the amplitude of the output signal if the 30khz input signal has amplitude of 1v.

Given:

\[ \begin{cases} f = 30\,\text{kHz} \\ V_{\text{in}} = 1\,\text{V} \\ \text{Attenuation} = 90\,\text{dB} \\ \text{Find } V_{\text{out}} \end{cases} \]

Attenuation is given by:

\[ \text{Attenuation (dB)} = 20 \log \left( \frac{V_{\text{out}}}{V_{\text{in}}} \right) \]

Since \( V_{\text{in}} = 1\,\text{V} \), this reduces to:

\[ \text{Attenuation (dB)} = 20 \log \left( V_{\text{out}} \right) \]

Substitute the given value:

\[ -90 = 20 \log \left( V_{\text{out}} \right) \]

Solve for \( V_{\text{out}} \):

\[ \log \left( V_{\text{out}} \right) = \frac{-90}{20} = -4.5 \]

\[ V_{\text{out}} = 10^{-4.5} \approx 3.16 \times 10^{-5}\ \text{V} \]

Final Answer:

\[ V_{\text{out}} \approx 31.6\, \mu\text{V} \]