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Here is another - rather simple - method for finding the 3db-cutoff frequencies (see the s polynominal as given by Chu in his answer):

1.) From the denominator of the bandpass transfer function you easily can derive the expressions for the bandpass center frequency wo=SQRT(1/T1T2) with T1=R1C1 and T2=R2C2.

2.) The same applies to the quality factor Q=SQRT(T1T2)/(T1+T2+R1C2)

3.) Because of the definition Q=wo/(w2-w1) and wo=SQRT(w1w2) we can find two equations for the two unknown cutoff frequencies w1 and w2 (Q and wo are known values).

4.) Note that the selectivity of this bandpass is rather poor because the maximum quality factor is Q=0.5 (bandwidth is twice the center frequency). The most common set of values (R1=R2, C1=C2) gives a quality factor of only Q=1/3. Note that for all RC bandpass configurations the quality factor never exceeds Q=0.5.

Here is another - rather simple - method for finding the 3db-cutoff frequencies:

1.) From the bandpass transfer function you easily can derive the expressions for the bandpass center frequency wo=SQRT(1/T1T2) with T1=R1C1 and T2=R2C2.

2.) The same applies to the quality factor Q=SQRT(T1T2)/(T1+T2+R1C2)

3.) Because of Q=wo/(w2-w1) and wo=SQRT(w1w2) we can find two equations for the two unknown cutoff frequencies w1 and w2 (Q and wo are known values).

4.) Note that the selectivity of this bandpass is rather poor because the maximum quality factor is Q=0.5 (bandwidth is twice the center frequency). The most common set of values (R1=R2, C1=C2) gives a quality factor of only Q=1/3.

Here is another - rather simple - method for finding the 3db-cutoff frequencies (see the s polynominal as given by Chu in his answer):

1.) From the denominator of the bandpass transfer function you easily can derive the expressions for the bandpass center frequency wo=SQRT(1/T1T2) with T1=R1C1 and T2=R2C2.

2.) The same applies to the quality factor Q=SQRT(T1T2)/(T1+T2+R1C2)

3.) Because of the definition Q=wo/(w2-w1) and wo=SQRT(w1w2) we can find two equations for the two unknown cutoff frequencies w1 and w2 (Q and wo are known values).

4.) Note that the selectivity of this bandpass is rather poor because the maximum quality factor is Q=0.5 (bandwidth is twice the center frequency). The most common set of values (R1=R2, C1=C2) gives a quality factor of only Q=1/3. Note that for all RC bandpass configurations the quality factor never exceeds Q=0.5.

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Here is another - rather simple - method for finding the 3db-cutoff frequencies:

1.) From the bandpass transfer function you easily can derive the expressions for the bandpass center frequency wo=SQRT(1/T1T2) with T1=R1C1 and T2=R2C2.

2.) The same applies to the quality factor Q=SQRT(T1T2)/(T1+T2+R1C2)

3.) Because of Q=wo/(w2-w1) and wo=SQRT(w1w2) we can find two equations for the two unknown cutoff frequencies w1 and w2 (Q and wo are known values).

4.) Note that the selectivity of this bandpass is rather poor because the maximum quality factor is Q=0.5 (bandwidth is twice the center frequency). The most common set of values (R1=R2, C1=C2) gives a quality factor of only Q=1/3.