I would like to calculate the half power frequency of the circuit attached.
I have combined the impedances of R2 and C1 with the 1/Z = 1/Z_1 + 1/Z_2 ... forumla. To get R2 / (R2*j*w*C + 1).
Then use the voltage divider on this combination and R1 to find that,
Vin / Vout = 1 / ( R1jwC + (R1/R2 +1) )
I believe the gain now is |Vin / Vout| = 1 / sqrt( (R1wC)^2 + (R1/R2 + 1)^2 )
At this point, I'm unsure how to proceed. The Internet has told me that the half power frequency occurs when | Vin / Vout | = 1/sqrt(2). If I set what's contained the the radical above equal to 2 and solve for w, I can find the frequency f. I turns out to 141.5 Hz which doesn't agree with a computer generated Bode plot.
Can anyone suggest what I'm doing wrong?
Sorry for the poor Maths formatting.
Thanks for your time,
I have combined the impedances of R2 and C1 with the 1/Z = 1/Z_1 + 1/Z_2 ... forumla. To get R2 / (R2*j*w*C + 1).
Then use the voltage divider on this combination and R1 to find that,
Vin / Vout = 1 / ( R1jwC + (R1/R2 +1) )
I believe the gain now is |Vin / Vout| = 1 / sqrt( (R1wC)^2 + (R1/R2 + 1)^2 )
At this point, I'm unsure how to proceed. The Internet has told me that the half power frequency occurs when | Vin / Vout | = 1/sqrt(2). If I set what's contained the the radical above equal to 2 and solve for w, I can find the frequency f. I turns out to 141.5 Hz which doesn't agree with a computer generated Bode plot.
Can anyone suggest what I'm doing wrong?
Sorry for the poor Maths formatting.
Thanks for your time,