Question

Find the difference in gain magnitude for a filter ,if it is the response obtained for frequencies f1=200Hz and f2=3kHz. Specification: AF=2 and fH=1kHz.

(a) 4.28 dB

(b) 5.85 dB

(c) 1.56 dB

(d) None of the mentioned

I have been asked this question in exam.

Question is from First Order Low Pass Butterworth Filter in section Active Filters of Linear Integrated Circuits

Answer 1

Right option is (c) 1.56 dB

Here's an easy explanation: When f1=200Hz,  VO(1)/Vin =AF/√ [1+(f/fH)^2] =2/√ [1+(200/1kHz) ^2] =2/1.0198.

=> VO(1)/Vin =1.96

=>20log|(VO/Vin)|=5.85dB.

When f=700Hz, VO(2)/Vin= 2/√ [1+(700/1kHz) ^2] =2/1.22=1.638.

 => VO(2)/Vin =20log|(VO/Vin|=20log(1.638) = 4.28.

Therefore, the difference in the gain magnitude is given as VO(1)/Vin-VO(2)/Vin =5.85-4.28 =1.56 dB.