Hi!
Here is my task:
Opamps in circuit are ideal and R1=100 KOhm, C=1uF. Calculate gain A(s)=Vi(s)/Vu(s) [dB], in passband range, where Vu(s)=V2(s)-V1(s).
Here is schematic and my attempt:
First you have to know what kind of filter you have, then you can look for the gain in the 'passband'.
This means you might have to plot it for frequency vs gain or frequency vs output to see what kind of filter it is, then determine where the passband is.
For a few examples, a low pass filter will have a passband gain specified at 0Hz or some low freuqency.
A high pass filter will have it at infinite frequency or some high frequency.
A bandpass will have it at some specific frequency other than 0 or infinity, somewhere in between.
The passband may be spread over some range of frequencies, but you choose the one that is appropriate for the filter. For example you could have a low pass filter that peaks at a gain higher than the normal passband, but you sort of ignore that and go with the dominate range and choose one in there or a range. To get the gain, you choose the highest in the appropriate range while sometimes ignoring the peak for filters that peak sharply.
For a quick example, 1/(s*R*C+1) is a low pass filter and the passband is 0 to the -3db cutoff frequency, but you would choose the gain at 0Hz as the set point for determining the -3db cutoff and to determine the passband gain.
Try plotting your filter gain across frequencies and see if you can figure it out for this filter.
Well for simpler filters there are set forms where the terms in the numerator and denominator will match one of the set forms and thus you can know the filter type from that. That's the fastest way.
Finding the poles and zeros you can then use the ideas of Bode to figure out where the response shoots up, becomes horizontal, or shoots down, and at what approximate rates, in order to figure out the basic filter type. For more complicated filters though it may becomes more and more difficult to do this.
In this day and age it is probably best to have some way to plot the response using some computer program. That way you can see the whole response (without any approximations) and figure out how you want to interpret the regions of interest. For example, if you have a higher order filter that has ripple in the passband you may prefer to average that out in order to determine the gain because it is very unlikely you'd want to prefer one frequency point over another in the determination of what the gain should be.
If you look over the transfer function of some of the more basic filter types like low pass, high pass, band pass, and band stop, you might start to get a feel for the more common ones. First and second order filters are the most common, but higher order passive and active filters are becoming more popular too these days. The main components being resistors, capacitors, inductors, and op amps.
Thanks.
I draw bode plot for this transfer function. This is highpass filter, it's passband is from 10rad/s (pole) up to infinity. So gain in passband is Av=10, or in dB, AVdb=20log10=20db.