# Why would an 8-order LPF switched capacitor have a less steep roll-off curve (MAX7405)?

As as I understand it, a higher order LPF will have a steeper roll-off curve. Something like below would happen if we increase the number of order for the LPF:

Normal LPF frequency response curve:

However, when I tried to check the frequency response curve for the 8-order LPF switched capacitor, MAX7405 datasheet page 5, it shows a less steep curve behavior which is similar to a normal second-order LPF.

8-order LPF MAX7405 frequency response curve:

For a 1k cut-off, I expect a -40dB drop at 2kHz - but the 8-order does not seem to behave like that. Does anyone know why?

• Your expectation isn't accurate. Your example graphs have a log frequency scale, and your datasheet chart has a linear scale. Your filter is prettty steep. Jul 23, 2014 at 10:27

## 2 Answers

For a lowpass with order n=8 you can expect a magnitude drop (far above the cut-off frequency) of 48dB/Octacve. I think, the presented curve does show such a slope - however, only approximately. Why do you expect a damping of 40 dB at 2 kHz?

More than that, Bessel filters are optimized with respect to their phase response (linear). The price paid for this linearized phase response is a magnitude which exhibits a relatively broad transition between passband and stopband.

The picture above with the frequency responses of 5 different order LPF filters is actually frequency response of a Butterworth filter (http://en.wikipedia.org/wiki/Butterworth_filter) and Butterworth filters are designed to have really steep transition between passband and stopband. However MAX7405 IC that you have is a Bessel filter (http://en.wikipedia.org/wiki/Bessel_filter) and as LvW mentioned above, Bessel filters are not designed for such a steep transition, rather they are optimized for having a linear phase response.

If you want to have a steeper transition between passband and stopband (as a Butterworth filter offers), you can use LTC1064 (http://cds.linear.com/docs/en/datasheet/10642fa.pdf), which is basically an 8th order Butterworth filter, or you can use another Maxim part MAX7480 (http://datasheets.maximintegrated.com/en/ds/MAX7480.pdf), which is also an 8th order Butterworth filter.

• Butterworths are maximally flat in the passband, but not particularly steep. Chebychevs can be pretty steep Jul 23, 2014 at 10:30
• Oh, actually you are right, that is the feature of Chebychevs. Thanks a lot, for the clarification.
– acm
Jul 23, 2014 at 10:53
• Also, note that the first set of curves uses log scale for frequency, while the others use linear. This will greatly change your perception of how they behave. Jul 23, 2014 at 12:37
• Gentlemen - the steepness of a filter (that is the slope far above the corner frequency) depends ONLY on the filter degree and NOT on the particular characteristic (Butterworth, Chebyshev, Bessel,...). It is only the passband (ripple yes/no) and the transition region between the passband and the stopband which depends on the kind of approximation/characteristic.
– LvW
Jul 23, 2014 at 19:23