# which one is better for smoothing a sine wave: Low pass filters or a serially connected inductor?

Smoothing a sine wave is my main concern in this question. I have a sine wave made by DDS that in higher frequencies shows some steps. Normally in every electronic class it is heard that the best solution is a low pass filter but low pass filters have a big drawback: amplitude reduction.

On the other hand by putting an inductor along with the signal we can obtain even a better result but I have not seen this solution in any books or nobody talks about that (At least those teachers I had!). Is there any problem with this method?

• A series inductor is a low-pass filter. – Pete Becker Oct 7 '13 at 20:55
• What is the "best" solution? Cheapest? Smallest? Most energy efficient? The most free of noise and distortion, at any cost? ...? – Kaz Oct 7 '13 at 21:05
• An LPF can be designed with arbitrarily small insertion loss (amplitude reduction) in the pass band, if you have ideal components. Who told you that an LPF must have "amplitude reduction" and what did they say is the alternate solution that doesn't have it? – The Photon Oct 7 '13 at 21:21
• I think that they read about an LPF having amplitude reduction (the theory), but then tested a series inductor ("Non-LPF", experimental) and got a good result with minimal insertion loss. Edit: Aug - If you are experimentally using a method that works to your liking, it almost by definition has no problem. We'll need a bit more detail about your system to see if we can't see any issues. – scld Oct 7 '13 at 21:31
• @Aug All filters have some phase shift. Filters can be designed to minimize phase shift (or other parameters), but there are tradeoffs. Minimum phase shift filters have a very gradual roll-off in response. If the frequencies you want to sharply cut off are very close to the frequency you want to pass, and you want the filter to be very flat up to your pass frequency, then the requirement for little or no phase shift is a lot to ask for. RC filtering stages do have little phase shift, but only in those frequency areas where they also don't attenuate much. Where they chop, they shift! – Kaz Oct 7 '13 at 21:45

You can construct a low-pass filter with a series inductor and capacitor from its output to ground. This will be a 2nd order low pass filter and if you are trying to filter out harmonics of the DDS process I'm fairly confident you'll need a higher order filter, something like an 8th order.

As the signal you want approaches nyquist, the fundamental content of that frequency reduces dramatically so you'll also need an approximation to a sinc-compensation filter. This can be achieved without too much amplitude error with one 2nd order LC low pass filter but like I said you'll need maybe another three stages of 2nd order filtering to remove the higher frequency artifacts brought about by sampling.

Depending on the frequency you wish to recover you'll get pretty decent results with sallen key op-amp filters but they have to be fast op-amps - gain-bandwidth-product of about 100MHz and these are not common or garden devices.

I'm suggesting op-amps because there are a stack of good formulas around that can help you. For instance there's a very good calculator here and produces this sort of information: -

Because the sallen-key has a low output impedance you could cut down on the number of op-amp stages by inserting inductor-capacitor filters in between but this can be a little tricky because the input of the next stage will load the output thus disturbing the frequency response.

If you go to this page (same author as the sallen key calculator you can choose all maneer of filters but the passive type you want will be under the heading RLC filters - choose the type with R and L in series feeding a capacitor down to ground.

• Thanks! According to the link you provided (Filter Design and Analysis), I assume the inductor in series with the signal is a RLC filter. R is the resistance in the wire, and C is a small capacitor expected around the circuit( something like quantized electron tunneling phenomenon into the air?). by putting R=0.1 ohm , c= 1pF and L=56uH, I saw a 21MHz cutoff frequency that is compatible with my result. Is this assumption correct? – Aug Oct 7 '13 at 22:16
• @Aug - No this will be a terrible filter - you want the bode diagram to be flat not have a giant peak in it. 100 ohm, 560nH and 100pF is the type of response you need for a well-behaved low pass filter - notice that there is no gigantic peak in the bode plot as in with you values. part from anything else it would be impractical to expect 1pF to be used because that will be of the same order as the wires connecting the components. – Andy aka Oct 8 '13 at 7:10