Getting An RF Low-Pass Filter Right

If you are in any way connected with radio, you will have encountered the low pass filter as a means to remove unwanted harmonics from the output of your transmitters. It’s a network of capacitors and inductors usually referred to as a pi-network after the rough resemblance of the schematic to a capital Greek letter Pi, and getting them right has traditionally been something of a Black Art. There are tables and formulae, but even after impressive feats of calculation the result can often not match the expectation.

The 30MHz low-pass filter, as QUCS delivered it.
The 30MHz low-pass filter, as QUCS delivered it.

Happily as with so many other fields, in recent decades the advent of affordable high-power computing has brought with it the ability to take the hard work out of filter design, Simply tell some software what the characteristics of your desired filter are, and it will do the rest. The results are good, and anyone can become a filter designer, but as is so often the case there remains a snag. The software calculates ideal inductances and capacitances for the desired cut-off and impedance, and in selecting the closest preferred values we modify the characteristics of the result and possibly even ruin our final filter. So it’s worth taking a look at the process here, and examining the effect of tweaking component values in this way.

The idealised graph produced by QUCS for our filter.
The idealised graph produced by QUCS for our filter.

The filter we’re designing is simple enough, a 5th-order Bessel filter, and the software is the easy-to-use QUCS package on an Ubuntu Linux machine. Plug in the required figures and it spits out a circuit diagram, which we can then simulate to show a nice curve with a 3dB point right on 30MHz. It’s an extremely idealised graph, and experience has taught me that real-world filters using these designs have a lower-frequency cut-off point, but for our purposes here it’s a good enough start.

As previously mentioned, the component values are not preferred ones from a commercially available series, so I can’t buy them off the shelf. I can wind my own inductors, but therein lies a whole world of pain of its own and I’d rather not go there. RS, Mouser, Digikey, Farnell et al exist to save me from such pits of electronic doom, why on earth would I do anything else but buy ready-made?

My revised filter circuit with off-the-shelf component values.
My revised filter circuit with off-the-shelf component values.

So each of the components in the above schematic needs moving up or down a little way to a preferred value. What effect will that have on the performance of my filter? Changing each value and re-running the simulation shows us the graph changing subtly each time, and it can sometimes be a challenge to adjust them without destroying the filter entirely. Particularly with the higher-order filters with more components in the network you can observe the effect of individual components on the gradient at different parts of the graph, but as a rule of thumb making values higher reduces the cut-off frequency and making them lower increases it. In my case I always pick higher values for that reason: my nearest harmonic I wish to filter is at double the frequency so I have quite some headroom to play with.

The revised curve from the filter with preferred values.
The revised curve from the filter with preferred values.

Having replaced my component values with preferred ones I can run the simulation again, and I can see from the resulting graph that I’ve been quite fortunate in not damaging its characteristics too much. As expected the cut-off frequency has shifted up a little, but the same curve shape has been preserved without any ripples appearing or it being made shallower.

If I were using this filter with a real transmitter I would ensure that I designed it with a cut-off at least a quarter higher than the transmission frequency. In practice I find the cut-off to be sharper and lower than the simulation leads one to expect, and for example,¬†were I to use this one with a 30 MHz transmitter I’d find it attenuated the carrier by more than I’d consider acceptable. It must also be admitted that changing the component values in this way will also change the impedance of the filter from the calculated 50 ohms, however in practice this does not seem to be significant enough to cause a problem as long as the value changes are modest.

We haven’t made this filter, but in the past we’ve featured another one I did make, and by coincidence it was in the same frequency range. When I wrote a feature on automating oscilloscope readings, the example I used was the characterisation of a 7th-order 30 MHz low-pass filter. It might even be one of the ones in the header image, pulled from my random bag of filter boards for the occasion.