The first three values of the table, G(1), G(2), and G(3) correspond to component values from left to right. Before doing any math, let’s draw the architecture of our filter: Choosing the third-order line on the above table, we are given 4 numbers: G(1), G(2), and G(3). That seems like a pretty worthless filter, but we will later extrapolate these numbers to find components values for our desired filter. What do these tables represent? The normalized values tables represent component values necessary for a low-pass filter with a cutoff frequency of 1 radian/s, and for an 1 Ohm input impedance. Below is a copy of the necessary table, taken from my copy of the ARRL Handbook: Otherwise, you can find them on page 7 of this PDF. If you have a copy of the ARRL Handbook, you’ll find them in the Filters chapter (at least mine does). These are actually not that easy to find. So, how do we get around to designing a third-order Butterworth filter? First, we need to find a table of normalized components values for the Butterworth family of filters. The 50dB/decade of power attenuation can be achieved with a 3rd order filter. a flat bandpass response for maximum linearity.Ī Butterworth filter seems like it would work nicely with these constraints.I don’t need a steep roll-off, but an attenuation of at least 50dB/decade would be preferable.What do we want our filter to accomplish? Let’s say I want to design a filter with The first step to designing a low-pass filter, or any filter for that matter, is to determine our design constraints. While filter design software are are powerful tools, it’s a good idea to go over how filter design works manually at least once. This way, a huge part of the complexity is abstracted away. Instead, filter design relies on using tables of normalized values, then extrapolating these values to fit your design case. Fortunately, most of that complexity will be transparent to you! Good news, you’ll never have to work from scratch when designing filters. The math behind filter design is actually very complex, and the equations that determine component values are complicated. More specifically, we’ll learn how to design low-pass filters, high-pass filters, and band-pass filters. In this post we’ll go over how to design the most common passive filters, step by step.
Now that you have a basic grasp on filter theory, let’s get down to actually designing one.