# Passive filter design with input load

I took several DSP courses years ago, but never actually designed a filter in real life (just solved equations.) Now, in my human job, I have been tasked with designing a filter that has an input load (R4) in an already existing filter chain (see the picture of the SPICE model I have created.)

My filter needs to go inside filter 1, and needs to filter out noise above .4MHz - I tried adding a simple RC filter with the specified corner frequency and it did not produce the expected results. I then tried trying to calculated the effective cutoff frequency of the cable, filter 2, and load but did not find anything that made sense.

How can I go about designing this filter in a "smart" way? My instructions from a coworker were to just plug in RLC filters and tweak them until they work, but that seems wrong. I have MATLAB and used it to do DSP before but I don't know how to translate a physical, passive circuit into MATLAB and generate a real circuit with actual capacitors, inductors, etc.

Clarification: R4 is the input resistance from the driving device. The Load section is the device, which is measured to have L2, C3, and R3 (it is an electrode on a device). Filter 2 is what is connected on board the device, and cannot be changed. Thus why only Filter 1 can be changed.

• There are any number of filter design calculators on the Web. Look for one that allows you to specify input and output impedance. Commented Nov 11, 2021 at 20:28
• Can you redesign the filters in Filter 1 and Load? To make a multisection RLC filter, all the different sections must play together to realize the desired response. There are a number of books and calculators to design multisection filers. My favorite book is "Simplified Modern Filter Design" by Philip R. Geffe. This book gives an easy to understand discussion of how RLC filters work as well as table approach to designing filters.
– qrk
Commented Nov 11, 2021 at 20:48
• @user287001 Adding clarification to post Commented Nov 11, 2021 at 21:24
• Insert also how part R4 in practice is L2 DCR?
– user136077
Commented Nov 11, 2021 at 21:35
• @qrk: The question title says "passive filter" so unfortunately I presume op-amps are not permissible. Commented Nov 11, 2021 at 22:11

Due to the interaction between the different components in an RLC filter, empirically determining the LC values of the added stage in LTSpice is probably the quickest way if Filter 1 can't be changed.

If you can change Filter 1 values, you can make a textbook filter. In the SPICE simulation below, I show your original filter and two textbook filters (minus the loss resistors) in a Butterworth and 2dB Chebychev configuration. With inductor and wiring loss resistances added, the slope of the filter won't be as good.

I'm using a bespoke filter program that is based off of "Simplified Modern Filter Design" by Philip R. Geffe. This is my favorite book on RLC filters since it has an easy to understand discussion of how RLC filters work, something many filter books avoid. This book can be found in university technical libraries.

You cannot just cascade filters and expect that the response will be the individual responses multiplied together. If you can, adding op amp unity gain buffers between sections -will- allow you to design this way, and usually does not cost much. If you can’t buffer between the sections, though, the advice of your coworker is good, and the most practical. You know from the circuit that the current response has five poles. Adding an rc section will give you another one, or an rlc section will give you two more. In general, the pole positions will depend on every part in the circuit, so trying to design from first principles is not practical.

Try this:

to get this:

Explanation: Looking at the component values, what you currently have (ignoring the pH of inductance and few ohms of resistance) looks like a filter with a final shunt element of 1.2nF, preceded by a series 47uH and then a shunt 90pF. i.e.:

This would seem to constrain you until you realize that C2 (90pF) is small enough to be pretty high impedance, so we may get away with ignoring it for the synthesis, and seeing what effect it has when we simulate the final design.

So let's try to turn it into a 4th order butterworth singly terminated filter:

from Williams Electronic Filter Design Handbook,

if we want a 400kHz cutoff, then the 1.2nF final C corresponds to a 500 ohm driving impedance. This is then the prototype:

and the rough approximation is to split the 314uH inductor across the existing 47uH and an extra 267uH. This ignores the 90pF shunt C, but it doesn't seem to have a great effect, but I'm sure there is room for optimization.

Here's the sim, it's quite a good approximation to the 4th order Butterworth I based it on, and the effect of the 90pF C2 that we ignored in designing it seems to be a bit of a bump in the rolloff at around -50dB.:

• I was about to suggest a Y topology also. My first guess was to do an RC in the usual way, accounting for the fact there is already 160 ohms resistance, and then place another 160 ohm resistor at the output because the next stage expects a 160 ohm source. This is of course not exactly correct because it ignores the output impedance of the first stage, but should work better than dropping in a plain RC ignoring the source impedance. Interesting to hear where you came up with your component values. A Smith chart would help if there were only one important frequency... Commented Nov 11, 2021 at 22:10