# How to properly design LC bandpass filters?

A little disclaimer. Electronics is a hobby to me so I learn it on my spare time. This leads to certain knowledge gaps that professionals might not have.

I want to build a good filter using SMD components. I started from some existing design I found online and trying to modify components and parameters in order to achieve the good results. I lack in theory heavily so I would welcome a good literature references.

I found LTSpice and started playing around. I learned how to step through parameters.

The only thing that concerns me is impedance matching. CT/CB are forming the divider and I want to optimize schematic for optimal Q while preserving 50 Ohm i/o impedance.

The problem here I don't know how to do these optimizations while I remain within assortment of available components. Plus there are tolerances on them which also should keep the schematic working fine.

My question is - what I should read or where to find an information or methodology to design such filters properly and suitable for manufacturing?

Answers for questions:

Type of the filter - band pass filter for ham-radio transceiver. So I have low signal levels. Low losses are very important because the signal will come from the antenna.

Frequency range: HF, 1.5MHz-30MHz. Bandwidth depends on the band. I am not sure about the ripple, the lower the better but I think 1db should be ok.

Source has a series resistance set to 50 Ohm in Parasitic Impedances section. My load is a resistor of 50 Ohm.

With regards to the components Q - ideally I want to use a inductances table from manufacturer which already has a Q measured. But I don't know how to use this table inside LTSpice because it has inductance+DCR+Q at the same time. Plus, there are tolerances that affect filter performance.

Also, the filter works at the higher impedance than its input output (CT/CB make a some sort of capacitive transformer).

Right now I am pretty much lost because I am trying to find the best fitting curve with lowest losses. Plus how to keep input/output impedance the same 50 Ohm?

This is what I have simulated so far:

• It would depend a lot what the filter is for. Is it for 20 kHz audio or 20 GHz RF? What voltage/current/power levels are involved? May 21 at 21:32
• What is this Q that you are talking about? What type of filter are you looking for? Not lastly, you have a few things in there that need correcting: the .meas command should be .meas VR1 param V(R1), and the exponentiation in LTspice is **; ^ means XOR (unless it's in Laplace expressions, not the case here). Also, your source is directly across an inductor, this might not be what you want (unless you add some series resistance). If you don't hink it's too much, try this link. May 21 at 22:07
• The source termination resistor (50R between V1 and L4) seems to be missing May 21 at 22:51
• If you have a college library nearby, see if they have "Simplified Modern Filter Design" by Philip Geffe (copyright1963). It's a wonderful book on designing LC filters and takes you through converting low-pass prototypes to the filter type of your choice, plus, normalization; all using tables.
– qrk
May 22 at 22:40
• Looks like I found a good book archive.org/details/HandbookOfFilterSynthesis/page/n69/mode/2up May 23 at 2:35

## 2 Answers

You have given enough parameters to design the required filter:

• source termination 50 ohms
• load termination 50 ohms
• bandwidth 200 kHz
• center frequency 1.81 Mhz

Any number of "applets" can design this filter. I have used "ttc08" that was included with EMRFD Experimental Methods for Radio Frequency Design. One is given a choice of inductor values (all inductors are the same). Capacitor values are internally calculated to achieve the desired filter.

In this case, a "standard value" inductor of 4.7 uH is chosen. One must be careful to choose a low-loss inductor so that its "Q" is far higher than the filter "Q". The filter Q in this case is roughly center frequency divided by bandwidth (about ten). An inductor Q of about 100 is assumed. Capacitor Q is usually assumed infinite at this low frequency:

simulate this circuit – Schematic created using CircuitLab
Could this be built with surface-mount components? 4.7uH of sufficiently-high Q might be a bit of a problem sourcing.
Those odd-value capacitors may have to be parallel or series combinations of standard values. All component tolerances should be tight with this fairly high-Q filter. Filter bandwidth is slightly less than the desired 200 kHz due to finite component Q. A filter having higher Q than 10 might benefit from trimming components added to C2, C6. All capacitor values here are fairly well-defined by bulk capacitors. At higher frequency, stray coupling and stray capacitance make trimmers/tuning mandatory.

LTspice is a good tool to verify a filter. One can vary component tolerances to gain a sense of how badly filter characteristics are degraded. But LTspice is not adequate to show how a filter should be constructed to reduce component-to-component coupling, or estimating reactance of printed-circuit traces that you think are inconsequential. That is a matter of experience.

It may seem that this filter differs from the capacitive-tap matching used in the OP's schematic. It is really not so different...C1 and C2 have roughly similar ratio to OP's C1 & C2.
What is missing from OP's schematic is the 50 ohm source resistance. Note that V1 generates a voltage that divides between R1 (50 ohms) and R5 (50 ohms), so that filter output within the pass band never rises above 0.5V when V1 is 1V. The resistive losses of the three inductors add about another 1 dB attenuation to this -6dB. (total of -7dB)

A brain fart caused me to choose the (above) filter's center frequency to be 1.81 MHz., instead of geometric mean of lower & upper frequency edge - which should be near 1.9 MHz. That's $$\ \sqrt{1.8 \times 2.0} \$$
This error is an opportunity to see how/which components change value, and by how much. Re-evaluating the resulting filter helps give you a feeling for component sensitivity. The "Q" value for the standard-value inductor was also reduced from 100 to 60, to reflect achievable Q of SMT inductors:

simulate this circuit

Note that R2,R3,R5 in this revised filter are equivalent loss resistance of the associated inductor, and are not components to be added. These increased losses added another few decibels to filter passband attenuation.

• That's a lot of elements in there. This might be less costly (and the values are not too far away from the standards, at least for the caps). May 22 at 15:54
• @aconcernedcitizen yes, very nice & simple! Released from using a "standard" inductor, one has the freedom to eliminate coupling reactances. But doing so increases the number of critical-value components - each one of the components of this simpler filter requires fairly tight variation in value. I'd hazard a guess that the OP's filter requirements are near the edge of what's build-able without trimming, no matter what topology. May 22 at 16:07
• I also think OP is ambitious, but I like ambition. :-) May 22 at 16:09

If you're a hobbyist, you might have a copy of Practical Electronics for Inventors. Chapter 9 (of the 4th edition) would likely have a lot of great information for guys like you.