# Dealing With Capacitor Tolerances on Passive Bandpass Filter

#### apt403

Joined Aug 8, 2014
2
I've been having some fun with an Analog Devices' AD8307 log. amp, using it for general RF monitoring. I've now got the desire to increase its selectivity (specifically to center it @ 216mhz). I'm thinking the easiest way is to put together a passive bandpass filter and put it inline between the physical antenna and the antenna input on the AD8307.

The design for the bandpass filter I'm studying at the moment is detailed here and here.

I can't seem to wrap my head around how to go about selecting the capacitors for the circuit - It took some playing around to find capacitor and resistor values that are actually available commercially, what trips me up are the tolerances.

For example: a 100 Ohm resistor and 7.4 pF capacitor would result in the lowpass side of my filter having a cutoff frequency of 215mhz. Perfect, because I want the highpass side to cut off at 217 (so my center freq. equals sqrt(215*217) = approx. 216). However, the tightest tolerance I can find for a 7.4pF ceramic cap. is +/- .1pF - So unless I bought a bunch and binned them myself to find one that's dead nuts on @ 7.4pF, my lowpass side is actually going to have a cutoff at anywhere from 212MHz (7.3pF) to 218MHz (7.5pF). Best case I skew the center frequency off its mark, worse case I end up with a bandpass filter without a passband.

How do I deal with this? Is this design more of a theoretical construct, and is there perhaps a similarly simple design that can use components with less stringent tolerances?

#### #12

Joined Nov 30, 2010
18,223
Do you know what a squib is?
Two pieces of wire that you twist together to tune the circuit.
I don't think you can buy a variable capacitor less than 10pf.

You seem to be educated enough to know that picofarads sneak in at various places on a circuit board. Trying to buy something closer than 0.1 pf is a fools errand because larger errors than that happen when you get your face next to the circuit. This is the kind of circuit that ends up in a metal box because you can't trust it with people moving around in the neighborhood.

Have you calculated the RL type of filter? or a CL filter?
You might get better numbers there or still be stuck with using a diddle stick on a tunable coil.

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#### AnalogKid

Joined Aug 1, 2013
9,354
2 MHz out of 216 MHz is a very narrow band. Two RC sections will not get you much selectivity. If this is for a continuous signal, think about an LC resonant tank. Depending on the inductor it can have a very high Q and give you much larger out-of-band attenuation. And with a variable inductor it is easy to tune without high-precision parts.

ak

#12

#### apt403

Joined Aug 8, 2014
2
Thanks for the replies. You're totally right, #12. The AD8307 is destined for a fully shielded enclosure (machined alu.), but even parasitic capacitance and inductance between adjacent traces on the PCB will negate any crazy precision binning.

I did some reading on tank circuits, and I believe I'm getting there. Going off the formula here, the schematic for a series resonant tank here, and assuming I want this filter on a separate PCB between the antenna itself and the antenna input on the AD8307 PCB, am I right in assuming this sort of thing would work? The formula I used for calculating the resonant frequency doesn't seem to take into account the impedance of the load or the characteristic impedance of coax, antenna, etc. Is that important?

I also ran across schematics that seem to chain together series and parallel LC circuits such as here. What are the advantages of using those topologies rather than a single LC circuit?

Assuming I can get away with this sort of filter, I ran across a few different models of serial programmable capacitors. If I added a little uC, it might be fun to use one along with a keypad and LCD to program the filter, instead of using a screwdriver on the trimmer cap.

#### #12

Joined Nov 30, 2010
18,223
LC in parallel is a, "Don't pass this frequency". In series..."Do pass this frequency".
More than one such circuit is supposed to improve the Q, but you can get crazy high Q with a low resistance inductor.
The simplification in my mind is that Xc = Xl at required frequency. Your circuit seems to do that.
It seems to me that making the values big enough to swamp out parasitic effects of the circuit board is a good thing. Theoretically, any L has a C with the same impedance at some frequency of your choice. Less L requires more C.
I don't know enough to tell you about impedance matching, but I can tell you to use a plastic screwdriver on an adjustable capacitor.

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#### SgtWookie

Joined Jul 17, 2007
22,221
Google "Elsie Tonne" - Tonne Software wrote
a mighty nifty lumped-element LC filter design program for Windows that can be used for free for filters of 7 stages or less. You do need to know your input & output impedances.

Caps are generally tested for their value at less than 10MHz; as frequency increases so do parasitics. A multilayer SMT cap might measure 47pF at 10MHz, but by 500MHz it could more than double.

With an LC filter, you generally try to get the C within around 5%, and then tune the inductor. You can also add usually by soldering) "gimmics"; short pieces of tinned, very thin copper strips that you trim and bend to tune. This process can be very "fiddly", as an Englishman might say. Inductors will couple signals to each other, which can lead to very strange results. Circuit board layout is critical. So is shielding. The higher in frequency you go, the more magic-like it seems.