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PCB trace capacitors and inductors

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DrMag:
I'm thinking through a very small radio design (ultimately for model rocket telemetry) and am a little befuddled by the small capacitances or inductances needed to filter a 2m or 70cm frequency. I have an idea--does anyone know if this is a bad one?

Here's my thinking:
Oscillator is an Si5351A (operating at 146Mhz to start). This is a square wave, so I need a filter to get a sine wave. Looking at a one-pole butterworth filter, that requires a series inductor and capacitor of about 1 uH and 1 pF, respectively.

At those levels (parallel filter would make the inductor small; ~2.6 nH in this case), the pcb traces themselves start making a significant contribution. So here's what I'm thinking: pcb is built with the Si5351A, short trace to a 1 uH inductor, short trace to a capacitor created by parallel 6.35x6.35 mm fill regions on opposite sides of the board. This would be followed by a voltage divider to move the oscillation to 0-Vcc so a single supply amplifier can be used.

An LTSpice simulation shows this working; but is it a bad idea in terms of pcb design?  If I were to use a narrow, short trace (or maybe a loop with vias?) as a small inductor, are there issues with that?

Quick edit:
I'm aware the below circuit is not tuned for 146 MHz; that comes from rounding off the inductor and capacitor sizes, of course.

T3sl4co1l:
1. Simulation quirks.

Your source has zero ohms ESR (as far as I can tell, anyway; LTSpice hides that kind of thing, sadly).  This is rather unrealistic!

2. Your filter has a suspiciously high impedance.  Can you even get a "1uH" inductor that's still an inductor at 146MHz?  (A: Yes, actually.  But you'll need to check carefully to make sure!)

3. Reality quirks.

There are no wires at RF.  Everything is transmission lines, and transmission lines have equivalent inductance and capacitance (at frequencies below the electrical length, which will be the case for any reasonably compact layout at this frequency).

Important factor: you won't have a series resonant tank, if you built that.  What you will have is extra capacitance to ground, on the middle (L-C) node.  Which creates a capacitor divider between ground and the output, changing the resonant frequency and impedance matching.

You can work this out by estimating the capacitance of that node -- it should be under 1pF for a typical SMT PCB layout, but also won't be under 0.2pF, even with ground plane removed around the connection.  So, it'll be important to the circuit response.

(Also, FR-4 has a nasty tempco, so it won't be very stable either.)

And yeah, using the parallel equivalent (assuming your source and load are happy with that impedance) might work out better, but similarly, a couple nH is comparable to the physical length of a chip capacitor, so again you will get a divider, this time an inductor divider (part of the inductance is the body of the capacitor itself, the rest is the loop that you can actually couple into), and again it will be poorly defined (depends on manufacturing and assembly tolerances) and drifty (due to mechanical expansion rates).

4. So how do you cook something like this, anyway?

Try a coupled resonator design.

A resonator is a parallel LC tank, grounded at one end.  Or, well, it doesn't really matter what it's attached to, it can be floating in space for all that matters (for non-contact coupling methods).

You can make a resonator with a length of wire or transmission line, a helix (helical resonator -- kind of big at this frequency, though!), or an LC.  (I mean, to be fair, these are all equivalent to, a sufficient degree of equivalency.)  There's absolutely no problem making a resonator for any arbitrary frequency, no worries.  What we are worried about, is the ratio of impedances: the resonator impedance Z = sqrt(L/C) compared to the system or coupling impedance Zo (usually 50 ohms).

It's typically easiest to make a parallel resonator with highish impedances (100s to 1000s of ohms), so we should work with that.

What we are really after, by shuffling around the impedance ratios, is setting the Q factor of the components.  A series resonant tank, Z = 1kohm, tied between two 50 ohm ports (100 ohms in series), is a Q of 10, and thus a bandpass of 10% (or 146MHz +/- 7MHz at -3dB).

For a generalized resonator, it doesn't matter that we have an electrical connection, just that we couple the same ratio of signal into it.

What does "coupling" look like, in circuit?  Lots of things!  You can connect a port to the "top" or "hot end" of a resonator, through a large series impedance (usually a small capacitor, since a resistor is lossy, and a very large inductor is impractical).  You can connect to the "middle" of the resonator, by dividing the capacitor into pieces (a capacitor divider -- a matching network), or dividing the inductor into pieces (inductor divider), or tapping the inductor, or coupling to it (mutual inductance).

Since the coupling capacitances, or coupling factors, are typically quite small, it often suffices to simply have the coils near each other.  A pair of "square" coils (i.e., height = diameter) have a coupling factor about 0.2 when positioned in line (parallel axes) with the same distance between them.

Relevant:
http://www.changpuak.ch/electronics/Direct-Coupled-Resonator-Bandpass.php


Tim

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