Electronic – Analyzing this RF circuit

RF

I'm trying to analyze this RF circuit:

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This circuit is designed for about 915 MHz operation. I'd be happy in fact understanding this smaller section of the circuit:

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  1. I have been trying to find the transfer function of this section. I bet it's some kind of filter, and while I did take classes on electronics, I unfortunately never paid attention in them. What analysis method could I use to determine the transfer function of this section? I tried figuring out Vout/Vin via impedances but I couldn't figure out anything meaningful. The grounded connection is confusing me. How is the grounded L304-C303 impedance modeled as a transfer function with respect to the rest of the circuit?

  2. For the schematic as a whole, I'm trying to figure out if the connection into the antenna (off the right of C304) is matched to 50Ω, since I'm going to use a different antenna system from what is in the schematic. It probably is, but I would rather make sure, if that's possible. What analysis approach could I use to figure this out?

CC430 datasheet.

Best Answer

It's just been so long that I don't know how to begin with the topological analysis that would let me frame it mathematically

Firstly, ignore the parallel tuned circuit formed by L304 and C303 (just for a little while why I look at the series tuned circuits)

A 1.5pF capacitor in series with a 15nH inductor is a series tuned circuit at 1.061 GHz: -

F = \$\dfrac{1}{2\pi\sqrt{LC}}\$

But with stray capacitance and non-ideal inductors it'll be a little lower and probably align itself with 0.915 GHz very nicely. So it's resonant and it will behave like a low resistive impedance at this frequency - this will make the input port impedance look like 50 ohm if there is 50 ohm on the output port. In fact it will look like 100 ohm if there was 100 ohm on the output.

Note that there are two of these circuits in series but this doesn't alter things - the pair will resonate exactly the same.

And now the parallel tuned circuit. It's theoretical resonance is at 1.18 GHz but like I mentioned before, stray capacitance will lower this and given that the ground plane on the circuit board will likely offer great stray capacitance than it would to the series tuned circuits, I would be surprised if it didn't resonate fairly well aligned to 0.915 GHz.

At resonance, a parallel tuned circuit has infinite impedance and in practice (given inductor losses) I would expect it to look like a resistor of a few kohms in value.

In summary, in the operating band of 915 MHz, the network will be virtually transparent to the signal.