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I have this RLC filter. Theoretically the center frequency is 1600 Hz and the 3 dB bandwidth 161 Hz.

I built it on breadboard. I used the Picoscope 2204A together with the FRA4Picoscope software to measure these two figures. For this purpose I connected the AWG output via a 50 ohm BNC cable to the input and channel 1. The output was connected via a probe to channel 2.

The center frequency turned out to be about 1530 Hz, which is close enough to the theoretical 1600 Hz.

However, the bandwidth turned out to be 532 Hz, much larger than the 161 Hz of above.

What causes this? The inductor has a resistance of ~19,2 ohm. If I add this to the 10 ohm I get a bandwidth of 490 Hz. Reasonably close to the 532 Hz.

But shouldn't I also include the output impedance of 600 ohm of the AWG? However, if I do this, the bandwidth is much to large~ 9.8 kHz.

The wider-than-expected bandwidth is most likely caused by the real-world resistance and loading of the circuit rather than the ideal RLC calculation. The inductor’s approximately 19.2 Ω winding resistance adds to the circuit’s effective series resistance, reducing the quality factor and increasing the 3 dB bandwidth, which explains why the measured 532 Hz is reasonably close to your revised estimate. The AWG’s 600 Ω output impedance should not automatically be added as a simple series resistance; its actual effect depends on how the generator, filter, and measurement setup are connected, and the 50 Ω output configuration and PicoScope input/probe loading should also be considered. Breadboard wiring, component tolerances, and measurement connections can further shift the results. For other measurement-related calculations, tools such as Days Between Dates Calculator https://alarabictools.com/days-between-dates/ can also be useful when organizing test dates and experimental records.

The extra bandwidth you're seeing is fully explained by the inductor's series resistance, and you should not add the AWG's 600 ohm output impedance on top of that — the reason is how the transfer function is actually being measured, not a missing resistance term. A series RLC bandpass filter's 3 dB bandwidth is set by BW = R_total / (2πL), where R_total is the sum of all resistances that are physically part of the filter's current loop: your design resistor plus the inductor's own DC resistance (19.2 Ω here). That alone brings your calculated bandwidth to about 490 Hz, very close to the 532 Hz you measured like https://comparingtwolists.com/duplicate-checker, so that resistance is doing almost all of the work already. The AWG's output impedance behaves differently: FRA4PicoScope computes the response as Vout(f)/Vin(f), where Vin is the voltage measured directly at the filter's input node by Channel 1 — not the generator's open-circuit source voltage. Because Channel 1 is sensing the voltage after any division caused by the source impedance, that loading effect is already baked into the Vin measurement itself, so folding the 600 Ω into the filter's own R_total double-counts it and inflates the predicted bandwidth to the ~9.8 kHz you saw. In short: only resistances inside the LC loop (your resistor and the inductor's parasitic resistance) belong in the bandwidth formula, while the source's output impedance affects signal amplitude but not the measured transfer function when Vin is probed directly at the input terminals.

A 0.4 V signal is usually too weak to drive a 5 V relay directly. You'll likely need a small interface circuit, such as a transistor or MOSFET stage (or an optocoupler if isolation is important), powered by a separate 5 V supply. That circuit can detect the low-voltage pulse and switch the relay safely. If you can measure whether the 0.4 V signal is just a brief pulse or stays high during the chime, it will be much easier to recommend the right components. fnf