David L - Thanks for the images of the power kit and the link back to the oscilloscope measurements.
OK, so the power kit has some electronics to it. It's not just a simple resistor as I had suspected. The board images aren't high enough resolution to zoom in and read part numbers, but I can envision what the circuit may be designed to do based on the images and the oscilloscope measurements.
The power kit IS wired in parallel with the chime. That's the connection made by the provided wiring harness. The diagrams show the parallel connection. The HikVision quick start guide and installation video also show that. The combination of the chime & power kit is then wired in SERIES with the power transformer and the doorbell button. But the power kit is in parallel with the chime.
As background, the quiescent chime noise and buzzing common to many video doorbells is caused by the fact that video doorbells, unlike the original mechanical buttons, continue to draw current that passes through the chime even when the doorbell is inactive. As that current changes (as doorbell processor loading changes due to motion processing, as network communication changes, as IR LEDs turn on/off, as the doorbell audio starts playback, etc.), that current changes, the magnetic field in the chime solenoid coil changes, and the chime solenoid piston moves in and out. Maybe only slightly, but enough to make noise in some chimes. In my original experimenting with our NSC-DB1 doorbell, I could actually see the solenoid core moving in and out in sync with the audio speak from the video doorbell, much like the cone in a loudspeaker does when it is driven by audio.
The "classic" way of silencing the noise/buzzing from the mechanical chimes in a video doorbell setup is to connect a power resistor across the terminals on the mechanical chime. This bypasses some of the current from flowing through the chime solenoid coil, which in turn helps to silence it. The bad side of this, however, is that when the doorbell is active the resistor is still bypassing current from the solenoid coil, meaning the chime likely won't strike as hard. It might even chime with one tone when it used to chime with two. Experimenting with different resistor values might be necessary to, for a particular transformer and chime, come to an acceptable trade-off between quiescent state noise and chime strike strength.
And now the power kit...
The image of the power kit shows a number of components marked with a "100". These are sizable surface mount 10-ohm resistor chips. They're likely wired in some parallel/serial fashion to form a fairly high power resistor, likely similar to the 5-watt or 10-watt resistors that are often included with other video doorbell kits and used to shunt across the chime solenoid coil.
Now let's talk about the oscilloscope measurements. The post isn't specific on how the measurements were being made, and there are some flaws in the conclusions made. In particular, for the case where the doorbell is inactive, the author misses the point on the oscilloscope graph where he states that "every half period is chopped away" and the waveform is spikey-looking. He missed the fact that the voltage across the power kit is really small (3V peak-to-peak) compared what it is across the doorbell button (40V peak-to-peak).
Here's my theory - the power kit acts as a "smart" resistor. When the doorbell isn't active, there isn't much current flowing in the circuit. I believe the power kit senses that condition and applies a low-resistance load across the chime to shunt or bypass current away from the chime to help silence it. It can't just short out the chime since the power kit needs to derive some of it's own power to work with - hence the low voltage waveform observed by the oscilloscope when the doorbell was inactive. Further, the waveform is "spikey" in this case since the only time current is flowing through the circuit is on voltage peaks where the video doorbell is recharging it's power supply filtering capacitors. Anyone who's built a linear, full-wave rectified power supply is familiar with this kind of current profile. Seeing it here in the oscilloscope graphs as a spikey voltage across the power kit is no surprise.
When the doorbell button is pressed, the current in the circuit goes up significantly. My theory is that the power kit in turn senses that and disables the shunt resistor across the chime. Removing the shunt maximizes how much power can be applied to the chime coil, help the chime drive as loud as can.
If I'm right, I think it's actually a fairly novel idea, and the power kit would go a long ways towards removing the problem of a video doorbell having to work with who-knows-what for a transformer and who-knows-what for a mechanical chime.