I realize that full RFID is overkill for your application,
so I hope you won't mind me linking to pages that are focused on RFID when I think the principles also apply to your system.
You might also want to look at
Acousto-magnetic tags and other electronic article surveillance tags
which I hear are simpler and may be lower cost than full RFID systems.
I'm really just speculating, but I suspect that the controller you disassembled transmits at many frequencies, and each of the tags resonates at some unique frequency.
Perhaps something like this:
How do I design the controller antenna ?
Entire books have been written on antenna design.
Have you seen "AN710: Antenna Circuit Design for RFID Applications" ?
It's part of the
"Microchip microID 125 kHz RFID System Design Guide".
What circuit does the controller use to detect the tag?
Perhaps the controller uses coil-driver and envelope-detection circuit like one of these:
from
scanlime: SIMPLEST RFID READER?.
similar circuits: "Simple Low Cost UHF RFID Reader"; "Proximity Security System"; "Arduino based RFID reader"; etc.
When we look at just the inductor+cap tank circuit:
drive ---- coil ---(sense point)--- capacitor ----GND.
The sense point voltage has very large amplitude swings when everything is in resonance (perhaps several times the peak-to-peak voltage of the drive signal), and much smaller amplitude swings when it is out of resonance.
How does it work?
I speculate that the controller you disassembled works in one of these three ways:
frequency vs impedance
The controller puts some signal, perhaps a squarewave, on one side of the coil+capacitor tank circuit,
and measures the analog amplitude of the response at the connection between the coil and the capacitor
-- perhaps using an envelope-detection circuit as above.
After driving the circuit a few dozen cycles at one frequency, pausing, then driving a few cycles at some other frequency, randomly jumping between frequencies until they have all been measured -- or perhaps gradually sweeping the frequency in a chirp -- the controller has measured the analog response at many different frequencies.
Since the effective inductance of the coil depends on which coil is close by,
each tag (hopefully) produces a unique frequency-vs-response-amplitude graph.
resonance detection
Perhaps the controller has some sort of feedback oscillator with a frequency influenced by the particular tag in the range.
The controller occasionally pulses the oscillator circuit to give it a bit of a shove, and then the effective inductance of the coil -- which depends on which tag is close by -- controls the frequency of the feedback oscillator.
The oscillator frequency measured by the controller is (hopefully) unique for each tag.
pulse and listen:
Perhaps the controller sends out a sharp pulse or two, exciting the LC resonance of any tag in range, and then tries to measure the frequency of the return signal.
The frequency heard by the controller is (hopefully) unique for each tag.
These components are SMT components, most likely 0402 size (seeing as there are smaller SMT passives on the board which are probably 0201's).
The device with the mark next to the pulled of SMT's is most likely a sot666 package.
The black one is a resistor.
The tan one is a capacitor.
By the looks of the top layer copper, they are in an RC configuration with both connected to the sot666
There is no way to know the value of a resistor by inspection.
You'll need to measure the resistor with a DMM (in ohms mode) to find its value.
While capacitors do have color codes, in many instances these are manufactuer specific, the best way would be to measure it. It's most likely that the capacitor is lower than 0.1uF in value.
If the intention is to repair the board, then you probably don't need to find new components, just clean the pads off the old components (as they have been ripped off of the board). Scrape the copper off of the traces and find a very very small gauge wire to connect them all back. This will be a difficult repair due to the size of the components.
Best Answer
Let's review the evidence...
"D801" and "D802" are wired in parallel, but only one is populated. This hints at power diodes, designers thought maybe two would be required to take the required current, but one ended up being enough so they only populated D802. So we're probably looking at the circuitry that PWMs the razor's motor, and D802 is the flywheel diode.
"M801" hints at a MOSFET. There is a "Q301" so if it was a bipolar transistor, they'd have used a "Q" designator. Also, a MOSFET fits with my "PWM the motor" hypothesis. And the "801" hints that the designer perhaps thought it was part of the same bit of circuit than the diodes.
The squiggly trace isn't an antenna, since the device is a razor, it doesn't have radio. I'm betting on a cheapo way to implement a low value (milliohms) resistor for motor current sensing, or maybe add a bit of inductance for EMI purposes, who knows.
Also, if we have a MOSFET and a flywheel diode... and you inverted the supply voltage polarity... then both diodes were in series and shorting the supply, so the FET popped, which makes sense.
So I'll bet on a MOSFET. You still have to identify its polarity, get a rough idea on RdsON, and decide whether it's single or maybe dual !
First thing to do is check if the rest of the circuit still works. So, desolder the FET. Test D802 and desolder it if it is shorted too.
Then try to power up the razor. If you get no smoke and some kind of life signs, like LEDs blinking or whatever, then good news, the micro isn't fried... you can try to probe pins with a scope, see if you find a clock or something. The idea is to check if the circuit is still good before spending time on replacing the FET.
After removing the burned FET, next thing to do would be to check the PCB connections between its pins, to try to confirm it is a single FET. You'll get the polarity by checking how it is connected with the supply and the diode. It's probably N, but who knows. If you have a scope, check the gate to get an idea of switching frequency, then check the motor's resistance and current, then pic a FET that will do the job.