Electronics 01
Why Do Transformers Hum? It's 100 or 120 Hz, Not 50 or 60
Transformer hum comes from magnetostriction: the core stretches about 2 micrometres per metre twice every cycle. Why 100/120 Hz, and what makes it louder.
Electronics
Electronics 02
Why 100nF Decoupling Capacitors? The Impedance Math
Why is every decoupling capacitor 100 nF? Impedance plots with ESL and via inductance show what the value really does and when 1 µF is better.
Electronics 03
Can You Use a Voltage Divider as a Power Supply?
A 7 kΩ / 5 kΩ divider makes 5 V from 12 V until you load it: at 20 mA it gives 0.39 V. The Thevenin math, the efficiency limit, and when a divider is fine.
Electronics 04
Relay Flyback Diode: Why You Need One and Which to Use
A relay coil can kick back 1,000 V at turn-off. A flyback diode stops it but slows contact release about 5x. Here is the math and the diode plus zener fix.
Electronics 05
Why Is the RC Time Constant 63%? The Math of 1 − 1/e
63.2% is 1 minus 1/e, the point where an RC curve would have finished if it kept its starting slope. Why e appears, and why 5τ is not always enough.
Electronics 06
RC Low Pass Filter Cutoff Frequency: What −3 dB Means
fc = 1/(2πRC) is where the output is 0.707 of the input, half power and −45°. Why the slope there is only 10 dB/decade, and how loading moves it.