Articles that do not fit on the calculator pages: the background of the formulas, component variation, how parasitic capacitance and inductance show up as symptoms on real hardware, and the judgement calls that come up in design review, each backed by standards and numbers.
2026-10-18
The three types differ in whether the diodes sit in the op-amp feedback, go to ground after a gain stage, or whether the transistors themselves saturate. Four classic circuits were solved in ngspice with the same guitar signal so you can hear the difference.
2026-10-18
A 1970s distortion amplifies once with an op-amp and clips with diodes, while modern high gain like Friedman's BE-OD clips a little at a time at three points across four gain stages, cutting lows and highs in between. It has more gain than a RAT, yet the gaps between palm-muted chugs survived better.
2026-10-18
A guitar's output is a weak signal of under 0.4 V and 1 µA; at the speaker it becomes 15 V and 2 A. We solve the whole chain connected together in ngspice and follow what each device receives and passes on, by waveform, voltage, current and impedance.
2026-10-02
A triode is a device that chokes plate current with the grid voltage; its input is voltage only and almost no current flows. Its small-signal equivalent circuit, a current source gm·vgk in parallel with an internal resistance rp, has the same form as an N-channel JFET, so grounded stages, followers, differential pairs and op amps can all be built in the same form with tubes (the differences are an operating voltage one to two orders of magnitude higher, and the heater).
2026-09-23
Making differential 100Ω by placing two 50Ω traces side by side is a common mistake. Bring them close and their fields couple, so the odd-mode impedance Zodd falls below the single-ended Z0, and Zdiff = 2×Zodd ends up below 2×Z0.
2026-09-23
"I checked the length in the calculator and the CAD. They match within 0.5mm, so it is fine." If the trace crosses outer and inner layers, it may not be. The outer layer leaks part of its field into air, lowering its effective permittivity, so the same length arrives sooner than on an inner layer.
2026-09-23
D = Vout/Vin is the formula for an ideal switch with no losses and no dead time. Stepping 24V down to 1.0V at 2MHz needs an on-time of about 21ns, below the minimum on-time of most controllers (typically 50-100ns), and the controller cannot make the intended voltage.
2026-09-23
In a buck converter making 6V from 12V, the RMS ripple current in the input capacitor is half the output current. D = 0.5 in Irms = Iout√(D(1−D)) is the worst case, so the closer Vout/Vin is to 1/2, the harder the input capacitor is to choose.
2026-09-23
A datasheet's "output resistance about 10Ω" is a single typical value. An IBIS file carries V-I tables for all three typ/min/max corners, and just reading the slope near the origin gives a good first estimate of Ro and the damping resistor for each corner.
2026-09-23
"8mA drive strength" does not mean the pin can deliver only 8mA; it is the current guaranteed at the VOL/VOH test point. What it really sets is the number of parallel transistors in the output stage, that is, output resistance and slew rate, so stronger drive adds ringing and ground bounce and weaker drive slows charging of trace capacitance.
2026-09-23
A long clip-style ground lead forms a series resonant circuit with the probe tip's input capacitance, and a 15cm lead resonates at 100-150MHz. Measure a fast edge and the screen shows ringing that the board does not have.
2026-09-23
The "600Ω at 100MHz" on a ferrite bead datasheet makes it look like an inductor, but in that band the bead is a resistor that turns current into heat. Below it the bead is an inductor, above it a capacitor, and DC current saturates it and weakens the resistive effect; paired with a capacitor downstream it can even amplify noise.
2026-09-23
The "load capacitance CL = 12.5pF" on a crystal datasheet is not a value to write on two capacitors, C1 and C2. It says the whole board must look like exactly 12.5pF from the crystal's two legs. Get this wrong and the frequency moves by a few to tens of ppm, which for a clock is tens of seconds a month.
2026-09-23
The "300mA output current" on a datasheet comes with the condition that the heat can be removed: multiplying the 0.51W of 5V-to-3.3V at 300mA by a SOT-23-5's θJA puts the junction above 150°C at 50°C ambient. Board copper area is what helps, but it has a ceiling.
2026-09-23
Plugging in a live adapter can destroy an input rated for 30V. The cable inductance and a low-ESR MLCC form a series LC circuit that resonates on the voltage step at the moment of plug-in, and the input voltage briefly jumps to nearly twice the supply voltage.
2026-09-23
A SAR ADC input pin is just a sample switch of a few hundred Ω to a few kΩ and a sampling capacitor C_sh of a few pF, and if the input does not settle within 1/2 LSB during the sample period, the shortfall becomes measurement error. Adding an external C "to be safe" can also cut the conversion rate by orders of magnitude if it is the wrong size.
2026-09-23
A strap pin reads its voltage only at the instant reset is released to choose the boot mode, and afterward works as an ordinary GPIO or LED driver. Even one LED is a heavy enough load for the internal pull resistor (tens of kΩ) to push the node into a band that is neither H nor L, and the chip boots in the wrong mode.
2026-09-23
The clamping voltage in a TVS datasheet is measured at the TVS's own terminals. If the voltage reaching the IC pin is higher, the cause is not the trace from the connector to the TVS but the inductance of the stub branching off the signal line to the TVS and of the TVS's ground via, the last few mm before the current reaches ground.
2026-09-23
A memory access is just placing or fetching data at an address, but inside DDR4 and LPDDR4 the address is split into row and column, several devices are selected with CS, and data is captured against a reference signal called DQS. Following this also shows where length matching on the board matters.
2026-09-22
The "output current" on a regulator datasheet is the current it sources from input to output; its ability to sink current flowing into the output, down to GND, is zero for an ordinary LDO. When a protection diode or another supply pushes current into a 3.3V rail, the LDO can only close, and the rail rises until it balances what the load can absorb.
2026-09-19
An inductor can't change its current suddenly, and it will put out whatever voltage it takes to keep the current flowing. The V in V = L·dI/dt is that voltage; it flips direction between rising and falling current, which gives both the spike when you switch off and the principle of the boost converter.
2026-09-19
"Active is just higher performance" isn't right. An active filter can't be used on a power rail or at RF, and a passive filter alone isn't enough ahead of an ADC, so the signal's frequency, power, and impedance decide the topology.
2026-09-19
Op-amp circuits look like a zoo, but two rules read them all: with negative feedback the two inputs sit at the same voltage, and no current flows into the inputs. With them you can trace an inverting circuit, a non-inverting circuit, or a 2nd-order filter.
2026-09-15
32768 is 2 multiplied by itself 15 times, so passing it through a halving circuit 15 times yields exactly one pulse per second. A crystal that vibrates once a second would seem simpler, but why it can't be built is the very reason this frequency was chosen.
2026-09-14
"I want 50 ohms, so tell me the trace width" cannot be answered as asked. The width is set by the dielectric thickness under the trace, so the stack-up must be fixed first.
2026-09-14
R = (Vcc − Vf) / I gives a nominal resistor. Supply, forward-voltage and resistance variation determine whether it also meets the required minimum and maximum current.
2026-09-14
A fab's design rules come in mm, a component footprint in mil, and copper weight in oz. Three unit systems on one drawing is an ordinary day in PCB design, and rounding at the wrong point means a rule violation or a board that won't take the part.
2026-09-14
Placing 0.1uF at an IC's power pin does not place a capacitor. It places "a capacitor with a small inductor attached." More than half of that inductance comes not from the capacitor but from the via and the trace feeding it.
2026-09-14
"At high frequency, current only flows near the surface" is true, but what counts as "high frequency" depends on the conductor's thickness. For 1oz copper on a PCB that is around 4MHz; for a power winding, it starts at 100kHz.
2026-09-14
Even a 1MHz clock will ring on a 30mm trace if the driver's edge is 500ps. What decides whether a trace behaves as a transmission line is not frequency but the ratio between the edge speed and the time it takes to travel the trace and back.
2026-09-14
Told to "match clock and data lengths," plenty of boards end up with every trace tuned to 0.1mm. But 1mm is 6.5ps. If that signal's timing margin is 5ns, a 100mm mismatch is not a problem at all.
2026-09-14
4.7kΩ is a rule of thumb from 5V, 100kHz, small buses; at 3.3V and 400kHz with five modules and a 30cm cable it can't keep up. The resistor has a floor and a ceiling, both calculable.
2026-09-14
A divider built from R1 and R2 scales the voltage by R2/(R1+R2) on paper. In practice, tolerance, the load's input resistance, temperature and the ADC's sampling capacitor move the output a few percent, so check that the divider is not adding more error than the ADC's resolution.
2026-09-14
Route a power trace off a table that says "0.3mm for 1A" and a long run will bite you with voltage drop. The width set by temperature rise and the width set by voltage drop are two separate calculations, and the longer the trace, the more the second one dominates.
2026-09-14
In a buck converter running at 92% efficiency, tracing where the remaining 8% turns into heat sets your priorities. Lower the MOSFET's RDS(on) alone, and switching loss and the inductor still account for 70% of the total.
2026-09-14
Told something "dropped 6dB," if you can't immediately say whether that means the voltage halved or the power fell to a quarter, you'll misread both filter calculations and EMI limits. A dB expresses a ratio on a log scale, with a coefficient of 10 for power and 20 for voltage.
2026-09-14
Put 3.3 V on a 0402, 10µF/6.3V part, about half its rating, and only about 3µF is left. The "10µF" on the datasheet is the value with no voltage applied.
2026-09-14
A 1.6kHz RC filter cuts 100kHz noise to 1/60 (-36dB). Not to zero. A filter attenuates rather than cuts off, and for a first-order stage the amount is set by the frequency ratio.
2026-09-14
The inverting amplifier is easy to analyze thanks to the virtual ground, but forget that the same virtual ground means "input impedance = Rin" and the gain halves the moment you connect a sensor.
2026-09-14
A 50pF load takes 20ns to charge to 3.3V from an 8mA driver. Toggled at 50MHz it burns 27mW. Trace capacitance gets called "parasitic," but it has a clear, numeric effect on both timing and power.
2026-09-14
A 10,000mAh power bank can't charge a 3,000mAh phone three times, and that's not false advertising but a units problem. The 10,000mAh is rated at 3.7V; convert to 5V and subtract the losses, and you get about two charges.
2026-09-14
A board specified as er = 4.3 is, underneath, a weave of er = 6 glass bundles and er = 3 resin. A 0.15mm trace crosses that pattern at a 0.5mm pitch, and if the two lines of a differential pair sit on different parts, you get skew.
2026-09-14
A humbucker's "fatter" tone comes from its inductance doubling, which pulls the resonant frequency down by about 1.3kHz, and the hum cancels because the two coils oppose an external field while adding for the string signal. Both can be put into numbers with the equivalent circuit.
2026-09-14
There's no memory that is "non-volatile, rewritable, and fast" all at once. Every memory gives up endurance, capacity, speed, or price, so this is organized to be looked up by application.
2026-09-10
If 20 V appeared the moment you plugged in, every 5 V-only device would die on first contact. USB PD avoids that with a stage settled by resistors alone, and a stage where nothing moves until the sink asks.
2026-09-10
Many non-PoE devices plug into an RJ45 port, so a PSE does not just put 48 V out: it checks who is there with a few volts, asks how much power they need, and only then switches on.
2026-09-07
It gets you an indicator LED without a 3PDT, which is why it turns up so often in home-built pedals. The circuit is simple, but it creates one node at a very high impedance, and the quirks all follow from that.
