Electronics

What separates conductors, insulators and semiconductors is the band gap between the full valence band and the empty conduction band. Widen and shrink the gap and watch the free-carrier count hang on exp(-Eg/2kT).

A pentavalent donor makes electrons the majority; a trivalent acceptor makes holes the majority. Swap the central atom and see the impurity valence set the majority carrier while the crystal stays neutral.

Carriers move by drift, pushed by a field, and by diffusion, spread by a concentration difference. Switch each mechanism on alone and see how the total current J = qnμE + qD(dn/dx) is completed.

Join n-type and p-type and majority carriers cross by diffusion, exposing fixed dopant ions that raise a depletion layer and a built-in potential barrier. Step through how drift cancels diffusion to reach zero-net-current equilibrium.

Put a voltage across a pn junction and it flows only one way. Sweep the bias from reverse to forward and see the basis of rectification: current surging exponentially in forward, blocked in reverse.

Reshape a signal with one one-way valve. Lower the threshold to slice off peaks (clipping), then follow a series capacitor that shifts the whole waveform (clamping): two uses of the same principle.

A Zener diode is operated on purpose in reverse breakdown. Raise the input voltage and see how, past the breakdown voltage Vz, the output stops following and is held at Vz: voltage regulation.

Four diodes fold even the negative half-cycles upward for full-wave rectification. Grow the smoothing capacitor and see the bumpy pulsation shaped into nearly flat DC.

A BJT is two pn junctions around a thin base. Raise the base current and see how carriers poured in by the emitter sweep across the thin base into the collector, so a small base current controls a β-times larger collector current.

Before amplifying, park the transistor at a point on the load line. Change the bias to move the operating point Q and see that the swing headroom is largest at the center, where Vce is half of Vcc.

To a small signal about the operating point, the transistor is linear. Shrink the signal amplitude and see the exponential curve look straight, giving ic = gm vbe and turning the transistor into a small-signal model of rπ and a current source.

Put the small-signal model in a circuit to make a voltage gain for the first time. Grow the collector resistor and see the signal current become a voltage across Rc, so the output grows to -gm Rc times the input and inverts.

An amplifier sits between a source and a load. Change the load resistor and see the input impedance rπ and output impedance Rc form a divider and a parallel, trimming the actual gain Av = -gm (Rc || RL) below the unloaded value.

A MOSFET opens its channel with the gate voltage, not current. Raise the gate voltage and see that the insulated gate gives a very large input impedance, and that a channel linking source and drain appears the moment Vgs crosses the threshold Vth.

Once the channel exists, the current is decided by the drain voltage Vds. Raise Vds and see it split into a linear (resistor) region at small Vds and a saturation (current-source) region where Vds exceeds the overdrive and the channel pinches off.

About a saturation operating point the MOSFET is linear. Move the overdrive and see the slope of the square curve, gm = k Vov = √(2k Id), grow only as the square root of current (unlike the BJT), with an open input from the insulated gate.

Put the MOSFET small-signal model in a circuit to make a voltage gain. Grow the drain resistor and see the output invert by -gm Rd, in the same form as the common-emitter, while the insulated gate gives a nearly infinite input impedance.

See the CMOS inverter, a complementary pair of NMOS and PMOS. Sweep the input voltage and see why the output inverts cleanly while, in any stable state, one side is off and the static power is almost zero.

See the differential pair, the input stage of an op-amp. Spread the two inputs and watch the shared tail current steer to one side to make a differential output vod=Ad vdiff, while a common signal is rejected because the sum stays constant (CMRR).

A real op-amp gain is neither infinite nor flat. Lower the closed-loop gain and see the bandwidth widen by the same factor, with the product GBW=Acl·fc staying constant at the unity-gain frequency.

If GBW is a small-signal limit, large signals have a wall called the slew rate. Raise the input frequency and see the output unable to change faster than SR=Imax/C, distorting a sine into a triangle, plus the rail clipping that completes the large-signal limits.

See the active filter, which combines a capacitor’s frequency-dependent impedance with an op-amp. Sweep the input frequency and see frequencies below the cutoff fc=1/(2πRC) pass and those above roll off at -20 dB/dec, with the op-amp adding gain and a buffer.

An ideal switch has zero voltage when on and zero current when off, so it dissipates almost no power. Sweep the conversion ratio and see that, unlike a linear approach that burns the difference as heat (η=Vout/Vin), switching, which chops the input and averages it with an LC (Vout=D·Vin), keeps efficiency high regardless of the ratio.

A power MOSFET is F1’s ideal switch but loses power two ways. Sweep the switching frequency and see how a conduction loss independent of frequency (P_cond=I²Ron·D) and a switching loss proportional to it (P_sw=½VI·tsw·fsw) set the ceiling on efficiency and the heat, and why devices with lower Ron and faster transitions (GaN, SiC) are chased.