The translation problem: one-way DC, back-and-forth AC
Picture a river that only flows downhill. That is direct current's twin — DC — the steady, one-direction push you get from a battery or a solar panel. Now picture the tide: water rushing in, pausing, rushing back out, sixty times a minute. That rhythmic reversal is alternating current, the language of your wall socket and the entire power grid. In the last few rungs you mastered the buck, the boost, and the buck converter — circuits that take a DC voltage and hand back a *different* DC voltage. The inverter asks a harder question: how do you take a flat, one-way DC supply and make it slosh back and forth like the tide?
The answer is almost embarrassingly simple in concept: if you can't make the current reverse, *reverse the wires instead*. Connect a load to your DC source one way, then a moment later flip the connections so current runs the opposite direction through the load. Do that flipping fast and rhythmically and the load never knows it was fed by DC — it feels AC. The whole art of inverter design is in *how* you flip, *how fast*, and *how cleanly*. A crude flip gives you an ugly square wave full of harmonics that overheat motors and upset the grid. A clever flip gives you something a sensitive load can mistake for a pure sine.
The H-bridge: four switches and a flip
The machine that does the flipping is the full-bridge or H-bridge inverter, named for the letter its schematic draws. You stack two transistors on the left leg and two on the right, with the load hung across the middle like the crossbar of the H. Call them Q1 (top-left), Q2 (bottom-left), Q3 (top-right), Q4 (bottom-right). The DC supply +V sits at the top rail, ground at the bottom. Each transistor is just a switch you can open and close electrically.
+V ───┬─────────────┬───
│ │
[Q1] [Q3]
│ │
A ────┼──[ LOAD ]───┼──── B
│ │
[Q2] [Q4]
│ │
GND ───┴─────────────┴───
Phase 1: Q1 + Q4 ON → current A→B (load sees +V)
Phase 2: Q3 + Q2 ON → current B→A (load sees −V)
Dead-time: ALL OFF for ~1 µs between phases- Phase 1: Close Q1 and Q4 (the diagonal). Current flows from +V, down through Q1, left-to-right across the load (A→B), out through Q4 to ground. The load sees +V.
- Phase 2: Open those, close Q3 and Q2 (the other diagonal). Now current flows down through Q3, right-to-left across the load (B→A), out through Q2. The load sees −V — same magnitude, opposite polarity.
- Alternate between Phase 1 and Phase 2 at, say, 50 or 60 times a second, and the load experiences a voltage that swings +V, −V, +V, −V… — a square-wave AC at your chosen frequency.
From square to sine: sinusoidal PWM
A bare square wave technically *is* AC, but it is a brute. Its sharp edges carry a thicket of harmonics — energy at 3×, 5×, 7× the fundamental frequency — that cook motor windings, buzz audibly, and fail every grid-connection rule. We need a smooth sine. The breakthrough is to remember a trick from earlier rungs: pulse-width modulation. You already know that switching a load fully on for, say, 30% of each tiny time-slice and off for 70% delivers an *average* of 30% of the supply voltage. PWM lets you synthesize any average value between 0 and +V just by choosing the duty cycle.
Sinusoidal PWM (SPWM) applies that idea across a whole AC cycle. Instead of a fixed duty cycle, you *vary* the duty cycle from pulse to pulse so that the *average* of the switched output traces a sine. Near the peak of the desired sine, the pulses are wide (high duty cycle); near the zero-crossing, they're narrow. The switching itself happens fast — typically 4 kHz to 20 kHz, far above the 50/60 Hz output. The load's own inductance acts as a low-pass filter, smoothing the fast chopping into a clean low-frequency sine and rejecting the high-frequency switching ripple.
Compare a slow SINE reference against a fast TRIANGLE carrier:
+1 ┤ ___ ___
│ / \ /\ /\ /\ / \
│ / SINE \ /\/\/ \/ \/ \ / \ ← reference
0 ┼──/─────────\────────────────/─────────\──
│ / /\/\/\ \ carrier / /\/\/\ \
−1 ┤/__________ \____________/__________ \
Gate = HIGH whenever sine > triangle
Output pulse width: WIDE near sine peak, NARROW near zero.
Wider pulses → higher local average → output tracks the sine.The IGBT: the muscle behind the switching
Switching a sub-watt LED is easy. Switching the 100 kW that spins a train motor — at 10,000 times a second — needs a special device. The IGBT (insulated-gate bipolar transistor) is the workhorse that made high-power inverters practical. It's a hybrid: it has the voltage-controlled gate of a MOSFET — meaning you steer it with voltage, drawing almost no current to hold it on — bolted onto the low conduction loss of a bipolar transistor, which carries hundreds of amps with a small voltage drop. You get the easy drive of one and the brawn of the other.
Where does each device reign? Below a few hundred volts and at very high switching speeds — laptop adapters, low-power drives — the MOSFET wins. From ~600 V up to several kilovolts, at currents from tens to thousands of amps — EV traction, industrial drives, grid inverters — the IGBT dominates. And at the bleeding edge, wide-bandgap SiC and GaN devices are now displacing IGBTs in EVs and fast chargers because they switch faster with lower loss, shrinking the heatsinks and magnetics around them.
Worked intuition: how PWM spins a motor
Here's the payoff. An AC motor's speed is set by the *frequency* of the AC feeding it, and its torque/flux by the *voltage*. An inverter controls both independently — that's the whole reason variable-speed drives exist. The key insight for a motor is the V/f ratio: to keep the magnetic flux in the iron constant (and thus available torque steady) as you change speed, you must change voltage and frequency *together*, in proportion. Drop the frequency to slow the motor, and you must drop the voltage by the same factor, or the flux saturates the core and the windings overheat.
Both knobs live inside the SPWM scheme. Frequency is just how fast the sine *reference* sweeps through its cycle — speed up the reference and the synthesized AC speeds up. Voltage is the modulation index — how tall the sine reference is compared to the triangle carrier. A short reference produces narrow pulses everywhere, a low average, a small effective AC voltage. Push the reference up toward the carrier's full height and the average swings closer to the full bus voltage.
Run a 4-pole induction motor from a 540 V DC bus.
Rated point: 400 V (line) at 50 Hz.
→ keep V/f ≈ 400 / 50 = 8 V per Hz
Want HALF speed? Set output frequency = 25 Hz
required voltage = 8 V/Hz × 25 Hz = 200 V
→ drop the modulation index to ~½ AND
sweep the sine reference at 25 Hz.
Want a soft start from standstill?
ramp frequency 0 → 50 Hz over a few seconds,
ramp voltage 0 → 400 V in lock-step.
No inrush surge — torque stays controlled the whole way up.Where inverters live: solar, the grid, and EVs
Look up at a rooftop solar array. Each panel is a DC source — a solar cell only ever pushes current one way. To put that energy into your home or sell it back, a grid-tie inverter converts the panels' DC into AC that exactly matches the grid: right voltage, right 50/60 Hz frequency, and crucially *in phase* with the grid's own sine. A grid-tie inverter doesn't just make AC — it makes AC synchronized to a wave it didn't create, locking onto the grid's rhythm like a musician joining a band already mid-song. Lose synchrony and you fight the grid instead of feeding it.
The same silicon underpins the electric car. An EV's battery is a big DC pack — often 400 V or 800 V. The motor that drives the wheels is AC (usually a permanent-magnet synchronous machine). Between them sits a traction inverter: a three-phase bridge — three legs of two IGBTs or SiC devices instead of two — that synthesizes three sine waves 120° apart to make a smoothly rotating magnetic field. Press the accelerator and you're commanding that inverter's frequency and modulation index; lift off or brake and the inverter *runs backward*, turning the motor into a generator and pumping energy back into the battery. That's regenerative braking — the inverter is the bidirectional gate between mechanical motion and stored charge.