F2 · power electronics

The Switching Device: A Real Switch Heats Up Two Ways

In the previous unit, the switch was treated as ideal. The power MOSFET is that switch, but a real switch loses power in its small on-resistance while it is on, and in the stretch where voltage and current overlap at each turn-on and turn-off. You sweep the switching frequency yourself and see how conduction loss, which does not depend on frequency, and switching loss, which is proportional to frequency, set the ceiling on efficiency.

Change the switching frequency and find where the two losses cross

The waveforms are the voltage Vds across the device and the current Id through it during one switching period. While the device is on, the voltage is nearly 0, so only a small conduction loss (amber) arises; in the brief moments of turning on and off, voltage and current are large together and a red loss peak rises. Raising the switching frequency shortens each period, so the transition peaks take a larger share and the switching loss overtakes the conduction loss. The indicator shows the two losses, their sum, and the efficiency relative to the output power.

Switching frequency fswfsw = 200 kHz

Loss and efficiency

P_cond = 0.48 W    P_sw = 0.96 W

P_tot = 1.44 W  ·  η = 98.2%

The switching frequency is in the middle. The frequency at which the two losses on the indicator become equal lies near the start of this range, so the switching loss catches up with the conduction loss and begins to pass it. Whether to raise the frequency further is decided here.

The two losses are comparable

The on cost: on-resistance makes the conduction loss

An ideal switch has 0 voltage across it when on, but a real power MOSFET keeps a small on-resistance Ron even when on. So when a current Io flows, a voltage of Io·Ron appears across the device, and while it is on the conduction loss P_cond = Io²·Ron turns into heat. The fraction of each period during which it is on is the duty ratio D, so on average P_cond = Io²·Ron·D. This loss does not depend on how often the device switches; it is set only by the current and the on-resistance, and it grows with the square of the current. For the same current, a device with lower Ron runs cooler.

The flip cost: overlap makes the switching loss

A transition does not finish in an instant. Turning the device on and off takes a short time, and during it the voltage has not fully fallen while the current is already rising, so the two overlap. In that moment when voltage and current are both large, P = Vds·Id spikes. If tsw is the sum of the turn-on and turn-off times, each period loses an energy E_sw = ½·Vds·Io·tsw as heat. This loss occurs once per period, so switching fsw times per second gives a switching loss P_sw = E_sw·fsw, directly proportional to frequency. Unlike the conduction loss, the faster you switch, the more often it leaks away.

The trade, and why faster and lower-resistance is chased

Then why raise the frequency at all? As seen in F1, the switching output is set by the duty ratio, and the inductor and capacitor do the work of smoothing the pieces. Raising the frequency lets a smaller inductor and capacitor achieve the same smoothing, so the power supply becomes smaller and lighter. The price is switching loss, so design is always a trade. Raise the frequency to shrink the circuit and the switching loss grows; lower the frequency to cut the loss and the circuit grows. The way to resolve this tug-of-war at once is a better device. A lower on-resistance cuts the conduction loss, and a faster transition (shorter tsw) cuts the switching loss. Wide-bandgap devices such as gallium nitride (GaN) and silicon carbide (SiC) withstand the same voltage with a thinner layer, lowering both losses together and making power electronics smaller and more efficient.

ObserveP_cond = I² Ron D

Conduction loss is the current squared times the on-resistance and the duty ratio.

ChooseE_sw = ½ Vds Io ?

The transition loss in one period is proportional to the time during which voltage and current overlap.

Fill inP_sw = E_sw ?

Switching loss is the transition energy per period times the switching frequency.

On your ownP_tot = P_cond ?

Total loss is the sum of conduction and switching losses, and this sum sets the ceiling on efficiency.

Back to the first screen

When the switching frequency was low, the loss was almost only the amber conduction loss; as you raised the frequency, red transition peaks rose often and the switching loss overtook the conduction loss. The on-state cost was P_cond = Io²·Ron·D from the on-resistance, and the switching cost was P_sw = E_sw·fsw from the overlap of voltage and current. This is what the switch assumed to be ideal in F1 really looks like. The way to lower both losses together is a lower on-resistance and faster transitions, that is, a better device, and what sets such devices apart goes back to the energy bands seen in the first unit of this track. The single thread that ran from bands to carriers, to junctions and diodes, and to transistors that amplify and switch, closes here.

The power MOSFET is the switch of F1, but it is not ideal. While on, its small on-resistance Ron causes a conduction loss P_cond = Io²·Ron·D, which is independent of frequency. In the brief moments of switching on and off, voltage and current overlap and E_sw = ½·Vds·Io·tsw leaks away each period, so the switching loss P_sw = E_sw·fsw is proportional to frequency. Raising the frequency shrinks the inductor and capacitor but increases switching loss, so the total loss P_cond + P_sw sets the ceiling on efficiency and the heat. The way to lower both losses together is a lower Ron and faster transitions, that is, better devices such as GaN and SiC.

Closing the track

The electronics track ends here. It started from the question the energy bands posed, what lets a material conduct, and went on: doping set the carriers, drift and diffusion moved them, and the pn junction became a one-way valve. With that valve we rectified and shaped waveforms, and the thin-base BJT and the insulated-gate MOSFET gave rise to amplification, controlling a large flow with a small input. Differential stages and op-amps, their limits of bandwidth and slew rate, and filters handled signals, and finally the same transistor, used as a switch, came to handle power itself efficiently. A single thread, how to handle electrons, ran through all 24 units from start to finish.