AC-AC · Matrix Converter · Virtual Lab

Sparse Matrix Converter Simulator

An advanced, physics-accurate simulator of the sparse matrix converter (SMC) — a reduced-switch realisation of the indirect matrix converter (here 12 IGBTs and 30 diodes) with an imaginary DC link and no capacitor. Watch every waveform on a real-time oscilloscope: input voltages and currents, the imaginary DC-link voltage, the PWM output phase voltage tracking its reference sine, the line-to-line voltage and the balanced sinusoidal output currents — validated live against Vo = q·Vim with the maximum voltage transfer ratio q = √3/2 ≈ 0.866, plus %THD and a real harmonic FFT.

Sparse matrix converter circuit diagram: an LC input filter, a reduced-switch rectifier of six bidirectional cells forming an imaginary DC link with no capacitor, and a six-switch voltage-source inverter driving a three-phase motor — output Vo = q·Vim, q ≤ 0.866
Sparse matrix converter — an LC filter, a reduced-switch (12 IGBT / 30 diode) rectifier forming an imaginary DC link, and a six-switch inverter. Vo = q·Vim, q ≤ √3/2 ≈ 0.866.

Parameters

V
Per-phase RMS. Peak Vim = √2·Vs.
A matrix converter can output above or below fi (unlike a cycloconverter).
Vo(peak) = q·Vim. Linear limit q = √3/2 ≈ 0.866; above it over-modulates.

Modulation & load

Carrier is synchronised to — pulses per output cycle.

Display

Presets

Waveforms to display

Waveforms fo = 30 Hz · q = 0.80

LIVE

Voltage transfer ratio & topology (topic-specific)

The sparse matrix converter keeps the indirect converter's behaviour but with fewer, cheaper devices (here 12 IGBTs and 30 diodes). Its rectifier stage carries unidirectional DC-link current, so it commutates at zero DC-link current. The voltage ceiling stays q ≤ √3/2 ≈ 0.866 with sinusoidal input currents — the same performance as the direct and indirect converters at a lower switch count. The DC-link panel below shows the imaginary link voltage — always positive, six pulses per input cycle.

Harmonic spectrum

Output-voltage THD (relative to fundamental)—
Harmonics are multiples of the output frequency fo. Bar 1 = fundamental; switching harmonics cluster near fsw/fo.

Measurements

Live accuracy check — simulation vs closed-form theory

What is a sparse matrix converter?

A sparse matrix converter (SMC) is a reduced-switch version of the indirect matrix converter. It keeps the same two-stage structure — a rectifier that forms an imaginary DC link (no capacitor) and a six-switch inverter — but uses fewer active devices. The version shown here is built from 12 IGBTs and 30 diodes, compared with 18 IGBTs in the direct/indirect converters.

Same performance, fewer switches

Because the rectifier stage only needs to carry unidirectional DC-link current, several bidirectional switches can be replaced by a single IGBT inside a diode bridge. The result matches the indirect converter's waveforms and its q ≤ 0.866 voltage ceiling while cutting cost, gate-drive count and control complexity. Variants include the very sparse (VSMC) and ultra-sparse matrix converters.

Output voltage and the 0.866 limit

Vo(peak) = q·Vim , q(max) = √3/2 ≈ 0.866 → Vo(rms) = q·Vim/√2

The inverter uses space-vector modulation referenced to the imaginary DC link, so each output phase tracks q·Vim·sin(ωot). This simulator confirms Vo = q·Vim by FFT of the real switched waveform.

Zero-current commutation & control — topic-specific

Like the indirect converter, the SMC commutates while the DC-link current is zero, which simplifies protection. Its low device count also makes it a favourite test-bed for advanced control such as model-predictive current control. It keeps the matrix-converter advantages: no DC-link capacitor, sinusoidal input currents and near-unity input power factor.

Applications

Cost-sensitive capacitor-free drives and research platforms for predictive control. Compare the direct matrix converter and the indirect matrix converter.

Frequently asked questions

What is a sparse matrix converter?

A reduced-switch version of the indirect matrix converter. It forms an imaginary DC link with no capacitor and drives a six-switch inverter, using fewer active devices (here 12 IGBTs and 30 diodes) than the 18-IGBT direct/indirect converters.

What is the maximum voltage transfer ratio?

Vo = q·Vim with a linear-range maximum of q = √3/2 ≈ 0.866, the same as the direct and indirect matrix converters.

How is it different from the indirect matrix converter?

It has the same two-stage behaviour but fewer switches, because the rectifier carries only unidirectional DC-link current. This lowers cost and control complexity while keeping the same performance and 0.866 voltage ceiling.

What are very sparse and ultra-sparse matrix converters?

Further reduced-switch variants of the sparse matrix converter that trade a little flexibility for even fewer devices, used where cost and size matter most.

Power4All · Sparse Matrix Converter interactive simulator. All waveforms are produced by numerical synthesis of the actual space-vector-modulated converter and validated against closed-form theory.