Class E Chopper (Four Quadrant Chopper)

The full H-bridge: four switches, four diodes, and a machine that can motor and brake in both directions. The complete DC drive — and the end of the chopper family.

Table of Contents:

Introduction — the complete drive

Four pages of build-up come together here. A Class A motors one way; a Class B brakes one way; a Class C does both in one direction; a Class D reverses the voltage. Each fills in part of the voltage–current plane. The Class E chopper fills in all of it.

It can drive a motor forwards, brake it forwards, drive it in reverse, and brake it in reverse — and slide between any of those without a contactor, a pause, or a change of circuit. It is the four-quadrant drive, the topology inside a servo, a rolling mill, an electric-vehicle traction inverter's DC cousin, and every application where a motor has to be fully commanded in both directions.

And it is not a new idea to learn. A Class E is simply two Class C legs — a full H-bridge. Everything you already know about a half-bridge chopper applies twice over.

What is a Class E Chopper?

A Class E chopper — Type E, four-quadrant chopper, or simply the H-bridge (full-bridge) drive — uses four switches and four diodes, arranged as two legs across the supply with the load bridging their midpoints:

  • Left leg: S1 (top) and S4 (bottom), each with an antiparallel diode (D1, D4). Its midpoint is node A.
  • Right leg: S3 (top) and S2 (bottom), with diodes D3, D2. Its midpoint is node B.
  • The R–L–E machine sits between A and B. The output is vo = vA − vB.

Each leg is a complete Class C half-bridge: it can clamp its own midpoint to Vs or to 0, and it does so for either direction of current, because each switch has a diode ready to take over when the current reverses. Two such legs, working independently, give you complete control of both ends of the load — and therefore of both the sign of the voltage across it and the sign of the current through it.

That is the whole idea, and it is worth stating cleanly. One leg controls one terminal. Two legs control both terminals. With both terminals free to be at Vs or 0, the voltage across the load can be +Vs, 0, or −Vs, and the diodes let the current be either sign in every case. Voltage either sign, current either sign — that is all four quadrants, by construction.

The four-quadrant capability is usually summarised by which pair of devices conducts:

Conducting pairvoioQuadrantMachine
S1 + S2+Vs+IForward motoring
D1 + D2+Vs−IIForward braking
S3 + S4−Vs−IIIReverse motoring
D3 + D4−Vs+IVReverse braking

All Four Quadrants

Voltage-current plane with all four quadrants highlighted, each carrying one operating point, showing that a Class E chopper reaches every quadrant: forward motoring, forward braking, reverse motoring and reverse braking.
Figure 1: A Class E chopper reaches every quadrant — the complete plane

Every previous page in this series could only shade part of this plane. A Class C owned the top half (I & II); a Class D owned the right half (I & IV). Lay those two over each other and you cover everything — which is exactly what adding the second pair of switches does. A Class E is a Class C and a Class D in the same four devices.

The practical meaning of "four quadrants" is a machine under total command. It can be accelerated or decelerated, run clockwise or anticlockwise, and made to deliver or absorb torque in either direction — and the controller can move the operating point anywhere on this plane continuously, with no boundary to stop at and no mode to switch.

Block Diagram

Block diagram of a Class E chopper: a DC source feeds a full H-bridge of two legs driving an R-L-E machine that can run in either direction, with double-headed arrows because power flows both ways and a controller driving all four switches.
Figure 2: Block diagram of a Class E chopper

The extra structure over the earlier pages is the two-leg bridge. Because both legs are driven, both diagonals of the bridge are available — and it is having both diagonals that lets the output voltage take either sign. As always in this series, every arrow is double-headed: power can flow from source to machine or machine to source, now with the machine turning either way.

Circuit Diagram & Construction

Circuit diagram of a Class E chopper as a full H-bridge: left leg S1 over S4, right leg S3 over S2, each switch with an antiparallel diode, and the R-L-E dc machine load between the two midpoints A and B.
Figure 3: Class E chopper — a full H-bridge (two Class C legs)
Left leg — S1, S4 (+ D1, D4)A complete half-bridge. Drives node A to Vs (S1 on) or to 0 (S4 on), for either current direction.
Right leg — S3, S2 (+ D3, D2)The second half-bridge. Drives node B the same way.
The diagonalsS1+S2 together apply +Vs; S3+S4 together apply −Vs. The diode diagonals D1+D2 and D3+D4 handle the reverse-current cases.
LoadR–L–E between A and B. vo = vA − vB, free to be +Vs, 0 or −Vs.
Shoot-throughEach leg has two switches in series across the supply, so — exactly as in a Class C — dead time is mandatory and getting it wrong shorts the rail. There are now two legs to protect.

This is the single most common power circuit in all of power electronics. The same four-switch bridge is a single-phase inverter, a full-bridge DC-DC converter, and the output stage of countless motor drives. Building a Class E chopper means buying a standard H-bridge module — the parts are ordinary and come pre-packaged in exactly this arrangement.

Principle of Operation

There are two ways to run the bridge, and it is worth being clear which is which because textbooks mix them up.

The direction is chosen by which leg chops. To go forward, hold the right leg with S2 on (B tied to 0) and chop the left leg — S1 for a fraction D of each cycle. The load sees +Vs for DT and 0 for the rest, so Vo = +D·Vs. To go in reverse, swap the roles: hold A at 0 and chop the right leg, giving Vo = −D·Vs.

The quadrant within that direction is chosen by the machine, not by you. Once Vo is set, the current is whatever (Vo − E)/R makes it — and its sign decides whether the switches or their antiparallel diodes actually carry it. Positive current forward is Quadrant I through S1/S2; negative current forward is Quadrant II through D1/D2. The hardware sorts itself out, exactly as it did on the Class C page — just now in either direction.

So a Class E is controlled by two decisions: a direction bit (which leg chops) and a duty ratio (how hard). Together they place Vo anywhere from −Vs to +Vs, and the machine's response places the current. A single signed current reference, fed to a controller that works out both, commands the entire plane.

The Four Quadrants, Device by Device

The cleanest way to see a Class E is one quadrant at a time, each as the device pair that carries the current in it. Highlighted loop = current path, green = conducting.

Quadrant I — S1 + S2 (forward motoring, vo = +Vs, io > 0)

Class E chopper Quadrant I: switches S1 and S2 conduct, connecting the source across the load from A to B. The output voltage is plus the supply voltage and the current is positive: forward motoring.
Figure 4: Quadrant I — S1 + S2 conducting, forward motoring

The S1–S2 diagonal is closed. The source drives current from A, through the load to B, and back — the machine motors forwards and the battery delivers. This is the Class A case, sitting inside the bridge.

Quadrant II — D1 + D2 (forward braking, vo = +Vs, io < 0)

Class E chopper Quadrant II: diodes D1 and D2 conduct while the machine still turns forwards, so the reversed current is forced back into the source. The output voltage stays positive but the current is negative: forward braking.
Figure 5: Quadrant II — D1 + D2 conducting, forward braking

Same forward direction, but now the machine's current has reversed — it is generating. The switches cannot carry reverse current, so the D1–D2 diodes do, forcing it back into the battery. The machine turns forwards while being braked and regenerated: the Class B case, inside the bridge.

Quadrant III — S3 + S4 (reverse motoring, vo = −Vs, io < 0)

Class E chopper Quadrant III: switches S3 and S4 conduct, applying minus the supply voltage across the load and driving current from B to A. Both voltage and current are negative: reverse motoring.
Figure 6: Quadrant III — S3 + S4 conducting, reverse motoring

The other diagonal closes. Now B is at Vs and A at 0, so vo = −Vs and current is driven the other way through the load. The machine motors in reverse. This is Quadrant I again, mirrored — the same behaviour as Quadrant I but with everything's sign flipped.

Quadrant IV — D3 + D4 (reverse braking, vo = −Vs, io > 0)

Class E chopper Quadrant IV: diodes D3 and D4 conduct while the machine turns in reverse, returning the reversed current to the source. The voltage is negative but the current is positive: reverse braking.
Figure 7: Quadrant IV — D3 + D4 conducting, reverse braking

The mirror of Quadrant II. The machine turns in reverse, its current reverses relative to Quadrant III, and the D3–D4 diodes return that energy to the battery. Reverse braking, regenerating.

Read the four figures as two symmetric pairs. Quadrants I and II are the forward direction (vo = +Vs), switches for motoring and diodes for braking — that pair is a Class C. Quadrants III and IV are the reverse direction (vo = −Vs), the same story mirrored. Two Class C's, one for each direction, sharing four devices. That is a Class E.

Waveforms Explained in Detail

Here is the actual switching for forward operation on the usual armature — 100 V, 0.25 Ω, 1.5 mH, 1 kHz — computed from the exponential solutions. The left leg chops at D = 0.6 and the right leg is held low, so Vo = +60 V. The machine's emf is +50 V, so the current comes out positive: Quadrant I.

Class E chopper waveforms for forward motoring at duty 0.6: one gate signal, an output voltage chopping between plus 100 and 0 volts averaging plus 60 volts, a load current entirely positive between about 32 and 48 amperes averaging plus 40 amperes with about 16 amperes of ripple, a device band showing S1 plus S2 during the on time and freewheeling during the off time, and a positive source current averaging about 24 amperes meaning the battery delivers power.
Figure 8: Forward motoring — D = 0.6, Vo = +60 V, Io = +40 A (Quadrant I)

Two things are worth pulling out. First, vo chops between +Vs and 0, not between +Vs and −Vs. That is unipolar switching — only the one leg is moving — and it keeps the ripple down to 16.0 A, the same as a Class C and half what a Class D would produce. A four-quadrant drive does not have to pay the Class D ripple penalty; it only would if you switched both legs together (see below).

Second, the reverse and braking quadrants look exactly like this figure with signs flipped. Quadrant III is this trace with vo and io both negated; Quadrants II and IV have the current negative while the voltage keeps its sign, so is goes negative and the battery is charged. Rather than repeat the figure four times, the worked example tabulates all four.

Control & the Four-Quadrant Map

Output voltage against duty ratio for a Class E chopper: two straight lines, forward giving plus D times Vs and reverse giving minus D times Vs, together covering the full range from minus 100 to plus 100 volts. Each line serves two quadrants because the current may be either sign.
Figure 9: The direction bit picks the line, the duty picks the point — two lines cover the whole plane

This is how a Class E is actually commanded. The direction bit chooses which leg chops, which selects one of the two lines — forward (Vo = +D·Vs) or reverse (Vo = −D·Vs). The duty ratio slides the operating point along that line. And because the current is free to be either sign, each line serves two quadrants: the forward line covers I and II, the reverse line covers III and IV. Between them they reach every point on the plane.

In practice you never set D by hand. A real four-quadrant drive closes a current (torque) loop: the speed controller outputs a signed torque demand, that becomes a signed current reference, and an inner PI loop works out the direction bit and the duty. Command +40 A and it motors forward; sweep the reference down through zero to −40 A and the drive passes smoothly from motoring, through braking, into reverse — crossing quadrant boundaries without the controller doing anything special, because the plant is linear across all of them.

Unipolar vs Bipolar Switching

There is one genuine design choice in a Class E, and it is the difference between it behaving like a Class C or like a Class D.

Unipolar switchingBipolar switching
What switchesOne leg chops; the other is heldBoth diagonals switch together (S1S2 ↔ S3S4)
vo swings+Vs ↔ 0 (or 0 ↔ −Vs)+Vs ↔ −Vs
RippleLow — like a Class CDouble — like a Class D
Effective ripple frequencyHigher (one leg per half-cycle)The switching frequency
Control near zeroSlightly more complexSimple — one duty sets everything
Usual choiceYes, for the lower rippleWhere simplicity matters more

The waveform above is unipolar, which is why its ripple matched a Class C. Switch bipolar instead — drive the S1S2 diagonal against the S3S4 diagonal with one duty — and the load sees the full ±Vs swing, the ripple doubles, and Vo = (2D−1)Vs exactly as on the Class D page. Same hardware, two firmware choices. A Class E contains both a Class C and a Class D and lets you pick which one to be.

Key Formulas

Unipolar operation, continuous conduction, ideal devices; τ = L/R and "dir" is +1 forward, −1 reverse.

Average output voltage

Vo = dir · D · Vs    range: −Vs … +Vs

Average current and quadrant

Io = (Vo − E)/R    sign of Vo → direction; sign of Io → motor / brake Vo>0, Io>0 → Q I  ·  Vo>0, Io<0 → Q II  ·  Vo<0, Io<0 → Q III  ·  Vo<0, Io>0 → Q IV

Ripple (unipolar)

Δio ≈ Vs D(1−D) T / L    (bipolar: twice this, like a Class D)

Source side and power

Is ≈ dir · D · Io    Pin = VsIs = 〈voio〉 = E·Io + Io,rms²R

Positive Pin = motoring (source delivers); negative = regenerating (source absorbs). True in all four quadrants.

Device ratings

all eight devices block Vs  ·  all carry |I|max  ·  dead time mandatory in both legs

Worked Example

The usual armature — Vs = 100 V, R = 0.25 Ω, L = 1.5 mH, f = 1 kHz, D = 0.6 — taken once into every quadrant. Only the emf (the machine's speed and direction) and the chopping leg change.

QuantityQ I motoringQ II brakingQ III motoringQ IV braking
Machine emf E+50 V+70 V−50 V−70 V
Directionforwardforwardreversereverse
Vo = dir·D·Vs+60 V+60 V−60 V−60 V
Io = (Vo−E)/R+40 A-40 A-40 A+40 A
Ripple |Δi|16.0 A16.0 A16.0 A16.0 A
Source current Is+24.1 A-23.9 A+24.1 A-23.9 A
Battery VsIs+2,405 W-2,395 W+2,405 W-2,395 W
deliversabsorbsdeliversabsorbs
Shaft E·Io+2,000 W-2,800 W+2,000 W-2,800 W
Balance VsIs = E·Io + Irms²Rcloses in all four quadrants ✔

The symmetry is the whole point. |Vo| = 60 V and |Io| = 40 A in every column; the ripple is 16.0 A in every column; only the signs move — and those signs are the quadrant. The forward-motoring column is the Class A example; the forward-braking column matches Class B; the two reverse columns are their mirrors. One circuit, one duty ratio, all four quadrants, every number balancing.

Advantages & Disadvantages

Advantages

  • Complete four-quadrant control — motor and brake, forwards and backwards, from one circuit.
  • Seamless transitions across every quadrant boundary; the plant is linear throughout, so a single current loop covers everything.
  • Regenerates in both directions, recovering braking energy whichever way the machine turns.
  • Low ripple available — unipolar switching gives Class C ripple, not the doubled Class D figure.
  • Standard hardware — it is just an H-bridge module, the most common power stage there is.
  • Contains every simpler chopper: run one leg and it is a Class A/B/C; switch bipolar and it is a Class D.

Disadvantages

  • The most devices — four switches and four diodes, twice a Class C.
  • Two legs to protect from shoot-through: dead time is mandatory in both, and the gate drive is the most complex in the family (two high-side drivers).
  • Most expensive chopper, and overkill unless you genuinely need all four quadrants.
  • The supply must absorb regenerated energy in both braking quadrants, as with Class B and D.
  • Dead-time distortion in both legs, needing compensation in precision drives.

Applications

  • Reversing DC servo drives — machine tools, robotics, positioning systems that must run and hold in both directions with full torque control.
  • Rolling mills and paper machines, where tension and speed must be controlled through zero and in reverse.
  • Traction that runs both ways with regenerative braking — some locomotives, hoists and elevators.
  • Elevators and cranes, motoring up, regenerating down, and holding a load either way.
  • Test dynamometers that must both drive and load a machine under test in either direction.
  • Battery test equipment and any bidirectional DC-DC role — the same bridge charges and discharges.

The rule is simple and it closes the series: if the machine must be fully commanded — both directions, motoring and braking — use a Class E. If it needs less, a simpler class is cheaper. A Class E is the answer when the requirement is "total control", and the wrong answer when it is anything less.

The Whole Family, Side by Side

ClassQuadrantsDevicesvoioWhat it does
AI1 sw + 1 di++Motor one way (step-down)
BII1 sw + 1 di+−Brake one way (step-up regen)
CI & II2 sw + 2 di+±Motor & brake, one direction
DI & IV2 sw + 2 di±+Voltage reverses; reverse braking
EI, II, III & IV4 sw + 4 di±±Everything — the full drive

And the tidy way to remember how they build up: C = A + B (motor and brake one way); D adds voltage reversal; E = two C's = C + D — both legs driven, both diagonals live, every quadrant reachable. The chopper family starts with one switch and one diode doing one job, and ends here, with four of each doing all of them.

Frequently Asked Questions – FAQs

Because it can reach every one of the four regions of the voltage-current plane. The output voltage can be either sign and the current can be either sign, independently, so the machine can motor forwards, brake forwards, motor in reverse, and brake in reverse. No other chopper class reaches more than two quadrants; the Class E reaches all four, which is why it is the complete drive.

Yes — a Class E chopper is a full H-bridge (full-bridge) with a DC machine as the load. The same four-switch, four-diode bridge is also a single-phase inverter and a full-bridge DC-DC converter; what makes it a "Class E chopper" is that it is driving an R-L-E machine to give four-quadrant DC drive. It is built from two identical legs, each of which is a Class C half-bridge.

Two decisions do it. The direction bit — which leg chops — sets the sign of the output voltage: chop the left leg for +D·Vs (forward), chop the right leg for -D·Vs (reverse). Then the machine's emf decides the current, and its sign decides whether the switches or their antiparallel diodes carry it: positive current uses the switch diagonal (motoring), negative current uses the diode diagonal (braking). Voltage sign times current sign gives the four quadrants: S1+S2 is Quadrant I, D1+D2 is Quadrant II, S3+S4 is Quadrant III, and D3+D4 is Quadrant IV.

In unipolar switching only one leg chops while the other is held, so the load voltage swings between +Vs and 0 (or 0 and -Vs). In bipolar switching both diagonals switch together, so the load swings the full +Vs to -Vs. Unipolar gives lower current ripple — the same as a Class C — and is the usual choice; bipolar doubles the ripple, exactly like a Class D, but is simpler to control near zero. A Class E can do either from the same hardware; it is a firmware choice.

Each leg of the bridge is a half-bridge with a switch and an antiparallel diode top and bottom — which is exactly a Class C chopper, able to clamp its midpoint to Vs or 0 for either current direction. A Class E has two of them, one driving each end of the load. One leg alone gives you Class A/B/C behaviour in one direction; the second leg lets you reverse the voltage, adding the other two quadrants. So a Class E is literally a Class C plus a second Class C leg, which is why it costs twice the devices and reaches twice the quadrants.

Only if you run it bipolar. With unipolar switching — the usual choice — the load voltage swings between Vs and 0, so the ripple is Vs·D(1-D)·T/L, the same as a Class A or C. It is only when both diagonals switch together (bipolar) that the load sees the full ±Vs swing and the ripple doubles to the Class D value. So a four-quadrant drive does not have to accept the Class D ripple penalty; it chooses.

Because each leg has two switches in series directly across the supply. If the top and bottom switch of a leg are ever on together, even briefly, they short the battery through themselves and are destroyed — that is shoot-through. Real switches turn off slower than they turn on, so a small dead time (both switches of a leg off) must be inserted at every transition. A Class E has two legs, so this must be done twice. The trade-off is dead-time distortion, a small error in the output voltage that precision drives compensate for.

Yes — this is the first chopper in the family that can. Because the output voltage can be made negative (chop the right leg instead of the left), the machine can be driven in reverse, which is Quadrant III. It can also brake in reverse (Quadrant IV). A Class C could only run one direction, and a Class D could reverse the voltage but not motor in reverse under load in a useful way; only the Class E gives genuine, controllable operation in both directions.

Use a Class E only when you genuinely need all four quadrants — the machine must run and brake in both directions under full control, as in a reversing servo, a rolling mill, or a hoist. If you only need to motor and brake in one direction, a Class C does it with half the devices. If you only motor, a Class A is enough. A Class E is the most capable and the most expensive chopper; it is the right answer for total control and overkill for anything less.

With a closed current (torque) loop, not by setting duty by hand. A speed controller outputs a signed torque demand, which becomes a signed current reference; an inner PI loop measures the actual armature current and works out both the direction bit and the duty ratio. Because the plant is linear across all four quadrants, one loop handles motoring, braking and reversing with no mode switching — sweep the current reference from +40 A through zero to -40 A and the drive passes smoothly from forward motoring through braking into reverse.

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