Alternating Current, Motors, & Controls — Bench

Notes from watching CaptiveAire — Alternating Current, Motors, & Controls.

Part 1 — Power Generation

Faraday’s Induction

Michael Faraday, 1831: move a magnet through a coil of wire and a voltage appears across the coil. More precisely — any change in the magnetic flux through a loop of conductor induces an EMF (electromotive force) in that loop.

The key word is change. A stationary magnet sitting in a coil does nothing. It’s the relative motion — the changing flux — that produces voltage. This is the operating principle of every electrical generator ever built.

The induced voltage is proportional to:

The rate of change of flux (faster motion = higher voltage)
The number of turns in the coil (more turns = higher voltage)

Lenz’s Law

The induced current flows in a direction that opposes the change that caused it. If you push a magnet into a coil, the coil generates a current that creates its own magnetic field — opposing your push. This is why turning a generator under load is harder than turning it unloaded. The electrical power you extract is paid for by the mechanical effort of overcoming that opposing force.

Lenz’s Law is conservation of energy expressed as electromagnetic behaviour. You can’t get electrical energy for free — the work you put in mechanically comes back out electrically, minus losses.

The First Generator

Faraday’s original device was a copper disk rotating between the poles of a permanent magnet — the Faraday disk generator. Inefficient but it worked.

The practical evolution: mount a rectangular coil of wire on a shaft (the armature), place it between the poles of a magnet, and spin the shaft. As the coil rotates, the angle between the coil and the magnetic field constantly changes — so the flux through the coil changes continuously — so a continuous voltage is induced.

Visualizing Alternating Current

As the coil rotates at constant speed:

When the coil is perpendicular to the field lines: flux is changing fastest → maximum voltage
When the coil is parallel to the field lines: flux is momentarily not changing → zero voltage
Half turn later: the same coil sides are back in the same field, but the motion is reversed → voltage in the opposite direction

This produces a smooth sine wave — naturally, from first principles. One full revolution of the coil = one complete cycle of AC.

 Voltage
   +│    ╭──╮
    │   ╱    ╲
    │──╱──────╲──────── time
    │           ╲    ╱
   −│            ╰──╯
    └──────────────────
        1 cycle = 1 Hz

Commutators

A commutator is a mechanical switch built into the shaft. It swaps the connection between the rotating coil and the external circuit every half-turn — exactly when the AC would reverse polarity. This converts the alternating output into unidirectional (pulsating) DC at the output terminals.

DC generators use commutators. AC generators (alternators) skip the commutator and let the AC out directly.

The downside of commutators: mechanical wear, arcing at brushes, maintenance. This is why AC systems eventually won over DC for power distribution.

Generator Types

Type	Output	Field	Notes
DC generator	Pulsating DC (via commutator)	Permanent or wound electromagnet	Brushes wear; used in small/automotive
AC alternator	Sinusoidal AC	Rotating field (rotor), fixed windings (stator)	More common for large-scale generation
Permanent magnet generator	AC	Permanent magnets on rotor	Simple, no field excitation needed
Wound field alternator	AC	Electromagnet rotor (field current adjustable)	Voltage output controlled by field current

Sinusoidal Waves

Key parameters of an AC waveform:

Frequency (Hz) — cycles per second. US standard: 60 Hz. Europe: 50 Hz.
Period (T) — time for one cycle. T = 1/f. At 60 Hz: T = 16.7 ms.
Peak voltage (Vpeak) — maximum positive (or negative) value. US household: ~170V peak.
Peak-to-peak — full swing from negative to positive peak. ~340V for US household.
Phase — where in the cycle a waveform is at a given moment. Multiple AC sources can be in phase, or offset by degrees.

Single vs. Multi-Phase Power

Single phase: one AC sine wave. Two wires (hot + neutral). What you find at standard household outlets.

Three phase: three AC sine waves, each 120° apart in phase. Three hot wires (+ neutral in some configurations).

Phase A:  ╭──╮         ╭──╮
Phase B:      ╭──╮         ╭──╮
Phase C:          ╭──╮         ╭──╮

Advantages of three phase:

At any given instant, the sum of all three phases is zero — the system is inherently balanced
Power delivery is smooth and constant (not pulsating like single phase)
Motors are naturally self-starting and more efficient
More power transmitted per conductor
Basis of commercial and industrial power supply worldwide

Part 2 — Power Transmission and Distribution

Mutual Induction

If two coils share a common magnetic field (or are on the same iron core), a changing current in one coil induces a voltage in the other. This is mutual induction — the operating principle of transformers.

No electrical connection between the coils is needed. Energy is transferred through the magnetic field. This allows electrical isolation between circuits while still transferring power.

Transformers

Two coils wound on a shared iron core.

Primary         Core         Secondary
                 ┌──┐
 ~AC ─────── N1 ─┤  ├─ N2 ─────── load
                 └──┘

The turns ratio determines the voltage ratio:

V1 / V2 = N1 / N2

If primary has 1000 turns and secondary has 100 turns (10:1 ratio):

240V in → 24V out (step-down)
Power is conserved (minus losses): V1 × I1 ≈ V2 × I2
So if voltage steps down 10×, current steps up 10×

Step-up transformer: fewer primary turns than secondary → voltage increases Step-down transformer: more primary turns than secondary → voltage decreases

Iron core concentrates and guides the magnetic flux between windings. Laminated steel (not solid) to minimise eddy current losses.

High Voltage Transmission

Transmitting power at high voltage dramatically reduces losses.

Power loss in a transmission line:

P_loss = I² × R_line

If you can transmit the same power at 10× the voltage, the current is 10× lower. Power loss drops by 100×. The resistance of the wire is the same, but the much lower current means far less heating.

This is why the grid operates at 115,000V–765,000V between generation and substation. Transformers step it up leaving the power plant, and step it back down at substations closer to consumers.

Wye vs. Delta Systems

Two ways to interconnect three-phase windings:

Wye (Y):

         A
         │
    ─────N─────
         │
   B─────┘─────C

All three phase windings share a common neutral point (N). Provides both phase-to-neutral voltage (e.g. 120V) and phase-to-phase voltage (e.g. 208V). Neutral wire is available.

Delta (Δ):

   A ─────── B
    ╲       ╱
     ╲     ╱
      ╲   ╱
       ─C─

Windings form a loop with no neutral point. Only phase-to-phase voltage available. More common on high-voltage transmission and on motor windings.

Wye provides a neutral (useful for single-phase loads off a three-phase supply). Delta handles unbalanced loads without affecting the neutral. Many transformers are Wye on secondary, Delta on primary.

Multitap Transformers

A secondary winding with multiple connection points along it. Different taps give different output voltages from the same transformer. Common in HVAC controls: a single multi-tap transformer provides 24V, 12V, and 5V from the same core.

Also used for motor speed: some motors have multiple voltage taps on the winding for different speed settings (though VFDs have largely replaced this).

AC vs. DC with Resistive Loads — RMS Explained

An AC sine wave’s average value is zero (positive and negative halves cancel). But it clearly delivers real power to a resistive load (a heater still heats).

RMS (Root Mean Square): the DC-equivalent value of an AC waveform in terms of power delivered to a resistive load.

V_rms = V_peak × (1/√2) ≈ V_peak × 0.707

US household outlet is rated 120V AC. That’s an RMS value. The actual peak is:

V_peak = 120V / 0.707 ≈ 170V

A 120V AC supply delivers the same heating power to a resistor as 120V DC. The RMS is the number you use in Ohm’s Law calculations for AC with resistive loads. For reactive components (capacitors, inductors, motors), it gets more complex — impedance, power factor, etc.

Part 3 — Motors

Motors Compared to Generators

A motor and a generator are the same physical machine — a coil of wire in a magnetic field, on a rotating shaft. The energy direction is reversed:

Generator: mechanical energy in → electrical energy out
Motor: electrical energy in → mechanical energy out

A generator forced to spin by external power generates back-EMF. A motor running under load generates back-EMF that limits current. They’re identical in principle.

Building a Motor In Real Life

The basic motor:

Fixed outer part (stator) with magnets or windings that create a magnetic field
Rotating inner part (rotor/armature) with windings that carry current
The interaction between stator field and rotor current creates torque — rotational force

The rotor current must be continuously switched (commutated) as it rotates to keep the torque always in the same direction. In a DC motor this is mechanical (brushes + commutator). In AC motors it’s done by the alternating current itself or electronically.

Synchronous Motors

The rotor contains a permanent magnet (or electromagnet). The stator creates a rotating magnetic field — in three-phase motors, the three phases sequentially energise stator poles, and the field rotates at the supply frequency.

The permanent magnet rotor locks onto this rotating field and is dragged around at exactly the same speed. Hence synchronous — rotor speed = field speed = supply frequency / pole pairs.

Synchronous speed (RPM) = (120 × f) / p

Where f = frequency (Hz), p = number of poles.

At 60 Hz with 2 poles: 3600 RPM. With 4 poles: 1800 RPM.

Limitation: synchronous motors can’t self-start easily (the rotor needs to already be near sync speed to lock in). Usually started as induction motors or with auxiliary means.

DC Motors

Stator has permanent or wound field magnets. Rotor windings carry current via brushes and commutator. Torque is proportional to current. Speed is proportional to applied voltage (minus back-EMF drop).

Speed control is straightforward — vary the voltage. This made DC motors dominant in variable-speed applications for a long time.

Downsides: brushes wear, commutator requires maintenance, carbon dust. Brushless DC (BLDC) solves this electronically.

The Induction Motor

The most common motor type in industrial and HVAC use. No brushes, no permanent magnets in the rotor.

The stator creates a rotating magnetic field. This rotating field induces currents in the rotor (by Faraday’s law — the field is changing relative to the rotor conductors). Those induced currents create their own magnetic field, which interacts with the stator field → torque.

The rotor never has a direct electrical connection. Power is transferred entirely by induction across an air gap.

Asynchronous Motors

The induction motor is also called asynchronous because the rotor can never reach exactly synchronous speed.

If the rotor caught up perfectly with the rotating field, there would be no relative motion, no changing flux, no induced current, no torque. The rotor always lags slightly behind the rotating field — this lag is called slip.

Slip (%) = (Synchronous speed − Rotor speed) / Synchronous speed × 100

Typical slip: 2–5% at full load. A 4-pole, 60 Hz motor (1800 RPM sync) runs at about 1750–1760 RPM under load.

Capacitor Start Motors

Problem: single-phase AC creates a pulsating (not rotating) magnetic field. A motor sitting in a pulsating field has no preferred direction of rotation and won’t self-start.

Solution: add a start winding electrically offset from the main winding. A capacitor in series with the start winding shifts its current by ~90° in phase. Now there are effectively two phases — enough to create a rotating field and produce starting torque.

Once up to speed, a centrifugal switch (or relay) disconnects the start capacitor. The motor continues on the main winding alone.

Variations:

Capacitor start — large capacitor only for starting
Capacitor start, capacitor run — two capacitors: a large start cap switched out, a smaller run cap that stays in for improved efficiency and power factor
Permanent split capacitor (PSC) — one run capacitor always in circuit; no start switch; simpler, quieter, but less starting torque

How Capacitors Work

Two conductive plates separated by an insulator (dielectric). Voltage across the plates creates an electric field, storing energy in that field.

     plate A    plate B
        ║          ║
 ───────╫──────────╫───────
        ║          ║
      dielectric

Key behaviours:

A capacitor blocks DC — once charged to supply voltage, no further current flows
A capacitor passes AC — alternating voltage continuously charges and discharges it; current flows continuously
Current through a capacitor leads voltage by 90° — the current peak arrives before the voltage peak

This 90° phase shift is what makes capacitor-start motors work — by putting a capacitor in series with one winding, that winding’s current is shifted relative to the main winding, creating two out-of-phase fields that combine into a rotating field.

Capacitance measured in Farads (F). Motor capacitors: microfarads (µF).

3-Phase Motor Advantages

Naturally self-starting — three phases inherently create a rotating field, no start capacitor needed
Smooth torque — power delivery at all instants (vs. pulsating in single phase)
Higher efficiency — no start winding losses, better power factor
Higher power density — more power per frame size
Simpler construction — no brushes, no commutator, no start switch
Better speed-torque characteristics

Three-phase induction motors are the workhorse of industry. Simple, robust, almost no maintenance.

Understanding Torque

Torque is rotational force — the tendency to cause angular acceleration.

T = F × r     (force × radius)

For a motor: torque is the output twist at the shaft. Units: Newton-metres (N·m) or foot-pounds (ft·lb).

Motor torque-speed curve:

At startup (zero speed): starting torque (lower for induction motors due to poor power factor)
As speed increases: torque rises to a breakdown torque peak
Above breakdown torque speed: torque falls off sharply
At no-load: motor runs near synchronous speed at very low torque (just overcoming friction)

Power = Torque × Angular velocity:

P = T × ω     (Watts = N·m × rad/s)

A motor can run at high torque low speed or low torque high speed. Power rating defines the limit of the product.

Belt Drive vs. Direct Drive

Belt drive:

Motor ──○── belt ──○── fan/load
       small       large
       pulley      pulley

Speed reduction by pulley ratio (larger driven pulley = slower fan)
Mechanical isolation absorbs vibration and misalignment
Belt slips under extreme overload (protects motor)
Maintenance: belt tension, belt wear, alignment, pulley wear
Some efficiency loss (~5–10%) at the belt

Direct drive:

Motor ──────── fan/load (on same shaft)

No mechanical losses from belt
Motor speed = load speed (or through a gearbox)
No belt maintenance
Requires motor speed to match desired load speed — traditionally required a separate motor for each speed
With a VFD, direct drive becomes variable speed without the belt ratio compromise

Trend in HVAC: direct drive with ECM motors and VFDs replacing belt-drive PSC motors.

Part 4 — Motor Controls

Soft Start

At startup, an induction motor draws inrush current — typically 6–8× its rated full-load current — for the first few seconds while accelerating.

This stresses windings, trips breakers, causes voltage sags on the supply, and puts mechanical stress on belts and couplings.

A soft starter gradually ramps up the voltage applied to the motor at startup, limiting inrush current to 2–4× rated. Once up to speed, full voltage is applied.

Soft starters don’t provide speed control during running — they’re only active during start and stop.

Why Speed Control Matters

The fan laws (affinity laws) govern centrifugal fans and pumps:

Airflow  ∝  speed          (linear)
Pressure ∝  speed²         (square)
Power    ∝  speed³         (cube)

Halving fan speed reduces airflow by 2×, but power consumption drops by 8×. This is enormous. An HVAC fan running at 80% speed uses only 51% of the power of the same fan at full speed.

In systems where demand varies (most of the time), fixed-speed motors are wasteful. Speed control directly translates to energy savings.

Rudimentary Speed Controls

Older/simpler methods before VFDs:

Switched winding taps — multiple voltage connections on the motor winding; select a tap to change effective impedance and speed (low, medium, high). Discrete steps only.
Autotransformer — reduces voltage to motor; lower voltage = lower torque = lower speed. Inefficient at low speeds; reduced torque may not drive load.
Series resistance — resistor in series with motor drops voltage. Wastes power as heat. Very inefficient.

None of these provide true variable-speed control with good efficiency. VFDs replaced them.

Variable Frequency Drives (VFD)

A VFD controls motor speed by varying both the frequency and voltage of the AC supply to the motor simultaneously.

Induction motor speed ≈ proportional to supply frequency

Lower frequency → slower rotating field → slower rotor. The V/Hz ratio is kept constant to maintain proper motor flux and torque.

A VFD is a power electronics system in three stages:

AC mains → [Rectifier] → DC bus → [Capacitor bank] → [Inverter] → AC to motor

Rectification

Converting AC to DC — the first VFD stage.

A single diode only passes one half-cycle (half-wave rectifier). A full wave bridge rectifier uses 4 diodes to redirect both half-cycles in the same direction:

        D1        D3
   ┌────►|────┬────►|────┐
   │          │          │
AC │          │ DC+       │
   │          │          │
   └────|◄────┘────|◄────┘
        D2        D4
                  │ DC−

Both the positive and negative half-cycles end up contributing to the positive output rail. Output is pulsating DC — all positive, but not flat.

Diodes

A diode allows current to flow in one direction only. PN junction semiconductor device.

Anode ──►|── Cathode

Forward biased (anode more positive than cathode): conducts, ~0.7V drop across it. Reverse biased: blocks current (until breakdown voltage is exceeded).

In rectifiers, diodes are selected for peak inverse voltage (PIV) rating and current rating matching the supply.

Capacitors as Filters

The rectifier output is pulsating DC — it rises and falls at 120 Hz (full-wave rectified 60 Hz). A large capacitor across the DC bus smooths this:

On voltage peaks: capacitor charges to peak value
Between peaks: capacitor slowly discharges into the load, maintaining voltage
Result: near-flat DC with small residual ripple

Larger capacitance = less ripple. VFD DC bus capacitors are typically large electrolytic capacitors, and are often the first component to fail in a VFD (capacitors age and degrade).

Inverters

The second half of the VFD: converts the smooth DC bus voltage back to AC at the desired output frequency and voltage.

The inverter uses high-speed switching transistors to chop the DC into a pattern that, when integrated by the motor’s inductance, resembles a sine wave at the target frequency.

Transistors and IGBTs

The VFD inverter switches use IGBTs — Insulated Gate Bipolar Transistors.

An IGBT is a voltage-controlled switch:

Apply a small voltage to the Gate → the Collector-Emitter path switches on (conducts high current)
Remove gate voltage → switches off

IGBTs combine the high-current, high-voltage handling of a bipolar transistor with the voltage-controlled (low drive power) gate of a MOSFET. Ideal for VFD inverter stages switching hundreds of volts at tens of amps, thousands of times per second.

Gate ─────────┐
              │ IGBT
Collector ────┤
              │
Emitter  ────────────

Pulse Width Modulation (PWM)

The inverter doesn’t produce a true sine wave. Instead it rapidly switches the output between the positive and negative DC bus rails at high frequency (typically 4–16 kHz), varying the duty cycle of each pulse.

PWM signal:
   ┌──┐  ┌────┐  ┌──────┐  ┌────┐  ┌──┐
───┘  └──┘    └──┘      └──┘    └──┘  └──

Average voltage follows a sine wave shape:
   ╭──────╮
──╱        ╲────────╱────
                  ╲      ╱
                   ╲────╱

Wide pulses (high duty cycle) → high average voltage
Narrow pulses → low average voltage
The duty cycle varies sinusoidally → the average output traces a sine wave

The motor’s own inductance acts as a low-pass filter — it integrates the PWM pulses into smooth current (and therefore smooth torque). The motor doesn’t “see” the high-frequency switching, only the fundamental sine wave below it.

Analyzing Inverter Signals

If you put a scope on a VFD output:

The raw voltage waveform looks like a fast PWM signal, swinging between +DC bus and −DC bus
The current waveform looks much more sinusoidal (inductance filtering)
The fundamental frequency is whatever you set on the VFD (e.g. 30 Hz for half speed)

VFD outputs are not suitable for measuring with a standard true-RMS voltmeter — the PWM switching confuses most meters. Dedicated VFD-compatible meters or a scope is needed.

Electronically Commutated Motors (ECM)

An ECM is a brushless DC motor with an integrated controller — effectively a motor + VFD in one unit.

The rotor contains permanent magnets. The stator has wound coils. The integrated electronics:

Sense rotor position (via Hall effect sensors or back-EMF sensing)
Switch the stator windings in sequence to always push the rotor forward
Vary the switching pattern to control speed and torque

This is electronic commutation — doing what a commutator and brushes do mechanically in a DC motor, but with transistors and software.

Advantages over traditional AC induction motors:

Dramatically higher efficiency (especially at part-load speeds)
Precise speed control across wide range
Soft start built in
No brushes, no wear
Can maintain constant airflow despite duct pressure changes (motor adjusts speed to hit target)
Quieter operation

ECMs are now standard in modern HVAC fans, furnace blowers, and refrigeration evaporator fans. The energy savings over a PSC motor running at fixed speed are substantial — often 30–60% reduction in motor energy consumption.