Electro-Magnetism for AC/DC engines

TL;DR

Post electro-magnetism 101 and electronics

Intro

Ive been doing additional electronics recaps before going all in with more electronics ideas

git clone /electronics-101/samples-motors

Circuits Recap

Electric Engines

Wondering about buying a car?

DC

DC motors are the easiest place to start because the electrical side maps cleanly to the mechanical side: more current means more torque, and more voltage usually means more speed until losses, back EMF, and heating catch up.

The classic brushed DC motor does the commutation mechanically with brushes and a segmented commutator.

That makes it cheap and intuitive, but the brushes wear, spark, add friction, and limit how cleanly you can control it at high power.

Brushless DC (BLDC) motors keep the useful DC control idea, but move the commutation into electronics.

The controller energizes the stator phases in sequence while the permanent-magnet rotor follows the rotating field.

That is why drones, fans, e-bikes, robots, and many EV auxiliaries use BLDC/PMSM-style machines instead of brushed motors.

AC

AC motors are built around a rotating magnetic field.

Instead of flipping current mechanically, the supply itself changes direction over time, and multi-phase windings create a field that rotates through the stator.

That makes AC machines very attractive at medium and large power: no brushes are needed, the construction can be rugged, and the grid already gives you AC.

The catch is that useful speed control usually needs power electronics, normally a variable-frequency drive (VFD) or an inverter.

Modelling Electrical Engines

Is the classical R-L model enough?

enough for what, right?

These are not powered by slider cranks and powerful combustions

But arent they simple, beautiful, elegant and massively efficient?

AC Engines

For an AC engine, the first question is not only “how much voltage?” but also “what frequency and phase relationship?”

Frequency sets the rotating field speed, and torque depends on the interaction between that field and the rotor.

An induction motor can start directly from AC because the rotating field induces currents in the rotor.

The rotor must lag the field slightly: that lag is slip, and slip is what creates torque.

This is why induction machines are robust and common in industry, but their control story gets interesting when you want precise speed or high efficiency over a wide range.

Synchronous motors do not rely on slip in the same way.

The rotor field locks to the stator field, so the machine runs at synchronous speed.

With permanent magnets, this becomes the PMSM family used in many EV traction systems because it can be compact, efficient, and very controllable with a good inverter.

Switched reluctance motors are a different branch: the rotor has no magnets and no windings, and torque comes from the magnetic circuit trying to reduce reluctance.

They are mechanically simple and heat-tolerant, but the control, noise, and torque ripple are the price.

DC Engines

These are the kind of motors propelling your DJi Tello Dron.

Yea, the same for which I was recently making a nicer desktop app with computer vision plugged in.

#git clone /dron
cd ./dron
uv sync
uv run main.py

In small drones the motor is usually called “brushless DC”, but electromagnetically it behaves much closer to a small permanent-magnet synchronous machine driven by an ESC.

The battery is DC, the controller creates timed phase currents, and the rotor follows the rotating field.

For brushed DC motors, a simple voltage source and PWM can already be enough for useful control. For BLDC/PMSM, the controller has to decide which phase to energize and when.

That decision can come from Hall sensors, back-EMF sensing, or full field-oriented control.

Yep, private video :)

The L-R

The L-R model is the smallest useful electrical model for a winding:

$$V = R i + L \frac{di}{dt} + e_{back}$$

Where:

• $R i$ is copper loss and voltage drop.
• $L \frac{di}{dt}$ is the winding fighting rapid current change.
• $e_{back}$ is the voltage generated by motion through the magnetic field.

This model is enough when you want intuition about current rise, PWM ripple, kickback, and why a coil cannot change current instantly.

It is not enough when geometry, saturation, rotor position, multi-phase coupling, thermal limits, or controller timing become the point of the analysis.

Equations Behind the Motor Types

The comparison table below is mostly justified by a few compact equations.

For a DC motor, the useful first-order model is:

$$ \begin{aligned} v &= Ri + L\frac{di}{dt} + e_b \ e_b &= K_e \omega \ \tau &= K_t i \end{aligned} $$

This is why DC motors feel intuitive: current creates torque, speed creates back EMF, and the winding inductance fights rapid current changes.

Mechanical power is the bridge between the electrical and rotating sides:

$$P_{mech} = \tau \omega$$

Copper loss explains why high current heats small motors quickly:

$$P_{cu} = i^2R$$

For AC machines, frequency matters because it sets the rotating field speed. In RPM:

$$n_s = \frac{120f}{p}$$

where $f$ is electrical frequency and $p$ is the number of poles. The same relation in angular speed is:

$$\omega_s = \frac{4\pi f}{p}$$

Induction motors need slip to make torque:

$$s = \frac{n_s - n_r}{n_s}$$

If $s = 0$, the rotor sees no changing field, no induced rotor current, and therefore no induction torque. That is the short mathematical reason why squirrel-cage motors are called asynchronous motors.

For synchronous and PMSM motors, the rotor tracks the rotating stator field. A simplified torque relationship is:

$$\tau \propto \Phi I \sin\delta$$

where $\Phi$ is magnetic flux, $I$ is stator current, and $\delta$ is the torque angle between rotor and stator fields. With field-oriented control, the common PMSM form is:

$$\tau = \frac{3}{2}p_p\lambda_m i_q$$

where $p_p$ is the number of pole pairs, $\lambda_m$ is permanent-magnet flux linkage, and $i_q$ is the torque-producing current component.

For BLDC/FPV motors, the KV rating is the speed constant:

$$\omega_{no-load} \approx K_V V$$

In drone terms, with KV in RPM/V:

$$RPM_{no-load} \approx KV \cdot V$$

That is the equation behind the practical rule: higher battery voltage or higher KV gives more no-load RPM, but the propeller load decides how much current and heat the motor must survive.

Conclusions

Why all of this?

Well, you can use this knowledge for fpv/drons:

See also this one.

The drone brushless DC motors will have present Faraday law with their Back EMF, same principle of the EMF kickback of the watering project.

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$

Remember: A changing magnetic field creates an electric field!

Or to understand electric cars before buying one

Total Energy Spent: Approximately 211 kWh. Efficiency: $211\text{ kWh} / 16.3\text{ (units of 100km)} = \mathbf{12.9\text{ kWh/100km}}$.

Note: You actually drove more efficiently than your initial 15 kWh estimate!

Unit Cost Comparison ($ USD per 1 kWh)

Durable Takeaways

• DC brushed motors are simple because mechanical commutation hides the switching problem, but the brushes become the maintenance limit.
• BLDC and PMSM motors are not magic DC motors; the battery is DC, but the controller creates rotating phase currents.
• AC induction motors are rugged because the rotor current is induced, but useful control depends on slip and frequency.
• Synchronous motors trade control complexity for efficiency, torque density, and precise field alignment.
• The L-R model is the first motor model, not the final one: it explains current dynamics, but not full electromagnetic geometry.

FAQ

AC vs DC Power Transmission

As experimented and summarized here:

Converting Electrical Energy

1. Rectifier (AC $\rightarrow$ DC)

A Rectifier converts Alternating Current (AC) into Direct Current (DC).

• How it works: It uses diodes (which act like one-way valves) to block or redirect the “backwards” part of the AC wave so the electricity only flows in one direction.
• Common Example: Your phone charger. It takes the AC from your wall and rectifies it into the DC your battery needs.

2. Inverter (DC $\rightarrow$ AC)

An Inverter converts Direct Current (DC) into Alternating Current (AC).

• How it works: It uses high-speed switches (transistors) to “chop up” the flat DC signal and flip its polarity back and forth to mimic the wave shape of AC.
• Common Example: Solar panels. They produce DC, but your home appliances need AC, so a “Solar Inverter” sits in the middle.

Home pv setups tend to have one of these!

3. Transformer (AC $\rightarrow$ AC)

You are exactly right—a Transformer stays within the same “lane” (AC to AC).

• How it works: It uses magnetic induction to change the voltage and current levels, but it cannot change the nature of the current. It cannot work with DC because it requires a changing magnetic field (which only AC provides).
• Common Example: Those big grey cans on utility poles. They take high-voltage AC from the power lines and “step it down” to the 110V/230V AC used in your house.

Pro Tip: If you want to go from DC to DC (like changing the voltage of a battery), you use something called a DC-DC Converter (often a “Buck” or “Boost” converter).

What is KV in motors

You are completely right to catch that! I snuck it into the component chart a few messages back when we built the initial blueprint for the indoor Whoop.

I wrote down: “0802SE 19500KV (Brushless)” for the motors.

Since KV is a highly specific and slightly confusing number in the drone world, let’s look at exactly what it means and why that specific number matters for your build:

What does “KV” actually mean?

In FPV drones, KV does not stand for kilovolts, and it has nothing to do with television.

It stands for the Velocity Constant of the motor.

Let’s look at the math for the 19500KV motors on a fully charged 1S drone battery ($4.2\text{V}$):

$$19,500 \text{ KV} \times 4.2 \text{ V} = 81,900 \text{ RPM}$$

Those tiny brushless motors are spinning the propellers at over 81,000 times per minute when you punch the throttle!

Why such a high KV for a small indoor drone?

• Small Propellers = Less Leverage: Indoor Whoop propellers are tiny (only 31mm wide). Because the blades are so small, they don’t grab a lot of air. To create enough thrust to lift the drone, they have to spin at astronomical speeds. High KV motors give you that raw speed.

• Low Voltage (1S): Since you are only using a single-cell battery ($3.7\text{V}$ to $4.2\text{V}$), the voltage is quite low. To get high RPMs out of low voltage, the motor needs a high KV rating.

• The Contrast: If you were building a massive 5-inch outdoor camera drone that runs on a heavy 6S battery ($25.2\text{V}$), you would use low KV motors (like 1700KV to 1900KV) because the larger propellers grab massive amounts of air and would burn out the motor if spun too fast.

When you go to buy your motors, sticking around 19500KV to 22000KV in the 0802 size is the absolute sweet spot for a snappy, controllable indoor flyer!

KV x Dron size

Choosing the right motor KV isn’t just about the drone’s size—it is a balancing act between Propeller Size and Battery Voltage (Cell Count / “S”).

The fundamental rule of thumb is: Big propellers and higher voltage need lower KV (more torque). Small propellers and lower voltage need higher KV (more raw RPM).

If you pair a big propeller with a high KV motor, the motor will try to spin way too fast, overheat, draw massive current, and likely burn out your ESC or the motor itself.

The drone’s “size” is typically measured by its propeller diameter (in inches).

💡 Understanding the Stator Numbers

When you see a motor size like 2207, the numbers stand for the internal dimensions in millimeters:

• 22 = Stator Width (Wider = more torque and efficiency at low RPM)
• 07 = Stator Height (Taller = more raw power and bite at high RPM)

DC vs BLDC vs AC Engines

The naming can be confusing because “DC” and “AC” can describe either the power source or the electromagnetic behavior.

So, a drone BLDC motor is “DC” from the battery perspective, but the useful physics inside the stator is a rotating multi-phase magnetic field.

An EV PMSM is similar: the pack is DC, the inverter creates controlled AC phase currents, and torque comes from field alignment.

The equations also reveal the naming problem:

$$\tau = K_t i$$

is a good DC-style control intuition, while:

$$n_s = \frac{120f}{p}$$

is the AC rotating-field intuition. BLDC/PMSM machines mix both worlds: a DC battery feeds an inverter, and the inverter creates the rotating field.

What is a squirrel-cage motor?

In Spanish, jaula de ardilla refers to the squirrel-cage induction motor.

So in the motor tables above, it corresponds to Induction (Squirrel Cage), also called:

• motor de induccion de jaula de ardilla
• motor asincrono de jaula de ardilla
• rotor de jaula de ardilla, when referring only to the rotor

The rotor is made of conductive bars shorted by end rings, visually similar to a cage.

There are no brushes, no permanent magnets, and no external electrical connection to the rotor.

The stator creates a rotating magnetic field, that field induces current in the rotor cage, and the interaction between both fields creates torque.

Using a ClampMeter