The Relationship Between PWM Duty Cycle and Average Voltage

If you've ever watched a robot's head pan smoothly to track an object, admired the delicate flutter of a model airplane's control surfaces, or wondered how a robotic arm knows just how far to reach, you've witnessed the silent, digital heartbeat of modern robotics: the micro servo motor. At the core of commanding these ubiquitous devices lies a deceptively simple concept with profound implications—the relationship between a PWM signal's duty cycle and its average voltage. This isn't just abstract electronics; it's the literal language we use to whisper commands to our mechanical creations.

What Exactly is a Micro Servo Motor?

Before we dive into the pulses, let's establish what makes a micro servo so special. Unlike a standard DC motor that spins continuously when power is applied, a micro servo motor is a compact, integrated package of magic. It contains: * A small DC motor * A gear train to reduce speed and increase torque * A control circuit * A potentiometer (or other sensor) attached to the output shaft

This last component is the key. The potentiometer provides real-time feedback to the control circuit about the shaft's exact angular position. The servo's entire purpose is to compare this feedback against an incoming command signal and move the motor to make them match. That command signal? It's almost universally a Pulse Width Modulation (PWM) signal.

The Language of Pulses: Understanding PWM

PWM is the digital world's clever hack for simulating analog control. Since microcontrollers (like those on an Arduino or Raspberry Pi) are brilliant at outputting simple ON (5V) and OFF (0V) signals, PWM uses this binary capability to create an effective intermediate voltage.

• Period and Frequency: The PWM signal repeats at a fixed interval called the period. Its inverse is the frequency (e.g., a 50Hz frequency has a 20ms period). Servos typically operate at frequencies between 40-300Hz.
• Pulse Width: This is the duration, usually measured in milliseconds (ms), that the signal is ON (high) during each period.
• Duty Cycle: This is the star of our show. Expressed as a percentage, it is the ratio of the pulse width to the total period. Duty Cycle (%) = (Pulse Width / Period) × 100

A 0% duty cycle means the signal is always OFF. A 100% duty cycle means it's always ON. A 50% duty cycle means it's ON for exactly half of each period.

From Duty Cycle to Average Voltage: The Fundamental Bridge

Here lies the first critical relationship. If your microcontroller's HIGH voltage is 5V, then: Average Voltage = Duty Cycle × Supply Voltage

• 10% Duty Cycle: Average Voltage = 0.10 × 5V = 0.5V
• 50% Duty Cycle: Average Voltage = 0.50 × 5V = 2.5V
• 90% Duty Cycle: Average Voltage = 0.90 × 5V = 4.5V

This average voltage is not what you'd measure with a standard voltmeter (which would show the peak voltage, 5V, due to the rapid switching). Instead, it's the effective voltage as "seen" by a slow-responding system—like a motor, an LED dimmer, or, crucially, the control circuitry inside a servo. The servo's internal electronics act as a low-pass filter, smoothing out the rapid pulses into this average DC voltage level.

Decoding the Servo's Pulse Protocol

Now, for a standard hobbyist micro servo (like the iconic SG90), this average voltage concept is applied in a very specific, calibrated way. The servo doesn't just respond to any average voltage; it responds to the pulse width that creates it within a strict protocol.

For a 50Hz signal (20ms period): * ~1.0 ms Pulse Width: This corresponds to a 5% duty cycle (1ms/20ms). The average voltage is 0.25V. This commands the servo to its minimum angular position (often 0° or -90°). * ~1.5 ms Pulse Width: This is a 7.5% duty cycle. Average voltage = 0.375V. This is the neutral position (often 90° or the center). * ~2.0 ms Pulse Width: This is a 10% duty cycle. Average voltage = 0.5V. This commands the servo to its maximum angular position (often 180° or +90°).

Why the Narrow Voltage Range? It's All About the Internal Comparator

You might notice the actual average voltage range we're talking about is tiny—from about 0.25V to 0.5V for a 5V system. Why such a small slice of the available voltage?

Inside the servo, the PWM signal is filtered and fed into one side of a comparator circuit. The potentiometer attached to the output shaft provides a reference voltage proportional to the current angle. The comparator's sole job is to drive the DC motor until these two voltages are equal.

• Scenario: Commanding a 90° Turn. You send a 1.5ms pulse. It's filtered to ~0.375V. The comparator checks this against the potentiometer's voltage. If the shaft is at 45°, the pot's voltage might be 0.3V. The comparator detects a difference (0.375V > 0.3V) and powers the motor to turn the shaft towards 90°, increasing the pot's voltage until it matches the command voltage.
• The Relationship is Linear: The servo's control board maps the entire pulse width range (e.g., 1.0ms to 2.0ms) linearly across its mechanical range (e.g., 0° to 180°). Therefore, a 1.25ms pulse (midway between min and neutral) will, in theory, command a 45° position.

Practical Implications for Hobbyists and Engineers

Understanding this relationship is not academic; it directly impacts your projects.

1. The Perils of Incorrect Frequency

If you change the PWM frequency, you break the servo's expected protocol. A 1.5ms pulse width at 100Hz (10ms period) is a 15% duty cycle, creating an average voltage of 0.75V—far outside the range the servo's comparator expects. This will cause erratic behavior, jitter, or failure to move. Stick to the standard 50Hz (20ms period) for analog servos.

2. Resolution and Jitter: The Digital Limitation

Your microcontroller's PWM capability has a finite resolution, defined by its bit depth (e.g., 8-bit, 16-bit). An 8-bit timer on a 20ms period can only define pulse widths in increments of 20ms / 256 ≈ 0.078ms. This limits the angular resolution of your commands. Lower resolution can also manifest as visible "jitter," where the servo vibrates trying to hold a position between two digital pulses it can't quite match.

How to Calculate Your System's Angular Resolution

Resolution (degrees) = (Total Angular Range) / (Number of Discrete Pulse Steps)

For a 180° servo using an 8-bit (256 step) PWM on a 20ms period, the pulse width range is 1ms (1000 steps of 1µs each on a good microcontroller). The number of discrete steps is 1000. Thus, resolution ≈ 180° / 1000 = 0.18°. In practice, servo mechanics and potentiometer quality limit this further.

3. Voltage Scaling and "Servo Rail" Power

The formula V_avg = Duty Cycle × V_supply reveals another nuance: if your signal's HIGH voltage (V_supply in this context) changes, the average voltage for a given pulse width changes. A 1.5ms pulse from a 3.3V microcontroller generates an average voltage of 0.2475V, not the 0.375V a 5V-powered servo expects. This can cause the servo's range of motion to shrink or shift. Always ensure your control signal's logic voltage is compatible with the servo's expected signal voltage. This is separate from the higher-current power needed for the servo motor itself (the "servo rail"), which should be supplied directly from a battery or regulated power supply.

Advanced Topic: Beyond Position - Controlling a Continuous Rotation Servo

A fascinating application of this principle is the continuous rotation servo. By modifying a standard servo (typically by removing the potentiometer's mechanical stop and fixing it to report a constant "neutral" voltage), you transform it from a position-controlled device to a speed-controlled one.

• 1.5ms Pulse (Neutral Average Voltage): The comparator sees a match. The motor receives no power. The servo is stopped.
• 1.0ms Pulse (Lower Average Voltage): The comparator sees a command voltage lower than the fixed pot voltage. It drives the motor in one direction to "correct" a non-existent error. The servo rotates continuously at full speed in one direction.
• 2.0ms Pulse (Higher Average Voltage): The comparator drives the motor in the opposite direction. The servo rotates at full speed the other way.
• Pulses in Between: The magnitude of the voltage difference dictates the speed. The relationship between pulse width and speed becomes roughly linear, turning the familiar position control into precise bidirectional speed control.

This elegant repurposing underscores the core principle: the micro servo is fundamentally a closed-loop system that strives to zero out the difference between the voltage implied by your PWM duty cycle and the voltage reported by its internal sensor. By mastering the simple, powerful relationship between duty cycle and average voltage, you gain the precise dialect needed to command the vast world of micro servos, from animatronic puppets to autonomous vehicle steering. The pulse, indeed, is the command.