Servo Drive Electronic Gear Ratio Calculation

Apr 10, 2026 Leave a message

A servo drive, also known as a servo amplifier, is the core component of an AC servo system. Its function is to convert the standard utility-frequency AC power supply into a variable-amplitude and variable-frequency AC power supply for the servo motor. When operating in speed control mode, the servo drive regulates the motor's speed by controlling the frequency of the output power; when in torque control mode, it controls the motor's torque by adjusting the amplitude of the output power; and when in position control mode, it determines the on/off timing of the output power based on incoming input pulses.

A servo drive

During operation, a servo drive requires connections to the servo motor, an encoder, control components, and a power supply unit. If software is used to configure parameters, a communication cable is required to connect the drive to a computer. The diagram below illustrates the wiring schematic connecting a servo drive to its auxiliary devices (for this tutorial, we will use a Mitsubishi servo drive as an example; future updates will cover Siemens and other servo brands).

a servo drive

In this installment, we will begin by explaining the "Electronic Gear" function-a topic of significant interest to many users-to provide practical guidance for real-world applications. (Subsequent updates will feature a more comprehensive summary of servo system learning and commissioning methods that I have compiled.)
In the servo drive's position control mode, a PLC generates input pulses to control the servo motor's rotational speed, thereby regulating the displacement of the actuated component. In other words, the greater the number of input pulses, the greater the number of rotations performed by the motor.
A servo motor's encoder generates a large number of pulses for every full rotation; the exact number of pulses per revolution depends on the specific device model and should be referenced in the product manual. Since the cumulative pulse count can become extremely high after the encoder has rotated multiple times, servo drives are equipped with an "Electronic Gear" function to address this issue by scaling (either reducing or increasing) the number of input pulses. (This concept is analogous to the large and small sprockets on a multi-speed bicycle.) Essentially, the Electronic Gear acts as a scaling multiplier; in Mitsubishi servo drives, it is configured using parameters P3 and P4, while in the Siemens V90 series, it is configured via parameters P29016 and P29017.

Formula: Electronic Gear Value = CMX / CDV

To facilitate understanding, let's examine a practical example to see how this concept is applied. As shown in the figure below, a servo motor drives a lead screw via a coupling; as the lead screw rotates, it drives the worktable to move horizontally. The lead screw has a pitch of 5 mm, meaning that for every full rotation of the screw, the worktable travels 5 mm. Suppose a pulse equivalent of 1 μm/pulse is required-that is, each pulse input to the servo drive causes the worktable to move by 1 μm. How many pulses must be input to the servo drive to achieve a worktable displacement of 5 mm? Furthermore, if the encoder resolution is 131,072 pulses per revolution, how should the electronic gear ratio be configured?

Electronic Gear Value

This scenario is an inevitable encounter in practical programming-particularly when driving a servo motor in position control mode-and necessitates the performance of specific calculations.

[Problem-Solving Approach and Steps]

Step 1: Calculate the number of command pulses required to move the load.

Our objective is to move the worktable by one pitch (5 mm). According to the requirements, one pulse corresponds to a displacement of 1 μm (i.e., 0.001 mm). Therefore, the number of command pulses required to move 5 mm (i.e., the number of pulses the PLC must output) is:
Number of Command Pulses = 5 mm / (0.001 mm/pulse) = 5,000 pulses. This implies:
We want the servo motor to complete exactly one full revolution when the PLC outputs 5,000 pulses.

Step 2: Determine the number of feedback pulses generated per motor revolution.

According to the motor's nameplate or manual, in this specific example, the encoder generates 131,072 pulses for every full revolution of the motor.

Step 3: Calculate the Electronic Gear Ratio.

The essence of the electronic gear function is to establish a proportional relationship between the "command pulses" and the "encoder feedback pulses."
Electronic Gear Value = Number of pulses generated by encoder / Number of input pulses
Substituting the values: Electronic Gear Value = 131,072 / 5,000

Step 4: Simplify the parameters.

We need to simplify the fraction obtained above into its simplest integer ratio form so that the values ​​can be entered as parameters:
131,072 / 5,000 = 16,384 / 625
Thus, the Electronic Gear Numerator is 16,384, and the Electronic Gear Denominator is 625. Once we have derived these two parameters, we can proceed to configure the settings within the servo amplifier.

Conclusion

Calculating the electronic gear ratio is a fundamental skill in servo system commissioning. By mastering it, you effectively master the "system of measurement" for position control. Although parameter codes may vary across different brands (some allow direct entry of pulses per revolution, while others require separate numerator and denominator values), the underlying physical logic remains universal.
To my colleagues in the industrial automation field: today's case study is based on the simplest model-one where the motor is directly coupled to the lead screw. However, in real-world applications, we frequently encounter more complex scenarios. If a reducer (e.g., with a reduction ratio of 1:3) or a synchronous belt drive is introduced between the motor and the lead screw, how should the electronic gear ratio be calculated?