**Reference to the chart reveals useful performance information valid for all MCP DC brushed servomotors.It shows speed n, current I, output power P and efficiency η plotted against torque M for a given supply voltage U.**

## Principles of Operation

Torque M is a function of the current I and the torque constant k (expressed in Nm/A). The motor develops its maximum torque Ms at stall (n=0), when the current is maximum and determined only by the supply voltage U and the rotor resistance R:

I_{s} = U/R

M_{s} = I_{s}·k

With increasing speed, an increasing back EMF E is induced in the armature which tends to reduce the current:

The value of E is the product of angular speed ω (expressed in rad/s) and the torque constant (expressed in V/rad/s=Vs=Nm/A):

E=kω

Thus the supply voltage splits into two parts: RI, necessary to establish the current I in the armature, which generates the torque M, and kω to overcome the induced voltage, in order to generate the speed ω:

U = RI + kω

No-load speed n_{0} is a function of the supply voltage and is reached when E becomes almost equal to U; no-load current I_{0} is a function of friction torque:

With increasing speed, an increasing back EMF E is induced in the armature which tends to reduce the current:

Power output P is the product of angular speed ω and torque M (P = M · ω); for a given voltage it reaches its maximum P_{max} at half the stall torque M_{s}, where efficiency is close to 50%. The maximum continuous output power is defined by an hyperbola delimiting the continuous and intermittent operation ranges.

Efficiency η is the mechanical to electrical power ratio (η = P_{m} / P_{el}). Maximum efficiency η_{max} occurs at relatively high speed. Its value depends upon the ratio of stall torque and friction torque and thus is a function of the supply voltage:

The maximum continuous torque depends upon dissipated power (I^{2}R), its maximum value is determined by:

Where T_{max} is the maximum tolerated armature temperature, T_{amb} is the ambient temperature, R_{max}is the rotor resistance at temperature T_{max} and R_{th} is the total thermal resistance (rotor-body-ambient).

At a given torque M, increasing or decreasing the supply voltage will increase or decrease the speed. The speed-torque function varies proportionally to the supply voltage U.