 In a closed loop system, a controller is used to amplify the amount of output change in proportion to the change that occurs at the input. Controllers provide amplification using one of two modes of proportional functions, proportional gain and proportional band. The ratio of the change in output to the change in input is defined as proportional gain. To illustrate the concept of gain, a common process of regulating the level of fluid in a tank with a float attached to a control valve is used. The float mechanism is designed so that when the tank level is half full, the flow valve is open to the position that causes the amount of fluid entering the tank to be equal to the amount leaving the tank. The float on the end of the rod is positioned to meet the minimum and maximum flow capability of the valve. The valve is actuated by the float to a fully open position when the tank level is low and fully closed when the tank level is full. Opening the drain valve increases the load demand which causes the tank level to drop by 25%. The float drops and the valve opens 25%, which allows more fluid flow to enter the tank. A gain of 1 is demonstrated in this mechanism since the 25% change of input or tank level results in a 25% change of output or valve position. Positioning the float to the midpoint of the bar increases the gain. The valve fully opens when the level drops to 25% and fully closes when the level rises to 75%. Opening the drain valve increases the load demand which causes the tank level to drop by 12.5% or 37.5% full. The float drops and the valve opens 25% which allows more fluid flow to enter the tank. A gain of 2 is demonstrated in this mechanism since the 12.5% change of tank level resulted in a 25% change of valve position. Proportional band is defined as the percentage of change in the controlled variable which causes the final control element to go through 100% of operating range. Proportional band is calculated by dividing the controlled variable percent change by the final control element percent change multiplied by 100. The width of proportional band determines how much of a controlled variable change is required to cause the final control element to move by a determined amount. By placing the float on the end of the rod the fluid level has to change 100% to cause the final control element to change 100%. By placing the float at the center of the rod the fluid level has to change 12.5% to cause the final control element to change 25%. The width of the proportional band is reduced by half.