you can see the wheel when the room lights are turned off. You sit directly in front of the wheel while a friend rotates the wheel. The view of the front of the wheel (real) and the top of the wheel (imaginary) tell you the position of the wheel. Pairs of real and imaginary values form a complex number explained as real and imaginary parts. Dynamic calibration is needed when there are long waveguide runs between the antenna and first down converter (see Superheterodyne receiver). This compensates for temperature changes that alter the size and length of wave-guide, which will cause phase variations that produce incorrect angle error signals for long wave-guide runs. The Cal term is created by injecting a calibration signal into the receive waveguide while the system is not active (sum and delta). The angle error of the calibration signal is used to evaluate angle error during normal operation. Antenna tuning is used to make adjustments that create the desired error signal when the antenna is calibrated on an antenna range. When the waveguide run is short between the antenna and receiver, the calibration signal can be omitted and the calibration term can be set to a fixed value. A fixed value may also be stored for systems with long wave-guide runs to allow degraded operation when RF calibration cannot be performed. The waveguide assembly may need to be tuned using an antenna range to obtain consistent results. Implementation for array antennas The four-quadrant array antenna consists of four sub-arrays. The sub-arrays are separated by a distance d. The angle θ (in either elevation or azimuth) is estimated from the monopulse ratio, which is the ratio of the difference signal over the sum signal. The estimation equation is given by: The derivation of a more general form of this equation is presented in. Antenna positioning Tracking systems produce constant aircraft position information, and the antenna position is part of this information. Antenna error signals are used to create feedback as part of a RADAR system that can track aircraft. The horizontal signal and the vertical signal created from antenna RF samples are called angle errors. These angle error signals indicate the angular distance between the center of the antenna beam and the position of the aircraft within the antenna beam. For a mechanically steered antenna, the horizontal signal and vertical signal are used to create a drive