Computing the distance from the phase differences,NOMINAL FREQUENCY & HALF WAVELENGTHS,FREQUENCY DIFFERENCES AND EQUIVALENT HALF WAVELENGTHS,SUMMATION OF DIATANCES CONTRIBUTION FROM PHASE DIFFERENCES,

 

ELECTRONIC DISTANCE MEASUREMENT 

Computing the distance from the phase differences

 One complete cycle at the modulation frequency corresponds to the time required for the signal to travel one half wavelengths in both directions. The distance being measured corresponds to many half wavelengths at the modulation frequency plus some fraction of a half wave length. All the instruments use data from several frequencies to overrun this ambiguity.

Four modulation frequencies are used in determining the total length being measured. Several measurements are made at one of these frequencies in order to reduce inherent electronic errors in the system. The four frequencies are f A , f B , f C and f D . The corresponding half lengths are λA/2, λB/2, λC/2  and λD/2 . The wavelength  λ is related to C, the velocity of propagation and the frequency f by

 Λ = C/f   ......(1)

NOMINAL FREQUENCY & HALF WAVELENGTHS

With the exception of λA , the modulation wavelengths are not useful directly, but the wavelengths associated with the frequency differences allow the ambiguity introduced by the long path to be resolved. These relations are given in next table. Phase differences needed in the determination of distance d can be derived as follows

A – B = 2d/λA - 2d / λB = 2d/λA ( 1 – λA/λB ) = 2d/λA( 1 – fB / fA ) ....... (2)

FREQUENCY DIFFERENCES AND EQUIVALENT HALF WAVELENGTHS

Equation (2) can be rearranged to obtain an expression for the distance  d .

A - B - 2d (fA/C - fB/C ) = 2d ( fA -fB )/C = d/( λ A-B/2)

d = (A - B )λA-B/2

In which half wavelengths are obtained from above mentioned table and the phase difference from the instrument readings. A hypothetical example of how distances are derived and total distance obtained shown in the following table.

SUMMATION OF DIATANCES CONTRIBUTION FROM PHASE DIFFERENCES

Modern EDMs use the decade modulation technique. When the modulation frequency is 15 MHz, the half wavelength is 10m. The phase meter reading then gives distance between 0 and 9.999m. When the modulation frequency is brought down to 1.5MHz, the half wavelength is 100m and the phase meter gives tens of meters. When it is still brought down to 0.15 MHz, the half wavelength is 1000m and we get hundreds of meters. The distance 13816.86 m will then be obtained as summation of 6.86, 10.00, 800 & 13000

Brief description of different types of instruments 

 Geodimeters:

All geodimeters employ visible light as the carrier. The measuring set consists of an active transmitter and receiver at one end of the line to be measured and a passive retro directive prism reflector at the other end. Continuous light emission in the transmitter is intensity (amplitude) modulated, using a precision radio frequency generator and an electro-optical shutter to form sinusoidal light intensity waves. The distance is obtained by comparing the phases of outgoing modu8lation waves with those received by the receiving component after reflection from the distant reflector. All reflectors in the modern instruments are based on the retro directivity principle. Each unit in the reflector is a retro directive prism made of three mutually perpendicular reflecting surfaces.

 Tellurimeters:

The tellurimeter uses microwaves at about 3, 10 or 35 GHz as the carrier. The measuring set consists of two active units with a transmitter or receiver; one is called the master and the other is called the remote unit. The carrier frequencies of the two units differ slightly making it possible to utilize intermediate frequency amplification. Because the carriers are microwaves and the beam widths are narrow - between 2 and 20°. Measuring can be carried on either at night or day time, through haze or light rain, although heavy rainfall may reduce the working range. The bare out lines of the measuring principle consists of a frequency modulated carrier wave from the master station being sent to the remote station where it is received or transmitted to the master station. There the phase difference between the transmitted and received modulation or pattern waves is compared. Knowing the phase difference or by decade modulation technique distance can be determined.

Hewlett-Packard 3800: This is a modern instrument. Block diagram is shown in Figure below. The transmitter uses a GaAs diode which emits amplitude modulated (AM) infrared light. Frequency of modulation is precisely controlled by a crystal oscillator. The intensity or amplitude variation is properly represented by sine waves, Environmental correction factor can be directly dialed into the transmitter to slightly vary the frequency so that a constant wavelength is maintained despite atmospheric variation. Hence no adjustment of distance is necessary at a later stage.

Fig :- General flow diagram of Hew left Packard 3800

                                                                                                                                                                                                                                         From matrix