#  Radar Basics

#### Doppler- Frequency Comparison

Since the Doppler- frequency (few Hertz) is small relatively to the transmitted frequency (much Mega-Hertz), therefore a phase comparison is more easily to carry out than a direct frequency comparison.

 fD = 2·v λ

The Doppler - frequency shall be calculated at a transmitted frequency of 2975 MHz and at a radial speed of the airplane of 650 kilometers per hour.
From the topic Doppler- effect this formula is still known to the calculation of the Doppler frequency.

 fD = 2·v·f c

By the relation λ=c/f  we calculate the wavelength or use this relation in the formula directly.

 fD = 2·v·f 3·108

The light speed is known but take the measurement unit of meters per seconds into account.

 fD = 2·v·2,975·109 3·108

We insert the frequency of the radar transmitter into the formula and shorten with the decades of the denominator.

 fD = 2·650·2.975·10 3·3.6

Notice that we need the radial speed in meters per second (m/s). Therefore we multiply by 1000 (meters) and divide by 3600 (seconds) - after shortening the value 3.6 is left in the denominator.

The rest of work doing at the pocket calculator: the Doppler-frequency is 3581 Hz. Although the radial speed was very high anyway, this value is very small compared one with the transmitted frequency. E.g. if the radial speed drops less than 10 km/h, then the Doppler-frequency becomes smaller than 110 Hz! At sufficiently good edge steepness favourable filters for such frequencies are digitally structured only.