RF amplifier is one that amplify the received low power radio frequency signal to high power signal ,isn't it ?
In mic the audio signal is power amplified to drive loudspeaker,like could you say why rf amplifier amplify rf signals?
i just want to know the purpose of the amplification
Low power and high power are relative attributes of any signal. A high power RF signal for a broadcast radio or television station might be tens or hundreds of kilowatts. However, this would be considered a low power signal for a ground-penetrating or missile tracking radar system whose power output is often measured in megawatts.
The purpose of amplification is to increase a lower power signal to a higher power level, as in your microphone > power amplifier > speaker example. Similar reasons apply to RF signals. For example, an RF signal received on an antenna might have less than a microwatt of power. An RF amplifier can make this signal large enough to perform some useful function as part of a radio receiver. For an RF transmitter, it is usually easier to generate and apply modulation to RF signals at lower power levels than at the power level applied to the transmitting antenna. It is for this purpose that linear RF amplifiers are made.
Back in "the good old days" of amateur radio, most radiotelephone communication used amplitude modulation (AM). In the absence of a linear RF amplifier, the audio modulation was applied at 50% of the power level of the RF carrier by inserting an audo power transformer in series with the plate power supply to the "final" amplifier operating as a Class C RF amplifier, to obtain 100% modulation, and hence the largest available signal at the receiver. Thus an amateur radio operator desiring to transmit a "full gallon" or 1000 watts of power needed a 500 watt audio power amplifier to modulate the power input to their 1 kW "final" RF amplifier. Some hams did build or buy lower power AM transmitters and add a linear RF amplifier to their rig, but that was not cheap either.
Most broadcast AM stations "bit the bullet" and built audio modulation amplifiers with power output equal to half of their transmitter carrier power. The vacuum tubes used by clear-channel AM radio station WLW (located in the USA near Cincinnati, Ohio) transmitted (at one time) a carrier power of 500,000 watts. The vacuum tubes were externally water-cooled from a recirculating water pond located outside the station. Today, WLW transmits AM with "only" 70,000 watt carrier.