Q5Microwave Theory And Techniques

Block diagram and function of each block:

• Transmitter: generates the high-power microwave pulse (via magnetron, klystron or solid-state amplifier chain) at the radar's operating frequency, delivered to the antenna via the duplexer.
• Duplexer (T-R switch): a fast electronic switch (commonly using a combination of circulators and gas-discharge/PIN-diode limiters) that connects the single shared antenna to the transmitter during pulse transmission and to the receiver during the (much longer) listening interval, protecting the sensitive receiver front-end from the transmitter's high power.
• Antenna: radiates the transmitted pulse in a narrow, highly directional beam (usually a rotating or electronically-scanned dish/array) and, on reception, collects the weak echo signal reflected from the target, with the same aperture used for both transmit and receive in a typical monostatic radar.
• Receiver: a low-noise, highly sensitive superheterodyne receiver chain (LNA, mixer, local oscillator, IF amplifier, detector) that amplifies and demodulates the extremely weak returned echo signal, whose power is often many orders of magnitude below the transmitted power due to the two-way propagation and reflection losses.
• Signal processor: extracts target information (range from pulse timing, velocity from Doppler shift, angle from antenna pointing) from the receiver output, and performs clutter rejection, pulse integration, and detection-threshold processing to distinguish genuine targets from noise and clutter.
• Display: presents processed target information to the operator (classically a PPI — plan position indicator — CRT display; in modern systems, a digital graphical display) showing target range, bearing and, in tracking radars, velocity/trajectory information.

Derivation of the radar range equation: consider a radar transmitting power Pt through an antenna of gain G. At a target located a distance R away, the power density (Poynting flux) incident on the target is, by the inverse-square law applied to the antenna's directional radiation:

The target intercepts and re-radiates (scatters) a portion of this incident power, characterized by its radar cross-section σ (an effective area, m², quantifying the target's reflectivity as seen by the radar), so the power scattered back toward the radar, treated as re-radiating isotropically from the target, has power density at the radar receiver (a further distance R back, so another inverse-square factor applies):

The receiving antenna (of the same gain G, using antenna reciprocity, with effective aperture Ae=Gλ²/4π) collects power:

Maximum detection range: the radar can detect the target only if the received power Pr is at least equal to the receiver's minimum detectable signal power Smin (set by receiver noise floor and required detection SNR); setting Pr=Smin and solving for R gives the maximum radar range:

This is the classical radar range equation, showing the characteristic fourth-root dependence on transmit power, antenna gain squared, and target cross-section — a direct consequence of the two independent inverse-square-law propagation legs (transmitter-to-target and target-to-receiver) each contributing an R⁻² factor, combining to the overall R⁻⁴ power falloff. This fourth-power relationship is the fundamental reason radar systems require disproportionately large increases in transmitter power or antenna gain to achieve modest increases in detection range (doubling range requires a 16-fold increase in transmit power for fixed antenna gain and target size), and it underlies every radar system design trade-off between power, antenna size, frequency (via λ) and achievable detection range for a given class of target.