Noise & Active Components Notes for Microwave-Engineering

• Dynamic Range and Compression Point: The linearity and deterministic features of all components can be satisfied in a range called Dynamic Range. The floor level of noise dominates the output power at very low frequencies. 1 dB Compression Point is defined as the input power for which the output is 1 dB below that of an ideal amplifier.
• Noise Power and Equivalent Noise Temperature: Rayleigh-Jeans approximation results Voltage Fluctuations as

        

• where k is Boltzmann’s constant, T ºK is temperature, B is bandwidth and R are resistance. Because of frequency independency, this is known as White Noise Source can be treated as Gaussian distributed variables. A noisy resistor R can be replaced with a noiseless resistor and a voltage source of RMS V_n. Then connecting a load resistor R results in maximum power transfer called Noise Power as

       

      

• If P_n is not strong function of frequency (White Noise), an Equivalent Noise Temperature is defined as

       

         where N₀ is Noise Power delivered to load R.

• A noisy amplifier with a source of resistor at a temperature of T = 0 ºK can be replaced with a noiseless amplifier and a resistor having Equivalent Noise Temperature T_e as

        

• where N₀ is output noise power and G is amplifier gain. Excess Noise Ratio (ENR) is also used to characterize Noise Power of active noise generator consisting of a diode or a tube as

        

• where N_g & T_g are Noise Power & Equivalent Temperature of the generator.
• Measurement of Noise Power: Y-factor method is applied as

       

       where Y should be determined via power measurement. Then

       

        where T₁ & T₂ are the temperature of hot & cold load, respectively.

Noise Figure, F

• It is a measure of the degradation in S/N ratio between the input and output as

        

        

        

        

         If the network is noiseless, .

• Noise Figure of a Two-Port Passive and Lossy Network: Having G < 1 such as attenuator (or lossy line) with a matched source resistor at T, overall system temperature also at T, noise factor

      

         where L = 1/G is lossy factor. The equivalent noise temperature

           

          If the line is at the temperature T_i, F = L.

         

         

         

        

        

        

        

        

        

       

         

        

         

• Noise Figure of a Mismatched Lossy Line: Previously, Noise Figure of a lossy line is calculated under assumptions of line is matched to its input and output circuits. Consider that line (L, T, Z₀, B) is mismatched to input circuit as

        

         Then

          

             When the line is matched  same as the matched lossy line.

Dynamic Range & Intermodulation Distortion

• All realistic devices are nonlinear at very low power levels due to noise effects and also practical components became nonlinear at high power levels. A given component (or network) can operate as desired between minimum and maximum realistic power ranges known as Dynamic Range. In the sense of intermodulation distortion, it is called as Spurious Free Dynamic Range. The output response of a nonlinear device (diode, transistor) by using a Taylor series expansion

        

        

       

       

• In most practical system, a₃ < 0, then gain tends to decrease named Gain Compression or Saturation.
• Intermodulation Distortion: 

       

        

• Passive Intermodulation: Connectors, cables, antennas, and every metal-metal contact can cause passive intermodulation due to poor mechanical contact, oxidation, contamination etc., and also thermal effects of high power source. This has generally lower power levels.  

RF Diode Characteristics

• Shottky Barrier Diode Detectors: This is a nonlinear device consisting of semiconductor-metal junction resulting lower junction capacitance can be used frequency conversion (rectification, detection, mixing). It has a

       

         with a Small Signal Model

       

         These diodes are used as rectifiers, detectors and demodulation of an AM modulated RF carrier.

• PIN Diode: This is used to construct an electronic switching for control circuits such as phase shifters and attenuators. These are preferable because of small size, high speed and inerrability with planar circuits. Especially single-pole PIN diode switches can be used in either a series or a shunt configuration to form a single pole RF switch. Insertion Loss of switches

        

          where Z_d is diode impedance as

         

• Varactor Diode: Junction capacitance varies with bias voltage used for electronically frequency tuning.
• Impatt Diode: Similar to PIN diode, but based on avalanche effects exhibiting negative resistance over a broad frequency range, therefore used to directly convert DC to RF power.
• Gunn Diode: It exhibits a negative differential resistance based on Gunn effect and used to generate RF power to DC.
• Baritt Diode: Similar to junction transistor without a base contact and useful for detector and mixer applications with advantages of lower AM noise.

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