Noise & Active Components Notes for Microwave-Engineering

By Rahul Ranjan|Updated : April 5th, 2020

In this article, go through the detail notes on Noise & Active Components for Microwave Engineering.  

Introduction to Noise

  • Noise is usually generated by random motions of charges (or charge carriers in devices and materials). Such motions can be caused by the mechanism of:
    • Thermal Noise: Thermal vibrations of bound charges.
    • Shot Noise: Random fluctuations of charge carriers.
    • Flicker Noise: 1/f noise.
    • Plasma Noise: Random motions of charges.
    • Quantum Noise: Quantized nature of charge carriers.
  • Noise is a random process and can be passed into a system from external sources or generated within the system itself. Noise level defining the system performance determines for minimum signal reliability detected by a receiver.
  • 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

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  • 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 Vn. Then connecting a load resistor R results in maximum power transfer called Noise Power as

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

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         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 Te as

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  • 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

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

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       where Y should be determined via power measurement. Then

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        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

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         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

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

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

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  • 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

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         Then

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             When the line is matched byjusexamprep 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

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

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  • 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

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         with a Small Signal Model

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         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

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          where Zd is diode impedance as

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  • 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.

Thanks.

Team Gradeup.

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