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# Theory of Linear and nonlinear circuits - Engberg J.

Engberg J. Theory of Linear and nonlinear circuits - Wiley & sons , 1995. - 154 p.
ISBN 0-47-94825
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After a short look at some power gain definitions the following noise quantities are introduced: effective input noise temperature, noise factor and operating noise temperature. The noise measure is defined in Chapter 5. Of these the operating noise temperature is intended to be used to describe the noise performance of a system including source and load generated noise. The other definitions are used to describe devices, stages and amplifiers and they are extended to cover negative immittances as well [1,2]. Then the average values of the noise quantities are defined. In a discussion of the noise quantities a definition of an output operating noise temperature is considered.
3.1 Power gains
Two types of power gain are often used in noise theory. One is the available power gain which is extended to include negative immittances and is then called the exchangeable power gam. i'he other is the transducer gain.
For a passive one-port source the available power P, is defined as the great-
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3. Noise characteristics of multi-ports
est power that can be drawn from the source by arbitrary variation of its terminal current (or voltage) [2]. This power is the maximum power delivered to the load when the load immittance is the complex conjugate of the source im-mittance. Extending the above definition to active sources gives no meaning as the “maximum” power is infinite and thus not a stationary value (extremum). However, a (negative) stationary value exists in this case so the exchangeable power Pe is defined as follows.
Definition 3.1 The exchangeable power of a one-port Pe is the stationary value (extremum) of the power output from the source, obtained by arbitrary variation of the terminal current (or voltage).
For a Thevenin equivalent of a one-port where Z = R -f j X and R ^ 0 definition
= TiT = [“I b'R*° <зл|
It is seen that Pe is negative when the one-port is active (Я < 0) and positive when passive (R > 0).
The extended version of the available power gain, which is defined as the available power at the output divided by the available power at the source, is the exchangeable power gain Gc defined by replacing the available powers by exchangeable powers.
Definition 3.2 The exchangeable power gain Gs is defined as
Ge = ^ (3.2)
-■ O’
[W]
|W!
where the exchangeable output power
p _ (Na>
4 iJ0
and the exchangeable power at the source
^
4 Rs
where e.g. e0, Rs / 0 and R„ / 0 are the Thevenin voltage at the source and output terminals and the corresponding resistances.
It is seen that
Ge > 0 when Rs! Ro > 0
Gn < 0 when Rs/Яо < 0
The transducer gain Gr is defined as the nnwpr delivered to the load divided by the power available from the source. As the available power is always positive then Gj > 0 for passive loads and Gt < 0 for active loads. If active sources are considered Gj — 0 as the available power approaches infinity. It is therefore necessarv to extend the definition in the same wav as above. This leads to
3.2. Definitions of noise quantities
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Definition 3.3 The extended transducer gain is defined as
G.r = £ (3,,)
where Pi is the power delivered to the load and PSts is the exchangeable power at the source.
It is seen that
Gej > 0 when Rs/Rl > 0
Ger < 0 when Rs/Rl < 0
where Й5 and Ri are the source and load resistances respectively.
3.2 Definitions of noise quantities
In this section the extended noise temperature, the extended noise factor (and figure) and the operating noise temperature which also is given in an extended version are defined. The extensions of the old definitions include the cases of active sources. This is very convenient as a stage in a cascade of stages as source immittance has the output immittance of the former stage. Often this stage is only stable when loaded which means that the output immittance can well be negative.
The definition of the noise measure will be given in Chapter 5.
Usually the available or exchangeable power gain is used for definitions of spot frequency noise quantities and the transducer or extended transducer gain for average noise quantities and this habit is maintained here. It is, however, not important which type of gain is used as all noise quantities are defined as ratios of powers and a change of e.g. exchangeable output, powers in numerator and denominator to powers delivered to the load does not change anything.
3.2.1 The effective noise temperature
The idea behind the definition of the noise temperature is to transfer the noise power generated in the two- or multi-port to the source or sources. As a one-port source with a known exchangeable noise power is characterized by its extended noise temperature this quantity is used to characterize the two- or multi-port.
Definition 3.4 The extended effective (input) noise temperature Tcc of a multi-port transducer is defined as the exchangeable output noise power density at a specified output frequency of the transducer with noise free sources, N: [W Hz-1] divided by Boltzmann's constant к = 1.3807 x iU-'1'3
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