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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
Download (direct link): noisetheoryoflinearandnonlinear1995.pdf
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3. Noise characteristics of multi-ports
J К x and by the sum of all exchangeable power gains from input responses that give an output at the output port on the specified frequency,
Гге ~ k zL fK1 (3'4)
where I is the number of responses from all the input ports and GCi, is the exchangeable power gain from port response i to the output port.
Note 1: There is only one output port and at that port only one frequency is considered. As the definition uses the exchangeable output noise power density any noise from the load has no influence on Tcc
Note 2: All other ports than the output port are considered input ports and they should be loaded with any passive or active immittances except short or open circuits.
Note 3: T„, is a function of the source iminittance(s).
The subscript ее stands for extended Te where Ts is the standard symbol for the IRE definition of effective input noise temperature [3].
For passive port terminations this definition is equivalent to the IRE definition. The IRE definition states that the effective (extended) input noise temperature of a multi-port transducer is the (extended) noise temperature which assigned simultaneously to all input ports of a noise free equivalent of the transducer yields the same available (exchangeable) output noise power density at a specified output frequency as the actual transducer with noise free sources.
With all input port terminations active, definition 3.4 gives a value of Tce which is negative and this corresponds to definition 2.3 of Tem. If, however, some input ports are terminated by passive immittances and some by active immittances Tee can be of both signs. This situation is discussed below. In these cases with some or all input terminations active the above IRE definition is equivalent to definition 3.4 when the alterations and the addition indicated in brackets are taken into account.
Figure 3.1: Illustration of me extended noise temperature definition for a single response transducer.
The definition is illustrated in Figure 3.1 for a single response two-port where at the right the noisy amplifier with a (fictitious) noise free source generates the
3.2. Definitions of noise quantities
exchangeable output noise power density Л". Tlie noise free - but otherwise equivalent - amplifier to the left is connected to a source of which the extended noise temperature is varied in such a way that the exchangeable noise power density of this amplifier is also N'e. Then the extended noise temperature of that source is defined to be the extended noise temperature of the noisy amplifier. As Лг' is a function of frequency the extended noise temperature is also a function of frequency.
As mentioned above the interpretation of Tee with both active and passive input terminations is a little difficult. Consider a three-port transducer with one output port and two input ports. The input ports are loaded with two immittances where one is passive and one active and the output immittance may be either passive
01 active. As Tee is the same at both input ports and the exchangeable power gains from the two ports have opposite signs, one of the input ports lias assigned an extended noise temperature of the opposite sign than the port resistance. It also seems that the noise power density at the output port consists of the difference between two noise power densities. This can be accepted as fictitious reference noise temperatures at the input ports, but it seems more natural if the temperature and resistance had the same sign and that the powers were added. If the input ports were loaded with either only active or only passive immittances, the noise powers at the output port from the input ports would all have the same sign. When this is not the case another - always positive - noise temperature is sometimes useful. It can be expressed from the extended noise temperature by
\t,< ZLgJ
Te„ = J----------j---------1 (3.5)
E,'=1 |Ge,i|
The idea behind Tep is that if all the input port responses are loaded by immittances with noise temperatures of ±Tep (+ for a passive load and — for an active load) and the transducer is replaced by a noise free equivalent, then the exchangeable output noise power density is the same as that from the actual transducer with noise free sources. It is seen that if and only if tlie loads to the input port responses are either all passive or all active then Tes - |T„|. One of the main reasons for choosing definition 3.4 instead of as the definition of the extended noise temperature is that for a single response two-port, the function Tce( Z<), where Zs is the source impedance, is the quadric surface of a hyperboloid of two sheets.1 This is a consequence of the simple relations - for single response two-ports - between the extended noise temperature and the extended noise factor defined below.
3.2.2 The noise factor
A much used noise characteristic for two-ports is the noise factor. It is, however, not very practical to use with multi-ports, where the noise temperature is preferable,
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